Applying an alternative mathematics pedagogy for students with weak mathematics: meta-analysis of alternative pedagogies

NASA Astrophysics Data System (ADS)

Lake, Warren; Wallin, Margie; Woolcott, Geoff; Boyd, Wendy; Foster, Alan; Markopoulos, Christos; Boyd, William

2017-02-01

Student mathematics performance and the need for work-ready graduates to be mathematics-competent is a core issue for many universities. While both student and teacher are responsible for learning outcomes, there is a need to explicitly acknowledge the weak mathematics foundation of many university students. A systematic literature review was undertaken of identified innovations and/or interventions that may lead to improvement in student outcomes for university mathematics-based units of study. The review revealed the importance of understanding the foundations of student performance in higher education mathematics learning, especially in first year. Pre-university mathematics skills were identified as significant in student retention and mathematics success at university, and a specific focus on student pre-university mathematics skill level was found to be more effective in providing help, rather than simply focusing on a particular at-risk group. Diagnostics tools were found to be important in identifying (1) student background and (2) appropriate intervention. The studies highlighted the importance of appropriate and validated interventions in mathematics teaching and learning, and the need to improve the learning model for mathematics-based subjects, communication and technology innovations.

Mathematical Modeling: Are Prior Experiences Important?

ERIC Educational Resources Information Center

Czocher, Jennifer A.; Moss, Diana L.

2017-01-01

Why are math modeling problems the source of such frustration for students and teachers? The conceptual understanding that students have when engaging with a math modeling problem varies greatly. They need opportunities to make their own assumptions and design the mathematics to fit these assumptions (CCSSI 2010). Making these assumptions is part…

Mathematics Teacher TPACK Standards and Development Model

ERIC Educational Resources Information Center

Niess, Margaret L.; Ronau, Robert N.; Shafer, Kathryn G.; Driskell, Shannon O.; Harper, Suzanne R.; Johnston, Christopher; Browning, Christine; Ozgun-Koca, S. Asli; Kersaint, Gladis

2009-01-01

What knowledge is needed to teach mathematics with digital technologies? The overarching construct, called technology, pedagogy, and content knowledge (TPACK), has been proposed as the interconnection and intersection of technology, pedagogy, and content knowledge. Mathematics Teacher TPACK Standards offer guidelines for thinking about this…

Mathematical modelling in developmental biology.

PubMed

Vasieva, Olga; Rasolonjanahary, Manan'Iarivo; Vasiev, Bakhtier

2013-06-01

In recent decades, molecular and cellular biology has benefited from numerous fascinating developments in experimental technique, generating an overwhelming amount of data on various biological objects and processes. This, in turn, has led biologists to look for appropriate tools to facilitate systematic analysis of data. Thus, the need for mathematical techniques, which can be used to aid the classification and understanding of this ever-growing body of experimental data, is more profound now than ever before. Mathematical modelling is becoming increasingly integrated into biological studies in general and into developmental biology particularly. This review outlines some achievements of mathematics as applied to developmental biology and demonstrates the mathematical formulation of basic principles driving morphogenesis. We begin by describing a mathematical formalism used to analyse the formation and scaling of morphogen gradients. Then we address a problem of interplay between the dynamics of morphogen gradients and movement of cells, referring to mathematical models of gastrulation in the chick embryo. In the last section, we give an overview of various mathematical models used in the study of the developmental cycle of Dictyostelium discoideum, which is probably the best example of successful mathematical modelling in developmental biology.

Interdisciplinary Education--A Predator-Prey Model for Developing a Skill Set in Mathematics, Biology and Technology

ERIC Educational Resources Information Center

van der Hoff, Quay

2017-01-01

The science of biology has been transforming dramatically and so the need for a stronger mathematical background for biology students has increased. Biological students reaching the senior or post-graduate level often come to realize that their mathematical background is insufficient. Similarly, students in a mathematics programme, interested in…

Program Helps Generate Boundary-Element Mathematical Models

NASA Technical Reports Server (NTRS)

Goldberg, R. K.

1995-01-01

Composite Model Generation-Boundary Element Method (COM-GEN-BEM) computer program significantly reduces time and effort needed to construct boundary-element mathematical models of continuous-fiber composite materials at micro-mechanical (constituent) scale. Generates boundary-element models compatible with BEST-CMS boundary-element code for anlaysis of micromechanics of composite material. Written in PATRAN Command Language (PCL).

A Mathematical Model Development for the Lateral Collapse of Octagonal Tubes

NASA Astrophysics Data System (ADS)

Ghazali Kamardan, M.; Sufahani, Suliadi; Othman, M. Z. M.; Che-Him, Norziha; Khalid, Kamil; Roslan, Rozaini; Ali, Maselan; Zaidi, A. M. A.

2018-04-01

Many researches has been done on the lateral collapse of tube. However, the previous researches only focus on cylindrical and square tubes. Then a research has been done discovering the collapse behaviour of hexagonal tube and the mathematic model of the deformation behaviour had been developed [8]. The purpose of this research is to study the lateral collapse behaviour of symmetric octagonal tubes and hence to develop a mathematical model of the collapse behaviour of these tubes. For that, a predictive mathematical model was developed and a finite element analysis procedure was conducted for the lateral collapse behaviour of symmetric octagonal tubes. Lastly, the mathematical model was verified by using the finite element analysis simulation results. It was discovered that these tubes performed different deformation behaviour than the cylindrical tube. Symmetric octagonal tubes perform 2 phases of elastic - plastic deformation behaviour patterns. The mathematical model had managed to show the fundamental of the deformation behaviour of octagonal tubes. However, further studies need to be conducted in order to further improve on the proposed mathematical model.

Modeling of processing technologies in food industry

NASA Astrophysics Data System (ADS)

Korotkov, V. G.; Sagitov, R. F.; Popov, V. P.; Bachirov, V. D.; Akhmadieva, Z. R.; TSirkaeva, E. A.

2018-03-01

Currently, the society is facing an urgent need to solve the problems of nutrition (products with increased nutrition value) and to develop energy-saving technologies for food products. A mathematical modeling of heat and mass transfer of polymer materials in the extruder is rather successful these days. Mathematical description of movement and heat exchange during extrusion of gluten-protein-starch-containing material similar to pasta dough in its structure, were taken as a framework for the mathematical model presented in this paper.

Creative Thinking Ability to Increase Student Mathematical of Junior High School by Applying Models Numbered Heads Together

ERIC Educational Resources Information Center

Lince, Ranak

2016-01-01

Mathematical ability of students creative thinking is a component that must be mastered by the student. Mathematical creative thinking plays an important role, both in solving the problem and well, even in high school students. Therefore, efforts are needed to convey ideas in mathematics. But the reality is not yet developed the ability to…

Mathematical biology modules based on modern molecular biology and modern discrete mathematics.

PubMed

Robeva, Raina; Davies, Robin; Hodge, Terrell; Enyedi, Alexander

2010-01-01

We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network.

Mathematical Biology Modules Based on Modern Molecular Biology and Modern Discrete Mathematics

PubMed Central

Davies, Robin; Hodge, Terrell; Enyedi, Alexander

2010-01-01

We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network. PMID:20810955

Building a Case for Blocks as Kindergarten Mathematics Learning Tools

ERIC Educational Resources Information Center

Kinzer, Cathy; Gerhardt, Kacie; Coca, Nicole

2016-01-01

Kindergarteners need access to blocks as thinking tools to develop, model, test, and articulate their mathematical ideas. In the current educational landscape, resources such as blocks are being pushed to the side and being replaced by procedural worksheets and academic "seat time" in order to address standards. Mathematics research…

The role of mathematical models in understanding pattern formation in developmental biology.

PubMed

Umulis, David M; Othmer, Hans G

2015-05-01

In a Wall Street Journal article published on April 5, 2013, E. O. Wilson attempted to make the case that biologists do not really need to learn any mathematics-whenever they run into difficulty with numerical issues, they can find a technician (aka mathematician) to help them out of their difficulty. He formalizes this in Wilsons Principle No. 1: "It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations." This reflects a complete misunderstanding of the role of mathematics in all sciences throughout history. To Wilson, mathematics is mere number crunching, but as Galileo said long ago, "The laws of Nature are written in the language of mathematics[Formula: see text] the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word." Mathematics has moved beyond the geometry-based model of Galileo's time, and in a rebuttal to Wilson, E. Frenkel has pointed out the role of mathematics in synthesizing the general principles in science (Both point and counter-point are available in Wilson and Frenkel in Notices Am Math Soc 60(7):837-838, 2013). We will take this a step further and show how mathematics has been used to make new and experimentally verified discoveries in developmental biology and how mathematics is essential for understanding a problem that has puzzled experimentalists for decades-that of how organisms can scale in size. Mathematical analysis alone cannot "solve" these problems since the validation lies at the molecular level, but conversely, a growing number of questions in biology cannot be solved without mathematical analysis and modeling. Herein, we discuss a few examples of the productive intercourse between mathematics and biology.

Interdisciplinary education - a predator-prey model for developing a skill set in mathematics, biology and technology

NASA Astrophysics Data System (ADS)

van der Hoff, Quay

2017-08-01

The science of biology has been transforming dramatically and so the need for a stronger mathematical background for biology students has increased. Biological students reaching the senior or post-graduate level often come to realize that their mathematical background is insufficient. Similarly, students in a mathematics programme, interested in biological phenomena, find it difficult to master the complex systems encountered in biology. In short, the biologists do not have enough mathematics and the mathematicians are not being taught enough biology. The need for interdisciplinary curricula that includes disciplines such as biology, physical science, and mathematics is widely recognized, but has not been widely implemented. In this paper, it is suggested that students develop a skill set of ecology, mathematics and technology to encourage working across disciplinary boundaries. To illustrate such a skill set, a predator-prey model that contains self-limiting factors for both predator and prey is suggested. The general idea of dynamics, is introduced and students are encouraged to discover the applicability of this approach to more complex biological systems. The level of mathematics and technology required is not advanced; therefore, it is ideal for inclusion in a senior-level or introductory graduate-level course for students interested in mathematical biology.

Higher Education in Sint Maarten: Fostering Growth of Teacher Knowledge in Mathematics and Science

ERIC Educational Resources Information Center

Sargeant, Marcel A.; Burton, Larry D.; Bailey, Andel

2010-01-01

A needs analysis conducted as part of the foundation-based education (FBE) innovation on the island territory of Sint Maarten indicated the need for additional training of early primary teachers (PK-2) in mathematics and science education. Seven in-service workshops, designed around the Joyce-Showers' Training Model, were implemented over the…

Beyond the Transcript: Factors Influencing the Pursuit of Science and Mathematics Coursework

ERIC Educational Resources Information Center

Haag, Susan; Megowan, Colleen

2012-01-01

The nation's middle schools suffer from a shortage of qualified science and mathematics teachers. To address this need, one university in the southwest has developed the Modeling Institute, a master's degree program for in-service elementary educators interested in teaching science and mathematics at the middle school level. Identifying the…

Examining the Implementation of an Innovative Mathematics Curriculum

ERIC Educational Resources Information Center

Hansen, Heidi Britte

2010-01-01

Reform in mathematics instruction at the college level has been slow to arrive (Dossey, Halvorson, & McCrone, 2008), and many institutions of higher learning still follow the calculus model, while fewer and fewer students need calculus for their chosen areas of study (Ganter & Barker, 2003). Instead, mathematics that is applicable and transferable…

Subject design and factors affecting achievement in mathematics for biomedical science

NASA Astrophysics Data System (ADS)

Carnie, Steven; Morphett, Anthony

2017-01-01

Reports such as Bio2010 emphasize the importance of integrating mathematical modelling skills into undergraduate biology and life science programmes, to ensure students have the skills and knowledge needed for biological research in the twenty-first century. One way to do this is by developing a dedicated mathematics subject to teach modelling and mathematical concepts in biological contexts. We describe such a subject at a research-intensive Australian university, and discuss the considerations informing its design. We also present an investigation into the effect of mathematical and biological background, prior mathematical achievement, and gender, on student achievement in the subject. The investigation shows that several factors known to predict performance in standard calculus subjects apply also to specialized discipline-specific mathematics subjects, and give some insight into the relative importance of mathematical versus biological background for a biology-focused mathematics subject.

Mathematics, Thermodynamics, and Modeling to Address Ten Common Misconceptions about Protein Structure, Folding, and Stability

ERIC Educational Resources Information Center

Robic, Srebrenka

2010-01-01

To fully understand the roles proteins play in cellular processes, students need to grasp complex ideas about protein structure, folding, and stability. Our current understanding of these topics is based on mathematical models and experimental data. However, protein structure, folding, and stability are often introduced as descriptive, qualitative…

Modeling Scientific Processes with Mathematics Equations Enhances Student Qualitative Conceptual Understanding and Quantitative Problem Solving

ERIC Educational Resources Information Center

Schuchardt, Anita M.; Schunn, Christian D.

2016-01-01

Amid calls for integrating science, technology, engineering, and mathematics (iSTEM) in K-12 education, there is a pressing need to uncover productive methods of integration. Prior research has shown that increasing contextual linkages between science and mathematics is associated with student problem solving and conceptual understanding. However,…

How to Enlarge the Scope of the Curriculum Integration of Mathematics and Science (CIMAS): A Delphi Study

ERIC Educational Resources Information Center

Kim, Minkee; Aktan, Tugba

2014-01-01

Studies have not yet consented whether integrating mathematics into science would enhance students' learning or confuse their understanding of abstract mathematical concepts. In spite of the social need for solving social-scientific problems with multiple facets, there has not been a holistic integration model of the disciplines. Hence, this study…

Professional Development for Secondary School Mathematics Teachers: A Peer Mentoring Model

ERIC Educational Resources Information Center

Kensington-Miller, Barbara

2012-01-01

Professional development is important for all teachers, and in low socio-economic schools where the challenges of teaching are greater this need is crucial. A model involving a combination of one-on-one peer mentoring integrated with group peer mentoring was piloted with experienced mathematics teachers of senior students in low socio-economic…

Realistic Real World Contexts: Model Eliciting Activities

ERIC Educational Resources Information Center

Doruk, Bekir Kürsat

2016-01-01

Researchers have proposed a variety of methods to make a connection between real life and mathematics so that it can be learned in a practical way and enable people to utilise mathematics in their daily lives. Model-eliciting activities (MEAs) were developed to fulfil this need and are very capable of serving this purpose. The reason MEAs are so…

The Urban Mathematics Collaborative Project: Report to the Ford Foundation on the 1986-87 School Year. Program Report 88-1.

ERIC Educational Resources Information Center

Webb, Norman L.; And Others

In 1984 the Urban Mathematics Collaborative (UMC) project was initiated to improve mathematics education in inner-city schools and to identify new models for meeting the ongoing professional needs of teachers. UMCs are located in Cleveland, Minneapolis-St. Paul, Los Angeles, Philadelphia, San Francisco, Durham, Pittsburgh, San Diego, St. Louis,…

Voluntary Medical Male Circumcision for HIV Prevention: New Mathematical Models for Strategic Demand Creation Prioritizing Subpopulations by Age and Geography.

PubMed

Hankins, Catherine; Warren, Mitchell; Njeuhmeli, Emmanuel

2016-01-01

Over 11 million voluntary medical male circumcisions (VMMC) have been performed of the projected 20.3 million needed to reach 80% adult male circumcision prevalence in priority sub-Saharan African countries. Striking numbers of adolescent males, outside the 15-49-year-old age target, have been accessing VMMC services. What are the implications of overall progress in scale-up to date? Can mathematical modeling provide further insights on how to efficiently reach the male circumcision coverage levels needed to create and sustain further reductions in HIV incidence to make AIDS no longer a public health threat by 2030? Considering ease of implementation and cultural acceptability, decision makers may also value the estimates that mathematical models can generate of immediacy of impact, cost-effectiveness, and magnitude of impact resulting from different policy choices. This supplement presents the results of mathematical modeling using the Decision Makers' Program Planning Tool Version 2.0 (DMPPT 2.0), the Actuarial Society of South Africa (ASSA2008) model, and the age structured mathematical (ASM) model. These models are helping countries examine the potential effects on program impact and cost-effectiveness of prioritizing specific subpopulations for VMMC services, for example, by client age, HIV-positive status, risk group, and geographical location. The modeling also examines long-term sustainability strategies, such as adolescent and/or early infant male circumcision, to preserve VMMC coverage gains achieved during rapid scale-up. The 2016-2021 UNAIDS strategy target for VMMC is an additional 27 million VMMC in high HIV-prevalence settings by 2020, as part of access to integrated sexual and reproductive health services for men. To achieve further scale-up, a combination of evidence, analysis, and impact estimates can usefully guide strategic planning and funding of VMMC services and related demand-creation strategies in priority countries. Mid-course corrections now can improve cost-effectiveness and scale to achieve the impact needed to help turn the HIV pandemic on its head within 15 years.

Use of open-ended problems as the basis for the mathematical creativity growth disclosure of student

NASA Astrophysics Data System (ADS)

Suyitno, A.; Suyitno, H.; Rochmad; Dwijanto

2018-03-01

Mathematical creativity is the essence of learning in mathematics. However, mathematical creativity had not yet grown among students. Means there was a gap between needs and reality. This gap must be bridged through by scientific studies, and there were novelty findings, namely the discovery of stages to cultivate of Mathematical Creativity. The problem formulation: How to use of open-ended problems as the basis for the mathematical creativity growth disclosure of student? The goal was to use of open issues as the basis for the mathematical creativity growth disclosure of student. Research method with a qualitative approach. After data was collected then activity in data analysis, include data reduction, data presentation, data interpretation, and conclusion/verification. The results of the research: After the learning by applying the modification of RTTW learning model, then the students were trained to do the open-ended problems and by looking at the UTS and UAS values then qualitatively the results: (1) There was a significant increase of the student's final score. (2) The category of the growth of mathematical creativity of students, the Very Good there were three students, the Good there were six students, There were 17 students, and there were six students. The validation of these results was reinforced by interviews and triangulation. (3) Stage to cultivate mathematical creativity: lecturers should need to provide inputs on student work; Apply an appropriate learning model, and train students to work on the continuing problems.

Systems oncology: towards patient-specific treatment regimes informed by multiscale mathematical modelling.

PubMed

Powathil, Gibin G; Swat, Maciej; Chaplain, Mark A J

2015-02-01

The multiscale complexity of cancer as a disease necessitates a corresponding multiscale modelling approach to produce truly predictive mathematical models capable of improving existing treatment protocols. To capture all the dynamics of solid tumour growth and its progression, mathematical modellers need to couple biological processes occurring at various spatial and temporal scales (from genes to tissues). Because effectiveness of cancer therapy is considerably affected by intracellular and extracellular heterogeneities as well as by the dynamical changes in the tissue microenvironment, any model attempt to optimise existing protocols must consider these factors ultimately leading to improved multimodal treatment regimes. By improving existing and building new mathematical models of cancer, modellers can play important role in preventing the use of potentially sub-optimal treatment combinations. In this paper, we analyse a multiscale computational mathematical model for cancer growth and spread, incorporating the multiple effects of radiation therapy and chemotherapy in the patient survival probability and implement the model using two different cell based modelling techniques. We show that the insights provided by such multiscale modelling approaches can ultimately help in designing optimal patient-specific multi-modality treatment protocols that may increase patients quality of life. Copyright © 2014 Elsevier Ltd. All rights reserved.

Authentic Integration: a model for integrating mathematics and science in the classroom

NASA Astrophysics Data System (ADS)

Treacy, Páraic; O'Donoghue, John

2014-07-01

Attempts at integrating mathematics and science have been made previously but no definitive, widely adopted teaching model has been developed to date. Research suggests that hands-on, practical, student-centred tasks should form a central element when designing an effective model for the integration of mathematics and science. Aided by this research, the author created a new model entitled 'Authentic Integration' which caters for the specific needs of integration of mathematics and science. This model requires that each lesson be based around a rich task which relates to the real world and ensures that hands-on group work, inquiry, and discussion are central to the lesson. It was found that Authentic Integration, when applied in four Irish post-primary schools, positively affected pupil understanding. The teachers who completed the intervention displayed a very positive attitude towards the approach, intimating that they would continue to implement the practice in their classrooms.

Mathematical Models of Breast and Ovarian Cancers

PubMed Central

Botesteanu, Dana-Adriana; Lipkowitz, Stanley; Lee, Jung-Min; Levy, Doron

2016-01-01

Women constitute the majority of the aging United States (US) population, and this has substantial implications on cancer population patterns and management practices. Breast cancer is the most common women's malignancy, while ovarian cancer is the most fatal gynecological malignancy in the US. In this review we focus on these subsets of women's cancers, seen more commonly in postmenopausal and elderly women. In order to systematically investigate the complexity of cancer progression and response to treatment in breast and ovarian malignancies, we assert that integrated mathematical modeling frameworks viewed from a systems biology perspective are needed. Such integrated frameworks could offer innovative contributions to the clinical women's cancers community, since answers to clinical questions cannot always be reached with contemporary clinical and experimental tools. Here, we recapitulate clinically known data regarding the progression and treatment of the breast and ovarian cancers. We compare and contrast the two malignancies whenever possible, in order to emphasize areas where substantial contributions could be made by clinically inspired and validated mathematical modeling. We show how current paradigms in the mathematical oncology community focusing on the two malignancies do not make comprehensive use of, nor substantially reflect existing clinical data, and we highlight the modeling areas in most critical need of clinical data integration. We emphasize that the primary goal of any mathematical study of women's cancers should be to address clinically relevant questions. PMID:27259061

Mathematical Metaphors: Problem Reformulation and Analysis Strategies

NASA Technical Reports Server (NTRS)

Thompson, David E.

2005-01-01

This paper addresses the critical need for the development of intelligent or assisting software tools for the scientist who is working in the initial problem formulation and mathematical model representation stage of research. In particular, examples of that representation in fluid dynamics and instability theory are discussed. The creation of a mathematical model that is ready for application of certain solution strategies requires extensive symbolic manipulation of the original mathematical model. These manipulations can be as simple as term reordering or as complicated as discovery of various symmetry groups embodied in the equations, whereby Backlund-type transformations create new determining equations and integrability conditions or create differential Grobner bases that are then solved in place of the original nonlinear PDEs. Several examples are presented of the kinds of problem formulations and transforms that can be frequently encountered in model representation for fluids problems. The capability of intelligently automating these types of transforms, available prior to actual mathematical solution, is advocated. Physical meaning and assumption-understanding can then be propagated through the mathematical transformations, allowing for explicit strategy development.

Representations and Rafts

ERIC Educational Resources Information Center

Hartweg, Kimberly Sipes

2011-01-01

To build on prior knowledge and mathematical understanding, middle school students need to be given the opportunity to make connections among a variety of representations. Graphs, tables, algebraic formulas, and models are just a few examples of representations that can help students explore quantitative relationships. As a mathematics educator,…

Molecular modeling: An open invitation for applied mathematics

NASA Astrophysics Data System (ADS)

Mezey, Paul G.

2013-10-01

Molecular modeling methods provide a very wide range of challenges for innovative mathematical and computational techniques, where often high dimensionality, large sets of data, and complicated interrelations imply a multitude of iterative approximations. The physical and chemical basis of these methodologies involves quantum mechanics with several non-intuitive aspects, where classical interpretation and classical analogies are often misleading or outright wrong. Hence, instead of the everyday, common sense approaches which work so well in engineering, in molecular modeling one often needs to rely on rather abstract mathematical constraints and conditions, again emphasizing the high level of reliance on applied mathematics. Yet, the interdisciplinary aspects of the field of molecular modeling also generates some inertia and perhaps too conservative reliance on tried and tested methodologies, that is at least partially caused by the less than up-to-date involvement in the newest developments in applied mathematics. It is expected that as more applied mathematicians take up the challenge of employing the latest advances of their field in molecular modeling, important breakthroughs may follow. In this presentation some of the current challenges of molecular modeling are discussed.

Use of mathematical modelling to assess the impact of vaccines on antibiotic resistance.

PubMed

Atkins, Katherine E; Lafferty, Erin I; Deeny, Sarah R; Davies, Nicholas G; Robotham, Julie V; Jit, Mark

2018-06-01

Antibiotic resistance is a major global threat to the provision of safe and effective health care. To control antibiotic resistance, vaccines have been proposed as an essential intervention, complementing improvements in diagnostic testing, antibiotic stewardship, and drug pipelines. The decision to introduce or amend vaccination programmes is routinely based on mathematical modelling. However, few mathematical models address the impact of vaccination on antibiotic resistance. We reviewed the literature using PubMed to identify all studies that used an original mathematical model to quantify the impact of a vaccine on antibiotic resistance transmission within a human population. We reviewed the models from the resulting studies in the context of a new framework to elucidate the pathways through which vaccination might impact antibiotic resistance. We identified eight mathematical modelling studies; the state of the literature highlighted important gaps in our understanding. Notably, studies are limited in the range of pathways represented, their geographical scope, and the vaccine-pathogen combinations assessed. Furthermore, to translate model predictions into public health decision making, more work is needed to understand how model structure and parameterisation affects model predictions and how to embed these predictions within economic frameworks. Copyright © 2018 Elsevier Ltd. All rights reserved.

Mathematical and Numerical Techniques in Energy and Environmental Modeling

NASA Astrophysics Data System (ADS)

Chen, Z.; Ewing, R. E.

Mathematical models have been widely used to predict, understand, and optimize many complex physical processes, from semiconductor or pharmaceutical design to large-scale applications such as global weather models to astrophysics. In particular, simulation of environmental effects of air pollution is extensive. Here we address the need for using similar models to understand the fate and transport of groundwater contaminants and to design in situ remediation strategies. Three basic problem areas need to be addressed in the modeling and simulation of the flow of groundwater contamination. First, one obtains an effective model to describe the complex fluid/fluid and fluid/rock interactions that control the transport of contaminants in groundwater. This includes the problem of obtaining accurate reservoir descriptions at various length scales and modeling the effects of this heterogeneity in the reservoir simulators. Next, one develops accurate discretization techniques that retain the important physical properties of the continuous models. Finally, one develops efficient numerical solution algorithms that utilize the potential of the emerging computing architectures. We will discuss recent advances and describe the contribution of each of the papers in this book in these three areas. Keywords: reservoir simulation, mathematical models, partial differential equations, numerical algorithms

Mathematical modeling of cancer metabolism.

PubMed

Medina, Miguel Ángel

2018-04-01

Systemic approaches are needed and useful for the study of the very complex issue of cancer. Modeling has a central position in these systemic approaches. Metabolic reprogramming is nowadays acknowledged as an essential hallmark of cancer. Mathematical modeling could contribute to a better understanding of cancer metabolic reprogramming and to identify new potential ways of therapeutic intervention. Herein, I review several alternative approaches to metabolic modeling and their current and future impact in oncology. Copyright © 2018 Elsevier B.V. All rights reserved.

Expanding your Horizons: a Program for Engaging Middle School Girls in Science and Mathematics

NASA Astrophysics Data System (ADS)

Jahnke, Tamera S.; Level, Allison V.

Gender equity in science, mathematics, and technology is an issue that has generated the creation of a number of programs. Young women need to be aware that there are a variety of careers in science, mathematics, and technology that they can actively pursue. This article highlights one example of a successful middle school science program in Southwest Missouri. Expanding Your Horizons in Science, Mathematics, and Technology (EYH) integrates keynote speakers, role model mentoring sessions, and small group experiments into a hands-on learning environment. Initial survey results of parents and teachers show support for the conference and indicate that the program helps motivate students to consider careers in science, mathematics, and technology. In addition to the goal of increasing awareness for these young people, there is a need for increased scientific literacy of the general public and an increased application of science to "real world" circumstances. This program addresses these issues.

Enhancing mathematics teachers' quality through Lesson Study.

PubMed

Lomibao, Laila S

2016-01-01

The efficiency and effectivity of the learning experience is dependent on the teacher quality, thus, enhancing teacher's quality is vital in improving the students learning outcome. Since, the usual top-down one-shot cascading model practice for teachers' professional development in Philippines has been observed to have much information dilution, and the Southeast Asian Ministers of Education Organization demanded the need to develop mathematics teachers' quality standards through the Southeast Asia Regional Standards for Mathematics Teachers (SEARS-MT), thus, an intensive, ongoing professional development model should be provided to teachers. This study was undertaken to determine the impact of Lesson Study on Bulua National High School mathematics teachers' quality level in terms of SEARS-MT dimensions. A mixed method of quantitative-qualitative research design was employed. Results of the analysis revealed that Lesson Study effectively enhanced mathematics teachers' quality and promoted teachers professional development. Teachers positively perceived Lesson Study to be beneficial for them to become a better mathematics teacher.

The Role of Mathematical Models in Understanding Pattern Formation in Developmental Biology

PubMed Central

Umulis, David M.

2016-01-01

In a Wall Street Journal article published on April 5, 2013, E. O. Wilson attempted to make the case that biologists do not really need to learn any mathematics—whenever they run into difficulty with numerical issues, they can find a technician (aka mathematician) to help them out of their difficulty. He formalizes this in Wilsons Principle No. 1: “It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations.” This reflects a complete misunderstanding of the role of mathematics in all sciences throughout history. To Wilson, mathematics is mere number crunching, but as Galileo said long ago, “The laws of Nature are written in the language of mathematics…the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word.” Mathematics has moved beyond the geometry-based model of Galileo’s time, and in a rebuttal to Wilson, E. Frenkel has pointed out the role of mathematics in synthesizing the general principles in science (Both point and counter-point are available in Wilson and Frenkel in Notices Am Math Soc 60(7):837–838, 2013). We will take this a step further and show how mathematics has been used to make new and experimentally verified discoveries in developmental biology and how mathematics is essential for understanding a problem that has puzzled experimentalists for decades—that of how organisms can scale in size. Mathematical analysis alone cannot “solve” these problems since the validation lies at the molecular level, but conversely, a growing number of questions in biology cannot be solved without mathematical analysis and modeling. Herein, we discuss a few examples of the productive intercourse between mathematics and biology. PMID:25280665

Application of mathematical modeling in sustained release delivery systems.

PubMed

Grassi, Mario; Grassi, Gabriele

2014-08-01

This review, presenting as starting point the concept of the mathematical modeling, is aimed at the physical and mathematical description of the most important mechanisms regulating drug delivery from matrix systems. The precise knowledge of the delivery mechanisms allows us to set up powerful mathematical models which, in turn, are essential for the design and optimization of appropriate drug delivery systems. The fundamental mechanisms for drug delivery from matrices are represented by drug diffusion, matrix swelling, matrix erosion, drug dissolution with possible recrystallization (e.g., as in the case of amorphous and nanocrystalline drugs), initial drug distribution inside the matrix, matrix geometry, matrix size distribution (in the case of spherical matrices of different diameter) and osmotic pressure. Depending on matrix characteristics, the above-reported variables may play a different role in drug delivery; thus the mathematical model needs to be built solely on the most relevant mechanisms of the particular matrix considered. Despite the somewhat diffident behavior of the industrial world, in the light of the most recent findings, we believe that mathematical modeling may have a tremendous potential impact in the pharmaceutical field. We do believe that mathematical modeling will be more and more important in the future especially in the light of the rapid advent of personalized medicine, a novel therapeutic approach intended to treat each single patient instead of the 'average' patient.

The effect of mathematical model development on the instruction of acceleration to introductory physics students

NASA Astrophysics Data System (ADS)

Sauer, Tim Allen

The purpose of this study was to evaluate the effectiveness of utilizing student constructed theoretical math models when teaching acceleration to high school introductory physics students. The goal of the study was for the students to be able to utilize mathematical modeling strategies to improve their problem solving skills, as well as their standardized scientific and conceptual understanding. This study was based on mathematical modeling research, conceptual change research and constructivist theory of learning, all of which suggest that mathematical modeling is an effective way to influence students' conceptual connectiveness and sense making of formulaic equations and problem solving. A total of 48 students in two sections of high school introductory physics classes received constructivist, inquiry-based, cooperative learning, and conceptual change-oriented instruction. The difference in the instruction for the 24 students in the mathematical modeling treatment group was that they constructed every formula they needed to solve problems from data they collected. In contrast, the instructional design for the control group of 24 students allowed the same instruction with assigned problems solved with formulas given to them without explanation. The results indicated that the mathematical modeling students were able to solve less familiar and more complicated problems with greater confidence and mental flexibility than the control group students. The mathematical modeling group maintained fewer alternative conceptions consistently in the interviews than did the control group. The implications for acceleration instruction from these results were discussed.

Our Prospective Mathematic Teachers Are Not Critical Thinkers Yet

ERIC Educational Resources Information Center

As'ari, Abdur Rahman; Mahmudi, Ali; Nuerlaelah, Elah

2017-01-01

In order to help students develop their critical thinking skills, teachers need to model the critical thinking skills and dispositions in front of their students. Unfortunately, very rare studies investigating prospective teachers' readiness in critical thinking dispositions are available in the field of mathematics education. This study was…

Mathematical modeling of reflectance and intrinsic fluorescence for cancer detection in human pancreatic tissue

NASA Astrophysics Data System (ADS)

Wilson, Robert H.; Chandra, Malavika; Scheiman, James; Simeone, Diane; McKenna, Barbara; Purdy, Julianne; Mycek, Mary-Ann

2009-02-01

Pancreatic adenocarcinoma has a five-year survival rate of only 4%, largely because an effective procedure for early detection has not been developed. In this study, mathematical modeling of reflectance and fluorescence spectra was utilized to quantitatively characterize differences between normal pancreatic tissue, pancreatitis, and pancreatic adenocarcinoma. Initial attempts at separating the spectra of different tissue types involved dividing fluorescence by reflectance, and removing absorption artifacts by applying a "reverse Beer-Lambert factor" when the absorption coefficient was modeled as a linear combination of the extinction coefficients of oxy- and deoxy-hemoglobin. These procedures demonstrated the need for a more complete mathematical model to quantitatively describe fluorescence and reflectance for minimally-invasive fiber-based optical diagnostics in the pancreas.

Unlocking the black box: teaching mathematical modeling with popular culture.

PubMed

Lofgren, Eric T

2016-10-01

Mathematical modeling is an important tool in biological research, allowing for the synthesis of results from many studies into an understanding of a system. Despite this, the need for extensive subject matter knowledge and complex mathematics often leaves modeling as an esoteric subspecialty. A 2-fold approach can be used to make modeling more approachable for students and those interested in obtaining a functional knowledge of modeling. The first is the use of a popular culture disease system-a zombie epidemic-to allow for exploration of the concepts of modeling using a flexible framework. The second is the use of available interactive and non-calculus-based tools to allow students to work with and implement models to cement their understanding. © FEMS 2016. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Interaction of mathematical modeling and social and behavioral HIV/AIDS research.

PubMed

Cassels, Susan; Goodreau, Steven M

2011-03-01

HIV is transmitted within complex biobehavioral systems. Mathematical modeling can provide insight to complex population-level outcomes of various behaviors measured at an individual level. HIV models in the social and behavioral sciences can be categorized in a number of ways; here, we consider two classes of applications common in the field generally, and in the past year in particular: those models that explore significant behavioral determinants of HIV disparities within and between populations; and those models that seek to evaluate the potential impact of specific social and behavioral interventions. We discuss two overarching issues we see in the field: the need to further systematize effectiveness models of behavioral interventions, and the need for increasing investigation of the use of behavioral data in epidemic models. We believe that a recent initiative by the National Institutes of Health will qualitatively change the relationships between epidemic modeling and sociobehavioral prevention research in the coming years.

The need for data science in epidemic modelling. Comment on: "Mathematical models to characterize early epidemic growth: A review" by Gerardo Chowell et al.

NASA Astrophysics Data System (ADS)

Danon, Leon; Brooks-Pollock, Ellen

2016-09-01

In their review, Chowell et al. consider the ability of mathematical models to predict early epidemic growth [1]. In particular, they question the central prediction of classical differential equation models that the number of cases grows exponentially during the early stages of an epidemic. Using examples including HIV and Ebola, they argue that classical models fail to capture key qualitative features of early growth and describe a selection of models that do capture non-exponential epidemic growth. An implication of this failure is that predictions may be inaccurate and unusable, highlighting the need for care when embarking upon modelling using classical methodology. There remains a lack of understanding of the mechanisms driving many observed epidemic patterns; we argue that data science should form a fundamental component of epidemic modelling, providing a rigorous methodology for data-driven approaches, rather than trying to enforce established frameworks. The need for refinement of classical models provides a strong argument for the use of data science, to identify qualitative characteristics and pinpoint the mechanisms responsible for the observed epidemic patterns.

Taguchi method for partial differential equations with application in tumor growth.

PubMed

Ilea, M; Turnea, M; Rotariu, M; Arotăriţei, D; Popescu, Marilena

2014-01-01

The growth of tumors is a highly complex process. To describe this process, mathematical models are needed. A variety of partial differential mathematical models for tumor growth have been developed and studied. Most of those models are based on the reaction-diffusion equations and mass conservation law. A variety of modeling strategies have been developed, each focusing on tumor growth. Systems of time-dependent partial differential equations occur in many branches of applied mathematics. The vast majority of mathematical models in tumor growth are formulated in terms of partial differential equations. We propose a mathematical model for the interactions between these three cancer cell populations. The Taguchi methods are widely used by quality engineering scientists to compare the effects of multiple variables, together with their interactions, with a simple and manageable experimental design. In Taguchi's design of experiments, variation is more interesting to study than the average. First, Taguchi methods are utilized to search for the significant factors and the optimal level combination of parameters. Except the three parameters levels, other factors levels other factors levels would not be considered. Second, cutting parameters namely, cutting speed, depth of cut, and feed rate are designed using the Taguchi method. Finally, the adequacy of the developed mathematical model is proved by ANOVA. According to the results of ANOVA, since the percentage contribution of the combined error is as small. Many mathematical models can be quantitatively characterized by partial differential equations. The use of MATLAB and Taguchi method in this article illustrates the important role of informatics in research in mathematical modeling. The study of tumor growth cells is an exciting and important topic in cancer research and will profit considerably from theoretical input. Interpret these results to be a permanent collaboration between math's and medical oncologists.

Voluntary Medical Male Circumcision for HIV Prevention: New Mathematical Models for Strategic Demand Creation Prioritizing Subpopulations by Age and Geography

PubMed Central

Hankins, Catherine; Warren, Mitchell

2016-01-01

Over 11 million voluntary medical male circumcisions (VMMC) have been performed of the projected 20.3 million needed to reach 80% adult male circumcision prevalence in priority sub-Saharan African countries. Striking numbers of adolescent males, outside the 15-49-year-old age target, have been accessing VMMC services. What are the implications of overall progress in scale-up to date? Can mathematical modeling provide further insights on how to efficiently reach the male circumcision coverage levels needed to create and sustain further reductions in HIV incidence to make AIDS no longer a public health threat by 2030? Considering ease of implementation and cultural acceptability, decision makers may also value the estimates that mathematical models can generate of immediacy of impact, cost-effectiveness, and magnitude of impact resulting from different policy choices. This supplement presents the results of mathematical modeling using the Decision Makers’ Program Planning Tool Version 2.0 (DMPPT 2.0), the Actuarial Society of South Africa (ASSA2008) model, and the age structured mathematical (ASM) model. These models are helping countries examine the potential effects on program impact and cost-effectiveness of prioritizing specific subpopulations for VMMC services, for example, by client age, HIV-positive status, risk group, and geographical location. The modeling also examines long-term sustainability strategies, such as adolescent and/or early infant male circumcision, to preserve VMMC coverage gains achieved during rapid scale-up. The 2016–2021 UNAIDS strategy target for VMMC is an additional 27 million VMMC in high HIV-prevalence settings by 2020, as part of access to integrated sexual and reproductive health services for men. To achieve further scale-up, a combination of evidence, analysis, and impact estimates can usefully guide strategic planning and funding of VMMC services and related demand-creation strategies in priority countries. Mid-course corrections now can improve cost-effectiveness and scale to achieve the impact needed to help turn the HIV pandemic on its head within 15 years. PMID:27783613

Modeling eBook acceptance: A study on mathematics teachers

NASA Astrophysics Data System (ADS)

Jalal, Azlin Abd; Ayub, Ahmad Fauzi Mohd; Tarmizi, Rohani Ahmad

2014-12-01

The integration and effectiveness of eBook utilization in Mathematics teaching and learning greatly relied upon the teachers, hence the need to understand their perceptions and beliefs. The eBook, an individual laptop completed with digitized textbook sofwares, were provided for each students in line with the concept of 1 student:1 laptop. This study focuses on predicting a model on the acceptance of the eBook among Mathematics teachers. Data was collected from 304 mathematics teachers in selected schools using a survey questionnaire. The selection were based on the proportionate stratified sampling. Structural Equation Modeling (SEM) were employed where the model was tested and evaluated and was found to have a good fit. The variance explained for the teachers' attitude towards eBook is approximately 69.1% where perceived usefulness appeared to be a stronger determinant compared to perceived ease of use. This study concluded that the attitude of mathematics teachers towards eBook depends largely on the perception of how useful the eBook is on improving their teaching performance, implying that teachers should be kept updated with the latest mathematical application and sofwares to use with the eBook to ensure positive attitude towards using it in class.

Mathematical modeling analysis of intratumoral disposition of anticancer agents and drug delivery systems.

PubMed

Popilski, Hen; Stepensky, David

2015-05-01

Solid tumors are characterized by complex morphology. Numerous factors relating to the composition of the cells and tumor stroma, vascularization and drainage of fluids affect the local microenvironment within a specific location inside the tumor. As a result, the intratumoral drug/drug delivery system (DDS) disposition following systemic or local administration is non-homogeneous and its complexity reflects the differences in the local microenvironment. Mathematical models can be used to analyze the intratumoral drug/DDS disposition and pharmacological effects and to assist in choice of optimal anticancer treatment strategies. The mathematical models that have been applied by different research groups to describe the intratumoral disposition of anticancer drugs/DDSs are summarized in this article. The properties of these models and of their suitability for prediction of the drug/DDS intratumoral disposition and pharmacological effects are reviewed. Currently available mathematical models appear to neglect some of the major factors that govern the drug/DDS intratumoral disposition, and apparently possess limited prediction capabilities. More sophisticated and detailed mathematical models and their extensive validation are needed for reliable prediction of different treatment scenarios and for optimization of drug treatment in the individual cancer patients.

SIMULATION MODELING OF GASTROINTESTINAL ABSORPTION

EPA Science Inventory

Mathematical dosimetry models incorporate mechanistic determinants of chemical disposition in a living organism to describe relationships between exposure concentration and the internal dose needed for PBPK models and human health risk assessment. Because they rely on determini...

A Mathematical Model of Marine Diesel Engine Speed Control System

NASA Astrophysics Data System (ADS)

Sinha, Rajendra Prasad; Balaji, Rajoo

2018-02-01

Diesel engine is inherently an unstable machine and requires a reliable control system to regulate its speed for safe and efficient operation. Also, the diesel engine may operate at fixed or variable speeds depending upon user's needs and accordingly the speed control system should have essential features to fulfil these requirements. This paper proposes a mathematical model of a marine diesel engine speed control system with droop governing function. The mathematical model includes static and dynamic characteristics of the control loop components. Model of static characteristic of the rotating fly weights speed sensing element provides an insight into the speed droop features of the speed controller. Because of big size and large time delay, the turbo charged diesel engine is represented as a first order system or sometimes even simplified to a pure integrator with constant gain which is considered acceptable in control literature. The proposed model is mathematically less complex and quick to use for preliminary analysis of the diesel engine speed controller performance.

Analysis mathematical literacy skills in terms of the students’ metacognition on PISA-CPS model

NASA Astrophysics Data System (ADS)

Ovan; Waluya, S. B.; Nugroho, S. E.

2018-03-01

This research was aimed to know the effectiveness of PISA-CPS model and desceibe the mathematical literacy skills (KLM) in terms of the students’ metacognition. This study used Mixed Methods approaches with the concurrent embedded desaign. The technique of data analysis on quantitative research done analysis of lesson plan, prerequisite test, test hypotesis 1 and hypotesis test. While qualitative research done data reduction, data presentation, and drawing conclution and data verification. The subject of this study was the students of Grade Eight (VIII) of SMP Islam Sultan Agung 4 Semarang, Central Java. The writer analyzed the data with quantitative and qualitative approaches based on the metacognition of the students in low, medium and high groups. Subsequently, taken the mathematical literacy skills (KLM) from students’ metacognition in low, medium, and high . The results of the study showed that the PISA-CPS model was complete and the students’ mathematical literacy skills in terms of the students’ metacognition taught by the PISA-CPS model was higher than the expository learning. metacognitions’ students classified low hadmathematical literacy skills (KLM) less good, metacognitions’ students classified medium had mathematical literacy skills (KLM) good enough, metacognitions’ students classified high had mathematical literacy skills (KLM) very good. Based onresult analysis got conclusion that the PISA-CPS model was effective toward the students’ mathematical literacy skills (KLM). To increase the students’ mathematical literacy skills (KLM), the teachers need to provide reinforcements in the form of the exercises so that the student’s mathematical literacy was achieved at level 5 and level 6.

Urban Middle-Grade Student Mathematics Achievement Growth under Comprehensive School Reform

ERIC Educational Resources Information Center

Mac Iver, Martha Abele; Mac Iver, Douglas J.

2009-01-01

Recognizing the need to implement standards-based instructional materials with school-wide coherence led some Philadelphia schools to adopt whole-school reform (WSR) models during the late 1990s. The authors report on the relation between mathematics achievement growth for middle-grade students on the Pennsylvania System of School Assessments and…

Relations among Brief Measures of Mathematics, Reading, and Processing Speed: A Construct Validity Study

ERIC Educational Resources Information Center

Maynard, Jennifer Leigh

2012-01-01

Emphasis on regular mathematics skill assessment, intervention, and progress monitoring under the RTI model has created a need for the development of assessment instruments that are psychometrically sound, reliable, universal, and brief. Important factors to consider when developing or selecting assessments for the school environment include what…

Developing teachers' models for assessing students' competence in mathematical modelling through lesson study

NASA Astrophysics Data System (ADS)

Aydogan Yenmez, Arzu; Erbas, Ayhan Kursat; Cakiroglu, Erdinc; Alacaci, Cengiz; Cetinkaya, Bulent

2017-08-01

Applications and modelling have gained a prominent role in mathematics education reform documents and curricula. Thus, there is a growing need for studies focusing on the effective use of mathematical modelling in classrooms. Assessment is an integral part of using modelling activities in classrooms, since it allows teachers to identify and manage problems that arise in various stages of the modelling process. However, teachers' difficulties in assessing student modelling work are a challenge to be considered when implementing modelling in the classroom. Thus, the purpose of this study was to investigate how teachers' knowledge on generating assessment criteria for assessing student competence in mathematical modelling evolved through a professional development programme, which is based on a lesson study approach and modelling perspective. The data was collected with four teachers from two public high schools over a five-month period. The professional development programme included a cyclical process, with each cycle consisting of an introductory meeting, the implementation of a model-eliciting activity with students, and a follow-up meeting. The results showed that the professional development programme contributed to teachers' knowledge for generating assessment criteria on the products, and the observable actions that affect the modelling cycle.

A mathematical programming method for formulating a fuzzy regression model based on distance criterion.

PubMed

Chen, Liang-Hsuan; Hsueh, Chan-Ching

2007-06-01

Fuzzy regression models are useful to investigate the relationship between explanatory and response variables with fuzzy observations. Different from previous studies, this correspondence proposes a mathematical programming method to construct a fuzzy regression model based on a distance criterion. The objective of the mathematical programming is to minimize the sum of distances between the estimated and observed responses on the X axis, such that the fuzzy regression model constructed has the minimal total estimation error in distance. Only several alpha-cuts of fuzzy observations are needed as inputs to the mathematical programming model; therefore, the applications are not restricted to triangular fuzzy numbers. Three examples, adopted in the previous studies, and a larger example, modified from the crisp case, are used to illustrate the performance of the proposed approach. The results indicate that the proposed model has better performance than those in the previous studies based on either distance criterion or Kim and Bishu's criterion. In addition, the efficiency and effectiveness for solving the larger example by the proposed model are also satisfactory.

Mathematical models to characterize early epidemic growth: A Review

PubMed Central

Chowell, Gerardo; Sattenspiel, Lisa; Bansal, Shweta; Viboud, Cécile

2016-01-01

There is a long tradition of using mathematical models to generate insights into the transmission dynamics of infectious diseases and assess the potential impact of different intervention strategies. The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing reliable models that capture the baseline transmission characteristics of specific pathogens and social contexts. More refined models are needed however, in particular to account for variation in the early growth dynamics of real epidemics and to gain a better understanding of the mechanisms at play. Here, we review recent progress on modeling and characterizing early epidemic growth patterns from infectious disease outbreak data, and survey the types of mathematical formulations that are most useful for capturing a diversity of early epidemic growth profiles, ranging from sub-exponential to exponential growth dynamics. Specifically, we review mathematical models that incorporate spatial details or realistic population mixing structures, including meta-population models, individual-based network models, and simple SIR-type models that incorporate the effects of reactive behavior changes or inhomogeneous mixing. In this process, we also analyze simulation data stemming from detailed large-scale agent-based models previously designed and calibrated to study how realistic social networks and disease transmission characteristics shape early epidemic growth patterns, general transmission dynamics, and control of international disease emergencies such as the 2009 A/H1N1 influenza pandemic and the 2014-15 Ebola epidemic in West Africa. PMID:27451336

Mathematical models to characterize early epidemic growth: A review

NASA Astrophysics Data System (ADS)

Chowell, Gerardo; Sattenspiel, Lisa; Bansal, Shweta; Viboud, Cécile

2016-09-01

There is a long tradition of using mathematical models to generate insights into the transmission dynamics of infectious diseases and assess the potential impact of different intervention strategies. The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing reliable models that capture the baseline transmission characteristics of specific pathogens and social contexts. More refined models are needed however, in particular to account for variation in the early growth dynamics of real epidemics and to gain a better understanding of the mechanisms at play. Here, we review recent progress on modeling and characterizing early epidemic growth patterns from infectious disease outbreak data, and survey the types of mathematical formulations that are most useful for capturing a diversity of early epidemic growth profiles, ranging from sub-exponential to exponential growth dynamics. Specifically, we review mathematical models that incorporate spatial details or realistic population mixing structures, including meta-population models, individual-based network models, and simple SIR-type models that incorporate the effects of reactive behavior changes or inhomogeneous mixing. In this process, we also analyze simulation data stemming from detailed large-scale agent-based models previously designed and calibrated to study how realistic social networks and disease transmission characteristics shape early epidemic growth patterns, general transmission dynamics, and control of international disease emergencies such as the 2009 A/H1N1 influenza pandemic and the 2014-2015 Ebola epidemic in West Africa.

EPAs Virtual Embryo: Modeling Developmental Toxicity

EPA Science Inventory

Embryogenesis is regulated by concurrent activities of signaling pathways organized into networks that control spatial patterning, molecular clocks, morphogenetic rearrangements and cell differentiation. Quantitative mathematical and computational models are needed to better unde...

Using models to manage systems subject to sustainability indicators

USGS Publications Warehouse

Hill, M.C.

2006-01-01

Mathematical and numerical models can provide insight into sustainability indicators using relevant simulated quantities, which are referred to here as predictions. To be useful, many concerns need to be considered. Four are discussed here: (a) mathematical and numerical accuracy of the model; (b) the accuracy of the data used in model development, (c) the information observations provide to aspects of the model important to predictions of interest as measured using sensitivity analysis; and (d) the existence of plausible alternative models for a given system. The four issues are illustrated using examples from conservative and transport modelling, and using conceptual arguments. Results suggest that ignoring these issues can produce misleading conclusions.

A survey on the measure of combat readiness

NASA Astrophysics Data System (ADS)

Wen, Kwong Fook; Nor, Norazman Mohamad; Soon, Lee Lai

2014-09-01

Measuring the combat readiness in military forces involves the measures of tangible and intangible elements of combat power. Though these measures are applicable, the mathematical models and formulae used focus mainly on either the tangible or the intangible elements. In this paper, a review is done to highlight the research gap in the formulation of a mathematical model that incorporates tangible elements with intangible elements to measure the combat readiness of a military force. It highlights the missing link between the tangible and intangible elements of combat power. To bridge the gap and missing link, a mathematical model could be formulated that measures both the tangible and intangible aspects of combat readiness by establishing the relationship between the causal (tangible and intangible) elements and its effects on the measure of combat readiness. The model uses multiple regression analysis as well as mathematical modeling and simulation which digest the capability component reflecting its assets and resources, the morale component reflecting human needs, and the quality of life component reflecting soldiers' state of satisfaction in life. The results of the review provide a mean to bridge the research gap through the formulation of a mathematical model that shows the total measure of a military force's combat readiness. The results also significantly identify parameters for each of the variables and factors in the model.

A user-friendly mathematical modelling web interface to assist local decision making in the fight against drug-resistant tuberculosis.

PubMed

Ragonnet, Romain; Trauer, James M; Denholm, Justin T; Marais, Ben J; McBryde, Emma S

2017-05-30

Multidrug-resistant and rifampicin-resistant tuberculosis (MDR/RR-TB) represent an important challenge for global tuberculosis (TB) control. The high rates of MDR/RR-TB observed among re-treatment cases can arise from diverse pathways: de novo amplification during initial treatment, inappropriate treatment of undiagnosed MDR/RR-TB, relapse despite appropriate treatment, or reinfection with MDR/RR-TB. Mathematical modelling allows quantification of the contribution made by these pathways in different settings. This information provides valuable insights for TB policy-makers, allowing better contextualised solutions. However, mathematical modelling outputs need to consider local data and be easily accessible to decision makers in order to improve their usefulness. We present a user-friendly web-based modelling interface, which can be used by people without technical knowledge. Users can input their own parameter values and produce estimates for their specific setting. This innovative tool provides easy access to mathematical modelling outputs that are highly relevant to national TB control programs. In future, the same approach could be applied to a variety of modelling applications, enhancing local decision making.

Mathematical modelling and quantitative methods.

PubMed

Edler, L; Poirier, K; Dourson, M; Kleiner, J; Mileson, B; Nordmann, H; Renwick, A; Slob, W; Walton, K; Würtzen, G

2002-01-01

The present review reports on the mathematical methods and statistical techniques presently available for hazard characterisation. The state of the art of mathematical modelling and quantitative methods used currently for regulatory decision-making in Europe and additional potential methods for risk assessment of chemicals in food and diet are described. Existing practices of JECFA, FDA, EPA, etc., are examined for their similarities and differences. A framework is established for the development of new and improved quantitative methodologies. Areas for refinement, improvement and increase of efficiency of each method are identified in a gap analysis. Based on this critical evaluation, needs for future research are defined. It is concluded from our work that mathematical modelling of the dose-response relationship would improve the risk assessment process. An adequate characterisation of the dose-response relationship by mathematical modelling clearly requires the use of a sufficient number of dose groups to achieve a range of different response levels. This need not necessarily lead to an increase in the total number of animals in the study if an appropriate design is used. Chemical-specific data relating to the mode or mechanism of action and/or the toxicokinetics of the chemical should be used for dose-response characterisation whenever possible. It is concluded that a single method of hazard characterisation would not be suitable for all kinds of risk assessments, and that a range of different approaches is necessary so that the method used is the most appropriate for the data available and for the risk characterisation issue. Future refinements to dose-response characterisation should incorporate more clearly the extent of uncertainty and variability in the resulting output.

Historical Analysis of the Battle of Little Bighorn Utilizing the Joint Conflict and Tactical Simulation (JCATS)

DTIC Science & Technology

2004-06-01

Frank Giordano , whose enlightening instruction and contagious enthusiasm in mathematical modeling provided us with the tools and concepts needed to...for each weapon, as taught by Brigadier General (Retired) Frank Giordano and Dr. Maurice Weir, authors of Mathematical Modeling and professors at...decision was to use the estimate given by Scott in a separate article he authored with Melissa A. Connor titled “Post-mortem at the Little Bighorn

Mathematical Modeling: Immune System Dynamics in the Presence of Cancer and Immunodeficiency in vivo

DTIC Science & Technology

2016-05-11

Control 2 Acknowledgments This research was sponsored by the United States Naval Academy’s Trident Scholar Program and the Department of Mathematics... experimental science which relies on qualitative observations; however, in the past decade the need for quantitative analysis has become much more...of Midshipman Research _________________________________________ ___________________________ USNA-1531-2 REPORT

Mathematical model describing the thyroids-pituitary axis with distributed time delays in hormone transportation

NASA Astrophysics Data System (ADS)

Neamţu, Mihaela; Stoian, Dana; Navolan, Dan Bogdan

2014-12-01

In the present paper we provide a mathematical model that describe the hypothalamus-pituitary-thyroid axis in autoimmune (Hashimoto's) thyroiditis. Since there is a spatial separation between thyroid and pituitary gland in the body, time is needed for transportation of thyrotropin and thyroxine between the glands. Thus, the distributed time delays are considered as both weak and Dirac kernels. The delayed model is analyzed regarding the stability and bifurcation behavior. The last part contains some numerical simulations to illustrate the effectiveness of our results and conclusions.

Optimal manpower allocation in aircraft line maintenance (Case in GMF AeroAsia)

NASA Astrophysics Data System (ADS)

Puteri, V. E.; Yuniaristanto, Hisjam, M.

2017-11-01

This paper presents a mathematical modeling to find the optimal manpower allocation in an aircraft line maintenance. This research focuses on assigning the number and type of manpower that allocated to each service. This study considers the licenced worker or Aircraft Maintenance Engineer Licence (AMEL) and non licenced worker or Aircraft Maintenance Technician (AMT). In this paper, we also consider the relationship of each station in terms of the possibility to transfer the manpower among them. The optimization model considers the number of manpowers needed for each service and the requirement of AMEL worker. This paper aims to determine the optimal manpower allocation using the mathematical modeling. The objective function of the model is to find the minimum employee expenses. The model was solved using the ILOG CPLEX software. The results show that the manpower allocation can meet the manpower need and the all load can be served.

Artificial intelligence: a new approach for prescription and monitoring of hemodialysis therapy.

PubMed

Akl, A I; Sobh, M A; Enab, Y M; Tattersall, J

2001-12-01

The effect of dialysis on patients is conventionally predicted using a formal mathematical model. This approach requires many assumptions of the processes involved, and validation of these may be difficult. The validity of dialysis urea modeling using a formal mathematical model has been challenged. Artificial intelligence using neural networks (NNs) has been used to solve complex problems without needing a mathematical model or an understanding of the mechanisms involved. In this study, we applied an NN model to study and predict concentrations of urea during a hemodialysis session. We measured blood concentrations of urea, patient weight, and total urea removal by direct dialysate quantification (DDQ) at 30-minute intervals during the session (in 15 chronic hemodialysis patients). The NN model was trained to recognize the evolution of measured urea concentrations and was subsequently able to predict hemodialysis session time needed to reach a target solute removal index (SRI) in patients not previously studied by the NN model (in another 15 chronic hemodialysis patients). Comparing results of the NN model with the DDQ model, the prediction error was 10.9%, with a not significant difference between predicted total urea nitrogen (UN) removal and measured UN removal by DDQ. NN model predictions of time showed a not significant difference with actual intervals needed to reach the same SRI level at the same patient conditions, except for the prediction of SRI at the first 30-minute interval, which showed a significant difference (P = 0.001). This indicates the sensitivity of the NN model to what is called patient clearance time; the prediction error was 8.3%. From our results, we conclude that artificial intelligence applications in urea kinetics can give an idea of intradialysis profiling according to individual clinical needs. In theory, this approach can be extended easily to other solutes, making the NN model a step forward to achieving artificial-intelligent dialysis control.

Understanding the Impact of Interventions to Prevent Antimicrobial Resistant Infections in the Long-Term Care Facility: A Review and Practical Guide to Mathematical Modeling.

PubMed

Rosello, Alicia; Horner, Carolyne; Hopkins, Susan; Hayward, Andrew C; Deeny, Sarah R

2017-02-01

OBJECTIVES (1) To systematically search for all dynamic mathematical models of infectious disease transmission in long-term care facilities (LTCFs); (2) to critically evaluate models of interventions against antimicrobial resistance (AMR) in this setting; and (3) to develop a checklist for hospital epidemiologists and policy makers by which to distinguish good quality models of AMR in LTCFs. METHODS The CINAHL, EMBASE, Global Health, MEDLINE, and Scopus databases were systematically searched for studies of dynamic mathematical models set in LTCFs. Models of interventions targeting methicillin-resistant Staphylococcus aureus in LTCFs were critically assessed. Using this analysis, we developed a checklist for good quality mathematical models of AMR in LTCFs. RESULTS AND DISCUSSION Overall, 18 papers described mathematical models that characterized the spread of infectious diseases in LTCFs, but no models of AMR in gram-negative bacteria in this setting were described. Future models of AMR in LTCFs require a more robust methodology (ie, formal model fitting to data and validation), greater transparency regarding model assumptions, setting-specific data, realistic and current setting-specific parameters, and inclusion of movement dynamics between LTCFs and hospitals. CONCLUSIONS Mathematical models of AMR in gram-negative bacteria in the LTCF setting, where these bacteria are increasingly becoming prevalent, are needed to help guide infection prevention and control. Improvements are required to develop outputs of sufficient quality to help guide interventions and policy in the future. We suggest a checklist of criteria to be used as a practical guide to determine whether a model is robust enough to test policy. Infect Control Hosp Epidemiol 2017;38:216-225.

The Determination of Production and Distribution Policy in Push-Pull Production Chain with Supply Hub as the Junction Point

NASA Astrophysics Data System (ADS)

Sinaga, A. T.; Wangsaputra, R.

2018-03-01

The development of technology causes the needs of products and services become increasingly complex, diverse, and fluctuating. This causes the level of inter-company dependencies within a production chains increased. To be able to compete, efficiency improvements need to be done collaboratively in the production chain network. One of the efforts to increase efficiency is to harmonize production and distribution activities in the production chain network. This paper describes the harmonization of production and distribution activities by applying the use of push-pull system and supply hub in the production chain between two companies. The research methodology begins with conducting empirical and literature studies, formulating research questions, developing mathematical models, conducting trials and analyses, and taking conclusions. The relationship between the two companies is described in the MINLP mathematical model with the total cost of production chain as the objective function. Decisions generated by the mathematical models are the size of production lot, size of delivery lot, number of kanban, frequency of delivery, and the number of understock and overstock lot.

Modeling Population Growth and Extinction

ERIC Educational Resources Information Center

Gordon, Sheldon P.

2009-01-01

The exponential growth model and the logistic model typically introduced in the mathematics curriculum presume that a population grows exclusively. In reality, species can also die out and more sophisticated models that take the possibility of extinction into account are needed. In this article, two extensions of the logistic model are considered,…

Improving mathematical problem solving skills through visual media

NASA Astrophysics Data System (ADS)

Widodo, S. A.; Darhim; Ikhwanudin, T.

2018-01-01

The purpose of this article was to find out the enhancement of students’ mathematical problem solving by using visual learning media. The ability to solve mathematical problems is the ability possessed by students to solve problems encountered, one of the problem-solving model of Polya. This preliminary study was not to make a model, but it only took a conceptual approach by comparing the various literature of problem-solving skills by linking visual learning media. The results of the study indicated that the use of learning media had not been appropriated so that the ability to solve mathematical problems was not optimal. The inappropriateness of media use was due to the instructional media that was not adapted to the characteristics of the learners. Suggestions that can be given is the need to develop visual media to increase the ability to solve problems.

On the mathematical modeling of the Reynolds stress's equations

NASA Technical Reports Server (NTRS)

Lin, Avi

1990-01-01

By considering the Reynolds stress equations as a possible descriptor of complex turbulent fields, pressure-velocity interaction and turbulence dissipation are studied as two of the main physical contributions to Reynolds stress balancing in turbulent flow fields. It is proven that the pressure interaction term contains turbulence generation elements. However, the usual 'return to isotropy' element appears more weakly than in the standard models. In addition, convection-like elements are discovered mathematically, but there is no mathematical evidence that the pressure fluctuations contribute to the turbulent transport mechanism. Calculations of some simple one-dimensional fields indicate that this extra convection, rather than the turbulent transport, is needed mathematically. Similarly, an expression for the turbulence dissipation is developed. The end result is a dynamic equation for the dissipation tensor which is based on the tensorial length scales.

EXPOSURE RELATED DOSE ESTIMATING MODEL (ERDEM)

EPA Science Inventory

ERDEM is a physiologically-based pharmacokinetic (PBPK) model with a graphical user interface (GUI) front end. Such a mathematical model was needed to make reliable estimates of the chemical dose to organs of animals or humans because of uncertainties of making route-to route, lo...

Relapse prediction in Graves´ disease: Towards mathematical modeling of clinical, immune and genetic markers.

PubMed

Langenstein, Christoph; Schork, Diana; Badenhoop, Klaus; Herrmann, Eva

2016-12-01

Graves' disease (GD) is an important and prevalent thyroid autoimmune disorder. Standard therapy for GD consists of antithyroid drugs (ATD) with treatment periods of around 12 months but relapse is frequent. Since predictors for relapse are difficult to identify the individual decision making for optimal treatment is often arbitrary. After reviewing the literature on this topic we summarize important factors involved in GD and with respect to their potential for relapse prediction from markers before and after treatment. This information was used to design a mathematical model integrating thyroid hormone parameters, thyroid size, antibody titers and a complex algorithm encompassing genetic predisposition, environmental exposures and current immune activity in order to arrive at a prognostic index for relapse risk after treatment. In the search for a tool to analyze and predict relapse in GD mathematical modeling is a promising approach. In analogy to mathematical modeling approaches in other diseases such as viral infections, we developed a differential equation model on the basis of published clinical trials in patients with GD. Although our model needs further evaluation to be applicable in a clinical context, it provides a perspective for an important contribution to a final statistical prediction model.

A model to predict accommodations needed by disabled persons.

PubMed

Babski-Reeves, Kari; Williams, Sabrina; Waters, Tzer Nan; Crumpton-Young, Lesia L; McCauley-Bell, Pamela

2005-09-01

In this paper, several approaches to assist employers in the accommodation process for disabled employees are discussed and a mathematical model is proposed to assist employers in predicting the accommodation level needed by an individual with a mobility-related disability. This study investigates the validity and reliability of this model in assessing the accommodation level needed by individuals utilizing data collected from twelve individuals with mobility-related disabilities. Based on the results of the statistical analyses, this proposed model produces a feasible preliminary measure for assessing the accommodation level needed for persons with mobility-related disabilities. Suggestions for practical application of this model in an industrial setting are addressed.

PASMet: a web-based platform for prediction, modelling and analyses of metabolic systems

PubMed Central

Sriyudthsak, Kansuporn; Mejia, Ramon Francisco; Arita, Masanori; Hirai, Masami Yokota

2016-01-01

PASMet (Prediction, Analysis and Simulation of Metabolic networks) is a web-based platform for proposing and verifying mathematical models to understand the dynamics of metabolism. The advantages of PASMet include user-friendliness and accessibility, which enable biologists and biochemists to easily perform mathematical modelling. PASMet offers a series of user-functions to handle the time-series data of metabolite concentrations. The functions are organised into four steps: (i) Prediction of a probable metabolic pathway and its regulation; (ii) Construction of mathematical models; (iii) Simulation of metabolic behaviours; and (iv) Analysis of metabolic system characteristics. Each function contains various statistical and mathematical methods that can be used independently. Users who may not have enough knowledge of computing or programming can easily and quickly analyse their local data without software downloads, updates or installations. Users only need to upload their files in comma-separated values (CSV) format or enter their model equations directly into the website. Once the time-series data or mathematical equations are uploaded, PASMet automatically performs computation on server-side. Then, users can interactively view their results and directly download them to their local computers. PASMet is freely available with no login requirement at http://pasmet.riken.jp/ from major web browsers on Windows, Mac and Linux operating systems. PMID:27174940

Cognitive predictors of children's development in mathematics achievement: A latent growth modeling approach.

PubMed

Xenidou-Dervou, Iro; Van Luit, Johannes E H; Kroesbergen, Evelyn H; Friso-van den Bos, Ilona; Jonkman, Lisa M; van der Schoot, Menno; van Lieshout, Ernest C D M

2018-04-24

Research has identified various domain-general and domain-specific cognitive abilities as predictors of children's individual differences in mathematics achievement. However, research into the predictors of children's individual growth rates, namely between-person differences in within-person change in mathematics achievement is scarce. We assessed 334 children's domain-general and mathematics-specific early cognitive abilities and their general mathematics achievement longitudinally across four time-points within the first and second grades of primary school. As expected, a constellation of multiple cognitive abilities contributed to the children's starting level of mathematical success. Specifically, latent growth modeling revealed that WM abilities, IQ, counting skills, nonsymbolic and symbolic approximate arithmetic and comparison skills explained individual differences in the children's initial status on a curriculum-based general mathematics achievement test. Surprisingly, however, only one out of all the assessed cognitive abilities was a unique predictor of the children's individual growth rates in mathematics achievement: their performance in the symbolic approximate addition task. In this task, children were asked to estimate the sum of two large numbers and decide if this estimated sum was smaller or larger compared to a third number. Our findings demonstrate the importance of multiple domain-general and mathematics-specific cognitive skills for identifying children at risk of struggling with mathematics and highlight the significance of early approximate arithmetic skills for the development of one's mathematical success. We argue the need for more research focus on explaining children's individual growth rates in mathematics achievement. © 2018 John Wiley & Sons Ltd.

Analysing the relationships between students and mathematics: a tale of two paradigms

NASA Astrophysics Data System (ADS)

Jorgensen, Robyn; Larkin, Kevin

2017-03-01

In this article, we argue the need to use inter-disciplinary paradigms to make sense of a range of findings from a research project. We developed a methodology using iPad diaries to uncover young students' thinking—mathematical, social and affective—so as to better understand their experiences of mathematics. These students, predominantly from year 3 to year 6, were drawn from economically and socially distinct schools in Queensland and New South Wales, Australia. This article builds on previous research, where we outlined the unique methodology that we developed over three iterations to collect student attitudinal comments regarding mathematics. The comments we collected gave significant insights into the experiences of, and possibilities for, the mathematics education of young learners. Here, we use these findings to explore the value of two paradigms to explain student experiences towards mathematics among primary school students from different social backgrounds. In so doing, we develop an explanatory model for the socially differentiated outcomes in students' responses and then use this explanatory model to analyse student responses from the two most socially disparate schools in our research.

Mathematical modeling of synthetic unit hydrograph case study: Citarum watershed

NASA Astrophysics Data System (ADS)

Islahuddin, Muhammad; Sukrainingtyas, Adiska L. A.; Kusuma, M. Syahril B.; Soewono, Edy

2015-09-01

Deriving unit hydrograph is very important in analyzing watershed's hydrologic response of a rainfall event. In most cases, hourly measures of stream flow data needed in deriving unit hydrograph are not always available. Hence, one needs to develop methods for deriving unit hydrograph for ungagged watershed. Methods that have evolved are based on theoretical or empirical formulas relating hydrograph peak discharge and timing to watershed characteristics. These are usually referred to Synthetic Unit Hydrograph. In this paper, a gamma probability density function and its variant are used as mathematical approximations of a unit hydrograph for Citarum Watershed. The model is adjusted with real field condition by translation and scaling. Optimal parameters are determined by using Particle Swarm Optimization method with weighted objective function. With these models, a synthetic unit hydrograph can be developed and hydrologic parameters can be well predicted.

What Teachers Need to Know to Teach Mathematics: An Argument for a Reconceptualised Model

ERIC Educational Resources Information Center

Hurrell, Derek P.

2013-01-01

Since Shulman's (1986) seminal work on Pedagogical Content Knowledge (PCK) was released, it has created opportunities for the creation of constructs to scaffold the knowledge and understandings that teachers need in order to be effective. Adapting this work from being a heuristic to an operational structure has seen the development of many models.…

A Cognitive Analysis of Students’ Mathematical Communication Ability on Geometry

NASA Astrophysics Data System (ADS)

Sari, D. S.; Kusnandi, K.; Suhendra, S.

2017-09-01

This study aims to analyze the difficulties of mathematical communication ability of students in one of secondary school on “three-dimensional space” topic. This research conducted by using quantitative approach with descriptive method. The population in this research was all students of that school and the sample was thirty students that was chosen by purposive sampling technique. Data of mathematical communication were collected through essay test. Furthermore, the data were analyzed with a descriptive way. The results of this study indicate that the percentage of achievement of student mathematical communication indicators as follows 1) Stating a situation, ideas, and mathematic correlation into images, graphics, or algebraic expressions is 35%; 2) Stating daily experience into a mathematic language / symbol, or a mathematic model is 35%; and 3) Associating images or diagrams into mathematical ideas is 53.3%. Based on the percentage of achievement on each indicator, it can be concluded that the level of achievement of students’ mathematical communication ability is still low. It can be caused the students were not used to convey or write their mathematical ideas systematically. Therefore students’ mathematical communication ability need to be improved.

Applying multibeam sonar and mathematical modeling for mapping seabed substrate and biota of offshore shallows

NASA Astrophysics Data System (ADS)

Herkül, Kristjan; Peterson, Anneliis; Paekivi, Sander

2017-06-01

Both basic science and marine spatial planning are in a need of high resolution spatially continuous data on seabed habitats and biota. As conventional point-wise sampling is unable to cover large spatial extents in high detail, it must be supplemented with remote sensing and modeling in order to fulfill the scientific and management needs. The combined use of in situ sampling, sonar scanning, and mathematical modeling is becoming the main method for mapping both abiotic and biotic seabed features. Further development and testing of the methods in varying locations and environmental settings is essential for moving towards unified and generally accepted methodology. To fill the relevant research gap in the Baltic Sea, we used multibeam sonar and mathematical modeling methods - generalized additive models (GAM) and random forest (RF) - together with underwater video to map seabed substrate and epibenthos of offshore shallows. In addition to testing the general applicability of the proposed complex of techniques, the predictive power of different sonar-based variables and modeling algorithms were tested. Mean depth, followed by mean backscatter, were the most influential variables in most of the models. Generally, mean values of sonar-based variables had higher predictive power than their standard deviations. The predictive accuracy of RF was higher than that of GAM. To conclude, we found the method to be feasible and with predictive accuracy similar to previous studies of sonar-based mapping.

Assessing metacognition of grade 2 and grade 4 students using an adaptation of multi-method interview approach during mathematics problem-solving

NASA Astrophysics Data System (ADS)

Kuzle, A.

2018-06-01

The important role that metacognition plays as a predictor for student mathematical learning and for mathematical problem-solving, has been extensively documented. But only recently has attention turned to primary grades, and more research is needed at this level. The goals of this paper are threefold: (1) to present metacognitive framework during mathematics problem-solving, (2) to describe their multi-method interview approach developed to study student mathematical metacognition, and (3) to empirically evaluate the utility of their model and the adaptation of their approach in the context of grade 2 and grade 4 mathematics problem-solving. The results are discussed not only with regard to further development of the adapted multi-method interview approach, but also with regard to their theoretical and practical implications.

Blooms' separation of the final exam of Engineering Mathematics II: Item reliability using Rasch measurement model

NASA Astrophysics Data System (ADS)

Fuaad, Norain Farhana Ahmad; Nopiah, Zulkifli Mohd; Tawil, Norgainy Mohd; Othman, Haliza; Asshaari, Izamarlina; Osman, Mohd Hanif; Ismail, Nur Arzilah

2014-06-01

In engineering studies and researches, Mathematics is one of the main elements which express physical, chemical and engineering laws. Therefore, it is essential for engineering students to have a strong knowledge in the fundamental of mathematics in order to apply the knowledge to real life issues. However, based on the previous results of Mathematics Pre-Test, it shows that the engineering students lack the fundamental knowledge in certain topics in mathematics. Due to this, apart from making improvements in the methods of teaching and learning, studies on the construction of questions (items) should also be emphasized. The purpose of this study is to assist lecturers in the process of item development and to monitor the separation of items based on Blooms' Taxonomy and to measure the reliability of the items itself usingRasch Measurement Model as a tool. By using Rasch Measurement Model, the final exam questions of Engineering Mathematics II (Linear Algebra) for semester 2 sessions 2012/2013 were analysed and the results will provide the details onthe extent to which the content of the item providesuseful information about students' ability. This study reveals that the items used in Engineering Mathematics II (Linear Algebra) final exam are well constructed but the separation of the items raises concern as it is argued that it needs further attention, as there is abig gap between items at several levels of Blooms' cognitive skill.

Understanding Calculus beyond Computations: A Descriptive Study of the Parallel Meanings and Expectations of Teachers and Users of Calculus

ERIC Educational Resources Information Center

Ferguson, Leann J.

2012-01-01

Calculus is an important tool for building mathematical models of the world around us and is thus used in a variety of disciplines, such as physics and engineering. These disciplines rely on calculus courses to provide the mathematical foundation needed for success in their courses. Unfortunately, due to the basal conceptions of what it means to…

Montgomery Blair Science, Mathematics and Computer Science Magnet Program: A Successful Model for Meeting the Needs of Highly Able STEM Learners

ERIC Educational Resources Information Center

Stein, David; Ostrander, Peter; Lee, G. Maie

2016-01-01

The Magnet Program at Montgomery Blair High School is an application-based magnet program utilizing a curriculum focused on science, mathematics, and computer science catering to interested, talented, and eager to learn students in Montgomery County, Maryland. This article identifies and discusses some of the unique aspects of the Magnet Program…

Modeling Zombie Outbreaks: A Problem-Based Approach to Improving Mathematics One Brain at a Time

ERIC Educational Resources Information Center

Lewis, Matthew; Powell, James A.

2016-01-01

A great deal of educational literature has focused on problem-based learning (PBL) in mathematics at the primary and secondary level, but arguably there is an even greater need for PBL in college math courses. We present a project centered around the Humans versus Zombies moderated tag game played on the Utah State University campus. We discuss…

Mathematics ability and related skills in preschoolers born very preterm.

PubMed

Hasler, Holly M; Akshoomoff, Natacha

2017-12-12

Children born very preterm (VPT) are at risk for academic, behavioral, and/or emotional problems. Mathematics is a particular weakness and better understanding of the relationship between preterm birth and early mathematics ability is needed, particularly as early as possible to aid in early intervention. Preschoolers born VPT (n = 58) and those born full term (FT; n = 29) were administered a large battery of measures within 6 months of beginning kindergarten. A multiple-mediation model was utilized to characterize the difference in skills underlying mathematics ability between groups. Children born VPT performed significantly worse than FT-born children on a measure of mathematics ability as well as full-scale IQ, verbal skills, visual-motor integration, phonological awareness, phonological working memory, motor skills, and executive functioning. Mathematics was significantly correlated with verbal skills, visual-motor integration, phonological processing, and motor skills across both groups. When entered into the mediation model, verbal skills, visual-motor integration, and phonological awareness were significant mediators of the group differences. This analysis provides insights into the pre-academic skills that are weak in preschoolers born VPT and their relationship to mathematics. It is important to identify children who will have difficulties as early as possible, particularly for VPT children who are at higher risk for academic difficulties. Therefore, this model may be used in evaluating VPT children for emerging difficulties as well as an indicator that if other weaknesses are found, an assessment of mathematics should be conducted.

Introduction: Occam’s Razor (SOT - Fit for Purpose workshop introduction)

EPA Science Inventory

Mathematical models provide important, reproducible, and transparent information for risk-based decision making. However, these models must be constructed to fit the needs of the problem to be solved. A “fit for purpose” model is an abstraction of a complicated problem that allow...

Countries with Higher Levels of Gender Equality Show Larger National Sex Differences in Mathematics Anxiety and Relatively Lower Parental Mathematics Valuation for Girls

PubMed Central

2016-01-01

Despite international advancements in gender equality across a variety of societal domains, the underrepresentation of girls and women in Science, Technology, Engineering, and Mathematics (STEM) related fields persists. In this study, we explored the possibility that the sex difference in mathematics anxiety contributes to this disparity. More specifically, we tested a number of predictions from the prominent gender stratification model, which is the leading psychological theory of cross-national patterns of sex differences in mathematics anxiety and performance. To this end, we analyzed data from 761,655 15-year old students across 68 nations who participated in the Programme for International Student Assessment (PISA). Most importantly and contra predictions, we showed that economically developed and more gender equal countries have a lower overall level of mathematics anxiety, and yet a larger national sex difference in mathematics anxiety relative to less developed countries. Further, although relatively more mothers work in STEM fields in more developed countries, these parents valued, on average, mathematical competence more in their sons than their daughters. The proportion of mothers working in STEM was unrelated to sex differences in mathematics anxiety or performance. We propose that the gender stratification model fails to account for these national patterns and that an alternative model is needed. In the discussion, we suggest how an interaction between socio-cultural values and sex-specific psychological traits can better explain these patterns. We also discuss implications for policies aiming to increase girls’ STEM participation. PMID:27100631

Countries with Higher Levels of Gender Equality Show Larger National Sex Differences in Mathematics Anxiety and Relatively Lower Parental Mathematics Valuation for Girls.

PubMed

Stoet, Gijsbert; Bailey, Drew H; Moore, Alex M; Geary, David C

2016-01-01

Despite international advancements in gender equality across a variety of societal domains, the underrepresentation of girls and women in Science, Technology, Engineering, and Mathematics (STEM) related fields persists. In this study, we explored the possibility that the sex difference in mathematics anxiety contributes to this disparity. More specifically, we tested a number of predictions from the prominent gender stratification model, which is the leading psychological theory of cross-national patterns of sex differences in mathematics anxiety and performance. To this end, we analyzed data from 761,655 15-year old students across 68 nations who participated in the Programme for International Student Assessment (PISA). Most importantly and contra predictions, we showed that economically developed and more gender equal countries have a lower overall level of mathematics anxiety, and yet a larger national sex difference in mathematics anxiety relative to less developed countries. Further, although relatively more mothers work in STEM fields in more developed countries, these parents valued, on average, mathematical competence more in their sons than their daughters. The proportion of mothers working in STEM was unrelated to sex differences in mathematics anxiety or performance. We propose that the gender stratification model fails to account for these national patterns and that an alternative model is needed. In the discussion, we suggest how an interaction between socio-cultural values and sex-specific psychological traits can better explain these patterns. We also discuss implications for policies aiming to increase girls' STEM participation.

An inverse problem for a mathematical model of aquaponic agriculture

NASA Astrophysics Data System (ADS)

Bobak, Carly; Kunze, Herb

2017-01-01

Aquaponic agriculture is a sustainable ecosystem that relies on a symbiotic relationship between fish and macrophytes. While the practice has been growing in popularity, relatively little mathematical models exist which aim to study the system processes. In this paper, we present a system of ODEs which aims to mathematically model the population and concetrations dynamics present in an aquaponic environment. Values of the parameters in the system are estimated from the literature so that simulated results can be presented to illustrate the nature of the solutions to the system. As well, a brief sensitivity analysis is performed in order to identify redundant parameters and highlight those which may need more reliable estimates. Specifically, an inverse problem with manufactured data for fish and plants is presented to demonstrate the ability of the collage theorem to recover parameter estimates.

Needs Assessment in STEM Disciplines: Reliability, Validity and Factor Structure of the Student Support Needs Scale (SSNS)

ERIC Educational Resources Information Center

Hardy, Precious; Aruguete, Mara

2014-01-01

Retention is a major problem in most colleges and universities. High dropout rates, especially in the STEM disciplines (science, technology, engineering and mathematics), have proved intractable despite the offering of supplemental instruction. A broad model of support systems that includes psychological factors is needed to address retention in…

A trend study of self-concept and mathematics achievement in a cross-cultural context

NASA Astrophysics Data System (ADS)

Wang, Jianjun

2007-12-01

The TIMSS 1995, 1999, and 2003 data have been gathered from Hong Kong before and after its sovereignty switch from the United Kingdom to China in 1997. Built on a reciprocal relation theory from the research literature, this investigation is designed to examine models of student self-concept and mathematics achievement during the political transition. Along with a perceived `brain drain' from the population migration, there was a non-monotonic change in the reciprocal relationship between self-concept and mathematics achievement. In addition, indicators of mathematics achievement and self-concept have demonstrated different linkages to the permanent emigration of Hong Kong residents with valued or desirable skills and qualifications. Interpretation of these empirical findings entails a need of enhancing cross-cultural understanding in mathematics education.

20171015 - Integrating Toxicity, Toxicokinetic, and Exposure Data for Risk-based Chemical Alternatives Assessment (ISES)

EPA Science Inventory

In order to predict the margin between the dose needed for adverse chemical effects and actual human exposure rates, data on hazard, exposure, and toxicokinetics are needed. In vitro methods, biomonitoring, and mathematical modeling have provided initial estimates for many extant...

Impacts of the Boston prekindergarten program on the school readiness of young children with special needs.

PubMed

Weiland, Christina

2016-11-01

Theory and empirical work suggest inclusion preschool improves the school readiness of young children with special needs, but only 2 studies of the model have used rigorous designs that could identify causality. The present study examined the impacts of the Boston Public prekindergarten program-which combined proven language, literacy, and mathematics curricula with coaching-on the language, literacy, mathematics, executive function, and emotional skills of young children with special needs (N = 242). Children with special needs benefitted from the program in all examined domains. Effects were on par with or surpassed those of their typically developing peers. Results are discussed in the context of their relevance for policy, practice, and theory. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Bi-objective approach for placing ground and air ambulance base and helipad locations in order to optimize EMS response.

PubMed

Shahriari, Milad; Bozorgi-Amiri, Ali; Tavakoli, Shayan; Yousefi-Babadi, Abolghasem

2017-12-01

Shortening the travel time of patient transfer has clinical implications for many conditions such as cardiac arrest, trauma, stroke and STEMI. As resources are often limited precise calculations are needed. In this paper we consider the location problem for both ground and aerial emergency medical services. Given the uncertainty of when patients are in need of prompt medical attention we consider these demand points to be uncertain. We consider various ways in which ground and helicopter ambulances can work together to make the whole process go faster. We develop a mathematical model that minimizes travel time and maximizes service level. We use a compromising programming method to solve this bi-objective mathematical model. For numerical experiments we apply our model to a case study in Lorestan, Iran, using geographical and population data, and the location of the actual hospital based in the capital of the province. Results show that low-accessibility locations are the main focus of the proposed problem and with mathematical modeling access to a hospital is vastly improved. We also found out that once the budget reaches a certain point which suffices for building certain ambulance bases more investments does not necessarily result in less travel time. Copyright © 2017 Elsevier Inc. All rights reserved.

A Model for Assessing and Meeting Needs in Instructional Computing: Procedures and Results of a Multi-State Needs Assessment.

ERIC Educational Resources Information Center

Roblyer, M. D., Ed.

The Appalachia Educational Laboratory (AEL) conducted an assessment of microcomputer-related needs for basic mathematics in the four-state areas of Kentucky, Tennessee, Virginia, and West Virginia in 1984-85. The primary input came from teachers from each of the states who participated in a needs conference in their home state. When each of the…

Development of innovative problem based learning model with PMRI-scientific approach using ICT to increase mathematics literacy and independence-character of junior high school students

NASA Astrophysics Data System (ADS)

Wardono; Waluya, B.; Kartono; Mulyono; Mariani, S.

2018-03-01

This research is very urgent in relation to the national issue of human development and the nation's competitiveness because of the ability of Indonesian Junior High School students' mathematics literacy results of the Programme for International Student Assessment (PISA) by OECD field of Mathematics is still very low compared to other countries. Curriculum 2013 launched one of them reflect the results of PISA which is still far from the expectations of the Indonesian nation and to produce a better quality of education, PISA ratings that reflect the nation's better competitiveness need to be developed innovative, interactive learning models such as innovative interactive learning Problem Based Learning (PBL) based on the approach of Indonesian Realistic Mathematics Education (PMRI) and the Scientific approach using Information and Communication Technology (ICT).The research was designed using Research and Development (R&D), research that followed up the development and dissemination of a product/model. The result of the research shows the innovative interactive learning PBL model based on PMRI-Scientific using ICT that developed valid, practical and effective and can improve the ability of mathematics literacy and independence-character of junior high school students. While the quality of innovative interactive learning PBL model based on PMRI-Scientific using ICT meet the good category.

A Multifaceted Mathematical Approach for Complex Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alexander, F.; Anitescu, M.; Bell, J.

2012-03-07

Applied mathematics has an important role to play in developing the tools needed for the analysis, simulation, and optimization of complex problems. These efforts require the development of the mathematical foundations for scientific discovery, engineering design, and risk analysis based on a sound integrated approach for the understanding of complex systems. However, maximizing the impact of applied mathematics on these challenges requires a novel perspective on approaching the mathematical enterprise. Previous reports that have surveyed the DOE's research needs in applied mathematics have played a key role in defining research directions with the community. Although these reports have had significantmore » impact, accurately assessing current research needs requires an evaluation of today's challenges against the backdrop of recent advances in applied mathematics and computing. To address these needs, the DOE Applied Mathematics Program sponsored a Workshop for Mathematics for the Analysis, Simulation and Optimization of Complex Systems on September 13-14, 2011. The workshop had approximately 50 participants from both the national labs and academia. The goal of the workshop was to identify new research areas in applied mathematics that will complement and enhance the existing DOE ASCR Applied Mathematics Program efforts that are needed to address problems associated with complex systems. This report describes recommendations from the workshop and subsequent analysis of the workshop findings by the organizing committee.« less

The Social Process of Analyzing Real Water Resource Systems Plans and Management Policies

NASA Astrophysics Data System (ADS)

Loucks, Daniel

2016-04-01

Developing and applying systems analysis methods for improving the development and management of real world water resource systems, I have learned, is primarily a social process. This talk is a call for more recognition of this reality in the modeling approaches we propose in the papers and books we publish. The mathematical models designed to inform planners and managers of water systems that we see in many of our journals often seem more complex than they need be. They also often seem not as connected to reality as they could be. While it may be easier to publish descriptions of complex models than simpler ones, and while adding complexity to models might make them better able to mimic or resemble the actual complexity of the real physical and/or social systems or processes being analyzed, the usefulness of such models often can be an illusion. Sometimes the important features of reality that are of concern or interest to those who make decisions can be adequately captured using relatively simple models. Finding the right balance for the particular issues being addressed or the particular decisions that need to be made is an art. When applied to real world problems or issues in specific basins or regions, systems modeling projects often involve more attention to the social aspects than the mathematical ones. Mathematical models addressing connected interacting interdependent components of complex water systems are in fact some of the most useful methods we have to study and better understand the systems we manage around us. They can help us identify and evaluate possible alternative solutions to problems facing humanity today. The study of real world systems of interacting components using mathematical models is commonly called applied systems analyses. Performing such analyses with decision makers rather than of decision makers is critical if the needed trust between project personnel and their clients is to be developed. Using examples from recent and ongoing modeling projects in different parts of the world, this talk will attempt to show the dependency on the degree of project success with the degree of attention given to the communication between project personnel, the stakeholders and decision making institutions. It will also highlight how initial project terms-of-reference and expected outcomes can change, sometimes in surprising ways, during the course of such projects. Changing project objectives often result from changing stakeholder values, emphasizing the need for analyses that can adapt to this uncertainty.

Sifting noisy data for truths about noisy systems. Comment on "Extracting physics of life at the molecular level: A review of single-molecule data analyses" by W. Colomb and S.K. Sarkar

NASA Astrophysics Data System (ADS)

Flyvbjerg, Henrik; Mortensen, Kim I.

2015-06-01

With each new aspect of nature that becomes accessible to quantitative science, new needs arise for data analysis and mathematical modeling. The classical example is Tycho Brahe's accurate and comprehensive observations of planets, which made him hire Kepler for his mathematical skills to assist with the data analysis. We all learned what that lead to: Kepler's three laws of planetary motion, phenomenology in purely mathematical form. Newton built on this, and the scientific revolution was over, completed.

Validation of an instrument for mathematics enhancement teaching efficacy of Pacific Northwest agricultural educators

NASA Astrophysics Data System (ADS)

Jansen, Daniel J.

Teacher efficacy continues to be an important area of study in educational research. This study tested an instrument designed to assess the perceived efficacy of agricultural education teachers when engaged in lessons involving mathematics instruction. The study population of Oregon and Washington agricultural educators utilized in the validation of the instrument revealed important demographic findings and specific results related to teacher efficacy for the study population. An instrument was developed from the assimilation of three scales previously used and validated in efficacy research. Participants' mathematics teaching efficacy was assessed using a portion of the Mathematics Teaching Efficacy Beliefs Instrument (MTEBI), and personal mathematics efficacy was evaluated by the mathematics self-belief instrument which was derived from the Betz and Hackett's Mathematics Self-Efficacy Scale. The final scale, the Teachers' Sense of Efficacy Scale (TSES) created by Tschannen-Moran and Woolfolk Hoy, examined perceived personal teaching efficacy. Structural equation modeling was used as the statistical analyses tool to validate the instrument and examine correlations between efficacy constructs used to determine potential professional development needs of the survey population. As part of the data required for validation of the Mathematics Enhancement Teaching Efficacy instrument, demographic information defining the population of Oregon and Washington agricultural educators was obtained and reported. A hypothetical model derived from teacher efficacy literature was found to be an acceptable model to verify construct validity and determine strength of correlations between the scales that defined the instrument. The instrument produced an alpha coefficient of .905 for reliability. Both exploratory and confirmatory factor analyses were used to verify construct and discriminate validity. Specifics results related to the survey population of agricultural educators concluded that personal mathematics efficacy has a stronger correlation with mathematics teaching efficacy than personal teaching efficacy of teachers for this population. The implications of such findings suggest that professional development and pre-service preparation should be more focused on mathematics content knowledge rather than pedagogical knowledge when the objective is to enhance mathematics in interdisciplinary lessons.

Does one size fit all? A study of beginning science and mathematics teacher induction

NASA Astrophysics Data System (ADS)

Kralik, Jeffrey M.

Over the past few years, many induction programs have been implemented across the country, primarily designed to limit the amount beginning teacher attrition. Few of these programs have focused on improving teacher quality or identifying the specific needs of individual teachers. Research suggests that beginning science and mathematics teachers have specific needs that are not being met by current induction models, possibly resulting in higher rates of attrition. Harry and Janet Knowles created the Knowles Science Teaching Foundation (KSTF) to identify and support young scientists and mathematicians as they dedicate their lives to teaching young people. Through financial, curricular, and emotional support, KSTF encourages new teachers to remain in teaching and become leaders in their schools and districts. This dissertation is a sequential explanatory study, which first establishes national estimates for beginning teacher attrition rates and the reasons for the migration based on subject area taught, with an emphasis on mathematics and science teachers. This study then evaluates the KSTF model through multiple methods---analysis of KSTF survey data and interviews with KSTF participants and stakeholders.

Nutritional models for a Controlled Ecological Life Support System (CELSS): Linear mathematical modeling

NASA Technical Reports Server (NTRS)

Wade, Rose C.

1989-01-01

The NASA Controlled Ecological Life Support System (CELSS) Program is involved in developing a biogenerative life support system that will supply food, air, and water to space crews on long-duration missions. An important part of this effort is in development of the knowledge and technological capability of producing and processing foods to provide optimal diets for space crews. This involves such interrelated factors as determination of the diet, based on knowledge of nutrient needs of humans and adjustments in those needs that may be required as a result of the conditions of long-duration space flight; determination of the optimal mixture of crops required to provide nutrients at levels that are sufficient but not excessive or toxic; and consideration of the critical issues of spacecraft space and power limitations, which impose a phytomass minimization requirement. The complex interactions among these factors are examined with the goal of supplying a diet that will satisfy human needs while minimizing the total phytomass requirement. The approach taken was to collect plant nutritional composition and phytomass production data, identify human nutritional needs and estimate the adjustments to the nutrient requirements likely to result from space flight, and then to generate mathematical models from these data.

[Mathematic modeling for prediction of waning immunity and timing of booster doses].

PubMed

Matuo, Fujio; Okada, Kenji

2008-10-01

Under an environment that a vaccination rate is low and an infectious disease is prevalent, it is thought that most vaccinee got additional immunity by natural infection. On the other hand, in the area where the incidence of disease has been reduced by high rate vaccination, it is also decreased the chance of additional immunity by natural infection. Therefore susceptible individuals are increased because of the waning immunity. In the community where a vaccination rate is high, it may be necessary to consider the booster vaccination for adolescent and adult even if one completed the primary vaccinations. It may also be important to explore the timing of booster dose. In this paper, we attempt to give a comprehensive explanation of mathematical model for predicting the antibody duration, and we introduce the role of mathematical model on a consideration to the need and timing of booster doses after the primary series.

The Interface between ChE and Mathematics: What Do Students Really Need?

ERIC Educational Resources Information Center

Graham, Michael D.; Ganter, Susan L.

2001-01-01

Summarizes the report given to the Committee on the Undergraduate Program in Mathematics of the Mathematical Association of America (MAA) who is developing new guidelines for instruction in mathematics with a chemical engineering group at Clemson University in order to list specific knowledge and skills in mathematics needed by engineering…

The Preparation Experiences of Elementary Mathematics Specialists: Examining Influences on Beliefs, Content Knowledge, and Teaching Practices

ERIC Educational Resources Information Center

Swars, Susan L.; Smith, Stephanie Z.; Smith, Marvin E.; Carothers, Jody; Myers, Kayla

2018-01-01

Many in the field of mathematics education call for elementary schools to have elementary mathematics specialists (EMSs) who provide needed mathematical expertise and support for children and teachers. EMSs serve as a reasonable, immediate alternative to the challenges generated by elementary teachers needing improved mathematical knowledge for…

Fielding an After-School Mathematics Lab

ERIC Educational Resources Information Center

Punches-Guntsch, Christina M.; Kenney, Erin N.

2012-01-01

Many students will need remedial work in mathematics during their high school years. Some sort of help will be needed to fulfill the National Council of Teachers of Mathematics' (NCTM's) (2000) vision of a mathematics classroom that involves students having access to mathematically rich problems and being engaged in solving them. The high school…

Current status and future needs of the BehavePlus Fire Modeling System

Treesearch

Patricia L. Andrews

2014-01-01

The BehavePlus Fire Modeling System is among the most widely used systems for wildland fire prediction. It is designed for use in a range of tasks including wildfire behaviour prediction, prescribed fire planning, fire investigation, fuel hazard assessment, fire model understanding, communication and research. BehavePlus is based on mathematical models for fire...

Modeling Processes of 4th-Year Middle-School Students and the Difficulties Encountered

ERIC Educational Resources Information Center

Eraslan, Ali; Kant, Sinem

2015-01-01

Mathematics teachers have recently begun to stress the need for teaching models and modeling approaches that encompass cognitive and meta-cognitive thought processes for every level of schooling, starting from primary school through to higher education. The objective of this study is to examine modeling processes with the help of modeling…

The Development of a Model of Culturally Responsive Science and Mathematics Teaching

ERIC Educational Resources Information Center

Hernandez, Cecilia M.; Morales, Amanda R.; Shroyer, M. Gail

2013-01-01

This qualitative theoretical study was conducted in response to the current need for an inclusive and comprehensive model to guide the preparation and assessment of teacher candidates for culturally responsive teaching. The process of developing a model of culturally responsive teaching involved three steps: a comprehensive review of the…

Methods of Technological Forecasting,

DTIC Science & Technology

1977-05-01

Trend Extrapolation Progress Curve Analogy Trend Correlation Substitution Analysis or Substitution Growth Curves Envelope Curve Advances in the State of...the Art Technological Mapping Contextual Mapping Matrix Input-Output Analysis Mathematical Models Simulation Models Dynamic Modelling. CHAPTER IV...Generation Interaction between Needs and Possibilities Map of the Technological Future — (‘ross- Impact Matri x Discovery Matrix Morphological Analysis

Tailoring Mathematical Models to Stem-Cell Derived Cardiomyocyte Lines Can Improve Predictions of Drug-Induced Changes to Their Electrophysiology.

PubMed

Lei, Chon Lok; Wang, Ken; Clerx, Michael; Johnstone, Ross H; Hortigon-Vinagre, Maria P; Zamora, Victor; Allan, Andrew; Smith, Godfrey L; Gavaghan, David J; Mirams, Gary R; Polonchuk, Liudmila

2017-01-01

Human induced pluripotent stem cell derived cardiomyocytes (iPSC-CMs) have applications in disease modeling, cell therapy, drug screening and personalized medicine. Computational models can be used to interpret experimental findings in iPSC-CMs, provide mechanistic insights, and translate these findings to adult cardiomyocyte (CM) electrophysiology. However, different cell lines display different expression of ion channels, pumps and receptors, and show differences in electrophysiology. In this exploratory study, we use a mathematical model based on iPSC-CMs from Cellular Dynamic International (CDI, iCell), and compare its predictions to novel experimental recordings made with the Axiogenesis Cor.4U line. We show that tailoring this model to the specific cell line, even using limited data and a relatively simple approach, leads to improved predictions of baseline behavior and response to drugs. This demonstrates the need and the feasibility to tailor models to individual cell lines, although a more refined approach will be needed to characterize individual currents, address differences in ion current kinetics, and further improve these results.

A Delphi Study: Identifying Strategies That Promote Student Self-Efficacy in the Middle Level Mathematics Classroom

ERIC Educational Resources Information Center

Kieschnick, Lauren E.

2013-01-01

This dissertation examines the strategies that promote mathematical self-efficacy in the middle level mathematics classroom. The need for more self-efficacious students to pursue mathematics is prevalent in the United States due to the need of workers in the STEM fields. Finding strategies to promote mathematical self-efficacy will provide…

Applying an Alternative Mathematics Pedagogy for Students with Weak Mathematics: Meta-Analysis of Alternative Pedagogies

ERIC Educational Resources Information Center

Lake, Warren; Wallin, Margie; Woolcott, Geoff; Boyd, Wendy; Foster, Alan; Markopoulos, Christos; Boyd, William

2017-01-01

Student mathematics performance and the need for work-ready graduates to be mathematics-competent is a core issue for many universities. While both student and teacher are responsible for learning outcomes, there is a need to explicitly acknowledge the weak mathematics foundation of many university students. A systematic literature review was…

Light, temperature, and leaf nitrogen distribution in the tropical rain forest of Biosphere 2 and their importance in the mathematical models for global environmental changes

NASA Technical Reports Server (NTRS)

Tohda, Motofumi

1997-01-01

As the environmental changes occur throughout the world in rapid rate, we need to have further understandings for our planet. Since the ecosystems are so complex, it is almost impossible for us to integrate every factor. However, mathematical models are powerful tools which can be used to simulate those ecosystems with limited data. In this project, I collected light intensity, canopy leaf temperature and Air Handler (AHU) temperature, and nitrogen concentration in the leaves for different profiles in the rainforest mesocosm. These data will later be put into mathematical models such as "big-leaf" and "sun/shade" models to determine how these factors will affect CO2 exchange in the rainforest. As rainforests are diminishing from our planet and their existence is very important for all living things on earth, it is necessary for us to learn more about the unique system of rainforests and how we can co-exist rather than destroy.

Selection Criteria for Mathematical Models Used in Exposure Assessments: Atmospheric Dispersion Models

EPA Science Inventory

Before the U.S. Environmental Protection Agency issued the 1988 Guidelines for Estimating Exposures, it published proposed guidelines in the Federal Register for public review and comment. he guidelines are intended to give risk analysis a basic framework and the tools they need ...

Measuring Middle Grades Teachers' Understanding of Rational Numbers with the Mixture Rasch Model

ERIC Educational Resources Information Center

Izsak, Andrew; Orrill, Chandra Hawley; Cohen, Allan S.; Brown, Rachael Eriksen

2010-01-01

We report the development of a multiple-choice instrument that measures the mathematical knowledge needed for teaching arithmetic with fractions, decimals, and proportions. In particular, the instrument emphasizes the knowledge needed to reason about such arithmetic when numbers are embedded in problem situations. We administered our instrument to…

Intelligent Information Retrieval: Diagnosing Information Need. Part II. Uncertainty Expansion in a Prototype of a Diagnostic IR Tool.

ERIC Educational Resources Information Center

Cole, Charles; Cantero, Pablo; Sauve, Diane

1998-01-01

Outlines a prototype of an intelligent information-retrieval tool to facilitate information access for an undergraduate seeking information for a term paper. Topics include diagnosing the information need, Kuhlthau's information-search-process model, Shannon's mathematical theory of communication, and principles of uncertainty expansion and…

Determining the Products of Inertia for Small Scale UAVs

NASA Technical Reports Server (NTRS)

Lorenzetti, Joseph S.; Banuelos, Leonel C.; Clarke, Robert; Murillo, Oscar J.; Bowers, Albion H.

2017-01-01

Moments of inertia and products of inertia often need to be determined for aircraft. As complex bodies, their mass properties need to be determined experimentally for best accuracy. While several moment of inertia experimental techniques have been developed, there are few to determine the products of inertia. Products of inertia can be easily determined mathematically if the angle between the aircraft x body axis and principal x axis is known. This method finds the principal inclination angle by mathematically correlating the measured moments of inertia about a range of axes of the aircraft. This correlation uses a least squares error minimization of a mathematical model that describes the ellipse of inertia in the aircraft's x-z axes plane. Results from a test conducted on a small scale UAV (Unmanned Aerial Vehicle) at NASA Armstrong Flight Research Center is also presented, which is an example of the intended application of this technique.

Using Mathematical Transmission Modelling to Investigate Drivers of Respiratory Syncytial Virus Seasonality in Children in the Philippines

PubMed Central

Paynter, Stuart; Yakob, Laith; Simões, Eric A. F.; Lucero, Marilla G.; Tallo, Veronica; Nohynek, Hanna; Ware, Robert S.; Weinstein, Philip; Williams, Gail; Sly, Peter D.

2014-01-01

We used a mathematical transmission model to estimate when ecological drivers of respiratory syncytial virus (RSV) transmissibility would need to act in order to produce the observed seasonality of RSV in the Philippines. We estimated that a seasonal peak in transmissibility would need to occur approximately 51 days prior to the observed peak in RSV cases (range 49 to 67 days). We then compared this estimated seasonal pattern of transmissibility to the seasonal patterns of possible ecological drivers of transmissibility: rainfall, humidity and temperature patterns, nutritional status, and school holidays. The timing of the seasonal patterns of nutritional status and rainfall were both consistent with the estimated seasonal pattern of transmissibility and these are both plausible drivers of the seasonality of RSV in this setting. PMID:24587222

Predicting human chronically paralyzed muscle force: a comparison of three mathematical models.

PubMed

Frey Law, Laura A; Shields, Richard K

2006-03-01

Chronic spinal cord injury (SCI) induces detrimental musculoskeletal adaptations that adversely affect health status, ranging from muscle paralysis and skin ulcerations to osteoporosis. SCI rehabilitative efforts may increasingly focus on preserving the integrity of paralyzed extremities to maximize health quality using electrical stimulation for isometric training and/or functional activities. Subject-specific mathematical muscle models could prove valuable for predicting the forces necessary to achieve therapeutic loading conditions in individuals with paralyzed limbs. Although numerous muscle models are available, three modeling approaches were chosen that can accommodate a variety of stimulation input patterns. To our knowledge, no direct comparisons between models using paralyzed muscle have been reported. The three models include 1) a simple second-order linear model with three parameters and 2) two six-parameter nonlinear models (a second-order nonlinear model and a Hill-derived nonlinear model). Soleus muscle forces from four individuals with complete, chronic SCI were used to optimize each model's parameters (using an increasing and decreasing frequency ramp) and to assess the models' predictive accuracies for constant and variable (doublet) stimulation trains at 5, 10, and 20 Hz in each individual. Despite the large differences in modeling approaches, the mean predicted force errors differed only moderately (8-15% error; P=0.0042), suggesting physiological force can be adequately represented by multiple mathematical constructs. The two nonlinear models predicted specific force characteristics better than the linear model in nearly all stimulation conditions, with minimal differences between the two nonlinear models. Either nonlinear mathematical model can provide reasonable force estimates; individual application needs may dictate the preferred modeling strategy.

Knowing and Learning Mathematics for Teaching: Proceedings of a Workshop (March 19-21, 1999).

ERIC Educational Resources Information Center

National Academy of Sciences - National Research Council, Washington, DC. Mathematical Sciences Education Board.

The Mathematics Teacher Preparation Content Workshop, held March 19-21, 1999, focused on two questions: (1) What is the mathematical knowledge teachers need to know in order to teach well? and (2) How can teachers develop the mathematical knowledge they need to teach well? Chapters include: (1) "Knowledge of Fundamental Mathematics for Teaching"…

Test-and-treat approach to HIV/AIDS: a primer for mathematical modeling.

PubMed

Nah, Kyeongah; Nishiura, Hiroshi; Tsuchiya, Naho; Sun, Xiaodan; Asai, Yusuke; Imamura, Akifumi

2017-09-05

The public benefit of test-and-treat has induced a need to justify goodness for the public, and mathematical modeling studies have played a key role in designing and evaluating the test-and-treat strategy for controlling HIV/AIDS. Here we briefly and comprehensively review the essence of contemporary understanding of the test-and-treat policy through mathematical modeling approaches and identify key pitfalls that have been identified to date. While the decrease in HIV incidence is achieved with certain coverages of diagnosis, care and continued treatment, HIV prevalence is not necessarily decreased and sometimes the test-and-treat is accompanied by increased long-term cost of antiretroviral therapy (ART). To confront with the complexity of assessment on this policy, the elimination threshold or the effective reproduction number has been proposed for its use in determining the overall success to anticipate the eventual elimination. Since the publication of original model in 2009, key issues of test-and-treat modeling studies have been identified, including theoretical problems surrounding the sexual partnership network, heterogeneities in the transmission dynamics, and realistic issues of achieving and maintaining high treatment coverage in the most hard-to-reach populations. To explicitly design country-specific control policy, quantitative modeling approaches to each single setting with differing epidemiological context would require multi-disciplinary collaborations among clinicians, public health practitioners, laboratory technologists, epidemiologists and mathematical modelers.

Methods to achieve accurate projection of regional and global raster databases

USGS Publications Warehouse

Usery, E. Lynn; Seong, Jeong Chang; Steinwand, Dan

2002-01-01

Modeling regional and global activities of climatic and human-induced change requires accurate geographic data from which we can develop mathematical and statistical tabulations of attributes and properties of the environment. Many of these models depend on data formatted as raster cells or matrices of pixel values. Recently, it has been demonstrated that regional and global raster datasets are subject to significant error from mathematical projection and that these errors are of such magnitude that model results may be jeopardized (Steinwand, et al., 1995; Yang, et al., 1996; Usery and Seong, 2001; Seong and Usery, 2001). There is a need to develop methods of projection that maintain the accuracy of these datasets to support regional and global analyses and modeling

Supercomputer modeling of hydrogen combustion in rocket engines

NASA Astrophysics Data System (ADS)

Betelin, V. B.; Nikitin, V. F.; Altukhov, D. I.; Dushin, V. R.; Koo, Jaye

2013-08-01

Hydrogen being an ecological fuel is very attractive now for rocket engines designers. However, peculiarities of hydrogen combustion kinetics, the presence of zones of inverse dependence of reaction rate on pressure, etc. prevents from using hydrogen engines in all stages not being supported by other types of engines, which often brings the ecological gains back to zero from using hydrogen. Computer aided design of new effective and clean hydrogen engines needs mathematical tools for supercomputer modeling of hydrogen-oxygen components mixing and combustion in rocket engines. The paper presents the results of developing verification and validation of mathematical model making it possible to simulate unsteady processes of ignition and combustion in rocket engines.

Characterizing mercury concentrations and flux dynamics in a coastal plain watershed using multiple models

EPA Science Inventory

The primary goal was to asess Hg cycling within a small coastal plain watershed (McTier Creek) using multiple watershed models with distinct mathematical frameworks that emphasize different system dynamics; a secondary goal was to identify current needs in watershed-scale Hg mode...

Effects of soil moisture on the diurnal pattern of pesticide emission: Numerical simulation and sensitivity analysis

USDA-ARS?s Scientific Manuscript database

Accurate prediction of pesticide volatilization is important for the protection of human and environmental health. Due to the complexity of the volatilization process, sophisticated predictive models are needed, especially for dry soil conditions. A mathematical model was developed to allow simulati...

Estimating tuberculosis incidence from primary survey data: a mathematical modeling approach.

PubMed

Pandey, S; Chadha, V K; Laxminarayan, R; Arinaminpathy, N

2017-04-01

There is an urgent need for improved estimations of the burden of tuberculosis (TB). To develop a new quantitative method based on mathematical modelling, and to demonstrate its application to TB in India. We developed a simple model of TB transmission dynamics to estimate the annual incidence of TB disease from the annual risk of tuberculous infection and prevalence of smear-positive TB. We first compared model estimates for annual infections per smear-positive TB case using previous empirical estimates from China, Korea and the Philippines. We then applied the model to estimate TB incidence in India, stratified by urban and rural settings. Study model estimates show agreement with previous empirical estimates. Applied to India, the model suggests an annual incidence of smear-positive TB of 89.8 per 100 000 population (95%CI 56.8-156.3). Results show differences in urban and rural TB: while an urban TB case infects more individuals per year, a rural TB case remains infectious for appreciably longer, suggesting the need for interventions tailored to these different settings. Simple models of TB transmission, in conjunction with necessary data, can offer approaches to burden estimation that complement those currently being used.

Evidence of the Need to Prepare Prospective Teachers to Engage in Mathematics Consultations

ERIC Educational Resources Information Center

van Ingen, Sarah; Eskelson, Samuel L.; Allsopp, David

2016-01-01

The mathematics consultation represents a powerful opportunity for mathematics teachers to leverage the knowledge base of special education professionals to advance equity for students with special education needs. Yet, most teacher preparation programs do not specifically prepare prospective teachers to engage in mathematics-specific…

Caring teaching practices in multiethnic mathematics classrooms: attending to health and well-being

NASA Astrophysics Data System (ADS)

Averill, Robin

2012-06-01

Factors that contribute to strong teacher-student relationships are vital to understand because of the influence these relationships have on achievement and motivation, particularly for minority group students. This article draws from a substantial quantity of empirical data, grounded in a wide theoretical and cultural base, regarding aspects of caring teacher practice to discuss mathematics teacher behaviours in relation to an existing model of health and well-being that encompasses cognitive, social, spiritual, and physical dimensions. Drawing from 100 Year 10 mathematics lesson observations involving six teachers and their classes across three urban schools, evidence emerged that for many indigenous (Māori), New Zealand Pacific, and New Zealand European students, caring teacher behaviours important for student engagement and achievement both include, and range beyond, traditional teaching practices. Examples include capitalising on student reactions and shared endeavours within the context of mathematics learning, expecting mathematical progress, showing respect for students and for their mathematics learning, being explicit about practice and expectations, incorporating one-to-one interactions, making opportunities within mathematics learning for sharing personal identities, and incorporating movement. This research illustrates how mathematics educators can attend to the specific and holistic mathematical learning needs of their students, including those often marginalised.

Temperature Coefficient for Modeling Denitrification in Surface Water Sediments Using the Mass Transfer Coefficient

Treesearch

T. W. Appelboom; G. M. Chescheir; R. W. Skaggs; J. W. Gilliam; Devendra M. Amatya

2006-01-01

Watershed modeling has become an important tool for researchers with the high costs of water quality monitoring. When modeling nitrate transport within drainage networks, denitrification within the sediments needs to be accounted for. Birgand et. al. developed an equation using a term called a mass transfer coefficient to mathematically describe sediment...

Analysis and Management of Animal Populations: Modeling, Estimation and Decision Making

USGS Publications Warehouse

Williams, B.K.; Nichols, J.D.; Conroy, M.J.

2002-01-01

This book deals with the processes involved in making informed decisions about the management of animal populations. It covers the modeling of population responses to management actions, the estimation of quantities needed in the modeling effort, and the application of these estimates and models to the development of sound management decisions. The book synthesizes and integrates in a single volume the methods associated with these themes, as they apply to ecological assessment and conservation of animal populations. KEY FEATURES * Integrates population modeling, parameter estimation and * decision-theoretic approaches to management in a single, cohesive framework * Provides authoritative, state-of-the-art descriptions of quantitative * approaches to modeling, estimation and decision-making * Emphasizes the role of mathematical modeling in the conduct of science * and management * Utilizes a unifying biological context, consistent mathematical notation, * and numerous biological examples

Concepts and tools for predictive modeling of microbial dynamics.

PubMed

Bernaerts, Kristel; Dens, Els; Vereecken, Karen; Geeraerd, Annemie H; Standaert, Arnout R; Devlieghere, Frank; Debevere, Johan; Van Impe, Jan F

2004-09-01

Description of microbial cell (population) behavior as influenced by dynamically changing environmental conditions intrinsically needs dynamic mathematical models. In the past, major effort has been put into the modeling of microbial growth and inactivation within a constant environment (static models). In the early 1990s, differential equation models (dynamic models) were introduced in the field of predictive microbiology. Here, we present a general dynamic model-building concept describing microbial evolution under dynamic conditions. Starting from an elementary model building block, the model structure can be gradually complexified to incorporate increasing numbers of influencing factors. Based on two case studies, the fundamentals of both macroscopic (population) and microscopic (individual) modeling approaches are revisited. These illustrations deal with the modeling of (i) microbial lag under variable temperature conditions and (ii) interspecies microbial interactions mediated by lactic acid production (product inhibition). Current and future research trends should address the need for (i) more specific measurements at the cell and/or population level, (ii) measurements under dynamic conditions, and (iii) more comprehensive (mechanistically inspired) model structures. In the context of quantitative microbial risk assessment, complexity of the mathematical model must be kept under control. An important challenge for the future is determination of a satisfactory trade-off between predictive power and manageability of predictive microbiology models.

The effectiveness of a head-heart-hands model for natural and environmental science learning in urban schools.

PubMed

Jagannathan, Radha; Camasso, Michael J; Delacalle, Maia

2018-02-01

We describe an environmental and natural science program called Nurture thru Nature (NtN) that seeks to improve mathematics and science performance of students in disadvantaged communities, and to increase student interest in Science, Technology, Engineering and Mathematics (STEM) careers. The program draws conceptual guidance from the Head-Heart-Hands model that informs the current educational movement to foster environmental understanding and sustainability. Employing an experimental design and data from seven cohorts of students, we find some promising, albeit preliminary, indications that the program can increase students' science knowledge and grades in mathematics, science and language arts. We discuss the special adaptations that environmental and sustainability education programs need to incorporate if they are to be successful in today's resource depleted urban schools. Copyright © 2017 Elsevier Ltd. All rights reserved.

Using confirmatory factor analysis to understand executive control in preschool children: sources of variation in emergent mathematic achievement

PubMed Central

Bull, Rebecca; Espy, Kimberly Andrews; Wiebe, Sandra A.; Sheffield, Tiffany D.; Nelson, Jennifer Mize

2010-01-01

Latent variable modeling methods have demonstrated utility for understanding the structure of executive control (EC) across development. These methods are utilized to better characterize the relation between EC and mathematics achievement in the preschool period, and to understand contributing sources of individual variation. Using the sample and battery of laboratory tasks described in Wiebe, Espy and Charak (2008), latent EC was related strongly to emergent mathematics achievement in preschool, and was robust after controlling for crystallized intellectual skills. The relation between crystallized skills and emergent mathematics differed between girls and boys, although the predictive association between EC and mathematics did not. Two dimensions of the child’s social environment contributed to mathematics achievement: social network support through its relation to EC and environmental stressors through its relation with crystallized skills. These findings underscore the need to examine the dimensions, mechanisms, and individual pathways that influence the development of early competence in basic cognitive processes that underpin early academic achievement. PMID:21676089

Using confirmatory factor analysis to understand executive control in preschool children: sources of variation in emergent mathematic achievement.

PubMed

Bull, Rebecca; Espy, Kimberly Andrews; Wiebe, Sandra A; Sheffield, Tiffany D; Nelson, Jennifer Mize

2011-07-01

Latent variable modeling methods have demonstrated utility for understanding the structure of executive control (EC) across development. These methods are utilized to better characterize the relation between EC and mathematics achievement in the preschool period, and to understand contributing sources of individual variation. Using the sample and battery of laboratory tasks described in Wiebe, Espy and Charak (2008), latent EC was related strongly to emergent mathematics achievement in preschool, and was robust after controlling for crystallized intellectual skills. The relation between crystallized skills and emergent mathematics differed between girls and boys, although the predictive association between EC and mathematics did not. Two dimensions of the child 's social environment contributed to mathematics achievement: social network support through its relation to EC and environmental stressors through its relation with crystallized skills. These findings underscore the need to examine the dimensions, mechanisms, and individual pathways that influence the development of early competence in basic cognitive processes that underpin early academic achievement. © 2010 Blackwell Publishing Ltd.

Experimental evolution in silico: a custom-designed mathematical model for virulence evolution of Bacillus thuringiensis.

PubMed

Strauß, Jakob Friedrich; Crain, Philip; Schulenburg, Hinrich; Telschow, Arndt

2016-08-01

Most mathematical models on the evolution of virulence are based on epidemiological models that assume parasite transmission follows the mass action principle. In experimental evolution, however, mass action is often violated due to controlled infection protocols. This "theory-experiment mismatch" raises the question whether there is a need for new mathematical models to accommodate the particular characteristics of experimental evolution. Here, we explore the experimental evolution model system of Bacillus thuringiensis as a parasite and Caenorhabditis elegans as a host. Recent experimental studies with strict control of parasite transmission revealed that one-sided adaptation of B. thuringiensis with non-evolving hosts selects for intermediate or no virulence, sometimes coupled with parasite extinction. In contrast, host-parasite coevolution selects for high virulence and for hosts with strong resistance against B. thuringiensis. In order to explain the empirical results, we propose a new mathematical model that mimics the basic experimental set-up. The key assumptions are: (i) controlled parasite transmission (no mass action), (ii) discrete host generations, and (iii) context-dependent cost of toxin production. Our model analysis revealed the same basic trends as found in the experiments. Especially, we could show that resistant hosts select for highly virulent bacterial strains. Moreover, we found (i) that the evolved level of virulence is independent of the initial level of virulence, and (ii) that the average amount of bacteria ingested significantly affects the evolution of virulence with fewer bacteria ingested selecting for highly virulent strains. These predictions can be tested in future experiments. This study highlights the usefulness of custom-designed mathematical models in the analysis and interpretation of empirical results from experimental evolution. Copyright © 2016 The Authors. Published by Elsevier GmbH.. All rights reserved.

Student-Perceived Mothers' and Fathers' Beliefs, Mathematics and English Motivations, and Career Choices.

PubMed

Lazarides, Rebecca; Watt, Helen M G

2017-12-01

According to Eccles and Jacobs' (1986) parent socialization model, parents' gendered ability and value beliefs influence girls' and boys' interpretations of those beliefs, and hence students' domain-specific valuing of tasks and competence beliefs and subsequent career plans. Studies have rarely analyzed how both student-perceived mothers' and fathers' beliefs affect girls' and boys' task values, success expectancies, and career plans across domains. This study analyzed survey data of 459 students (262 boys) assessed through Grades 9, 10, and 11 from three coeducational secondary schools in Sydney, Australia. Longitudinal structural equation models revealed gendered value transmission pathways for girls in mathematics. Although mathematics test scores did not vary statistically significantly, girls reported statistically significantly lower mothers' ability beliefs for them in mathematics than boys at Time 1, which led to their statistically significantly lower mathematics intrinsic value at Time 2 and mathematics-related career plans at Time 3. Such gendered pathways did not occur in English. Matched same-gender effects and gendered pathways in parent socialization processes were evident; perceived mothers' value beliefs were more strongly related to girls' than boys' importance values in English. Student-perceived fathers' ability beliefs positively predicted boys', not girls', importance value in mathematics. Implications for educational practice emphasize the need to target girls' and boys' interest when aiming to enhance their mathematical career motivations. © 2017 The Authors. Journal of Research on Adolescence © 2017 Society for Research on Adolescence.

The modeling of reactive solute transport with sorption to mobile and immobile sorbents 1. Experimental evidence and model development

NASA Astrophysics Data System (ADS)

Knabner, P.; Totsche, K. U.; Kögel-Knabner, I.

Modeling carrier-influenced transport needs to take into account the reactivity of the carrier itself. This paper presents a mathematical model of reactive solute transport with sorption to mobile and immobile sorbents. The mobile sorbent is also considered to be reactive. To justify the assumptions and generality of our modeling approach, experimental findings are reviewed and analyzed. A transformation of the model in terms of total concentrations of solute and mobile sorbents is presented which simplifies the mathematical formulations. Breakthrough data on dissolved organic carbon are presented to exemplify the need to take into account the reactivity of the mobile sorbent. Data on hexachlorobiphenyl and cadmium are presented to demonstrate carrier-introduced increased mobility, whereas data on anthracene and pyrene are presented to demonstrate carrier-introduced reduced mobility. The experimental conditions leading to the different findings are pointed out. The sorption processes considered in the model are both equilibrium and nonequilibrium processes, allowing for different sorption sites and nonlinear isotherms and rate functions. Effective isotherms, which describe the sorption to the immobile sorbent in the presence of a mobile sorbent and rate functions, are introduced and their properties are discussed.

Addressing the Mathematics-Specific Needs of Beginning Mathematics Teachers

ERIC Educational Resources Information Center

Britton, Edward

2012-01-01

Beginning mathematics teachers at the secondary level (middle and high school grades) have mathematics-specific needs that induction programs should address more substantially. However, a number of issues in how programs can accomplish this are more complex than often framed in discussions occurring in the induction programs and the field of…

Mathematics Teachers' Support and Retention: Using Maslow's Hierarchy to Understand Teachers' Needs

ERIC Educational Resources Information Center

Fisher, Molly H.; Royster, David

2016-01-01

As part of a larger study, four mathematics teachers from diverse backgrounds and teaching situations report their ideas on teacher stress, mathematics teacher retention, and their feelings about the needs of mathematics teachers, as well as other information crucial to retaining quality teachers. The responses from the participants were used to…

Designing Differentiated Mathematics Games: "Discarding" the One-Size-Fits-All Approach to Educational Game Play

ERIC Educational Resources Information Center

Trinter, Christine P.; Brighton, Catherine M.; Moon, Tonya R.

2015-01-01

Primary grade students enter the mathematics classroom with a range of differences including students' mathematical readiness, mathematical conceptions, interests, and learning profiles. Addressing the learning needs of students is not a trivial task, but accounting for these needs is essential for supporting students as they continually work…

Mathematical formalisms based on approximated kinetic representations for modeling genetic and metabolic pathways.

PubMed

Alves, Rui; Vilaprinyo, Ester; Hernádez-Bermejo, Benito; Sorribas, Albert

2008-01-01

There is a renewed interest in obtaining a systemic understanding of metabolism, gene expression and signal transduction processes, driven by the recent research focus on Systems Biology. From a biotechnological point of view, such a systemic understanding of how a biological system is designed to work can facilitate the rational manipulation of specific pathways in different cell types to achieve specific goals. Due to the intrinsic complexity of biological systems, mathematical models are a central tool for understanding and predicting the integrative behavior of those systems. Particularly, models are essential for a rational development of biotechnological applications and in understanding system's design from an evolutionary point of view. Mathematical models can be obtained using many different strategies. In each case, their utility will depend upon the properties of the mathematical representation and on the possibility of obtaining meaningful parameters from available data. In practice, there are several issues at stake when one has to decide which mathematical model is more appropriate for the study of a given problem. First, one needs a model that can represent the aspects of the system one wishes to study. Second, one must choose a mathematical representation that allows an accurate analysis of the system with respect to different aspects of interest (for example, robustness of the system, dynamical behavior, optimization of the system with respect to some production goal, parameter value determination, etc). Third, before choosing between alternative and equally appropriate mathematical representations for the system, one should compare representations with respect to easiness of automation for model set-up, simulation, and analysis of results. Fourth, one should also consider how to facilitate model transference and re-usability by other researchers and for distinct purposes. Finally, one factor that is important for all four aspects is the regularity in the mathematical structure of the equations because it facilitates computational manipulation. This regularity is a mark of kinetic representations based on approximation theory. The use of approximation theory to derive mathematical representations with regular structure for modeling purposes has a long tradition in science. In most applied fields, such as engineering and physics, those approximations are often required to obtain practical solutions to complex problems. In this paper we review some of the more popular mathematical representations that have been derived using approximation theory and are used for modeling in molecular systems biology. We will focus on formalisms that are theoretically supported by the Taylor Theorem. These include the Power-law formalism, the recently proposed (log)linear and Lin-log formalisms as well as some closely related alternatives. We will analyze the similarities and differences between these formalisms, discuss the advantages and limitations of each representation, and provide a tentative "road map" for their potential utilization for different problems.

Quality Teaching in Mathematics

ERIC Educational Resources Information Center

Ediger, Marlow

2012-01-01

The best teaching possible needs to accrue in the mathematics curriculum. Pupils also need to become proficient in using mathematics in every day situations in life. Individuals buy goods and services. They pay for these in different ways, including cash. Here, persons need to be able to compute the total cost of items purchased and then pay for…

Climate change and health modeling: horses for courses.

PubMed

Ebi, Kristie L; Rocklöv, Joacim

2014-01-01

Mathematical and statistical models are needed to understand the extent to which weather, climate variability, and climate change are affecting current and may affect future health burdens in the context of other risk factors and a range of possible development pathways, and the temporal and spatial patterns of any changes. Such understanding is needed to guide the design and the implementation of adaptation and mitigation measures. Because each model projection captures only a narrow range of possible futures, and because models serve different purposes, multiple models are needed for each health outcome ('horses for courses'). Multiple modeling results can be used to bracket the ranges of when, where, and with what intensity negative health consequences could arise. This commentary explores some climate change and health modeling issues, particularly modeling exposure-response relationships, developing early warning systems, projecting health risks over coming decades, and modeling to inform decision-making. Research needs are also suggested.

Applied Mathematics at the U.S. Department of Energy: Past, Present and a View to the Future

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brown, D L; Bell, J; Estep, D

2008-02-15

Over the past half-century, the Applied Mathematics program in the U.S. Department of Energy's Office of Advanced Scientific Computing Research has made significant, enduring advances in applied mathematics that have been essential enablers of modern computational science. Motivated by the scientific needs of the Department of Energy and its predecessors, advances have been made in mathematical modeling, numerical analysis of differential equations, optimization theory, mesh generation for complex geometries, adaptive algorithms and other important mathematical areas. High-performance mathematical software libraries developed through this program have contributed as much or more to the performance of modern scientific computer codes as themore » high-performance computers on which these codes run. The combination of these mathematical advances and the resulting software has enabled high-performance computers to be used for scientific discovery in ways that could only be imagined at the program's inception. Our nation, and indeed our world, face great challenges that must be addressed in coming years, and many of these will be addressed through the development of scientific understanding and engineering advances yet to be discovered. The U.S. Department of Energy (DOE) will play an essential role in providing science-based solutions to many of these problems, particularly those that involve the energy, environmental and national security needs of the country. As the capability of high-performance computers continues to increase, the types of questions that can be answered by applying this huge computational power become more varied and more complex. It will be essential that we find new ways to develop and apply the mathematics necessary to enable the new scientific and engineering discoveries that are needed. In August 2007, a panel of experts in applied, computational and statistical mathematics met for a day and a half in Berkeley, California to understand the mathematical developments required to meet the future science and engineering needs of the DOE. It is important to emphasize that the panelists were not asked to speculate only on advances that might be made in their own research specialties. Instead, the guidance this panel was given was to consider the broad science and engineering challenges that the DOE faces and identify the corresponding advances that must occur across the field of mathematics for these challenges to be successfully addressed. As preparation for the meeting, each panelist was asked to review strategic planning and other informational documents available for one or more of the DOE Program Offices, including the Offices of Science, Nuclear Energy, Fossil Energy, Environmental Management, Legacy Management, Energy Efficiency & Renewable Energy, Electricity Delivery & Energy Reliability and Civilian Radioactive Waste Management as well as the National Nuclear Security Administration. The panelists reported on science and engineering needs for each of these offices, and then discussed and identified mathematical advances that will be required if these challenges are to be met. A review of DOE challenges in energy, the environment and national security brings to light a broad and varied array of questions that the DOE must answer in the coming years. A representative subset of such questions includes: (1) Can we predict the operating characteristics of a clean coal power plant? (2) How stable is the plasma containment in a tokamak? (3) How quickly is climate change occurring and what are the uncertainties in the predicted time scales? (4) How quickly can an introduced bio-weapon contaminate the agricultural environment in the US? (5) How do we modify models of the atmosphere and clouds to incorporate newly collected data of possibly of new types? (6) How quickly can the United States recover if part of the power grid became inoperable? (7) What are optimal locations and communication protocols for sensing devices in a remote-sensing network? (8) How can new materials be designed with a specified desirable set of properties? In comparing and contrasting these and other questions of importance to DOE, the panel found that while the scientific breadth of the requirements is enormous, a central theme emerges: Scientists are being asked to identify or provide technology, or to give expert analysis to inform policy-makers that requires the scientific understanding of increasingly complex physical and engineered systems. In addition, as the complexity of the systems of interest increases, neither experimental observation nor mathematical and computational modeling alone can access all components of the system over the entire range of scales or conditions needed to provide the required scientific understanding.« less

Mathematical Modeling of Food Supply for Long Term Space Missions Using Advanced Life Support

NASA Technical Reports Server (NTRS)

Cruthirds, John E.

2003-01-01

A habitat for long duration missions which utilizes Advanced Life Support (ALS), the Bioregenerative Planetary Life Support Systems Test Complex (BIO-Plex), is currently being built at JSC. In this system all consumables will be recycled and reused. In support of this effort, a menu is being planned utilizing ALS crops that will meet nutritional and psychological requirements. The need exists in the food system to identify specific physical quantities that define life support systems from an analysis and modeling perspective. Once these quantities are defined, they need to be fed into a mathematical model that takes into consideration other systems in the BIO-Plex. This model, if successful, will be used to understand the impacts of changes in the food system on the other systems and vice versa. The Equivalent System Mass (ESM) metric has been used to describe systems and subsystems, including the food system options, in terms of the single parameter, mass. There is concern that this approach might not adequately address the important issues of food quality and psychological impact on crew morale of a supply of fiesh food items. In fact, the mass of food can also depend on the quality of the food. This summer faculty fellow project will involve creating an appropriate mathematical model for the food plan developed by the Food Processing System for BIO-Plex. The desired outcome of this work will be a quantitative model that can be applied to the various options of supplying food on long-term space missions.

Development of a Model for Some Aspects of University Policy. Technical Report.

ERIC Educational Resources Information Center

Goossens, J. L. M.; And Others

A method to calculate the need for academic staff per faculty, based on educational programs and numbers of students, is described which is based on quantitative relations between programs, student enrollment, and total budget. The model is described schematically and presented in a mathematical form adapted to computer processing. Its application…

Fraction Multiplication and Division Models: A Practitioner Reference Paper

ERIC Educational Resources Information Center

Ervin, Heather K.

2017-01-01

It is well documented in literature that rational number is an important area of understanding in mathematics. Therefore, it follows that teachers and students need to have an understanding of rational number and related concepts such as fraction multiplication and division. This practitioner reference paper examines models that are important to…

Mathematical modeling and experimental testing of three bioreactor configurations based on windkessel models

PubMed Central

Ruel, Jean; Lachance, Geneviève

2010-01-01

This paper presents an experimental study of three bioreactor configurations. The bioreactor is intended to be used for the development of tissue-engineered heart valve substitutes. Therefore it must be able to reproduce physiological flow and pressure waveforms accurately. A detailed analysis of three bioreactor arrangements is presented using mathematical models based on the windkessel (WK) approach. First, a review of the many applications of this approach in medical studies enhances its fundamental nature and its usefulness. Then the models are developed with reference to the actual components of the bioreactor. This study emphasizes different conflicting issues arising in the design process of a bioreactor for biomedical purposes, where an optimization process is essential to reach a compromise satisfying all conditions. Two important aspects are the need for a simple system providing ease of use and long-term sterility, opposed to the need for an advanced (thus more complex) architecture capable of a more accurate reproduction of the physiological environment. Three classic WK architectures are analyzed, and experimental results enhance the advantages and limitations of each one. PMID:21977286

Model of Fluidized Bed Containing Reacting Solids and Gases

NASA Technical Reports Server (NTRS)

Bellan, Josette; Lathouwers, Danny

2003-01-01

A mathematical model has been developed for describing the thermofluid dynamics of a dense, chemically reacting mixture of solid particles and gases. As used here, "dense" signifies having a large volume fraction of particles, as for example in a bubbling fluidized bed. The model is intended especially for application to fluidized beds that contain mixtures of carrier gases, biomass undergoing pyrolysis, and sand. So far, the design of fluidized beds and other gas/solid industrial processing equipment has been based on empirical correlations derived from laboratory- and pilot-scale units. The present mathematical model is a product of continuing efforts to develop a computational capability for optimizing the designs of fluidized beds and related equipment on the basis of first principles. Such a capability could eliminate the need for expensive, time-consuming predesign testing.

Desegregating undergraduate mathematics and biology--interdisciplinary instruction with emphasis on ongoing biomedical research.

PubMed

Robeva, Raina

2009-01-01

The remarkable advances in the field of biology in the last decade, specifically in the areas of biochemistry, genetics, genomics, proteomics, and systems biology, have demonstrated how critically important mathematical models and methods are in addressing questions of vital importance for these disciplines. There is little doubt that the need for utilizing and developing mathematical methods for biology research will only grow in the future. The rapidly increasing demand for scientists with appropriate interdisciplinary skills and knowledge, however, is not being reflected in the way undergraduate mathematics and biology courses are structured and taught in most colleges and universities nationwide. While a number of institutions have stepped forward and addressed this need by creating and offering interdisciplinary courses at the juncture of mathematics and biology, there are still many others at which there is little, if any, interdisciplinary interaction between the curricula. This chapter describes an interdisciplinary course and a textbook in mathematical biology developed collaboratively by faculty from Sweet Briar College and the University of Virginia School of Medicine. The course and textbook are designed to provide a bridge between the mathematical and biological sciences at the lower undergraduate level. The course is developed for and is being taught in a liberal arts setting at Sweet Briar College, Virginia, but some of the advanced modules are used in a course at the University of Virginia for advanced undergraduate and beginning graduate students. The individual modules are relatively independent and can be used as stand-alone projects in conventional mathematics and biology courses. Except for the introductory material, the course and textbook topics are based on current biomedical research.

Correlation of spacecraft thermal mathematical models to reference data

NASA Astrophysics Data System (ADS)

Torralbo, Ignacio; Perez-Grande, Isabel; Sanz-Andres, Angel; Piqueras, Javier

2018-03-01

Model-to-test correlation is a frequent problem in spacecraft-thermal control design. The idea is to determine the values of the parameters of the thermal mathematical model (TMM) that allows reaching a good fit between the TMM results and test data, in order to reduce the uncertainty of the mathematical model. Quite often, this task is performed manually, mainly because a good engineering knowledge and experience is needed to reach a successful compromise, but the use of a mathematical tool could facilitate this work. The correlation process can be considered as the minimization of the error of the model results with regard to the reference data. In this paper, a simple method is presented suitable to solve the TMM-to-test correlation problem, using Jacobian matrix formulation and Moore-Penrose pseudo-inverse, generalized to include several load cases. Aside, in simple cases, this method also allows for analytical solutions to be obtained, which helps to analyze some problems that appear when the Jacobian matrix is singular. To show the implementation of the method, two problems have been considered, one more academic, and the other one the TMM of an electronic box of PHI instrument of ESA Solar Orbiter mission, to be flown in 2019. The use of singular value decomposition of the Jacobian matrix to analyze and reduce these models is also shown. The error in parameter space is used to assess the quality of the correlation results in both models.

Unresolved issues in theories of autoimmune disease using myocarditis as a framework

PubMed Central

Root-Bernstein, Robert; Fairweather, DeLisa

2014-01-01

Many theories of autoimmune disease have been proposed since the discovery that the immune system can attack the body. These theories include the hidden or cryptic antigen theory, modified antigen theory, T cell bypass, T cell-B cell mismatch, epitope spread or drift, the bystander effect, molecular mimicry, anti-idiotype theory, antigenic complementarity, and dual-affinity T cell receptors. We critically review these theories and relevant mathematical models as they apply to autoimmune myocarditis. All theories share the common assumption that autoimmune diseases are triggered by environmental factors such as infections or chemical exposure. Most, but not all, theories and mathematical models are unifactorial assuming single-agent causation of disease. Experimental and clinical evidence and mathematical models exist to support some aspects of most theories, but evidence/models that support one theory almost invariably supports other theories as well. More importantly, every theory (and every model) lacks the ability to account for some key autoimmune disease phenomena such as the fundamental roles of innate immunity, sex differences in disease susceptibility, the necessity for adjuvants in experimental animal models, and the often paradoxical effect of exposure timing and dose on disease induction. We argue that a more comprehensive and integrated theory of autoimmunity associated with new mathematical models is needed and suggest specific experimental and clinical tests for each major theory that might help to clarify how they relate to clinical disease and reveal how theories are related. PMID:25484004

Unresolved issues in theories of autoimmune disease using myocarditis as a framework.

PubMed

Root-Bernstein, Robert; Fairweather, DeLisa

2015-06-21

Many theories of autoimmune disease have been proposed since the discovery that the immune system can attack the body. These theories include the hidden or cryptic antigen theory, modified antigen theory, T cell bypass, T cell-B cell mismatch, epitope spread or drift, the bystander effect, molecular mimicry, anti-idiotype theory, antigenic complementarity, and dual-affinity T cell receptors. We critically review these theories and relevant mathematical models as they apply to autoimmune myocarditis. All theories share the common assumption that autoimmune diseases are triggered by environmental factors such as infections or chemical exposure. Most, but not all, theories and mathematical models are unifactorial assuming single-agent causation of disease. Experimental and clinical evidence and mathematical models exist to support some aspects of most theories, but evidence/models that support one theory almost invariably supports other theories as well. More importantly, every theory (and every model) lacks the ability to account for some key autoimmune disease phenomena such as the fundamental roles of innate immunity, sex differences in disease susceptibility, the necessity for adjuvants in experimental animal models, and the often paradoxical effect of exposure timing and dose on disease induction. We argue that a more comprehensive and integrated theory of autoimmunity associated with new mathematical models is needed and suggest specific experimental and clinical tests for each major theory that might help to clarify how they relate to clinical disease and reveal how theories are related. Copyright © 2014 Elsevier Ltd. All rights reserved.

The use of predictive models to optimize risk of decisions.

PubMed

Baranyi, József; Buss da Silva, Nathália

2017-01-02

The purpose of this paper is to set up a mathematical framework that risk assessors and regulators could use to quantify the "riskiness" of a particular recommendation (choice/decision). The mathematical theory introduced here can be used for decision support systems. We point out that efficient use of predictive models in decision making for food microbiology needs to consider three major points: (1) the uncertainty and variability of the used information based on which the decision is to be made; (2) the validity of the predictive models aiding the assessor; and (3) the cost generated by the difference between the a-priory choice and the a-posteriori outcome. Copyright © 2016 Elsevier B.V. All rights reserved.

Controlled grafting of vinylic monomers on polyolefins: a robust mathematical modeling approach

PubMed Central

Saeb, Mohammad Reza; Rezaee, Babak; Shadman, Alireza; Formela, Krzysztof; Ahmadi, Zahed; Hemmati, Farkhondeh; Kermaniyan, Tayebeh Sadat; Mohammadi, Yousef

2017-01-01

Abstract Experimental and mathematical modeling analyses were used for controlling melt free-radical grafting of vinylic monomers on polyolefins and, thereby, reducing the disturbance of undesired cross-linking of polyolefins. Response surface, desirability function, and artificial intelligence methodologies were blended to modeling/optimization of grafting reaction in terms of vinylic monomer content, peroxide initiator concentration, and melt-processing time. An in-house code was developed based on artificial neural network that learns and mimics processing torque and grafting of glycidyl methacrylate (GMA) typical vinylic monomer on high-density polyethylene (HDPE). Application of response surface and desirability function enabled concurrent optimization of processing torque and GMA grafting on HDPE, through which we quantified for the first time competition between parallel reactions taking place during melt processing: (i) desirable grafting of GMA on HDPE; (ii) undesirable cross-linking of HDPE. The proposed robust mathematical modeling approach can precisely learn the behavior of grafting reaction of vinylic monomers on polyolefins and be placed into practice in finding exact operating condition needed for efficient grafting of reactive monomers on polyolefins. PMID:29491797

Controlled grafting of vinylic monomers on polyolefins: a robust mathematical modeling approach.

PubMed

Saeb, Mohammad Reza; Rezaee, Babak; Shadman, Alireza; Formela, Krzysztof; Ahmadi, Zahed; Hemmati, Farkhondeh; Kermaniyan, Tayebeh Sadat; Mohammadi, Yousef

2017-01-01

Experimental and mathematical modeling analyses were used for controlling melt free-radical grafting of vinylic monomers on polyolefins and, thereby, reducing the disturbance of undesired cross-linking of polyolefins. Response surface, desirability function, and artificial intelligence methodologies were blended to modeling/optimization of grafting reaction in terms of vinylic monomer content, peroxide initiator concentration, and melt-processing time. An in-house code was developed based on artificial neural network that learns and mimics processing torque and grafting of glycidyl methacrylate (GMA) typical vinylic monomer on high-density polyethylene (HDPE). Application of response surface and desirability function enabled concurrent optimization of processing torque and GMA grafting on HDPE, through which we quantified for the first time competition between parallel reactions taking place during melt processing: (i) desirable grafting of GMA on HDPE; (ii) undesirable cross-linking of HDPE. The proposed robust mathematical modeling approach can precisely learn the behavior of grafting reaction of vinylic monomers on polyolefins and be placed into practice in finding exact operating condition needed for efficient grafting of reactive monomers on polyolefins.

A mathematical model of aortic aneurysm formation

PubMed Central

Hao, Wenrui; Gong, Shihua; Wu, Shuonan; Xu, Jinchao; Go, Michael R.; Friedman, Avner; Zhu, Dai

2017-01-01

Abdominal aortic aneurysm (AAA) is a localized enlargement of the abdominal aorta, such that the diameter exceeds 3 cm. The natural history of AAA is progressive growth leading to rupture, an event that carries up to 90% risk of mortality. Hence there is a need to predict the growth of the diameter of the aorta based on the diameter of a patient’s aneurysm at initial screening and aided by non-invasive biomarkers. IL-6 is overexpressed in AAA and was suggested as a prognostic marker for the risk in AAA. The present paper develops a mathematical model which relates the growth of the abdominal aorta to the serum concentration of IL-6. Given the initial diameter of the aorta and the serum concentration of IL-6, the model predicts the growth of the diameter at subsequent times. Such a prediction can provide guidance to how closely the patient’s abdominal aorta should be monitored. The mathematical model is represented by a system of partial differential equations taking place in the aortic wall, where the media is assumed to have the constituency of an hyperelastic material. PMID:28212412

Addressing the Impacts of Climate Change on U.S. Army Alaska with Decision Support Tools Developed Through Field Work and Modeling

DTIC Science & Technology

2016-02-01

Junction, Alaska provided field support and access to their myriad maps, surveys, and field measurements. The glaciology research group at the University of...designed to address the four Research Needs outlined in the SERDP Statement of Need SISON-11-01 as follows: 1) We conducted field measurements and... Research Center. 2014. ACIS Daily Data Browser. Alexiades, V., and A. D. Solomon . Mathematical Modeling of Melting and Freezing Processes. 1993

The Employment Equation: Why Our Young People Need More Maths for Today's Jobs

ERIC Educational Resources Information Center

Hodgen, Jeremy; Marks, Rachel

2013-01-01

This report reviews over 50 research studies to consider the level and type of mathematical skills needed by employers in today's economy. It considers five key questions: (1) What mathematics (level and content) is required in the workplace today?; (2) How and why have the mathematical needs of the workplace changed over time?; (3) In what ways…

Estimating tuberculosis incidence from primary survey data: a mathematical modeling approach

PubMed Central

Chadha, V. K.; Laxminarayan, R.; Arinaminpathy, N.

2017-01-01

SUMMARY BACKGROUND: There is an urgent need for improved estimations of the burden of tuberculosis (TB). OBJECTIVE: To develop a new quantitative method based on mathematical modelling, and to demonstrate its application to TB in India. DESIGN: We developed a simple model of TB transmission dynamics to estimate the annual incidence of TB disease from the annual risk of tuberculous infection and prevalence of smear-positive TB. We first compared model estimates for annual infections per smear-positive TB case using previous empirical estimates from China, Korea and the Philippines. We then applied the model to estimate TB incidence in India, stratified by urban and rural settings. RESULTS: Study model estimates show agreement with previous empirical estimates. Applied to India, the model suggests an annual incidence of smear-positive TB of 89.8 per 100 000 population (95%CI 56.8–156.3). Results show differences in urban and rural TB: while an urban TB case infects more individuals per year, a rural TB case remains infectious for appreciably longer, suggesting the need for interventions tailored to these different settings. CONCLUSIONS: Simple models of TB transmission, in conjunction with necessary data, can offer approaches to burden estimation that complement those currently being used. PMID:28284250

Examining Fourth-Grade Mathematics Writing: Features of Organization, Mathematics Vocabulary, and Mathematical Representations

ERIC Educational Resources Information Center

Hebert, Michael A.; Powell, Sarah R.

2016-01-01

Increasingly, students are expected to write about mathematics. Mathematics writing may be informal (e.g., journals, exit slips) or formal (e.g., writing prompts on high-stakes mathematics assessments). In order to develop an effective mathematics-writing intervention, research needs to be conducted on how students organize mathematics writing and…

Completing the Remedial Sequence and College-Level Credit-Bearing Math: Comparing Binary, Cumulative, and Continuation Ratio Logistic Regression Models

ERIC Educational Resources Information Center

Davidson, J. Cody

2016-01-01

Mathematics is the most common subject area of remedial need and the majority of remedial math students never pass a college-level credit-bearing math class. The majorities of studies that investigate this phenomenon are conducted at community colleges and use some type of regression model; however, none have used a continuation ratio model. The…

Predicting Flu Season Requirements: An Undergraduate Modeling Project

ERIC Educational Resources Information Center

Kramlich, Gary R., II; Braunstein Fierson, Janet L.; Wright, J. Adam

2010-01-01

This project was designed to be used in a freshman calculus class whose students had already been introduced to logistic functions and basic data modeling techniques. It need not be limited to such an audience, however; it has also been implemented in a topics in mathematics class for college upperclassmen. Originally intended to be presented in…

Mathematics Efficacy and Professional Development Needs of Wyoming Agricultural Education Teachers

ERIC Educational Resources Information Center

Haynes, J. Chris; Stripling, Christopher T.

2014-01-01

School-based agricultural education programs provide contextualized learning environments for the teaching of core academic subject matter. This study sought to examine the mathematics efficacy and professional development needs of Wyoming agricultural education teachers related to teaching contextualized mathematics. Wyoming agricultural…

Mathematics teachers' support and retention: using Maslow's hierarchy to understand teachers' needs

NASA Astrophysics Data System (ADS)

Fisher, Molly H.; Royster, David

2016-10-01

As part of a larger study, four mathematics teachers from diverse backgrounds and teaching situations report their ideas on teacher stress, mathematics teacher retention, and their feelings about the needs of mathematics teachers, as well as other information crucial to retaining quality teachers. The responses from the participants were used to develop a hierarchy of teachers' needs that resembles Maslow's hierarchy, which can be used to better support teachers in various stages of their careers. The interviews revealed both non content-specific and content-specific needs within the hierarchy. The responses show that teachers found different schools foster different stress levels and that as teachers they used a number of resources for reducing stress. Other mathematics-specific ideas are also discussed such as the amount of content and pedagogy courses required for certification.

Predictive factors of user acceptance on the primary educational mathematics aids product

NASA Astrophysics Data System (ADS)

Hidayah, I.; Margunani; Dwijanto

2018-03-01

Mathematics learning in primary schools requires instructional media. According to Piaget's theory, students are still in the concrete operational stage. For this reason, the development of the primary level mathematics aids is needed to support the development of successful mathematics learning. The stages of this research are the stages of commercialization with preparatory, marketing, and measurement analysis procedures. Promotion as part of marketing is done by doing a demonstration to the teacher. Measurements were performed to explore the predictive factors of user feasibility in adopting the product. Measurements were conducted using the concept of Technology Acceptance Model (TAM). Measurement variables include external variables, perceived usefulness, perceived ease of use, attitude, intention to use, and actual use. The result of this research shows that the contribution of predictive factors of mathematics teachers on the teaching aids product as follows: the external variable and perceived ease of use at 74%, perceived usefulness at 72%, intention to use (behavioral) at 58%, attitude at 52%, and the consequence factor (actual use) at 42%.

Model-Based Design of Biochemical Microreactors

PubMed Central

Elbinger, Tobias; Gahn, Markus; Neuss-Radu, Maria; Hante, Falk M.; Voll, Lars M.; Leugering, Günter; Knabner, Peter

2016-01-01

Mathematical modeling of biochemical pathways is an important resource in Synthetic Biology, as the predictive power of simulating synthetic pathways represents an important step in the design of synthetic metabolons. In this paper, we are concerned with the mathematical modeling, simulation, and optimization of metabolic processes in biochemical microreactors able to carry out enzymatic reactions and to exchange metabolites with their surrounding medium. The results of the reported modeling approach are incorporated in the design of the first microreactor prototypes that are under construction. These microreactors consist of compartments separated by membranes carrying specific transporters for the input of substrates and export of products. Inside the compartments of the reactor multienzyme complexes assembled on nano-beads by peptide adapters are used to carry out metabolic reactions. The spatially resolved mathematical model describing the ongoing processes consists of a system of diffusion equations together with boundary and initial conditions. The boundary conditions model the exchange of metabolites with the neighboring compartments and the reactions at the surface of the nano-beads carrying the multienzyme complexes. Efficient and accurate approaches for numerical simulation of the mathematical model and for optimal design of the microreactor are developed. As a proof-of-concept scenario, a synthetic pathway for the conversion of sucrose to glucose-6-phosphate (G6P) was chosen. In this context, the mathematical model is employed to compute the spatio-temporal distributions of the metabolite concentrations, as well as application relevant quantities like the outflow rate of G6P. These computations are performed for different scenarios, where the number of beads as well as their loading capacity are varied. The computed metabolite distributions show spatial patterns, which differ for different experimental arrangements. Furthermore, the total output of G6P increases for scenarios where microcompartimentation of enzymes occurs. These results show that spatially resolved models are needed in the description of the conversion processes. Finally, the enzyme stoichiometry on the nano-beads is determined, which maximizes the production of glucose-6-phosphate. PMID:26913283

Development Mathematic Assessment to Increase Mathematical Prerequisite Ability on The Student with Learning Disabilities in Inclusive Elementary School

NASA Astrophysics Data System (ADS)

Robiansyah, S. T. U.; Nanang, F.; Hidayat

2018-01-01

The purpose of this study was to introduce about mathematic assessment is a process of obtaining data or information about the mastery of a student's mathematical skills as an ingredient in preparing a learning program. With this mathematics assessment can be known obstacles, difficulties and needs of students especially in the field of mathematic, so that the learning program will be in accordance with the potential students because it is tailored to what is required of students. This research study was conducted at elementary school of inclusive precisely at SDN Sukagalih I Bandung City based learning in setting of inclusive education. This research study is motivated by the existence of a first-grade student who has disabilities learning in mathematics, the ability of the mathematical prerequisite mastery of the classification of objects by color. The results of the research can provide a profile picture of student data information, the data obtained from the results of the development of systematic and formal mathematical assessment. After doing the development of mathematics assessment then the teacher gets important related information: 1. process the analysis of students’ learning needs, especially in the field of mathematics, 2. preparing the learning program planning according to student learning needs, 3. Designing procedural of method remedial program.

Modeling Criminal Activity in Urban Landscapes

NASA Astrophysics Data System (ADS)

Brantingham, Patricia; Glässer, Uwe; Jackson, Piper; Vajihollahi, Mona

Computational and mathematical methods arguably have an enormous potential for serving practical needs in crime analysis and prevention by offering novel tools for crime investigations and experimental platforms for evidence-based policy making. We present a comprehensive formal framework and tool support for mathematical and computational modeling of criminal behavior to facilitate systematic experimental studies of a wide range of criminal activities in urban environments. The focus is on spatial and temporal aspects of different forms of crime, including opportunistic and serial violent crimes. However, the proposed framework provides a basis to push beyond conventional empirical research and engage the use of computational thinking and social simulations in the analysis of terrorism and counter-terrorism.

The Mathematical Modeling and Computer Simulation of Electrochemical Micromachining Using Ultrashort Pulses

NASA Astrophysics Data System (ADS)

Kozak, J.; Gulbinowicz, D.; Gulbinowicz, Z.

2009-05-01

The need for complex and accurate three dimensional (3-D) microcomponents is increasing rapidly for many industrial and consumer products. Electrochemical machining process (ECM) has the potential of generating desired crack-free and stress-free surfaces of microcomponents. This paper reports a study of pulse electrochemical micromachining (PECMM) using ultrashort (nanoseconds) pulses for generating complex 3-D microstructures of high accuracy. A mathematical model of the microshaping process with taking into consideration unsteady phenomena in electrical double layer has been developed. The software for computer simulation of PECM has been developed and the effects of machining parameters on anodic localization and final shape of machined surface are presented.

A mathematical model for jet engine combustor pollutant emissions

NASA Technical Reports Server (NTRS)

Boccio, J. L.; Weilerstein, G.; Edelman, R. B.

1973-01-01

Mathematical modeling for the description of the origin and disposition of combustion-generated pollutants in gas turbines is presented. A unified model in modular form is proposed which includes kinetics, recirculation, turbulent mixing, multiphase flow effects, swirl and secondary air injection. Subelements of the overall model were applied to data relevant to laboratory reactors and practical combustor configurations. Comparisons between the theory and available data show excellent agreement for basic CO/H2/Air chemical systems. For hydrocarbons the trends are predicted well including higher-than-equilibrium NO levels within the fuel rich regime. Although the need for improved accuracy in fuel rich combustion is indicated, comparisons with actual jet engine data in terms of the effect of combustor-inlet temperature is excellent. In addition, excellent agreement with data is obtained regarding reduced NO emissions with water droplet and steam injection.

Mathematics as a Conduit for Translational Research in Post-Traumatic Osteoarthritis

PubMed Central

Ayati, Bruce P.; Kapitanov, Georgi I.; Coleman, Mitchell C.; Anderson, Donald D.; Martin, James A.

2016-01-01

Biomathematical models offer a powerful method of clarifying complex temporal interactions and the relationships among multiple variables in a system. We present a coupled in silico biomathematical model of articular cartilage degeneration in response to impact and/or aberrant loading such as would be associated with injury to an articular joint. The model incorporates fundamental biological and mechanical information obtained from explant and small animal studies to predict post-traumatic osteoarthritis (PTOA) progression, with an eye toward eventual application in human patients. In this sense, we refer to the mathematics as a “conduit of translation”. The new in silico framework presented in this paper involves a biomathematical model for the cellular and biochemical response to strains computed using finite element analysis. The model predicts qualitative responses presently, utilizing system parameter values largely taken from the literature. To contribute to accurate predictions, models need to be accurately parameterized with values that are based on solid science. We discuss a parameter identification protocol that will enable us to make increasingly accurate predictions of PTOA progression using additional data from smaller scale explant and small animal assays as they become available. By distilling the data from the explant and animal assays into parameters for biomathematical models, mathematics can translate experimental data to clinically relevant knowledge. PMID:27653021

Project CLIMB.

ERIC Educational Resources Information Center

DeLucca, Adolph

1982-01-01

As a state and national model for a basic skills curriculum for Kindergarten through grade 12 students, Coordination Learning Integration--Middlesex Basics (Project CLIMB) is described. The unified system was developed by teachers with administrative support to accomodate all students' reading and mathematics needs. Project CLIMB's development and…

Mathematical Model of Seasonal Influenza with Treatment in Constant Population

NASA Astrophysics Data System (ADS)

Kharis, M.; Arifudin, R.

2017-04-01

Seasonal Influenza is one of disease that outbreaks periodically at least once every year. This disease caused many people hospitalized. Many hospitalized people as employers would infect production quantities, distribution time, and some economic aspects. It will infect economic growth. Infected people need treatments to reduce infection period and cure the infection. In this paper, we discussed about a mathematical model of seasonal influenza with treatment. Factually, the disease was held in short period, less than one year. Hence, we can assume that the population is constant at the disease outbreak time. In this paper, we analyzed the existence of the equilibrium points of the model and their stability. We also give some simulation to give a geometric image about the results of the analysis process.

The language of mathematics: investigating the ways language counts for children's mathematical development.

PubMed

Vukovic, Rose K; Lesaux, Nonie K

2013-06-01

This longitudinal study examined how language ability relates to mathematical development in a linguistically and ethnically diverse sample of children from 6 to 9 years of age. Study participants were 75 native English speakers and 92 language minority learners followed from first to fourth grades. Autoregression in a structural equation modeling (SEM) framework was used to evaluate the relation between children's language ability and gains in different domains of mathematical cognition (i.e., arithmetic, data analysis/probability, algebra, and geometry). The results showed that language ability predicts gains in data analysis/probability and geometry, but not in arithmetic or algebra, after controlling for visual-spatial working memory, reading ability, and sex. The effect of language on gains in mathematical cognition did not differ between language minority learners and native English speakers. These findings suggest that language influences how children make meaning of mathematics but is not involved in complex arithmetical procedures whether presented with Arabic symbols as in arithmetic or with abstract symbols as in algebraic reasoning. The findings further indicate that early language experiences are important for later mathematical development regardless of language background, denoting the need for intensive and targeted language opportunities for language minority and native English learners to develop mathematical concepts and representations. Copyright © 2013. Published by Elsevier Inc.

Why physics needs mathematics

NASA Astrophysics Data System (ADS)

Rohrlich, Fritz

2011-12-01

Classical and the quantum mechanical sciences are in essential need of mathematics. Only thus can the laws of nature be formulated quantitatively permitting quantitative predictions. Mathematics also facilitates extrapolations. But classical and quantum sciences differ in essential ways: they follow different laws of logic, Aristotelian and non-Aristotelian logics, respectively. These are explicated.

A cost-effectiveness model to personalize antiviral therapy in naive patients with genotype 1 chronic hepatitis C.

PubMed

Iannazzo, Sergio; Colombatto, Piero; Ricco, Gabriele; Oliveri, Filippo; Bonino, Ferruccio; Brunetto, Maurizia R

2015-03-01

Rapid virologic response is the best predictor of sustained virologic response with dual therapy in genotype-1 chronic hepatitis C, and its evaluation was proposed to tailor triple therapy in F0-F2 patients. Bio-mathematical modelling of viral dynamics during dual therapy has potentially higher accuracy than rapid virologic in the identification of patients who will eventually achieve sustained response. Study's objective was the cost-effectiveness analysis of a personalized therapy in naïve F0-F2 patients with chronic hepatitis C based on a bio-mathematical model (model-guided strategy) rather than on rapid virologic response (guideline-guided strategy). A deterministic bio-mathematical model of the infected cell dynamics was validated in a cohort of 135 patients treated with dual therapy. A decision-analytic economic model was then developed to compare model-guided and guideline-guided strategies in the Italian setting. The outcomes of the cost-effectiveness analysis with model-guided and guideline-guided strategy were 19.1-19.4 and 18.9-19.3 quality-adjusted-life-years. Total per-patient lifetime costs were €25,200-€26,000 with model-guided strategy and €28,800-€29,900 with guideline-guided strategy. When comparing model-guided with guideline-guided strategy the former resulted more effective and less costly. The adoption of the bio-mathematical predictive criterion has the potential to improve the cost-effectiveness of a personalized therapy for chronic hepatitis C, reserving triple therapy for those patients who really need it. Copyright © 2014 Editrice Gastroenterologica Italiana S.r.l. Published by Elsevier Ltd. All rights reserved.

Suspended Sediment Modeling of Dredge-Disposal Effluent in the GREAT-II Study Reach,

DTIC Science & Technology

1980-03-01

Illinois site. Ky = 1000 cm2/sec .... .......... 81 5-11 Model prediction vs. field observation for centerline Rock Island site ..... ............. 82 5-12...Model prediction vs. field observation for centerline Keithsburg site ...... ............. 83 5-13 Deposition rate at all points in plume for Rock...material disposal to be examined were impairment of the water column and the covering of benthic communities. The need for mathematical models to predict

DMPy: a Python package for automated mathematical model construction of large-scale metabolic systems.

PubMed

Smith, Robert W; van Rosmalen, Rik P; Martins Dos Santos, Vitor A P; Fleck, Christian

2018-06-19

Models of metabolism are often used in biotechnology and pharmaceutical research to identify drug targets or increase the direct production of valuable compounds. Due to the complexity of large metabolic systems, a number of conclusions have been drawn using mathematical methods with simplifying assumptions. For example, constraint-based models describe changes of internal concentrations that occur much quicker than alterations in cell physiology. Thus, metabolite concentrations and reaction fluxes are fixed to constant values. This greatly reduces the mathematical complexity, while providing a reasonably good description of the system in steady state. However, without a large number of constraints, many different flux sets can describe the optimal model and we obtain no information on how metabolite levels dynamically change. Thus, to accurately determine what is taking place within the cell, finer quality data and more detailed models need to be constructed. In this paper we present a computational framework, DMPy, that uses a network scheme as input to automatically search for kinetic rates and produce a mathematical model that describes temporal changes of metabolite fluxes. The parameter search utilises several online databases to find measured reaction parameters. From this, we take advantage of previous modelling efforts, such as Parameter Balancing, to produce an initial mathematical model of a metabolic pathway. We analyse the effect of parameter uncertainty on model dynamics and test how recent flux-based model reduction techniques alter system properties. To our knowledge this is the first time such analysis has been performed on large models of metabolism. Our results highlight that good estimates of at least 80% of the reaction rates are required to accurately model metabolic systems. Furthermore, reducing the size of the model by grouping reactions together based on fluxes alters the resulting system dynamics. The presented pipeline automates the modelling process for large metabolic networks. From this, users can simulate their pathway of interest and obtain a better understanding of how altering conditions influences cellular dynamics. By testing the effects of different parameterisations we are also able to provide suggestions to help construct more accurate models of complete metabolic systems in the future.

A life skills approach to mathematics instruction: preparing students with learning disabilities for the real-life math demands of adulthood.

PubMed

Patton, J R; Cronin, M E; Bassett, D S; Koppel, A E

1997-01-01

Current mathematics instruction does not address the day-to-day needs of many students with learning disabilities. Although the vast majority of students with learning disabilities are not college bound, much of mathematics instruction provides college preparation. Too often, classes in mathematics ignore the skills needed in home and community and on the job. The present article examines the ways in which general mathematics instruction, focused on daily living skills, can easily be integrated into the classrooms of students with learning disabilities.

Mathematization Competencies of Pre-Service Elementary Mathematics Teachers in the Mathematical Modelling Process

ERIC Educational Resources Information Center

Yilmaz, Suha; Tekin-Dede, Ayse

2016-01-01

Mathematization competency is considered in the field as the focus of modelling process. Considering the various definitions, the components of the mathematization competency are determined as identifying assumptions, identifying variables based on the assumptions and constructing mathematical model/s based on the relations among identified…

Comparing the cognitive differences resulting from modeling instruction: Using computer microworld and physical object instruction to model real world problems

NASA Astrophysics Data System (ADS)

Oursland, Mark David

This study compared the modeling achievement of students receiving mathematical modeling instruction using the computer microworld, Interactive Physics, and students receiving instruction using physical objects. Modeling instruction included activities where students applied the (a) linear model to a variety of situations, (b) linear model to two-rate situations with a constant rate, (c) quadratic model to familiar geometric figures. Both quantitative and qualitative methods were used to analyze achievement differences between students (a) receiving different methods of modeling instruction, (b) with different levels of beginning modeling ability, or (c) with different levels of computer literacy. Student achievement was analyzed quantitatively through a three-factor analysis of variance where modeling instruction, beginning modeling ability, and computer literacy were used as the three independent factors. The SOLO (Structure of the Observed Learning Outcome) assessment framework was used to design written modeling assessment instruments to measure the students' modeling achievement. The same three independent factors were used to collect and analyze the interviews and observations of student behaviors. Both methods of modeling instruction used the data analysis approach to mathematical modeling. The instructional lessons presented problem situations where students were asked to collect data, analyze the data, write a symbolic mathematical equation, and use equation to solve the problem. The researcher recommends the following practice for modeling instruction based on the conclusions of this study. A variety of activities with a common structure are needed to make explicit the modeling process of applying a standard mathematical model. The modeling process is influenced strongly by prior knowledge of the problem context and previous modeling experiences. The conclusions of this study imply that knowledge of the properties about squares improved the students' ability to model a geometric problem more than instruction in data analysis modeling. The uses of computer microworlds such as Interactive Physics in conjunction with cooperative groups are a viable method of modeling instruction.

Helicopter mathematical models and control law development for handling qualities research

NASA Technical Reports Server (NTRS)

Chen, Robert T. N.; Lebacqz, J. Victor; Aiken, Edwin W.; Tischler, Mark B.

1988-01-01

Progress made in joint NASA/Army research concerning rotorcraft flight-dynamics modeling, design methodologies for rotorcraft flight-control laws, and rotorcraft parameter identification is reviewed. Research into these interactive disciplines is needed to develop the analytical tools necessary to conduct flying qualities investigations using both the ground-based and in-flight simulators, and to permit an efficient means of performing flight test evaluation of rotorcraft flying qualities for specification compliance. The need for the research is particularly acute for rotorcraft because of their mathematical complexity, high order dynamic characteristics, and demanding mission requirements. The research in rotorcraft flight-dynamics modeling is pursued along two general directions: generic nonlinear models and nonlinear models for specific rotorcraft. In addition, linear models are generated that extend their utilization from 1-g flight to high-g maneuvers and expand their frequency range of validity for the design analysis of high-gain flight control systems. A variety of methods ranging from classical frequency-domain approaches to modern time-domain control methodology that are used in the design of rotorcraft flight control laws is reviewed. Also reviewed is a study conducted to investigate the design details associated with high-gain, digital flight control systems for combat rotorcraft. Parameter identification techniques developed for rotorcraft applications are reviewed.

Choosing High-Yield Tasks for the Mathematical Development of Practicing Secondary Teachers

ERIC Educational Resources Information Center

Epperson, James A. Mendoza; Rhoads, Kathryn

2015-01-01

Many mathematics teacher educators encounter the challenge of creating or choosing mathematical tasks that evoke important mathematical insights and connections yet remain firmly grounded in school mathematics. This challenge increases substantially when trying to meet the needs of practicing secondary mathematics teachers pursuing graduate work…

Role of mathematical models in assessment of risk and in attempts to define management strategy.

PubMed

Flamm, W G; Winbush, J S

1984-06-01

Risk assessment of food-borne carcinogens is becoming a common practice at FDA. Actual risk is not being estimated, only the upper limit of risk. The risk assessment process involves a large number of steps and assumptions, many of which affect the numerical value estimated. The mathematical model which is to be applied is only one of the factors which affect these numerical values. To fulfill the policy objective of using the "worst plausible case" in estimating the upper limit of risk, recognition needs to be given to a proper balancing of assumptions and decisions. Interaction between risk assessors and risk managers should avoid making or giving the appearance of making specific technical decisions such as the choice of the mathematical model. The importance of this emerging field is too great to jeopardize it by inappropriately mixing scientific judgments with policy judgments. The risk manager should understand fully the points and range of uncertainty involved in arriving at the estimates of risk which must necessarily affect the choice of the policy or regulatory options available.

Flight dynamics analysis and simulation of heavy lift airships. Volume 2: Technical manual

NASA Technical Reports Server (NTRS)

Ringland, R. F.; Tischler, M. B.; Jex, H. R.; Emmen, R. D.; Ashkenas, I. L.

1982-01-01

The mathematical models embodied in the simulation are described in considerable detail and with supporting evidence for the model forms chosen. In addition the trimming and linearization algorithms used in the simulation are described. Appendices to the manual identify reference material for estimating the needed coefficients for the input data and provide example simulation results.

Abrupt Strategy Change Underlies Gradual Performance Change: Bayesian Hierarchical Models of Component and Aggregate Strategy Use

ERIC Educational Resources Information Center

Wynton, Sarah K. A.; Anglim, Jeromy

2017-01-01

While researchers have often sought to understand the learning curve in terms of multiple component processes, few studies have measured and mathematically modeled these processes on a complex task. In particular, there remains a need to reconcile how abrupt changes in strategy use can co-occur with gradual changes in task completion time. Thus,…

Optimization and Control of Agent-Based Models in Biology: A Perspective.

PubMed

An, G; Fitzpatrick, B G; Christley, S; Federico, P; Kanarek, A; Neilan, R Miller; Oremland, M; Salinas, R; Laubenbacher, R; Lenhart, S

2017-01-01

Agent-based models (ABMs) have become an increasingly important mode of inquiry for the life sciences. They are particularly valuable for systems that are not understood well enough to build an equation-based model. These advantages, however, are counterbalanced by the difficulty of analyzing and using ABMs, due to the lack of the type of mathematical tools available for more traditional models, which leaves simulation as the primary approach. As models become large, simulation becomes challenging. This paper proposes a novel approach to two mathematical aspects of ABMs, optimization and control, and it presents a few first steps outlining how one might carry out this approach. Rather than viewing the ABM as a model, it is to be viewed as a surrogate for the actual system. For a given optimization or control problem (which may change over time), the surrogate system is modeled instead, using data from the ABM and a modeling framework for which ready-made mathematical tools exist, such as differential equations, or for which control strategies can explored more easily. Once the optimization problem is solved for the model of the surrogate, it is then lifted to the surrogate and tested. The final step is to lift the optimization solution from the surrogate system to the actual system. This program is illustrated with published work, using two relatively simple ABMs as a demonstration, Sugarscape and a consumer-resource ABM. Specific techniques discussed include dimension reduction and approximation of an ABM by difference equations as well systems of PDEs, related to certain specific control objectives. This demonstration illustrates the very challenging mathematical problems that need to be solved before this approach can be realistically applied to complex and large ABMs, current and future. The paper outlines a research program to address them.

Computing Surface Coordinates Of Face-Milled Spiral-Bevel Gear Teeth

NASA Technical Reports Server (NTRS)

Handschuh, Robert F.; Litvin, Faydor L.

1995-01-01

Surface coordinates of face-milled spiral-bevel gear teeth computed by method involving numerical solution of governing equations. Needed to generate mathematical models of tooth surfaces for use in finite-element analyses of stresses, strains, and vibrations in meshing spiral-bevel gears.

Mathematical and Computational Aspects Related to Soil Modeling and Simulation

DTIC Science & Technology

2017-09-26

and simulation challenges at the interface of applied math (homogenization, handling of discontinuous behavior, discrete vs. continuum representations...applied math tools need to be established and used to figure out how to impose compatible boundary conditions, how to better approximate the gradient

76 FR 57017 - Submission for OMB Review; Comment Request

Federal Register 2010, 2011, 2012, 2013, 2014

2011-09-15

...) Predict or detect trends in disease occurrence and movement, (4) Understand the risk factors for disease... mathematical models of animal disease to evaluate potential control scenarios, (7) Make recommendation for..., and diagnostic testing needs. Description of Respondents: Business or other for-profit. Number of...

Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches

ERIC Educational Resources Information Center

Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem

2014-01-01

Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…

Elementary Preservice Teachers' and Elementary Inservice Teachers' Knowledge of Mathematical Modeling

ERIC Educational Resources Information Center

Schwerdtfeger, Sara

2017-01-01

This study examined the differences in knowledge of mathematical modeling between a group of elementary preservice teachers and a group of elementary inservice teachers. Mathematical modeling has recently come to the forefront of elementary mathematics classrooms because of the call to add mathematical modeling tasks in mathematics classes through…

HELIOGate, a Portal for the Heliophysics Community

NASA Astrophysics Data System (ADS)

Pierantoni; Gabriele; Carley, Eoin

2014-10-01

Heliophysics is the branch of physics that investigates the interactions between the Sun and the other bodies of the solar system. Heliophysicists rely on data collected from numerous sources scattered across the Solar System. The data collected from these sources is processed to extract metadata and the metadata extracted in this fashion is then used to build indexes of features and events called catalogues. Heliophysicists also develop conceptual and mathematical models of the phenomena and the environment of the Solar System. More specifically, they investigate the physical characteristics of the phenomena and they simulate how they propagate throughout the Solar System with mathematical and physical abstractions called propagation models. HELIOGate aims at addressing the need to combine and orchestrate existing web services in a flexible and easily configurable fashion to tackle different scientific questions. HELIOGate also offers a tool capable of connecting to size! able computation and storage infrastructures to execute data processing codes that are needed to calibrate raw data and to extract metadata.

A Case Study of Teachers' Development of Well-Structured Mathematical Modelling Activities

ERIC Educational Resources Information Center

Stohlmann, Micah; Maiorca, Cathrine; Allen, Charlie

2017-01-01

This case study investigated how three teachers developed mathematical modelling activities integrated with content standards through participation in a course on mathematical modelling. The class activities involved experiencing a mathematical modelling activity, reading and rating example mathematical modelling activities, reading articles about…

Measuring Near-Infrared Spectroscopy Derived Cerebral Autoregulation in Neonates: From Research Tool Toward Bedside Multimodal Monitoring

PubMed Central

Thewissen, Liesbeth; Caicedo, Alexander; Lemmers, Petra; Van Bel, Frank; Van Huffel, Sabine; Naulaers, Gunnar

2018-01-01

Introduction: Cerebral autoregulation (CAR), the ability of the human body to maintain cerebral blood flow (CBF) in a wide range of perfusion pressures, can be calculated by describing the relation between arterial blood pressure (ABP) and cerebral oxygen saturation measured by near-infrared spectroscopy (NIRS). In literature, disturbed CAR is described in different patient groups, using multiple measurement techniques and mathematical models. Furthermore, it is unclear to what extent cerebral pathology and outcome can be explained by impaired CAR. Aim and methods: In order to summarize CAR studies using NIRS in neonates, a systematic review was performed in the PUBMED and EMBASE database. To provide a general overview of the clinical framework used to study CAR, the different preprocessing methods and mathematical models are described and explained. Furthermore, patient characteristics, definition of impaired CAR and the outcome according to this definition is described organized for the different patient groups. Results: Forty-six articles were included in this review. Four patient groups were established: preterm infants during the transitional period, neonates receiving specific medication/treatment, neonates with congenital heart disease and neonates with hypoxic-ischemic encephalopathy (HIE) treated with therapeutic hypothermia. Correlation, coherence and transfer function (TF) gain are the mathematical models most frequently used to describe CAR. The definition of impaired CAR is depending on the mathematical model used. The incidence of intraventricular hemorrhage in preterm infants is the outcome variable most frequently correlated with impaired CAR. Hypotension, disease severity, dopamine treatment, injury on magnetic resonance imaging (MRI) and long term outcome are associated with impaired CAR. Prospective interventional studies are lacking in all research areas. Discussion and conclusion: NIRS derived CAR measurement is an important research tool to improve knowledge about central hemodynamic fluctuations during the transitional period, cerebral pharmacodynamics of frequently used medication (sedatives-inotropes) and cerebral effects of specific therapies in neonatology. Uniformity regarding measurement techniques and mathematical models is needed. Multimodal monitoring databases of neonatal intensive care patients of multiple centers, together with identical outcome parameters are needed to compare different techniques and make progress in this field. Real-time bedside monitoring of CAR, together with conventional monitoring, seems a promising technique to improve individual patient care. PMID:29868521

Mild Disability Students and Everyday Mathematics: Serving the Needs of This Population

ERIC Educational Resources Information Center

Brehe Pixler, Priscilla

2009-01-01

No Child Left Behind requires school districts to demonstrate adequate yearly progress in mathematics for all students, including the sub-population of disabled students. Given that more than 200 Ohio school districts have implemented Everyday Mathematics (EM) to achieve this mandate, districts need to know if this standards-based program meets…

Teachers of Mathematics or Numeracy?

ERIC Educational Resources Information Center

Perso, Thelma

2006-01-01

According to this author, the solution to the "phonics versus whole language" debate over the teaching of reading is balance and a focus on the needs of all students. There is similarly a need, in developing numerate young people, to focus on the teaching and learning of mathematics and mathematics skills some of the time, and on…

The Academic Training of Two-Year College Mathematics Faculty.

ERIC Educational Resources Information Center

Long, Calvin T.

The academic training needs of two-year college mathematics faculty are discussed in this paper and appropriate courses of study are proposed. After introductory comments on the diversity of two-year college students' needs for mathematics education, an undergraduate course of study appropriate for two-year college math faculty is proposed. This…

Middle Grades Mathematics Engagement: How Action Research Informs What Counts

ERIC Educational Resources Information Center

Ivory, Pateakia Lachelle

2017-01-01

The purpose of the study was to examine how action research informs instructional changes that need to take place in the middle grades mathematics classroom. There is a need for an increase in engagement in middle grades mathematics by educators being critically reflective of their instructional practices. The research question addressed in this…

An Introduction to Turbulent Flow

NASA Astrophysics Data System (ADS)

Mathieu, Jean; Scott, Julian

2000-06-01

In recent years, turbulence has become a very lively area of scientific research and application, attracting many newcomers who need a basic introduction to the subject. Turbulent Flows ably meets this need, developing both physical insight and the mathematical framework needed to express the theory. The authors present basic theory and illustrate it with examples of simple turbulent flows and classical models of jets, wakes, and boundary layers. A deeper understanding of turbulence dynamics is provided by their treatment of spectral analysis and its applications.

Mathematical Modelling Approach in Mathematics Education

ERIC Educational Resources Information Center

Arseven, Ayla

2015-01-01

The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…

Mathematical Modelling in the Junior Secondary Years: An Approach Incorporating Mathematical Technology

ERIC Educational Resources Information Center

Lowe, James; Carter, Merilyn; Cooper, Tom

2018-01-01

Mathematical models are conceptual processes that use mathematics to describe, explain, and/or predict the behaviour of complex systems. This article is written for teachers of mathematics in the junior secondary years (including out-of-field teachers of mathematics) who may be unfamiliar with mathematical modelling, to explain the steps involved…

Mathematics teachers' conceptions about modelling activities and its reflection on their beliefs about mathematics

NASA Astrophysics Data System (ADS)

Shahbari, Juhaina Awawdeh

2018-07-01

The current study examines whether the engagement of mathematics teachers in modelling activities and subsequent changes in their conceptions about these activities affect their beliefs about mathematics. The sample comprised 52 mathematics teachers working in small groups in four modelling activities. The data were collected from teachers' Reports about features of each activity, interviews and questionnaires on teachers' beliefs about mathematics. The findings indicated changes in teachers' conceptions about the modelling activities. Most teachers referred to the first activity as a mathematical problem but emphasized only the mathematical notions or the mathematical operations in the modelling process; changes in their conceptions were gradual. Most of the teachers referred to the fourth activity as a mathematical problem and emphasized features of the whole modelling process. The results of the interviews indicated that changes in the teachers' conceptions can be attributed to structure of the activities, group discussions, solution paths and elicited models. These changes about modelling activities were reflected in teachers' beliefs about mathematics. The quantitative findings indicated that the teachers developed more constructive beliefs about mathematics after engagement in the modelling activities and that the difference was significant, however there was no significant difference regarding changes in their traditional beliefs.

Linear Mathematical Model for Seam Tracking with an Arc Sensor in P-GMAW Processes

PubMed Central

Liu, Wenji; Li, Liangyu; Hong, Ying; Yue, Jianfeng

2017-01-01

Arc sensors have been used in seam tracking and widely studied since the 80s and commercial arc sensing products for T and V shaped grooves have been developed. However, it is difficult to use these arc sensors in narrow gap welding because the arc stability and sensing accuracy are not satisfactory. Pulse gas melting arc welding (P-GMAW) has been successfully applied in narrow gap welding and all position welding processes, so it is worthwhile to research P-GMAW arc sensing technology. In this paper, we derived a linear mathematical P-GMAW model for arc sensing, and the assumptions for the model are verified through experiments and finite element methods. Finally, the linear characteristics of the mathematical model were investigated. In torch height changing experiments, uphill experiments, and groove angle changing experiments the P-GMAW arc signals all satisfied the linear rules. In addition, the faster the welding speed, the higher the arc signal sensitivities; the smaller the groove angle, the greater the arc sensitivities. The arc signal variation rate needs to be modified according to the welding power, groove angles, and weaving or rotate speed. PMID:28335425

Real-time control data wrangling for development of mathematical control models of technological processes

NASA Astrophysics Data System (ADS)

Vasilyeva, N. V.; Koteleva, N. I.; Fedorova, E. R.

2018-05-01

The relevance of the research is due to the need to stabilize the composition of the melting products of copper-nickel sulfide raw materials in the Vanyukov furnace. The goal of this research is to identify the most suitable methods for the aggregation of the real time data for the development of a mathematical model for control of the technological process of melting copper-nickel sulfide raw materials in the Vanyukov furnace. Statistical methods of analyzing the historical data of the real technological object and the correlation analysis of process parameters are described. Factors that exert the greatest influence on the main output parameter (copper content in matte) and ensure the physical-chemical transformations are revealed. An approach to the processing of the real time data for the development of a mathematical model for control of the melting process is proposed. The stages of processing the real time information are considered. The adopted methodology for the aggregation of data suitable for the development of a control model for the technological process of melting copper-nickel sulfide raw materials in the Vanyukov furnace allows us to interpret the obtained results for their further practical application.

An integrated theoretical-experimental approach to accelerate translational tissue engineering.

PubMed

Coy, Rachel H; Evans, Owen R; Phillips, James B; Shipley, Rebecca J

2018-01-01

Implantable devices utilizing bioengineered tissue are increasingly showing promise as viable clinical solutions. The design of bioengineered constructs is currently directed according to the results of experiments that are used to test a wide range of different combinations and spatial arrangements of biomaterials, cells and chemical factors. There is an outstanding need to accelerate the design process and reduce financial costs, whilst minimizing the required number of animal-based experiments. These aims could be achieved through the incorporation of mathematical modelling as a preliminary design tool. Here we focus on tissue-engineered constructs for peripheral nerve repair, which are designed to aid nerve and blood vessel growth and repair after peripheral nerve injury. We offer insight into the role that mathematical modelling can play within tissue engineering, and motivate the use of modelling as a tool capable of improving and accelerating the design of nerve repair constructs in particular. Specific case studies are presented in order to illustrate the potential of mathematical modelling to direct construct design. Copyright © 2016 The Authors Journal of Tissue Engineering and Regenerative Medicine Published by John Wiley & Sons Ltd. Copyright © 2016 The Authors Journal of Tissue Engineering and Regenerative Medicine Published by John Wiley & Sons Ltd.

Mathematics, thermodynamics, and modeling to address ten common misconceptions about protein structure, folding, and stability.

PubMed

Robic, Srebrenka

2010-01-01

To fully understand the roles proteins play in cellular processes, students need to grasp complex ideas about protein structure, folding, and stability. Our current understanding of these topics is based on mathematical models and experimental data. However, protein structure, folding, and stability are often introduced as descriptive, qualitative phenomena in undergraduate classes. In the process of learning about these topics, students often form incorrect ideas. For example, by learning about protein folding in the context of protein synthesis, students may come to an incorrect conclusion that once synthesized on the ribosome, a protein spends its entire cellular life time in its fully folded native confirmation. This is clearly not true; proteins are dynamic structures that undergo both local fluctuations and global unfolding events. To prevent and address such misconceptions, basic concepts of protein science can be introduced in the context of simple mathematical models and hands-on explorations of publicly available data sets. Ten common misconceptions about proteins are presented, along with suggestions for using equations, models, sequence, structure, and thermodynamic data to help students gain a deeper understanding of basic concepts relating to protein structure, folding, and stability.

Linear Mathematical Model for Seam Tracking with an Arc Sensor in P-GMAW Processes.

PubMed

Liu, Wenji; Li, Liangyu; Hong, Ying; Yue, Jianfeng

2017-03-14

Arc sensors have been used in seam tracking and widely studied since the 80s and commercial arc sensing products for T and V shaped grooves have been developed. However, it is difficult to use these arc sensors in narrow gap welding because the arc stability and sensing accuracy are not satisfactory. Pulse gas melting arc welding (P-GMAW) has been successfully applied in narrow gap welding and all position welding processes, so it is worthwhile to research P-GMAW arc sensing technology. In this paper, we derived a linear mathematical P-GMAW model for arc sensing, and the assumptions for the model are verified through experiments and finite element methods. Finally, the linear characteristics of the mathematical model were investigated. In torch height changing experiments, uphill experiments, and groove angle changing experiments the P-GMAW arc signals all satisfied the linear rules. In addition, the faster the welding speed, the higher the arc signal sensitivities; the smaller the groove angle, the greater the arc sensitivities. The arc signal variation rate needs to be modified according to the welding power, groove angles, and weaving or rotate speed.

Moving beyond Type I and Type II neuron types.

PubMed

Skinner, Frances K

2013-01-01

In 1948, Hodgkin delineated different classes of axonal firing.  This has been mathematically translated allowing insight and understanding to emerge.  As such, the terminology of 'Type I' and 'Type II' neurons is commonplace in the Neuroscience literature today.  Theoretical insights have helped us realize that, for example, network synchronization depends on whether neurons are Type I or Type II.  Mathematical models are precise with analyses (considering Type I/II aspects), but experimentally, the distinction can be less clear.  On the other hand, experiments are becoming more sophisticated in terms of distinguishing and manipulating particular cell types but are limited in terms of being able to consider network aspects simultaneously.   Although there is much work going on mathematically and experimentally, in my opinion it is becoming common that models are either superficially linked with experiment or not described in enough detail to appreciate the biological context.  Overall, we all suffer in terms of impeding our understanding of brain networks and applying our understanding to neurological disease.  I suggest that more modelers become familiar with experimental details and that more experimentalists appreciate modeling assumptions. In other words, we need to move beyond our comfort zones.

The conceptual basis of mathematics in cardiology IV: statistics and model fitting.

PubMed

Bates, Jason H T; Sobel, Burton E

2003-06-01

This is the fourth in a series of four articles developed for the readers of Coronary Artery Disease. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas. This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to cardiovascular medicine and biology.

Dependence of the firearm-related homicide rate on gun availability: a mathematical analysis.

PubMed

Wodarz, Dominik; Komarova, Natalia L

2013-01-01

In the USA, the relationship between the legal availability of guns and the firearm-related homicide rate has been debated. It has been argued that unrestricted gun availability promotes the occurrence of firearm-induced homicides. It has also been pointed out that gun possession can protect potential victims when attacked. This paper provides a first mathematical analysis of this tradeoff, with the goal to steer the debate towards arguing about assumptions, statistics, and scientific methods. The model is based on a set of clearly defined assumptions, which are supported by available statistical data, and is formulated axiomatically such that results do not depend on arbitrary mathematical expressions. According to this framework, two alternative scenarios can minimize the gun-related homicide rate: a ban of private firearms possession, or a policy allowing the general population to carry guns. Importantly, the model identifies the crucial parameters that determine which policy minimizes the death rate, and thus serves as a guide for the design of future epidemiological studies. The parameters that need to be measured include the fraction of offenders that illegally possess a gun, the degree of protection provided by gun ownership, and the fraction of the population who take up their right to own a gun and carry it when attacked. Limited data available in the literature were used to demonstrate how the model can be parameterized, and this preliminary analysis suggests that a ban of private firearm possession, or possibly a partial reduction in gun availability, might lower the rate of firearm-induced homicides. This, however, should not be seen as a policy recommendation, due to the limited data available to inform and parameterize the model. However, the model clearly defines what needs to be measured, and provides a basis for a scientific discussion about assumptions and data.

A Multiple Intelligence Pedagogical Approach in Fifth Grade Mathematics: A Mixed Method Study

ERIC Educational Resources Information Center

Davis, Claudine Davillier

2012-01-01

The need for mathematics intervention has increased tremendously over the years, particularly after the No Child Left Behind Act of 2001.Students who lack basic mathematics skills and students who experience mathematics difficulties greatly benefit from mathematics interventions. This study examined mathematics intervention through the use of the…

Some aspects on kinetic modeling of evacuation dynamics. Comment on "Human behaviours in evacuation crowd dynamics: From modelling to "big data" toward crisis management" by Nicola Bellomo et al.

NASA Astrophysics Data System (ADS)

Calvo, Juan; Nieto, Juanjo

2016-09-01

The management of human crowds in extreme situations is a complex subject which requires to take into account a variety of factors. To name a few, the understanding of human behaviour, the psychological and behavioural features of individuals, the quality of the venue and the stress level of the pedestrian need to be addressed in order to select the most appropriate action during an evacuation process on a complex venue. In this sense, the mathematical modeling of such complex phenomena can be regarded as a very useful tool to understand and predict these situations. As presented in [4], mathematical models can provide guidance to the personnel in charge of managing evacuation processes, by means of helping to design a set of protocols, among which the most appropriate during a given critical situation is then chosen.

Mathematical Model of Cardiovascular and Metabolic Responses to Umbilical Cord Occlusions in Fetal Sheep.

PubMed

Wang, Qiming; Gold, Nathan; Frasch, Martin G; Huang, Huaxiong; Thiriet, Marc; Wang, Xiaogang

2015-12-01

Fetal acidemia during labor is associated with an increased risk of brain injury and lasting neurological deficits. This is in part due to the repetitive occlusions of the umbilical cord (UCO) induced by uterine contractions. Whereas fetal heart rate (FHR) monitoring is widely used clinically, it fails to detect fetal acidemia. Hence, new approaches are needed for early detection of fetal acidemia during labor. We built a mathematical model of the UCO effects on FHR, mean arterial blood pressure (MABP), oxygenation and metabolism. Mimicking fetal experiments, our in silico model reproduces salient features of experimentally observed fetal cardiovascular and metabolic behavior including FHR overshoot, gradual MABP decrease and mixed metabolic and respiratory acidemia during UCO. Combined with statistical analysis, our model provides valuable insight into the labor-like fetal distress and guidance for refining FHR monitoring algorithms to improve detection of fetal acidemia and cardiovascular decompensation.

Thinking is believing.

PubMed

Kasturirangan, Rajesh

2008-01-01

Philosophers as well lay people often think of beliefs as psychological states with dubious epistemic properties. Beliefs are conceptualized as unregulated conceptual structures, for the most part hypothetical and often fanciful or deluded. Thinking and reasoning on the other hand are seen as rational activities regulated by rules and governed by norms. Computational modeling of the mind has focused on rule-governed behavior, ultimately trying to reduce them to rules of logic. What if thinking is less like reasoning and more like believing? I argue that the classical model of thought as rational is mistaken and that thinking is fundamentally constituted by believing. This new approach forces us to re-evaluate classical epistemic concepts like "truth", "justification" etc. Furthermore, if thinking is believing, then it is not clear how thoughts can be modeled computationally. We need new mathematical ideas to model thought, ideas that are quite different from traditional logic-based mathematical structures.

A mathematical model to describe the nonlinear elastic properties of the gastrocnemius tendon of chickens.

PubMed

Foutz, T L

1991-03-01

A phenomenological model was developed to describe the nonlinear elastic behavior of the avian gastrocnemius tendon. Quasistatic uniaxial tensile tests were used to apply a deformation and resulting load on the tendon at a deformation rate of 5 mm/min. Plots of deformation versus load indicated a nonlinear loading response. By calculating engineering stress and engineering strain, the experimental data were normalized for tendon shape. The elastic response was determined from stress-strain curves and was found to vary with engineering strain. The response to the applied engineering strain could best be described by a mathematical model that combined a linear function and a nonlinear function. Three parameters in the model were developed to represent the nonlinear elastic behavior of the tendon, thereby allowing analysis of elasticity without prior knowledge of engineering strain. This procedure reduced the amount of data needed for the statistical analysis of nonlinear elasticity.

A stochastic model for optimizing composite predictors based on gene expression profiles.

PubMed

Ramanathan, Murali

2003-07-01

This project was done to develop a mathematical model for optimizing composite predictors based on gene expression profiles from DNA arrays and proteomics. The problem was amenable to a formulation and solution analogous to the portfolio optimization problem in mathematical finance: it requires the optimization of a quadratic function subject to linear constraints. The performance of the approach was compared to that of neighborhood analysis using a data set containing cDNA array-derived gene expression profiles from 14 multiple sclerosis patients receiving intramuscular inteferon-beta1a. The Markowitz portfolio model predicts that the covariance between genes can be exploited to construct an efficient composite. The model predicts that a composite is not needed for maximizing the mean value of a treatment effect: only a single gene is needed, but the usefulness of the effect measure may be compromised by high variability. The model optimized the composite to yield the highest mean for a given level of variability or the least variability for a given mean level. The choices that meet this optimization criteria lie on a curve of composite mean vs. composite variability plot referred to as the "efficient frontier." When a composite is constructed using the model, it outperforms the composite constructed using the neighborhood analysis method. The Markowitz portfolio model may find potential applications in constructing composite biomarkers and in the pharmacogenomic modeling of treatment effects derived from gene expression endpoints.

Physically based modeling in catchment hydrology at 50: Survey and outlook

NASA Astrophysics Data System (ADS)

Paniconi, Claudio; Putti, Mario

2015-09-01

Integrated, process-based numerical models in hydrology are rapidly evolving, spurred by novel theories in mathematical physics, advances in computational methods, insights from laboratory and field experiments, and the need to better understand and predict the potential impacts of population, land use, and climate change on our water resources. At the catchment scale, these simulation models are commonly based on conservation principles for surface and subsurface water flow and solute transport (e.g., the Richards, shallow water, and advection-dispersion equations), and they require robust numerical techniques for their resolution. Traditional (and still open) challenges in developing reliable and efficient models are associated with heterogeneity and variability in parameters and state variables; nonlinearities and scale effects in process dynamics; and complex or poorly known boundary conditions and initial system states. As catchment modeling enters a highly interdisciplinary era, new challenges arise from the need to maintain physical and numerical consistency in the description of multiple processes that interact over a range of scales and across different compartments of an overall system. This paper first gives an historical overview (past 50 years) of some of the key developments in physically based hydrological modeling, emphasizing how the interplay between theory, experiments, and modeling has contributed to advancing the state of the art. The second part of the paper examines some outstanding problems in integrated catchment modeling from the perspective of recent developments in mathematical and computational science.

Evaluation Theory for Developmental Mathematics Practitioners

ERIC Educational Resources Information Center

Duranczyk, Irene Mary

2007-01-01

This article is designed to present an overview of critical theory, research, and evaluation for the developmental mathematics educator. Students caught in the gap between high school mathematics preparation and entry-level college mathematics expectations--developmental mathematics education students--need to have their personal narratives told…

Internationalizing the Mathematical Finance Course

ERIC Educational Resources Information Center

Okonkwo, Zephyrinus C.

2017-01-01

About the year 2000, the Department of Mathematics and Computer Science, Albany State University (ASU), Albany, Georgia, USA envisioned the need to have a comprehensive curriculum revision based on recommendations of the Conference Boards of The Mathematical Sciences, the American Mathematical Society, the Mathematical Association of American, and…

The 24-Hour Mathematical Modeling Challenge

ERIC Educational Resources Information Center

Galluzzo, Benjamin J.; Wendt, Theodore J.

2015-01-01

Across the mathematics curriculum there is a renewed emphasis on applications of mathematics and on mathematical modeling. Providing students with modeling experiences beyond the ordinary classroom setting remains a challenge, however. In this article, we describe the 24-hour Mathematical Modeling Challenge, an extracurricular event that exposes…

Validation of a mathematical model of the bovine estrous cycle for cows with different estrous cycle characteristics.

PubMed

Boer, H M T; Butler, S T; Stötzel, C; Te Pas, M F W; Veerkamp, R F; Woelders, H

2017-11-01

A recently developed mechanistic mathematical model of the bovine estrous cycle was parameterized to fit empirical data sets collected during one estrous cycle of 31 individual cows, with the main objective to further validate the model. The a priori criteria for validation were (1) the resulting model can simulate the measured data correctly (i.e. goodness of fit), and (2) this is achieved without needing extreme, probably non-physiological parameter values. We used a least squares optimization procedure to identify parameter configurations for the mathematical model to fit the empirical in vivo measurements of follicle and corpus luteum sizes, and the plasma concentrations of progesterone, estradiol, FSH and LH for each cow. The model was capable of accommodating normal variation in estrous cycle characteristics of individual cows. With the parameter sets estimated for the individual cows, the model behavior changed for 21 cows, with improved fit of the simulated output curves for 18 of these 21 cows. Moreover, the number of follicular waves was predicted correctly for 18 of the 25 two-wave and three-wave cows, without extreme parameter value changes. Estimation of specific parameters confirmed results of previous model simulations indicating that parameters involved in luteolytic signaling are very important for regulation of general estrous cycle characteristics, and are likely responsible for differences in estrous cycle characteristics between cows.

An Approach for a Mathematical Description of Human Root Canals by Means of Elementary Parameters.

PubMed

Dannemann, Martin; Kucher, Michael; Kirsch, Jasmin; Binkowski, Alexander; Modler, Niels; Hannig, Christian; Weber, Marie-Theres

2017-04-01

Root canal geometry is an important factor for instrumentation and preparation of the canals. Curvature, length, shape, and ramifications need to be evaluated in advance to enhance the success of the treatment. Therefore, the present study aimed to design and realize a method for analyzing the geometric characteristics of human root canals. Two extracted human lower molars were radiographed in the occlusal direction using micro-computed tomographic imaging. The 3-dimensional geometry of the root canals, calculated by a self-implemented image evaluation algorithm, was described by 3 different mathematical models: the elliptical model, the 1-circle model, and the 3-circle model. The different applied mathematical models obtained similar geometric properties depending on the parametric model used. Considering more complex root canals, the differences of the results increase because of the different adaptability and the better approximation of the geometry. With the presented approach, it is possible to estimate and compare the geometry of natural root canals. Therefore, the deviation of the canal can be assessed, which is important for the choice of taper of root canal instruments. Root canals with a nearly elliptical cross section are reasonably approximated by the elliptical model, whereas the 3-circle model obtains a good agreement for curved shapes. Copyright © 2017 American Association of Endodontists. Published by Elsevier Inc. All rights reserved.

Mathematical analysis of a nutrient-plankton system with delay.

PubMed

Rehim, Mehbuba; Zhang, Zhenzhen; Muhammadhaji, Ahmadjan

2016-01-01

A mathematical model describing the interaction of nutrient-plankton is investigated in this paper. In order to account for the time needed by the phytoplankton to mature after which they can release toxins, a discrete time delay is incorporated into the system. Moreover, it is also taken into account discrete time delays which indicates the partially recycled nutrient decomposed by bacteria after the death of biomass. In the first part of our analysis the sufficient conditions ensuring local and global asymptotic stability of the model are obtained. Next, the existence of the Hopf bifurcation as time delay crosses a threshold value is established and, meanwhile, the phenomenon of stability switches is found under certain conditions. Numerical simulations are presented to illustrate the analytical results.

Truth, models, model sets, AIC, and multimodel inference: a Bayesian perspective

USGS Publications Warehouse

Barker, Richard J.; Link, William A.

2015-01-01

Statistical inference begins with viewing data as realizations of stochastic processes. Mathematical models provide partial descriptions of these processes; inference is the process of using the data to obtain a more complete description of the stochastic processes. Wildlife and ecological scientists have become increasingly concerned with the conditional nature of model-based inference: what if the model is wrong? Over the last 2 decades, Akaike's Information Criterion (AIC) has been widely and increasingly used in wildlife statistics for 2 related purposes, first for model choice and second to quantify model uncertainty. We argue that for the second of these purposes, the Bayesian paradigm provides the natural framework for describing uncertainty associated with model choice and provides the most easily communicated basis for model weighting. Moreover, Bayesian arguments provide the sole justification for interpreting model weights (including AIC weights) as coherent (mathematically self consistent) model probabilities. This interpretation requires treating the model as an exact description of the data-generating mechanism. We discuss the implications of this assumption, and conclude that more emphasis is needed on model checking to provide confidence in the quality of inference.

Using Science to Promote Preservice Teacher Understanding of Problem Solving in Mathematics

ERIC Educational Resources Information Center

Tobias, Jennifer M.; Ortiz, Enrique

2007-01-01

Preservice elementary teachers need to be given the experiences of integrating mathematics with other subjects. They need to go into the classroom with the understanding that mathematics is not an isolated topic. This article describes a paper airplane activity that was presented in a class of preservice elementary education teachers to show how…

Academic Procrastination in Mathematics: Causes, Dangers and Implications of Counselling for Effective Learning

ERIC Educational Resources Information Center

Asikhia, Olubusayo A.

2010-01-01

This paper focused on causes and dangers of academic procrastination (a behavioural problem that involves delaying a task which needs to be accomplished) in mathematics and the need for counseling students who are procrastinators especially of mathematics. Thus, in order to have a comprehensive understanding of the topic, the meaning, causes and…

Decision support system in an international-voice-services business company

NASA Astrophysics Data System (ADS)

Hadianti, R.; Uttunggadewa, S.; Syamsuddin, M.; Soewono, E.

2017-01-01

We consider a problem facing by an international telecommunication services company in maximizing its profit. From voice services by controlling cost and business partnership. The competitiveness in this industry is very high, so that any efficiency from controlling cost and business partnership can help the company to survive in the very high competitiveness situation. The company trades voice traffic with a large number of business partners. There are four trading schemes that can be chosen by this company, namely, flat rate, class tiering, volume commitment, and revenue capped. Each scheme has a specific characteristic on the rate and volume deal, where the last three schemes are regarded as strategic schemes to be offered to business partner to ensure incoming traffic volume for both parties. This company and each business partner need to choose an optimal agreement in a certain period of time that can maximize the company’s profit. In this agreement, both parties agree to use a certain trading scheme, rate and rate/volume/revenue deal. A decision support system is then needed in order to give a comprehensive information to the sales officers to deal with the business partners. This paper discusses the mathematical model of the optimal decision for incoming traffic volume control, which is a part of the analysis needed to build the decision support system. The mathematical model is built by first performing data analysis to see how elastic the incoming traffic volume is. As the level of elasticity is obtained, we then derive a mathematical modelling that can simulate the impact of any decision on trading to the revenue of the company. The optimal decision can be obtained from these simulations results. To evaluate the performance of the proposed method we implement our decision model to the historical data. A software tool incorporating our methodology is currently in construction.

Mathematical model of organic substrate degradation in solid waste windrow composting.

PubMed

Seng, Bunrith; Kristanti, Risky Ayu; Hadibarata, Tony; Hirayama, Kimiaki; Katayama-Hirayama, Keiko; Kaneko, Hidehiro

2016-01-01

Organic solid waste composting is a complex process that involves many coupled physical, chemical and biological mechanisms. To understand this complexity and to ease in planning, design and management of the composting plant, mathematical model for simulation is usually applied. The aim of this paper is to develop a mathematical model of organic substrate degradation and its performance evaluation in solid waste windrow composting system. The present model is a biomass-dependent model, considering biological growth processes under the limitation of moisture, oxygen and substrate contents, and temperature. The main output of this model is substrate content which was divided into two categories: slowly and rapidly degradable substrates. To validate the model, it was applied to a laboratory scale windrow composting of a mixture of wood chips and dog food. The wastes were filled into a cylindrical reactor of 6 cm diameter and 1 m height. The simulation program was run for 3 weeks with 1 s stepwise. The simulated results were in reasonably good agreement with the experimental results. The MC and temperature of model simulation were found to be matched with those of experiment, but limited for rapidly degradable substrates. Under anaerobic zone, the degradation of rapidly degradable substrate needs to be incorporated into the model to achieve full simulation of a long period static pile composting. This model is a useful tool to estimate the changes of substrate content during composting period, and acts as a basic model for further development of a sophisticated model.

The Relationship between Students' Performance on Conventional Standardized Mathematics Assessments and Complex Mathematical Modeling Problems

ERIC Educational Resources Information Center

Kartal, Ozgul; Dunya, Beyza Aksu; Diefes-Dux, Heidi A.; Zawojewski, Judith S.

2016-01-01

Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…

Annual Perspectives in Mathematics Education 2016: Mathematical Modeling and Modeling Mathematics

ERIC Educational Resources Information Center

Hirsch, Christian R., Ed.; McDuffie, Amy Roth, Ed.

2016-01-01

Mathematical modeling plays an increasingly important role both in real-life applications--in engineering, business, the social sciences, climate study, advanced design, and more--and within mathematics education itself. This 2016 volume of "Annual Perspectives in Mathematics Education" ("APME") focuses on this key topic from a…

Upgrading geometry conceptual understanding and strategic competence through implementing rigorous mathematical thinking (RMT)

NASA Astrophysics Data System (ADS)

Nugraheni, Z.; Budiyono, B.; Slamet, I.

2018-03-01

To reach higher order thinking skill, needed to be mastered the conceptual understanding and strategic competence as they are two basic parts of high order thinking skill (HOTS). RMT is a unique realization of the cognitive conceptual construction approach based on Feurstein with his theory of Mediated Learning Experience (MLE) and Vygotsky’s sociocultural theory. This was quasi-experimental research which compared the experimental class that was given Rigorous Mathematical Thinking (RMT) as learning method and the control class that was given Direct Learning (DL) as the conventional learning activity. This study examined whether there was different effect of two learning model toward conceptual understanding and strategic competence of Junior High School Students. The data was analyzed by using Multivariate Analysis of Variance (MANOVA) and obtained a significant difference between experimental and control class when considered jointly on the mathematics conceptual understanding and strategic competence (shown by Wilk’s Λ = 0.84). Further, by independent t-test is known that there was significant difference between two classes both on mathematical conceptual understanding and strategic competence. By this result is known that Rigorous Mathematical Thinking (RMT) had positive impact toward Mathematics conceptual understanding and strategic competence.

Mathematical Abstraction: Constructing Concept of Parallel Coordinates

NASA Astrophysics Data System (ADS)

Nurhasanah, F.; Kusumah, Y. S.; Sabandar, J.; Suryadi, D.

2017-09-01

Mathematical abstraction is an important process in teaching and learning mathematics so pre-service mathematics teachers need to understand and experience this process. One of the theoretical-methodological frameworks for studying this process is Abstraction in Context (AiC). Based on this framework, abstraction process comprises of observable epistemic actions, Recognition, Building-With, Construction, and Consolidation called as RBC + C model. This study investigates and analyzes how pre-service mathematics teachers constructed and consolidated concept of Parallel Coordinates in a group discussion. It uses AiC framework for analyzing mathematical abstraction of a group of pre-service teachers consisted of four students in learning Parallel Coordinates concepts. The data were collected through video recording, students’ worksheet, test, and field notes. The result shows that the students’ prior knowledge related to concept of the Cartesian coordinate has significant role in the process of constructing Parallel Coordinates concept as a new knowledge. The consolidation process is influenced by the social interaction between group members. The abstraction process taken place in this group were dominated by empirical abstraction that emphasizes on the aspect of identifying characteristic of manipulated or imagined object during the process of recognizing and building-with.

Mathematical modelling of the influenced of diffusion rate on macro nutrient availability in paddy field

NASA Astrophysics Data System (ADS)

Renny; Supriyanto

2018-04-01

Nutrition is the chemical compounds that needed by the organism for the growth process. In plants, nutrients are organic or inorganic compounds that are absorbed from the roots of the soil. It consist of macro and micro nutrient. Macro nutrients are nutrition that needed by plants in large quantities, such as, nitrogen, calcium, pottacium, magnesium, and sulfur. The total soil nutrient is the difference between the input nutrient and the output nutrients. Input nutrients are nutrient that derived from the decomposition of organic substances. Meanwhile, the output nutrient consists of the nutrients that absorbed by plant roots (uptake), the evaporated nutrients (volatilized) and leached nutrients. The nutrient transport can be done through diffusion process. The diffusion process is essential in removing the nutrient from one place to the root surface. It will cause the rate of absorption of nutrient by the roots will be greater. Nutrient concept in paddy filed can be represented into a mathematical modelling, by making compartment models. The rate of concentration change in the compartment model forms a system of homogeneous linear differential equations. In this research, we will use Laplaces transformation to solve the compartment model and determined the dynamics of macro nutrition due to diffusion process.

Design of a Field Test for Probability of Hit by Antiaircraft Guns

DTIC Science & Technology

1973-02-01

not available. • The cost of conducting the numerous field test trials that would be needed to establish the loss rates of aircraft to antiaircraft...mathematical models provide a readily available and relatively inexpensive way to obtain estimates of aircraft losses to antiaircraft guns. Because these...aircraft losses to antiaircraft guns, the use of the models can contribute greatly to better decisions. But if the models produce invalid estimates

Enhancing the Math and Science Experiences of Latinas and Latinos: A Study of the Joaquin Bustoz Math-Science Honors Program

NASA Astrophysics Data System (ADS)

Escontrias, Gabriel, Jr.

Latinas and Latinos are currently underrepresented in terms of our 21 st century student academic attainment and workforce, compared to the total U.S. Hispanic population. In a field such as mathematical sciences, Hispanic or Latino U.S. citizenship doctoral recipients only accounted for 3.04% in 2009--2010. While there are various initiatives to engage underrepresented STEM populations through education, there is a need to give a voice to the experiences of Latinas and Latinos engaged in such programs. This study explored the experiences of seven Arizona State University undergraduate Latina and Latino Joaquin Bustoz Math-Science Honors Program (JBMSHP) participants as well as examined how the program enhanced their math and science learning experiences. Participants attended either a five-week or eight-week program and ranged in attendance from 2006 to 2011. Students were provided an opportunity to begin university mathematics and science studies before graduating high school. Through a demographic survey and one-on-one guided interview, participants shared their personal journey, their experience in the JBMSHP, and their goals. Using grounded theory, a qualitative research approach, this study focuses on the unique experiences of Latina and Latino participants. Four major themes emerged from the analysis of the data. Each participant applied to the program with a foundation in which they sought to challenge themselves academically through mathematics and/or science. Through their involvement it the JBMSHP, participants recognized benefits during and after the program. All participants recognized the value of these benefits and their participation and praised the program. Overall, the JBMSHP provided the students the resources to grow their academic capital and if they chose seek a STEM related bachelor degree. The results of this study emphasize the need to expand the JBMSHP both within Arizona and nationally. In addition, there is a need to explore the other components of their parent center, the Mathematical, Computational and Modeling Sciences Center (MCMSC), to determine if the suggested pipeline, MCMSC Model for Enhancing the Math and Science Experiences of Latinas and Latinos, can positively impact our 21st century workforce and the dire representational need of Latinas and Latinos in STEM fields.

Mathematical Modeling: A Bridge to STEM Education

ERIC Educational Resources Information Center

Kertil, Mahmut; Gurel, Cem

2016-01-01

The purpose of this study is making a theoretical discussion on the relationship between mathematical modeling and integrated STEM education. First of all, STEM education perspective and the construct of mathematical modeling in mathematics education is introduced. A review of literature is provided on how mathematical modeling literature may…

Education of a model student.

PubMed

Novikoff, Timothy P; Kleinberg, Jon M; Strogatz, Steven H

2012-02-07

A dilemma faced by teachers, and increasingly by designers of educational software, is the trade-off between teaching new material and reviewing what has already been taught. Complicating matters, review is useful only if it is neither too soon nor too late. Moreover, different students need to review at different rates. We present a mathematical model that captures these issues in idealized form. The student's needs are modeled as constraints on the schedule according to which educational material and review are spaced over time. Our results include algorithms to construct schedules that adhere to various spacing constraints, and bounds on the rate at which new material can be introduced under these schedules.

How students learn to coordinate knowledge of physical and mathematical models in cellular physiology

NASA Astrophysics Data System (ADS)

Lira, Matthew

This dissertation explores the Knowledge in Pieces (KiP) theory to account for how students learn to coordinate knowledge of mathematical and physical models in biology education. The KiP approach characterizes student knowledge as a fragmented collection of knowledge elements as opposed to stable and theory-like knowledge. This dissertation sought to use this theoretical lens to account for how students understand and learn with mathematical models and representations, such as equations. Cellular physiology provides a quantified discipline that leverages concepts from mathematics, physics, and chemistry to understand cellular functioning. Therefore, this discipline provides an exemplary context for assessing how biology students think and learn with mathematical models. In particular, the resting membrane potential provides an exemplary concept well defined by models of dynamic equilibrium borrowed from physics and chemistry. In brief, membrane potentials, or voltages, "rest" when the electrical and chemical driving forces for permeable ionic species are equal in magnitude but opposite in direction. To assess students' understandings of this concept, this dissertation employed three studies: the first study employed the cognitive clinical interview to assess student thinking in the absence and presence of equations. The second study employed an intervention to assess student learning and the affordances of an innovative assessment. The third student employed a human-computer-interaction paradigm to assess how students learn with a novel multi-representational technology. Study 1 revealed that students saw only one influence--the chemical gradient--and that students coordinated knowledge of only this gradient with the related equations. Study 2 revealed that students benefited from learning with the multi-representational technology and that the assessment detected performance gains across both calculation and explanation tasks. Last, Study 3 revealed how students shift from recognizing one influence to recognizing both the chemical and the electrical gradients as responsible for a cell's membrane potential reaching dynamic equilibrium. Together, the studies illustrate that to coordinate knowledge, students need opportunities to reflect upon relations between representations of mathematical and physical models as well as distinguish between physical quantities such as molarities for ions and transmembrane voltages.

Smart sensors and virtual physiology human approach as a basis of personalized therapies in diabetes mellitus.

PubMed

Fernández Peruchena, Carlos M; Prado-Velasco, Manuel

2010-01-01

Diabetes mellitus (DM) has a growing incidence and prevalence in modern societies, pushed by the aging and change of life styles. Despite the huge resources dedicated to improve their quality of life, mortality and morbidity rates, these are still very poor. In this work, DM pathology is revised from clinical and metabolic points of view, as well as mathematical models related to DM, with the aim of justifying an evolution of DM therapies towards the correction of the physiological metabolic loops involved. We analyze the reliability of mathematical models, under the perspective of virtual physiological human (VPH) initiatives, for generating and integrating customized knowledge about patients, which is needed for that evolution. Wearable smart sensors play a key role in this frame, as they provide patient's information to the models.A telehealthcare computational architecture based on distributed smart sensors (first processing layer) and personalized physiological mathematical models integrated in Human Physiological Images (HPI) computational components (second processing layer), is presented. This technology was designed for a renal disease telehealthcare in earlier works and promotes crossroads between smart sensors and the VPH initiative. We suggest that it is able to support a truly personalized, preventive, and predictive healthcare model for the delivery of evolved DM therapies.

Smart Sensors and Virtual Physiology Human Approach as a Basis of Personalized Therapies in Diabetes Mellitus

PubMed Central

Fernández Peruchena, Carlos M; Prado-Velasco, Manuel

2010-01-01

Diabetes mellitus (DM) has a growing incidence and prevalence in modern societies, pushed by the aging and change of life styles. Despite the huge resources dedicated to improve their quality of life, mortality and morbidity rates, these are still very poor. In this work, DM pathology is revised from clinical and metabolic points of view, as well as mathematical models related to DM, with the aim of justifying an evolution of DM therapies towards the correction of the physiological metabolic loops involved. We analyze the reliability of mathematical models, under the perspective of virtual physiological human (VPH) initiatives, for generating and integrating customized knowledge about patients, which is needed for that evolution. Wearable smart sensors play a key role in this frame, as they provide patient’s information to the models. A telehealthcare computational architecture based on distributed smart sensors (first processing layer) and personalized physiological mathematical models integrated in Human Physiological Images (HPI) computational components (second processing layer), is presented. This technology was designed for a renal disease telehealthcare in earlier works and promotes crossroads between smart sensors and the VPH initiative. We suggest that it is able to support a truly personalized, preventive, and predictive healthcare model for the delivery of evolved DM therapies. PMID:21625646

The effects of hard water consumption on kidney function: Insights from mathematical modelling

NASA Astrophysics Data System (ADS)

Tambaru, David; Djahi, Bertha S.; Ndii, Meksianis Z.

2018-03-01

Most water sources in Nusa Tenggara Timur contain higher concentration of calcium and magnesium ions, which is known as hard water. Long-term consumption of hard water can cause kidney dysfunction, which may lead to the other diseases such as cerebrovascular disease, diabetes and others. Therefore, understanding the effects of hard water consumption on kidney function is of importance. This paper studies the transmission dynamics of kidney dysfunction due to the consumption of hard water using a mathematical model. We propose a new deterministic mathematical model comprising human and water compartments and conduct a global sensitivity analysis to determine the most influential parameters of the model. The Routh-Hurwitz criterion is used to examine the stability of the steady states. The results shows that the model has two steady states, which are locally stable. Moreover, we found that the most influential parameters are the maximum concentration of magnesium and calcium in the water, the increase rate of calcium and magnesium concentration in the water and the rate of effectiveness of water treatment. The results suggest that better water treatments are required to reduce the concentration of magnesium and calcium in the water. This aid in minimizing the probability of humans to attract kidney dysfunction. Furthermore, water-related data need to be collected for further investigation.

Spline Laplacian estimate of EEG potentials over a realistic magnetic resonance-constructed scalp surface model.

PubMed

Babiloni, F; Babiloni, C; Carducci, F; Fattorini, L; Onorati, P; Urbano, A

1996-04-01

This paper presents a realistic Laplacian (RL) estimator based on a tensorial formulation of the surface Laplacian (SL) that uses the 2-D thin plate spline function to obtain a mathematical description of a realistic scalp surface. Because of this tensorial formulation, the RL does not need an orthogonal reference frame placed on the realistic scalp surface. In simulation experiments the RL was estimated with an increasing number of "electrodes" (up to 256) on a mathematical scalp model, the analytic Laplacian being used as a reference. Second and third order spherical spline Laplacian estimates were examined for comparison. Noise of increasing magnitude and spatial frequency was added to the simulated potential distributions. Movement-related potentials and somatosensory evoked potentials sampled with 128 electrodes were used to estimate the RL on a realistically shaped, MR-constructed model of the subject's scalp surface. The RL was also estimated on a mathematical spherical scalp model computed from the real scalp surface. Simulation experiments showed that the performances of the RL estimator were similar to those of the second and third order spherical spline Laplacians. Furthermore, the information content of scalp-recorded potentials was clearly better when the RL estimator computed the SL of the potential on an MR-constructed scalp surface model.

Sensory neural pathways revisited to unravel the temporal dynamics of the Simon effect: A model-based cognitive neuroscience approach.

PubMed

Salzer, Yael; de Hollander, Gilles; Forstmann, Birte U

2017-06-01

The Simon task is one of the most prominent interference tasks and has been extensively studied in experimental psychology and cognitive neuroscience. Despite years of research, the underlying mechanism driving the phenomenon and its temporal dynamics are still disputed. Within the framework of the review, we adopt a model-based cognitive neuroscience approach. We first go over key findings in the literature of the Simon task, discuss competing qualitative cognitive theories and the difficulty of testing them empirically. We then introduce sequential sampling models, a particular class of mathematical cognitive process models. Finally, we argue that the brain architecture accountable for the processing of spatial ('where') and non-spatial ('what') information, could constrain these models. We conclude that there is a clear need to bridge neural and behavioral measures, and that mathematical cognitive models may facilitate the construction of this bridge and work towards revealing the underlying mechanisms of the Simon effect. Copyright © 2017 Elsevier Ltd. All rights reserved.

The influence of mathematics learning using SAVI approach on junior high school students’ mathematical modelling ability

NASA Astrophysics Data System (ADS)

Khusna, H.; Heryaningsih, N. Y.

2018-01-01

The aim of this research was to examine mathematical modeling ability who learn mathematics by using SAVI approach. This research was a quasi-experimental research with non-equivalent control group designed by using purposive sampling technique. The population of this research was the state junior high school students in Lembang while the sample consisted of two class at 8th grade. The instrument used in this research was mathematical modeling ability. Data analysis of this research was conducted by using SPSS 20 by Windows. The result showed that students’ ability of mathematical modeling who learn mathematics by using SAVI approach was better than students’ ability of mathematical modeling who learn mathematics using conventional learning.

Space physiology IV: mathematical modeling of the cardiovascular system in space exploration.

PubMed

Keith Sharp, M; Batzel, Jerry Joseph; Montani, Jean-Pierre

2013-08-01

Mathematical modeling represents an important tool for analyzing cardiovascular function during spaceflight. This review describes how modeling of the cardiovascular system can contribute to space life science research and illustrates this process via modeling efforts to study postflight orthostatic intolerance (POI), a key issue for spaceflight. Examining this application also provides a context for considering broader applications of modeling techniques to the challenges of bioastronautics. POI, which affects a large fraction of astronauts in stand tests upon return to Earth, presents as dizziness, fainting and other symptoms, which can diminish crew performance and cause safety hazards. POI on the Moon or Mars could be more critical. In the field of bioastronautics, POI has been the dominant application of cardiovascular modeling for more than a decade, and a number of mechanisms for POI have been investigated. Modeling approaches include computational models with a range of incorporated factors and hemodynamic sophistication, and also physical models tested in parabolic and orbital flight. Mathematical methods such as parameter sensitivity analysis can help identify key system mechanisms. In the case of POI, this could lead to more effective countermeasures. Validation is a persistent issue in modeling efforts, and key considerations and needs for experimental data to synergistically improve understanding of cardiovascular responses are outlined. Future directions in cardiovascular modeling include subject-specific assessment of system status, as well as research on integrated physiological responses, leading, for instance, to assessment of subject-specific susceptibility to POI or effects of cardiovascular alterations on muscular, vision and cognitive function.

"Effective" Mathematics Teaching of African American Adolescents and the Development of a Mathematics Identity

ERIC Educational Resources Information Center

Green, Marcus Allen

2016-01-01

In order to increase mathematics achievement, persistence, and participation in mathematics-related careers and majors for African American adolescents, researchers have discussed the need for students to develop positive mathematical identities (English-Clarke, Slaughter-Defoe, & Martin, 2012; Gutstein, 2003; Larnell, 2013; Martin, 2000,…

Communication and Representation as Elements in Mathematical Literacy

ERIC Educational Resources Information Center

Thompson, Denisse R.; Chappell, Michaele F.

2007-01-01

The process standards of communication and representation in the "Principles and Standards for School Mathematics" are critical tools to help students develop mathematical literacy. In the mathematics classroom, students need to be encouraged to use speaking, listening, reading, and writing to communicate their understanding of mathematics words,…

Beyond Motivation: Exploring Mathematical Modeling as a Context for Deepening Students' Understandings of Curricular Mathematics

ERIC Educational Resources Information Center

Zbiek, Rose Mary; Conner, Annamarie

2006-01-01

Views of mathematical modeling in empirical, expository, and curricular references typically capture a relationship between real-world phenomena and mathematical ideas from the perspective that competence in mathematical modeling is a clear goal of the mathematics curriculum. However, we work within a curricular context in which mathematical…

An Investigation of Mathematical Modeling with Pre-Service Secondary Mathematics Teachers

ERIC Educational Resources Information Center

Thrasher, Emily Plunkett

2016-01-01

The goal of this thesis was to investigate and enhance our understanding of what occurs while pre-service mathematics teachers engage in a mathematical modeling unit that is broadly based upon mathematical modeling as defined by the Common Core State Standards for Mathematics (National Governors Association Center for Best Practices & Council…

Integrated Modeling of Complex Optomechanical Systems

NASA Astrophysics Data System (ADS)

Andersen, Torben; Enmark, Anita

2011-09-01

Mathematical modeling and performance simulation are playing an increasing role in large, high-technology projects. There are two reasons; first, projects are now larger than they were before, and the high cost calls for detailed performance prediction before construction. Second, in particular for space-related designs, it is often difficult to test systems under realistic conditions beforehand, and mathematical modeling is then needed to verify in advance that a system will work as planned. Computers have become much more powerful, permitting calculations that were not possible before. At the same time mathematical tools have been further developed and found acceptance in the community. Particular progress has been made in the fields of structural mechanics, optics and control engineering, where new methods have gained importance over the last few decades. Also, methods for combining optical, structural and control system models into global models have found widespread use. Such combined models are usually called integrated models and were the subject of this symposium. The objective was to bring together people working in the fields of groundbased optical telescopes, ground-based radio telescopes, and space telescopes. We succeeded in doing so and had 39 interesting presentations and many fruitful discussions during coffee and lunch breaks and social arrangements. We are grateful that so many top ranked specialists found their way to Kiruna and we believe that these proceedings will prove valuable during much future work.

Alternative Analysis of the Michaelis-Menten Equations

ERIC Educational Resources Information Center

Krogstad, Harald E.; Dawed, Mohammed Yiha; Tegegne, Tadele Tesfa

2011-01-01

Courses in mathematical modelling are always in need of simple, illustrative examples. The Michaelis-Menten reaction kinetics equations have been considered to be a basic example of scaling and singular perturbation. However, the leading order approximations do not easily show the expected behaviour, and this note proposes a different perturbation…

Recent Evolution of the Introductory Curriculum in Computing.

ERIC Educational Resources Information Center

Tucker, Allen B.; Garnick, David K.

1991-01-01

Traces the evolution of introductory computing courses for undergraduates based on the Association for Computing Machinery (ACM) guidelines published in "Curriculum 78." Changes in the curricula are described, including the role of discrete mathematics and theory; and the need for a broader model for designing introductory courses is…

Linking LEGO and Algebra

ERIC Educational Resources Information Center

Özgün-Koca, S. Asli; Edwards, Thomas G.; Chelst, Kenneth R.

2015-01-01

In mathematics, students should represent, model, and work with such real-world situations as those found in the physical world, the public policy realm, and society (CCSSI 2010). Additionally, students need to make decisions and be flexible enough to improve their decisions after analyzing realistic situations. The LEGO® Pets activity does just…

Predicting Successful Mathematics Remediation among Latina/o Students

ERIC Educational Resources Information Center

Crisp, Gloria; Reyes, Nicole Alia Salis; Doran, Erin

2017-01-01

This study examines Latina/o students' remedial math needs and outcomes. Data were drawn from a national sample of Latina/o students. Hierarchical generalized linear modeling techniques were used to predict three successful remediation outcomes. Results highlight the importance of providing financial aid and academic support to Latina/o students,…

Progress Report, June 1974: Reaching Out...

ERIC Educational Resources Information Center

Research for Better Schools, Inc., Philadelphia, PA.

This report reviews programs of individualized instruction in the basic skills of mathematics, language arts, science, and social education as well as in new curriculums which foster the skills needed for social education as well and emotional growth. The development and operation of an experience-based model for career education is described, and…

Reflective Modeling in Teacher Education.

ERIC Educational Resources Information Center

Shealy, Barry E.

This paper describes mathematical modeling activities from a secondary mathematics teacher education course taken by fourth-year university students. Experiences with mathematical modeling are viewed as important in helping teachers develop a more intuitive understanding of mathematics, generate and evaluate mathematical interpretations, and…

Primary School Pre-Service Mathematics Teachers' Views on Mathematical Modeling

ERIC Educational Resources Information Center

Karali, Diren; Durmus, Soner

2015-01-01

The current study aimed to identify the views of pre-service teachers, who attended a primary school mathematics teaching department but did not take mathematical modeling courses. The mathematical modeling activity used by the pre-service teachers was developed with regards to the modeling activities utilized by Lesh and Doerr (2003) in their…

Comparing Differences in Math Achievement and Attitudes toward Math in a Sixth Grade Mathematics Enrichment Pilot Program

ERIC Educational Resources Information Center

Tow, Tamara

2011-01-01

High-stakes assessments have encouraged educators to ignore the needs of the top performers. Therefore, the Oakwood School District decided to implement a mathematics pilot enrichment program in order to meet the needs of the advanced mathematics students. As a result, this study used quantitative data to determine if there was a significant…

An interdisciplinary collaboration between computer engineering and mathematics/bilingual education to develop a curriculum for underrepresented middle school students

NASA Astrophysics Data System (ADS)

Celedón-Pattichis, Sylvia; LópezLeiva, Carlos Alfonso; Pattichis, Marios S.; Llamocca, Daniel

2013-12-01

There is a strong need in the United States to increase the number of students from underrepresented groups who pursue careers in Science, Technology, Engineering, and Mathematics. Drawing from sociocultural theory, we present approaches to establishing collaborations between computer engineering and mathematics/bilingual education faculty to address this need. We describe our work through the Advancing Out-of-School Learning in Mathematics and Engineering project by illustrating how an integrated curriculum that is based on mathematics with applications in image and video processing can be designed and how it can be implemented with middle school students from underrepresented groups.

Professional development for teaching in higher education

NASA Astrophysics Data System (ADS)

Wood, Leigh N.; Vu, Tori; Bower, Matt; Brown, Natalie; Skalicky, Jane; Donovan, Diane; Loch, Birgit; Joshi, Nalini; Bloom, Walter

2011-10-01

Due to the changing nature of learning and teaching in universities, there is a growing need for professional development for lecturers and tutors teaching in disciplines in the mathematical sciences. Mathematics teaching staff receive some training in learning and teaching but many of the courses running at university level are not tailored to the mathematical sciences. This article reports on a collaborative research project aimed at investigating the type of professional development that Australian tertiary mathematics teachers need and their preference for delivery modes. Effective teaching promotes effective learning in our students and discipline-specific professional development will enhance outcomes for teachers, students, and mathematics.

Student and high-school characteristics related to completing a science, technology, engineering or mathematics (STEM) major in college

NASA Astrophysics Data System (ADS)

LeBeau, Brandon; Harwell, Michael; Monson, Debra; Dupuis, Danielle; Medhanie, Amanuel; Post, Thomas R.

2012-04-01

Background: The importance of increasing the number of US college students completing degrees in science, technology, engineering or mathematics (STEM) has prompted calls for research to provide a better understanding of factors related to student participation in these majors, including the impact of a student's high-school mathematics curriculum. Purpose: This study examines the relationship between various student and high-school characteristics and completion of a STEM major in college. Of specific interest is the influence of a student's high-school mathematics curriculum on the completion of a STEM major in college. Sample: The sample consisted of approximately 3500 students from 229 high schools. Students were predominantly Caucasian (80%), with slightly more males than females (52% vs 48%). Design and method: A quasi-experimental design with archival data was used for students who enrolled in, and graduated from, a post-secondary institution in the upper Midwest. To be included in the sample, students needed to have completed at least three years of high-school mathematics. A generalized linear mixed model was used with students nested within high schools. The data were cross-sectional. Results: High-school predictors were not found to have a significant impact on the completion of a STEM major. Significant student-level predictors included ACT mathematics score, gender and high-school mathematics GPA. Conclusions: The results provide evidence that on average students are equally prepared for the rigorous mathematics coursework regardless of the high-school mathematics curriculum they completed.

Persisting mathematics and science high school teachers: A Q-methodology study

NASA Astrophysics Data System (ADS)

Robbins-Lavicka, Michelle M.

There is a lack of qualified mathematics and science teachers at all levels of education in Arkansas. Lasting teaching initiative programs are needed to address retention so qualified teachers remain in the classroom. The dearth of studies regarding why mathematics and science teachers persist in the classroom beyond the traditional 5-year attrition period led this Q-methodological study to evaluate the subjective perceptions of persistent mathematics and science teachers to determine what makes them stay. This study sought to understand what factors persisting mathematics and science teachers used to explain their persistence in the classroom beyond 5 years and what educational factors contributed to persisting mathematics and science teachers. Q-methodology combines qualitative and quantitative techniques and provided a systematic means to investigate personal beliefs by collecting a concourse, developing a Q-sample and a person-sample, conducting a Q-sorting process, and analyzing the data. The results indicated that to encourage longevity within mathematics and science classrooms (a) teachers should remain cognizant of their ability to influence student attitudes toward teaching; (b) administrators should provide support for teachers and emphasize the role and importance of professional development; and (c) policy makers should focus their efforts and resources on developing recruitment plans, including mentorship programs, while providing and improving financial compensation. Significantly, the findings indicate that providing mentorship and role models at every level of mathematics and science education will likely encourage qualified teachers to remain in the mathematics and science classrooms, thus increasing the chance of positive social change.

The Mathematics Attitudes and Perceptions Survey: An Instrument to Assess Expert-Like Views and Dispositions among Undergraduate Mathematics Students

ERIC Educational Resources Information Center

Code, Warren; Merchant, Sandra; Maciejewski, Wes; Thomas, Matthew; Lo, Joseph

2016-01-01

One goal of an undergraduate education in mathematics is to help students develop a productive disposition towards mathematics. A way of conceiving of this is as helping mathematical novices transition to more expert-like perceptions of mathematics. This conceptualization creates a need for a way to characterize students' perceptions of…

The implementation of multiple intelligences based teaching model to improve mathematical problem solving ability for student of junior high school

NASA Astrophysics Data System (ADS)

Fasni, Nurli; Fatimah, Siti; Yulanda, Syerli

2017-05-01

This research aims to achieve some purposes such as: to know whether mathematical problem solving ability of students who have learned mathematics using Multiple Intelligences based teaching model is higher than the student who have learned mathematics using cooperative learning; to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using Multiple Intelligences based teaching model., to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using cooperative learning; to know the attitude of the students to Multiple Intelligences based teaching model. The method employed here is quasi-experiment which is controlled by pre-test and post-test. The population of this research is all of VII grade in SMP Negeri 14 Bandung even-term 2013/2014, later on two classes of it were taken for the samples of this research. A class was taught using Multiple Intelligences based teaching model and the other one was taught using cooperative learning. The data of this research were gotten from the test in mathematical problem solving, scale questionnaire of the student attitudes, and observation. The results show the mathematical problem solving of the students who have learned mathematics using Multiple Intelligences based teaching model learning is higher than the student who have learned mathematics using cooperative learning, the mathematical problem solving ability of the student who have learned mathematics using cooperative learning and Multiple Intelligences based teaching model are in intermediate level, and the students showed the positive attitude in learning mathematics using Multiple Intelligences based teaching model. As for the recommendation for next author, Multiple Intelligences based teaching model can be tested on other subject and other ability.

Using Mathematics, Mathematical Applications, Mathematical Modelling, and Mathematical Literacy: A Theoretical Study

ERIC Educational Resources Information Center

Mumcu, Hayal Yavuz

2016-01-01

The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…

Demand modelling of passenger air travel: An analysis and extension, volume 2

NASA Technical Reports Server (NTRS)

Jacobson, I. D.

1978-01-01

Previous intercity travel demand models in terms of their ability to predict air travel in a useful way and the need for disaggregation in the approach to demand modelling are evaluated. The viability of incorporating non-conventional factors (i.e. non-econometric, such as time and cost) in travel demand forecasting models are determined. The investigation of existing models is carried out in order to provide insight into their strong points and shortcomings. The model is characterized as a market segmentation model. This is a consequence of the strengths of disaggregation and its natural evolution to a usable aggregate formulation. The need for this approach both pedagogically and mathematically is discussed. In addition this volume contains two appendices which should prove useful to the non-specialist in the area.

Mathematical Modeling in Science: Using Spreadsheets to Create Mathematical Models and Address Scientific Inquiry

ERIC Educational Resources Information Center

Horton, Robert M.; Leonard, William H.

2005-01-01

In science, inquiry is used as students explore important and interesting questions concerning the world around them. In mathematics, one contemporary inquiry approach is to create models that describe real phenomena. Creating mathematical models using spreadsheets can help students learn at deep levels in both science and mathematics, and give…

[Research advances in mathematical model of coniferous trees cold hardiness].

PubMed

Zhang, Gang; Wang, Ai-Fang

2007-07-01

Plant cold hardiness has complicated attributes. This paper introduced the research advances in establishing the dynamic models of coniferous trees cold hardiness, with the advantages and disadvantages of the models presented and the further studies suggested. In the models established initially, temperature was concerned as the only environmental factor affecting the cold hardiness, and the concept of stationary level of cold hardiness was introduced. Due to the obvious prediction errors of these models, the stationary level of cold hardiness was modeled later by assuming the existence of an additive effect of temperature and photoperiod on the increase of cold hardiness. Furthermore, the responses of the annual development phases for cold hardiness to environment were considered. The model researchers have paid more attention to the additive effect models, and run some experiments to test the additivity principle. However, the research results on Scots pine (Pinus sylvestris) indicated that its organs did not support the presumption of an additive response of cold hardiness by temperature and photoperiod, and the interaction between environmental factors should be taken into account. The mathematical models of cold hardiness need to be developed and improved.

New Challenges in the Teaching of Mathematics.

ERIC Educational Resources Information Center

Bourguignon, Jean Pierre

The manifold but discrete presence of mathematics in many objects or services imposes new constraints to the teaching of mathematics. If citizens need to be comfortable in various situations with a variety of mathematical tools, the learning of mathematics requires that one starts with simple concepts. This paper proposes some solutions to solve…

Master's Students' Perceptions of Microsoft Word for Mathematical Typesetting

ERIC Educational Resources Information Center

Loch, Birgit; Lowe, Tim W.; Mestel, Ben D.

2015-01-01

It is widely recognized that mathematical typesetting is more difficult than typesetting in most other disciplines due to the need for specialized mathematical notation and symbols. While most mathematicians type mathematical documents using LaTeX, with varying levels of proficiency, students often use other options or handwrite mathematics. Here,…

Preparing Mathematics Teachers for Elementary High-Poverty Schools: Perceptions and Suggestions from Preservice Teachers

ERIC Educational Resources Information Center

McKinney, Sueanne E.; Berry, Robert Q., III; Jackson, Joan M.

2007-01-01

The National Council of Teachers of Mathematics articulates an ambitious vision of a high-quality mathematics program. Achieving this vision requires competent and knowledgeable teachers who can support all students in learning mathematics concepts with understanding. Effective mathematics teachers are especially needed for high-poverty schools…

Need for Equipping Student Teachers with Language of Mathematics

ERIC Educational Resources Information Center

Gafoor, K. Abdul; Sarabi, M. K.

2015-01-01

The significance of curriculum in building up language of mathematics which enables learners to construct and communicate knowledge of mathematics has not received due attention even as the pedagogical challenges faced by the students in learning mathematics have been discussed for years. Learning language of mathematics is not only valuable in…

The Use of Teachers' Baseline Normative Beliefs to Guide Professional Development in Teaching Mathematics

ERIC Educational Resources Information Center

Lloyd, Mary Elizabeth Riley; Veal, William; Howell, Malia

2016-01-01

This article describes the normative beliefs and the discursive claims related to mathematics and teaching mathematics made by approximately 50 middle-level and secondary mathematics teachers within four high-need local education associations participating in a Mathematics and Science Partnership with a southeastern college's Science and Math for…

Classroom Culture, Mathematics Culture, and the Failures of Reform: The Need for a Collective View of Culture

ERIC Educational Resources Information Center

Gill, Michele Gregoire; Boote, David

2012-01-01

Background/Context: Despite the tremendous amount of effort devoted by many mathematics educators to promote, defend, and implement reform-based mathematics education, procedural mathematics, which locates mathematical correctness in the procedures learned from textbooks and teachers, persists. Many researchers have identified school and classroom…

Pre-Service Secondary Mathematics Teachers Making Sense of Definitions of Functions

ERIC Educational Resources Information Center

Chesler, Joshua

2012-01-01

Definitions play an essential role in mathematics. As such, mathematics teachers and students need to flexibly and productively interact with mathematical definitions in the classroom. However, there has been little research about mathematics teachers' understanding of definitions. At an even more basic level, there is little clarity about what…

Finnish Mentor Mathematics Teachers' Views of the Teacher Knowledge Required for Teaching Mathematics

ERIC Educational Resources Information Center

Asikainen, Mervi A.; Pehkonen, Erkki; Hirvonen, Pekka E.

2013-01-01

Seven Finnish mentor mathematics teachers were interviewed about their views regarding the teacher knowledge required for teaching mathematics. The results of the interviews revealed not only the teachers' spontaneous views of the knowledge base needed for effective mathematics teaching but also their views of the particular types of teacher…

Dynamic Assessment of Algebraic Learning in Predicting Third Graders’ Development of Mathematical Problem Solving

PubMed Central

Fuchs, Lynn S.; Compton, Donald L.; Fuchs, Douglas; Hollenbeck, Kurstin N.; Craddock, Caitlin F.; Hamlett, Carol L.

2008-01-01

Dynamic assessment (DA) involves helping students learn a task and indexing responsiveness to that instruction as a measure of learning potential. The purpose of this study was to explore the utility of a DA of algebraic learning in predicting 3rd graders’ development of mathematics problem solving. In the fall, 122 3rd-grade students were assessed on language, nonverbal reasoning, attentive behavior, calculations, word-problem skill, and DA. On the basis of random assignment, students received 16 weeks of validated instruction on word problems or received 16 weeks of conventional instruction on word problems. Then, students were assessed on word-problem measures proximal and distal to instruction. Structural equation measurement models showed that DA measured a distinct dimension of pretreatment ability and that proximal and distal word-problem measures were needed to account for outcome. Structural equation modeling showed that instruction (conventional vs. validated) was sufficient to account for math word-problem outcome proximal to instruction; by contrast, language, pretreatment math skill, and DA were needed to forecast learning on word-problem outcomes more distal to instruction. Findings are discussed in terms of responsiveness-to-intervention models for preventing and identifying learning disabilities. PMID:19884957

Simulation of friction stir drilling process

NASA Astrophysics Data System (ADS)

Vijayabaskar, P.; Hynes, N. Rajesh Jesudoss

2018-05-01

The project is the study of the thermal drilling process. The process is a hole forming process in the sheet metals using the heat generated by means of friction. The main advantage of the process over the conventional drilling process is that the holes formed using this process does not need any backing arrangements such as weld nuts, rivet nuts etc. Because the extruded bush itself acts as a supporting structure for the fasteners. This eliminates the need for the access to the backside of the work material for fastening operations. The major factors contributing the thermal drilling operation are the spindle speed and the thrust force required for forming a hole. The process of finding out the suitable thrust force and the speed for drilling a particular material with particular thickness is a tedious process. The process can be simplified by forming a mathematical model by combining the empirical formulae from the literature. These formulae were derived in the literature from the experimental trials by following certain assumptions. In this paper a suitable mathematical model is formed by replicating the experiments and tried to be validated by the results from numerical analysis. The numerical analysis of the model is done using the ANSYS software.

The development of a model of culturally responsive science and mathematics teaching

NASA Astrophysics Data System (ADS)

Hernandez, Cecilia M.; Morales, Amanda R.; Shroyer, M. Gail

2013-12-01

This qualitative theoretical study was conducted in response to the current need for an inclusive and comprehensive model to guide the preparation and assessment of teacher candidates for culturally responsive teaching. The process of developing a model of culturally responsive teaching involved three steps: a comprehensive review of the literature; a synthesis of the literature into thematic categories to capture the dispositions and behaviors of culturally responsive teaching; and the piloting of these thematic categories with teacher candidates to validate the usefulness of the categories and to generate specific exemplars of behavior to represent each category. The model of culturally responsive teaching contains five thematic categories: (1) content integration, (2) facilitating knowledge construction, (3) prejudice reduction, (4) social justice, and (5) academic development. The current model is a promising tool for comprehensively defining culturally responsive teaching in the context of teacher education as well as to guide curriculum and assessment changes aimed to increase candidates' culturally responsive knowledge and skills in science and mathematics teaching.

Metrological traceability in education: A practical online system for measuring and managing middle school mathematics instruction

NASA Astrophysics Data System (ADS)

Torres Irribarra, D.; Freund, R.; Fisher, W.; Wilson, M.

2015-02-01

Computer-based, online assessments modelled, designed, and evaluated for adaptively administered invariant measurement are uniquely suited to defining and maintaining traceability to standardized units in education. An assessment of this kind is embedded in the Assessing Data Modeling and Statistical Reasoning (ADM) middle school mathematics curriculum. Diagnostic information about middle school students' learning of statistics and modeling is provided via computer-based formative assessments for seven constructs that comprise a learning progression for statistics and modeling from late elementary through the middle school grades. The seven constructs are: Data Display, Meta-Representational Competence, Conceptions of Statistics, Chance, Modeling Variability, Theory of Measurement, and Informal Inference. The end product is a web-delivered system built with Ruby on Rails for use by curriculum development teams working with classroom teachers in designing, developing, and delivering formative assessments. The online accessible system allows teachers to accurately diagnose students' unique comprehension and learning needs in a common language of real-time assessment, logging, analysis, feedback, and reporting.

Mathematical Modeling and Pure Mathematics

ERIC Educational Resources Information Center

Usiskin, Zalman

2015-01-01

Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…

Understanding Prospective Teachers' Mathematical Modeling Processes in the Context of a Mathematical Modeling Course

ERIC Educational Resources Information Center

Zeytun, Aysel Sen; Cetinkaya, Bulent; Erbas, Ayhan Kursat

2017-01-01

This paper investigates how prospective teachers develop mathematical models while they engage in modeling tasks. The study was conducted in an undergraduate elective course aiming to improve prospective teachers' mathematical modeling abilities, while enhancing their pedagogical knowledge for the integrating of modeling tasks into their future…

Estimating the Stoichiometry of HIV Neutralization

PubMed Central

Magnus, Carsten; Regoes, Roland R.

2010-01-01

HIV-1 virions infect target cells by first establishing contact between envelope glycoprotein trimers on the virion's surface and CD4 receptors on a target cell, recruiting co-receptors, fusing with the cell membrane and finally releasing the genetic material into the target cell. Specific experimental setups allow the study of the number of trimer-receptor-interactions needed for infection, i.e., the stoichiometry of entry and also the number of antibodies needed to prevent one trimer from engaging successfully in the entry process, i.e., the stoichiometry of (trimer) neutralization. Mathematical models are required to infer the stoichiometric parameters from these experimental data. Recently, we developed mathematical models for the estimations of the stoichiometry of entry [1]. In this article, we show how our models can be extended to investigate the stoichiometry of trimer neutralization. We study how various biological parameters affect the estimate of the stoichiometry of neutralization. We find that the distribution of trimer numbers—which is also an important determinant of the stoichiometry of entry—influences the estimated value of the stoichiometry of neutralization. In contrast, other parameters, which characterize the experimental system, diminish the information we can extract from the data about the stoichiometry of neutralization, and thus reduce our confidence in the estimate. We illustrate the use of our models by re-analyzing previously published data on the neutralization sensitivity [2], which contains measurements of neutralization sensitivity of viruses with different envelope proteins to antibodies with various specificities. Our mathematical framework represents the formal basis for the estimation of the stoichiometry of neutralization. Together with the stoichiometry of entry, the stoichiometry of trimer neutralization will allow one to calculate how many antibodies are required to neutralize a virion or even an entire population of virions. PMID:20333245

Numerical Modeling in Geodynamics: Success, Failure and Perspective

NASA Astrophysics Data System (ADS)

Ismail-Zadeh, A.

2005-12-01

A real success in numerical modeling of dynamics of the Earth can be achieved only by multidisciplinary research teams of experts in geodynamics, applied and pure mathematics, and computer science. The success in numerical modeling is based on the following basic, but simple, rules. (i) People need simplicity most, but they understand intricacies best (B. Pasternak, writer). Start from a simple numerical model, which describes basic physical laws by a set of mathematical equations, and move then to a complex model. Never start from a complex model, because you cannot understand the contribution of each term of the equations to the modeled geophysical phenomenon. (ii) Study the numerical methods behind your computer code. Otherwise it becomes difficult to distinguish true and erroneous solutions to the geodynamic problem, especially when your problem is complex enough. (iii) Test your model versus analytical and asymptotic solutions, simple 2D and 3D model examples. Develop benchmark analysis of different numerical codes and compare numerical results with laboratory experiments. Remember that the numerical tool you employ is not perfect, and there are small bugs in every computer code. Therefore the testing is the most important part of your numerical modeling. (iv) Prove (if possible) or learn relevant statements concerning the existence, uniqueness and stability of the solution to the mathematical and discrete problems. Otherwise you can solve an improperly-posed problem, and the results of the modeling will be far from the true solution of your model problem. (v) Try to analyze numerical models of a geological phenomenon using as less as possible tuning model variables. Already two tuning variables give enough possibilities to constrain your model well enough with respect to observations. The data fitting sometimes is quite attractive and can take you far from a principal aim of your numerical modeling: to understand geophysical phenomena. (vi) If the number of tuning model variables are greater than two, test carefully the effect of each of the variables on the modeled phenomenon. Remember: With four exponents I can fit an elephant (E. Fermi, physicist). (vii) Make your numerical model as accurate as possible, but never put the aim to reach a great accuracy: Undue precision of computations is the first symptom of mathematical illiteracy (N. Krylov, mathematician). How complex should be a numerical model? A model which images any detail of the reality is as useful as a map of scale 1:1 (J. Robinson, economist). This message is quite important for geoscientists, who study numerical models of complex geodynamical processes. I believe that geoscientists will never create a model of the real Earth dynamics, but we should try to model the dynamics such a way to simulate basic geophysical processes and phenomena. Does a particular model have a predictive power? Each numerical model has a predictive power, otherwise the model is useless. The predictability of the model varies with its complexity. Remember that a solution to the numerical model is an approximate solution to the equations, which have been chosen in believe that they describe dynamic processes of the Earth. Hence a numerical model predicts dynamics of the Earth as well as the mathematical equations describe this dynamics. What methodological advances are still needed for testable geodynamic modeling? Inverse (time-reverse) numerical modeling and data assimilation are new methodologies in geodynamics. The inverse modeling can allow to test geodynamic models forward in time using restored (from present-day observations) initial conditions instead of unknown conditions.

College Preparatory Mathematics: Change from Within.

ERIC Educational Resources Information Center

Kysh, Judith M.

1995-01-01

The College Preparatory Mathematics: Change from Within Project (CPM) was created to develop a rich, integrated mathematics curriculum, based on the best current wisdom of how people learn and the mathematics needed in an era of computers, and involving teachers in materials development. (MKR)

Introducing Modeling Transition Diagrams as a Tool to Connect Mathematical Modeling to Mathematical Thinking

ERIC Educational Resources Information Center

Czocher, Jennifer A.

2016-01-01

This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…

An Experimental Approach to Mathematical Modeling in Biology

ERIC Educational Resources Information Center

Ledder, Glenn

2008-01-01

The simplest age-structured population models update a population vector via multiplication by a matrix. These linear models offer an opportunity to introduce mathematical modeling to students of limited mathematical sophistication and background. We begin with a detailed discussion of mathematical modeling, particularly in a biological context.…

Changing Pre-Service Mathematics Teachers' Beliefs about Using Computers for Teaching and Learning Mathematics: The Effect of Three Different Models

ERIC Educational Resources Information Center

Karatas, Ilhan

2014-01-01

This study examines the effect of three different computer integration models on pre-service mathematics teachers' beliefs about using computers in mathematics education. Participants included 104 pre-service mathematics teachers (36 second-year students in the Computer Oriented Model group, 35 fourth-year students in the Integrated Model (IM)…

Consortium for Mathematics in the Geosciences (CMG++): Promoting the application of mathematics, statistics, and computational sciences to the geosciences

NASA Astrophysics Data System (ADS)

Mead, J.; Wright, G. B.

2013-12-01

The collection of massive amounts of high quality data from new and greatly improved observing technologies and from large-scale numerical simulations are drastically improving our understanding and modeling of the earth system. However, these datasets are also revealing important knowledge gaps and limitations of our current conceptual models for explaining key aspects of these new observations. These limitations are impeding progress on questions that have both fundamental scientific and societal significance, including climate and weather, natural disaster mitigation, earthquake and volcano dynamics, earth structure and geodynamics, resource exploration, and planetary evolution. New conceptual approaches and numerical methods for characterizing and simulating these systems are needed - methods that can handle processes which vary through a myriad of scales in heterogeneous, complex environments. Additionally, as certain aspects of these systems may be observable only indirectly or not at all, new statistical methods are also needed. This type of research will demand integrating the expertise of geoscientist together with that of mathematicians, statisticians, and computer scientists. If the past is any indicator, this interdisciplinary research will no doubt lead to advances in all these fields in addition to vital improvements in our ability to predict the behavior of the planetary environment. The Consortium for Mathematics in the Geosciences (CMG++) arose from two scientific workshops held at Northwestern and Princeton in 2011 and 2012 with participants from mathematics, statistics, geoscience and computational science. The mission of CMG++ is to accelerate the traditional interaction between people in these disciplines through the promotion of both collaborative research and interdisciplinary education. We will discuss current activities, describe how people can get involved, and solicit input from the broader AGU community.

Mathematical Modeling: A Structured Process

ERIC Educational Resources Information Center

Anhalt, Cynthia Oropesa; Cortez, Ricardo

2015-01-01

Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…

Mathematical Models of Elementary Mathematics Learning and Performance. Final Report.

ERIC Educational Resources Information Center

Suppes, Patrick

This project was concerned with the development of mathematical models of elementary mathematics learning and performance. Probabilistic finite automata and register machines with a finite number of registers were developed as models and extensively tested with data arising from the elementary-mathematics strand curriculum developed by the…

To Assess Students' Attitudes, Skills and Competencies in Mathematical Modeling

ERIC Educational Resources Information Center

Lingefjard, Thomas; Holmquist, Mikael

2005-01-01

Peer-to-peer assessment, take-home exams and a mathematical modeling survey were used to monitor and assess students' attitudes, skills and competencies in mathematical modeling. The students were all in a secondary mathematics, teacher education program with a comprehensive amount of mathematics studies behind them. Findings indicate that…

Mathematical Modeling in the Undergraduate Curriculum

ERIC Educational Resources Information Center

Toews, Carl

2012-01-01

Mathematical modeling occupies an unusual space in the undergraduate mathematics curriculum: typically an "advanced" course, it nonetheless has little to do with formal proof, the usual hallmark of advanced mathematics. Mathematics departments are thus forced to decide what role they want the modeling course to play, both as a component of the…

Teachers' Conceptions of Mathematical Modeling

ERIC Educational Resources Information Center

Gould, Heather

2013-01-01

The release of the "Common Core State Standards for Mathematics" in 2010 resulted in a new focus on mathematical modeling in United States curricula. Mathematical modeling represents a way of doing and understanding mathematics new to most teachers. The purpose of this study was to determine the conceptions and misconceptions held by…

Experimentation of cooperative learning model Numbered Heads Together (NHT) type by concept maps and Teams Games Tournament (TGT) by concept maps in terms of students logical mathematics intellegences

NASA Astrophysics Data System (ADS)

Irawan, Adi; Mardiyana; Retno Sari Saputro, Dewi

2017-06-01

This research is aimed to find out the effect of learning model towards learning achievement in terms of students’ logical mathematics intelligences. The learning models that were compared were NHT by Concept Maps, TGT by Concept Maps, and Direct Learning model. This research was pseudo experimental by factorial design 3×3. The population of this research was all of the students of class XI Natural Sciences of Senior High School in all regency of Karanganyar in academic year 2016/2017. The conclusions of this research were: 1) the students’ achievements with NHT learning model by Concept Maps were better than students’ achievements with TGT model by Concept Maps and Direct Learning model. The students’ achievements with TGT model by Concept Maps were better than the students’ achievements with Direct Learning model. 2) The students’ achievements that exposed high logical mathematics intelligences were better than students’ medium and low logical mathematics intelligences. The students’ achievements that exposed medium logical mathematics intelligences were better than the students’ low logical mathematics intelligences. 3) Each of student logical mathematics intelligences with NHT learning model by Concept Maps has better achievement than students with TGT learning model by Concept Maps, students with NHT learning model by Concept Maps have better achievement than students with the direct learning model, and the students with TGT by Concept Maps learning model have better achievement than students with Direct Learning model. 4) Each of learning model, students who have logical mathematics intelligences have better achievement then students who have medium logical mathematics intelligences, and students who have medium logical mathematics intelligences have better achievement than students who have low logical mathematics intelligences.

Quantum dots as contrast agents for endoscopy: mathematical modeling and experimental validation of the optimal excitation wavelength

NASA Astrophysics Data System (ADS)

Roy, Mathieu; DaCosta, Ralph S.; Weersink, Robert; Netchev, George; Davidson, Sean R. H.; Chan, Warren; Wilson, Brian C.

2007-02-01

Our group is investigating the use of ZnS-capped CdSe quantum dot (QD) bioconjugates combined with fluorescence endoscopy for improved early cancer detection in the esophagus, colon and lung. A major challenge in using fluorescent contrast agents in vivo is to extract the relevant signal from the tissue autofluorescence (AF). Our studies are aimed at maximizing the QD signal to AF background ratio (SBR) to facilitate detection. This work quantitatively evaluates the effect of the excitation wavelength on the SBR, using both experimental measurements and mathematical modeling. Experimental SBR measurements were done by imaging QD solutions placed onto (surface) or embedded in (sub-surface) ex vivo murine tissue samples (brain, kidney, liver, lung), using a polymethylmethacrylate (PMMA) microchannel phantom. The results suggest that the maximum contrast is reached when the excitation wavelength is set at 400+/-20 μm for the surface configuration. For the sub-surface configuration, the optimal excitation wavelength varies with the tissue type and QD emission wavelengths. Our mathematical model, based on an approximation to the diffusion equation, successfully predicts the optimal excitation wavelength for the surface configuration, but needs further modifications to be accurate in the sub-surface configuration.

Production of biofuels and biochemicals: in need of an ORACLE.

PubMed

Miskovic, Ljubisa; Hatzimanikatis, Vassily

2010-08-01

The engineering of cells for the production of fuels and chemicals involves simultaneous optimization of multiple objectives, such as specific productivity, extended substrate range and improved tolerance - all under a great degree of uncertainty. The achievement of these objectives under physiological and process constraints will be impossible without the use of mathematical modeling. However, the limited information and the uncertainty in the available information require new methods for modeling and simulation that will characterize the uncertainty and will quantify, in a statistical sense, the expectations of success of alternative metabolic engineering strategies. We discuss these considerations toward developing a framework for the Optimization and Risk Analysis of Complex Living Entities (ORACLE) - a computational method that integrates available information into a mathematical structure to calculate control coefficients. Copyright 2010 Elsevier Ltd. All rights reserved.

Mathematics make microbes beautiful, beneficial, and bountiful.

PubMed

Jungck, John R

2012-01-01

Microbiology is a rich area for visualizing the importance of mathematics in terms of designing experiments, data mining, testing hypotheses, and visualizing relationships. Historically, Nobel Prizes have acknowledged the close interplay between mathematics and microbiology in such examples as the fluctuation test and mutation rates using Poisson statistics by Luria and Delbrück and the use of graph theory of polyhedra by Caspar and Klug. More and more contemporary microbiology journals feature mathematical models, computational algorithms and heuristics, and multidimensional visualizations. While revolutions in research have driven these initiatives, a commensurate effort needs to be made to incorporate much more mathematics into the professional preparation of microbiologists. In order not to be daunting to many educators, a Bloom-like "Taxonomy of Quantitative Reasoning" is shared with explicit examples of microbiological activities for engaging students in (a) counting, measuring, calculating using image analysis of bacterial colonies and viral infections on variegated leaves, measurement of fractal dimensions of beautiful colony morphologies, and counting vertices, edges, and faces on viral capsids and using graph theory to understand self assembly; (b) graphing, mapping, ordering by applying linear, exponential, and logistic growth models of public health and sanitation problems, revisiting Snow's epidemiological map of cholera with computational geometry, and using interval graphs to do complementation mapping, deletion mapping, food webs, and microarray heatmaps; (c) problem solving by doing gene mapping and experimental design, and applying Boolean algebra to gene regulation of operons; (d) analysis of the "Bacterial Bonanza" of microbial sequence and genomic data using bioinformatics and phylogenetics; (e) hypothesis testing-again with phylogenetic trees and use of Poisson statistics and the Luria-Delbrück fluctuation test; and (f) modeling of biodiversity by using game theory, of epidemics with algebraic models, bacterial motion by using motion picture analysis and fluid mechanics of motility in multiple dimensions through the physics of "Life at Low Reynolds Numbers," and pattern formation of quorum sensing bacterial populations. Through a developmental model for preprofessional education that emphasizes the beauty, utility, and diversity of microbiological systems, we hope to foster creativity as well as mathematically rigorous reasoning. Copyright © 2012 Elsevier Inc. All rights reserved.

Predictability and preparedness in influenza control.

PubMed

Smith, Derek J

2006-04-21

The threat of pandemic human influenza looms as we survey the ongoing avian influenza pandemic and wonder if and when it will jump species. What are the risks and how can we plan? The nub of the problem lies in the inherent variability of the virus, which makes prediction difficult. However, it is not impossible; mathematical models can help determine and quantify critical parameters and thresholds in the relationships of those parameters, even if the relationships are nonlinear and obscure to simple reasoning. Mathematical models can derive estimates for the levels of drug stockpiles needed to buy time, how and when to modify vaccines, whom to target with vaccines and drugs, and when to enforce quarantine measures. Regardless, the models used for pandemic planning must be tested, and for this we must continue to gather data, not just for exceptional scenarios but also for seasonal influenza.

Biofiltration of volatile organic compounds using fungi and its conceptual and mathematical modeling.

PubMed

Vergara-Fernández, Alberto; Revah, Sergio; Moreno-Casas, Patricio; Scott, Felipe

Volatile organic compounds (VOCs) are ubiquitous contaminants that can be found both in outdoor and indoor air, posing risks to human health and the ecosystems. The treatment of air contaminated with VOCs in low concentrations can be effectively performed using biofiltration, especially when VOCs are hydrophilic. However, the performance of biofilters inoculated with bacteria has been found to be low with sparsely water soluble molecules when compared to biofilters where fungi develop. Using conceptual and mathematical models, this review presents an overview of the physical, chemical and biological mechanisms that explain the differences in the performance of fungal and bacterial biofilters. Moreover, future research needs are proposed, with an emphasis on integrated models describing the biological and chemical reactions with the mass transfer using high-resolution descriptions of the packing material. Copyright © 2018 Elsevier Inc. All rights reserved.

Optimal healthcare decision making under multiple mathematical models: application in prostate cancer screening.

PubMed

Bertsimas, Dimitris; Silberholz, John; Trikalinos, Thomas

2018-03-01

Important decisions related to human health, such as screening strategies for cancer, need to be made without a satisfactory understanding of the underlying biological and other processes. Rather, they are often informed by mathematical models that approximate reality. Often multiple models have been made to study the same phenomenon, which may lead to conflicting decisions. It is natural to seek a decision making process that identifies decisions that all models find to be effective, and we propose such a framework in this work. We apply the framework in prostate cancer screening to identify prostate-specific antigen (PSA)-based strategies that perform well under all considered models. We use heuristic search to identify strategies that trade off between optimizing the average across all models' assessments and being "conservative" by optimizing the most pessimistic model assessment. We identified three recently published mathematical models that can estimate quality-adjusted life expectancy (QALE) of PSA-based screening strategies and identified 64 strategies that trade off between maximizing the average and the most pessimistic model assessments. All prescribe PSA thresholds that increase with age, and 57 involve biennial screening. Strategies with higher assessments with the pessimistic model start screening later, stop screening earlier, and use higher PSA thresholds at earlier ages. The 64 strategies outperform 22 previously published expert-generated strategies. The 41 most "conservative" ones remained better than no screening with all models in extensive sensitivity analyses. We augment current comparative modeling approaches by identifying strategies that perform well under all models, for various degrees of decision makers' conservativeness.

Pre-Service Teachers' Modelling Processes through Engagement with Model Eliciting Activities with a Technological Tool

ERIC Educational Resources Information Center

Daher, Wajeeh M.; Shahbari, Juhaina Awawdeh

2015-01-01

Engaging mathematics students with modelling activities helps them learn mathematics meaningfully. This engagement, in the case of model eliciting activities, helps the students elicit mathematical models by interpreting real-world situation in mathematical ways. This is especially true when the students utilize technology to build the models.…

Interactive basic mathematics web using Wordpress

NASA Astrophysics Data System (ADS)

Septia, Tika; Husna; Cesaria, Anna

2017-12-01

Wordpress is a popular open source tool that can be used for developing learning media. Basic Mathematics is the difficult subject for a physics student. The students need an interactive learning to improve their knowledge. The aims of this study were to develop the interactive media using Wordpress and to know the effectiveness of web as a learning media to improve the ICT Literacy students. This study used ADDIE models. The effectiveness of interactive web can be described as the students’ equipness of ICT literacy. The population is physics students. The findings show that the interactive web is valid for the content, presentation, linguistic, and graphic aspects. The results concluded that basic mathematic interactive web is effective to equip the learners ICT literacy of categories of high, medium, and low with the observations and questionnaires are in very good criteria.

A review of mathematical modeling and simulation of controlled-release fertilizers.

PubMed

Irfan, Sayed Ameenuddin; Razali, Radzuan; KuShaari, KuZilati; Mansor, Nurlidia; Azeem, Babar; Ford Versypt, Ashlee N

2018-02-10

Nutrients released into soils from uncoated fertilizer granules are lost continuously due to volatilization, leaching, denitrification, and surface run-off. These issues have caused economic loss due to low nutrient absorption efficiency and environmental pollution due to hazardous emissions and water eutrophication. Controlled-release fertilizers (CRFs) can change the release kinetics of the fertilizer nutrients through an abatement strategy to offset these issues by providing the fertilizer content in synchrony with the metabolic needs of the plants. Parametric analysis of release characteristics of CRFs is of paramount importance for the design and development of new CRFs. However, the experimental approaches are not only time consuming, but they are also cumbersome and expensive. Scientists have introduced mathematical modeling techniques to predict the release of nutrients from the CRFs to elucidate fundamental understanding of the dynamics of the release processes and to design new CRFs in a shorter time and with relatively lower cost. This paper reviews and critically analyzes the latest developments in the mathematical modeling and simulation techniques that have been reported for the characteristics and mechanisms of nutrient release from CRFs. The scope of this review includes the modeling and simulations techniques used for coated, controlled-release fertilizers. Copyright © 2017 Elsevier B.V. All rights reserved.

TU-FG-209-09: Mathematical Estimation and Experimental Measurement of Patient Free-In-Air Skin Entrance Exposure During a Panoramic Dental X-Ray Procedure

DOE Office of Scientific and Technical Information (OSTI.GOV)

Errico, A; Behrman, R; Li, B

Purpose: To develop a simple mathematical model for estimating the patient free-in-air skin entrance exposure (SEE) during a panoramic dental x-ray that does not require the use of a head phantom. This eliminates issues associated with phantom centering and the mounting of a detector on the phantom for routine QC testing. Methods: We used a Sirona Orthophos XG panoramic radiographic unit and a Radcal Accu-Gold system for this study. A solid state detector was attached over the slit of the Orthophos’ sensor with the help of a custom-built jig. A single measurement of the free-in-air exposure at this position wasmore » taken over a full panoramic scan. A mathematical model for estimating the SEE was developed based upon this measurement, the system geometry, x-ray field beam width, and x-ray sweep angle. To validate the model, patient geometry was simulated by a 16 cm diameter PMMA CTDI phantom centered at the machine’s isocenter. Measurements taken on the phantom’s surface were made using a solid state detector with lead backing, an ion chamber, and the ion chamber with the phantom wrapped in lead to mitigate backscatter. Measurements were taken near the start position of the tube and at 90 degrees from the start position. Results: Using the solid state detector, the average SEE was 23.5+/−0.02 mR and 55.5+/−0.08 mR at 64 kVp and 73 kVp, respectively. With the lead-wrapping, the measurements from the ion chamber matched those of the solid state detector to within 0.1%. Preliminary results gave the difference between the mathematical model and the phantom measurements to be approximately 5% at both kVps. Conclusion: Reasonable estimates of patient SEE for panoramic dental radiography can be made using a simple mathematical model without the need for a head phantom.« less

South Carolina Guide for Mathematics for the Technologies (Applied Vocational Mathematics).

ERIC Educational Resources Information Center

Moore, Charles; And Others

In this instructional guide, a third-level, two-semester mathematics course specifically for the student who plans a career in a vocational field is presented. The course is designed to meet the needs of students with varying mathematical backgrounds and to teach the mathematical skills required by various technical areas. In this practical…

Addressing the Needs of a Developing Nation: Electronic Maps of Mathematical Learning Resources Accessible via the Internet

ERIC Educational Resources Information Center

Fathurrohman, Maman; Porter, Anne

2012-01-01

Teaching and learning of mathematics are integral parts of societies throughout the world. The fundamental or core nature of mathematics, its compulsory acquisition, requires high quality mathematics learning experiences. Moreover it is highly desirable that the emergence of new technology positively influences learning experiences in mathematics.…

Learning Mathematics in High School Courses beyond Mathematics: Combating the Need for Post-Secondary Remediation in Mathematics

ERIC Educational Resources Information Center

Young, R. Brent; Hodge, Angie; Edwards, M. Craig; Leising, James G.

2012-01-01

The purpose of this study was to empirically test the posit that students who participated in a contextualized, mathematics-enhanced high school agricultural power and technology (APT) curriculum and aligned instructional approach would develop a deeper and more sustained understanding of selected mathematics concepts than those students who…

A Synthesis of Technology-Mediated Mathematics Interventions for Students with or at Risk for Mathematics Learning Disabilities

ERIC Educational Resources Information Center

Kiru, Elisheba W.; Doabler, Christian T.; Sorrells, Audrey M.; Cooc, North A.

2018-01-01

With the increasing availability of technology and the emphasis on science, technology, engineering, and mathematics education, there is an urgent need to understand the impact of technology-mediated mathematics (TMM) interventions on student mathematics outcomes. The purpose of this study was to review studies on TMM interventions that target the…

Middle School Mathematics Students' Perspectives on the Study of Mathematics

ERIC Educational Resources Information Center

Vaughn, Christy H.

2012-01-01

This qualitative study addressed the perceptions toward the study of mathematics by middle school students who had formerly been in a remedial mathematics program. The purpose of the study was to explore the past experiences of nine students in order to determine what is needed for them to feel successful in mathematics. The conceptual framework…

Relationships of Mathematics Anxiety, Mathematics Self-Efficacy and Mathematics Performance of Adult Basic Education Students

ERIC Educational Resources Information Center

Watts, Beverly Kinsey

2011-01-01

Competent mathematical skills are needed in the workplace as well as in the college setting. Adults in Adult Basic Education classes and programs generally perform below high school level competency, but very few studies have been performed investigating the predictors of mathematical success for adults. The current study contributes to the…

Mathematical modeling in realistic mathematics education

NASA Astrophysics Data System (ADS)

Riyanto, B.; Zulkardi; Putri, R. I. I.; Darmawijoyo

2017-12-01

The purpose of this paper is to produce Mathematical modelling in Realistics Mathematics Education of Junior High School. This study used development research consisting of 3 stages, namely analysis, design and evaluation. The success criteria of this study were obtained in the form of local instruction theory for school mathematical modelling learning which was valid and practical for students. The data were analyzed using descriptive analysis method as follows: (1) walk through, analysis based on the expert comments in the expert review to get Hypothetical Learning Trajectory for valid mathematical modelling learning; (2) analyzing the results of the review in one to one and small group to gain practicality. Based on the expert validation and students’ opinion and answers, the obtained mathematical modeling problem in Realistics Mathematics Education was valid and practical.

Mathematical Problem Solving Ability of Junior High School Students through Ang’s Framework for Mathematical Modelling Instruction

NASA Astrophysics Data System (ADS)

Fasni, N.; Turmudi, T.; Kusnandi, K.

2017-09-01

This research background of this research is the importance of student problem solving abilities. The purpose of this study is to find out whether there are differences in the ability to solve mathematical problems between students who have learned mathematics using Ang’s Framework for Mathematical Modelling Instruction (AFFMMI) and students who have learned using scientific approach (SA). The method used in this research is a quasi-experimental method with pretest-postest control group design. Data analysis of mathematical problem solving ability using Indepent Sample Test. The results showed that there was a difference in the ability to solve mathematical problems between students who received learning with Ang’s Framework for Mathematical Modelling Instruction and students who received learning with a scientific approach. AFFMMI focuses on mathematical modeling. This modeling allows students to solve problems. The use of AFFMMI is able to improve the solving ability.

Investigating the Knowledge Needed for Teaching Mathematics: An Exploratory Validation Study Focusing on Teaching Practices

ERIC Educational Resources Information Center

Charalambous, Charalambos Y.

2016-01-01

Central in the frameworks proposed to capture the knowledge needed for teaching mathematics is the assumption that teachers need more than pure subject-matter knowledge. Validation studies exploring this assumption by recruiting contrasting populations are relatively scarce. Drawing on a sample of 644 Greek-Cypriots preservice and inservice…

Special Education Teachers' Views on Using Technology in Teaching Mathematics

ERIC Educational Resources Information Center

Baglama, Basak; Yikmis, Ahmet; Demirok, Mukaddes Sakalli

2017-01-01

Individuals with special needs require support in acquiring various academic and social skills and mathematical skills are one of the most important skills in which individuals with special needs need to acquire in order to maintain their daily lives. Current approaches in education emphasize the importance of integrating technology into special…

Mathematics: PROJECT DESIGN. Educational Needs, Fresno, 1968, Number 12.

ERIC Educational Resources Information Center

Smart, James R.

This report examines and summarizes the needs in mathematics of the Fresno City school system. The study is one in a series of needs assessment reports for PROJECT DESIGN, an ESEA Title III project administered by the Fresno City Unified School District. Theoretical concepts, rather than computational drill, would be emphasized in the proposed…

Human-System Technology: Human-Robot Interaction to Address Critical Navy Needs of the Present and Future

DTIC Science & Technology

2006-10-31

Articles: Danks , D. "Psychological Theories of Categorization as Probabilistic Graphical Models," Journal of Mathematical Psychology, submitted. Kyburg...and when there is no set of competent and authorized humans available to make the decisions themselves. Ultimately, it is a matter of expected utility

Vocational Assessment of Students with Disadvantages: Their Peculiar Needs.

ERIC Educational Resources Information Center

Nolte, Deborah

A study examined the underlying factor structure of the aptitude tests and work samples being completed by students with educational disadvantages (limited reading and mathematics skills) who were assessed with the current assessment model in the Akron (Ohio) Public Schools. The amount of variance accounted for by the factors was also…

STEM Strategies: Student Ambassadors and Equality in Higher Education

ERIC Educational Resources Information Center

Gartland, Clare

2014-01-01

More skilled young people are urgently needed in science, technology, engineering and mathematics in the UK. This book indicates how policy can be developed to encourage young people to consider STEM careers. It challenges widely held assumptions about how role models help raise aspirations and support progression to Higher Education and asks…

Characterizing STEM Teacher Education: Affordances and Constraints of Explicit STEM Preparation for Elementary Teachers

ERIC Educational Resources Information Center

Rinke, Carol R.; Gladstone-Brown, Wendy; Kinlaw, C. Ryan; Cappiello, Jean

2016-01-01

Although science, technology, engineering, and mathematics (STEM) education sits at the center of a national conversation, comparatively little attention has been given to growing need for STEM teacher preparation, particularly at the elementary level. This study analyzes the outcomes of a novel, preservice STEM teacher education model. Building…

Computer simulation of white pine blister rust epidemics

Treesearch

Geral I. McDonald; Raymond J. Hoff; William R. Wykoff

1981-01-01

A simulation of white pine blister rust is described in both word and mathematical models. The objective of this first generation simulation was to organize and analyze the available epidemiological knowledge to produce a foundation for integrated management of this destructive rust of 5-needle pines. Verification procedures and additional research needs are also...

The Effect of Teacher Beliefs on Student Competence in Mathematical Modeling--An Intervention Study

ERIC Educational Resources Information Center

Mischo, Christoph; Maaß, Katja

2013-01-01

This paper presents an intervention study whose aim was to promote teacher beliefs about mathematics and learning mathematics and student competences in mathematical modeling. In the intervention, teachers received written curriculum materials about mathematical modeling. The concept underlying the materials was based on constructivist ideas and…

Leaning on Mathematical Habits of Mind

ERIC Educational Resources Information Center

Sword, Sarah; Matsuura, Ryota; Cuoco, Al; Kang, Jane; Gates, Miriam

2018-01-01

Mathematical modeling has taken on increasing curricular importance in the past decade due in no small measure to the Common Core State Standards in Mathematics (CCSSM) identifying modeling as one of the Standards for Mathematical Practice (SMP 4, CCSSI 2010, p. 7). Although researchers have worked on mathematical modeling (Lesh and Doerr 2003;…

V/STOL tilt rotor study. Volume 5: A mathematical model for real time flight simulation of the Bell model 301 tilt rotor research aircraft

NASA Technical Reports Server (NTRS)

Harendra, P. B.; Joglekar, M. J.; Gaffey, T. M.; Marr, R. L.

1973-01-01

A mathematical model for real-time flight simulation of a tilt rotor research aircraft was developed. The mathematical model was used to support the aircraft design, pilot training, and proof-of-concept aspects of the development program. The structure of the mathematical model is indicated by a block diagram. The mathematical model differs from that for a conventional fixed wing aircraft principally in the added requirement to represent the dynamics and aerodynamics of the rotors, the interaction of the rotor wake with the airframe, and the rotor control and drive systems. The constraints imposed on the mathematical model are defined.

Pre-Service Teachers' Views of the Maths Talent Quest (MTQ): Connecting Mathematical Concepts to Everyday Tasks and Experiences

ERIC Educational Resources Information Center

Baum, Prudence; Perera, Radhika

2017-01-01

Mathematics needs to take on a real-world quality, and students need to be able to identify and connect the value of what they are learning within the classroom to life outside the classroom. Creating a connection between the mathematics learned within a classroom and its value to life in the outside world is critical to effectively engage…

Education of a model student

PubMed Central

Novikoff, Timothy P.; Kleinberg, Jon M.; Strogatz, Steven H.

2012-01-01

A dilemma faced by teachers, and increasingly by designers of educational software, is the trade-off between teaching new material and reviewing what has already been taught. Complicating matters, review is useful only if it is neither too soon nor too late. Moreover, different students need to review at different rates. We present a mathematical model that captures these issues in idealized form. The student’s needs are modeled as constraints on the schedule according to which educational material and review are spaced over time. Our results include algorithms to construct schedules that adhere to various spacing constraints, and bounds on the rate at which new material can be introduced under these schedules. PMID:22308334

Developing Students' Reflections on the Function and Status of Mathematical Modeling in Different Scientific Practices: History as a Provider of Cases

ERIC Educational Resources Information Center

Kjeldsen, Tinne Hoff; Blomhøj, Morten

2013-01-01

Mathematical models and mathematical modeling play different roles in the different areas and problems in which they are used. The function and status of mathematical modeling and models in the different areas depend on the scientific practice as well as the underlying philosophical and theoretical position held by the modeler(s) and the…

How Ordinary Meaning Underpins the Meaning of Mathematics.

ERIC Educational Resources Information Center

Ormell, Christopher

1991-01-01

Discusses the meaning of mathematics by looking at its uses in the real world. Offers mathematical modeling as a way to represent mathematical applications in real or potential situations. Presents levels of applicability, modus operandi, relationship to "pure mathematics," and consequences for education for mathematical modeling. (MDH)

Virtual Environments for Mathematics and Geometry Education

ERIC Educational Resources Information Center

Kaufmann, Hannes

2009-01-01

Since ancient times mathematicians and geometricians have used visualisations to describe, discuss, study and teach mathematics. In mathematics education, visualisations are still used whenever possible to support teaching, to inspire students and feed their need to actually see abstract mathematical facts. In our times, virtual reality presents a…

Restoring Scholarship to Collegiate Mathematics.

ERIC Educational Resources Information Center

Steen, Lynn Arthur

1986-01-01

Needs of collegiate mathematics across the nation are considered, and suggestions are offered to the National Science Foundation (NSF) by a professor of Mathematics at St. Olaf College (Minnesota). Changes in mathematics content, scope, and applications have implications for the college curriculum. Problems and challenges are posed by: increased…

Fostering Sex Equity in Math.

ERIC Educational Resources Information Center

Moody, Charles D.; Linn, Eleanor

1986-01-01

The role of mathematics as a critical determiner of employment is noted, and the "significant absence of women and minority students in mathematics classes" is given attention. The need to gain competence in mathematics skills and confidence in mathematical abilities calls for programs to increase student participation, motivation, and…

Standards for Reporting Mathematics Professional Development in Research Studies

ERIC Educational Resources Information Center

Sztajn, Paola

2011-01-01

This Research Commentary addresses the need for standards for describing mathematics professional development in mathematics education research reports. Considering that mathematics professional development is an emerging research field, it is timely to set expectations for what constitutes high-quality reporting in this field. (Contains 2 tables.)

Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century.

PubMed

Ganusov, Vitaly V

2016-01-01

While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest "strong inference in mathematical modeling" as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century.

A new mathematical neck model for a low-velocity rear-end impact dummy: evaluation of components influencing head kinematics.

PubMed

Linder, A

2000-03-01

A mathematical model of a new rear-end impact dummy neck was implemented using MADYMO. The main goal was to design a model with a human-like response of the first extension motion in the crash event. The new dummy neck was modelled as a series of rigid bodies (representing the seven cervical vertebrae and the uppermost thoracic element, T1) connected by pin joints, and supplemented by two muscle substitutes. The joints had non-linear stiffness characteristics and the muscle elements possessed both elastic stiffness and damping properties. The new model was compared with two neck models with the same number of vertebrae, but without muscle substitutes. The properties of the muscle substitutes and the need of these were evaluated by using three different modified neck models. The motion of T1 in the simulations was prescribed using displacement data obtained from volunteer tests. In a sensitivity analysis of the mathematical model the influence of different factors on the head-neck kinematics was evaluated. The neck model was validated against kinematics data from volunteer tests: linear displacement, angular displacement, and acceleration of the head relative to the upper torso at 7 km/h velocity change. The response of the new model was within the corridor of the volunteer tests for the main part of the time history plot. This study showed that a combination of elastic stiffness and damping in the muscle substitutes, together with a non-linear joint stiffness, resulted in a head-neck response similar to human volunteers, and superior to that of other tested neck models.

Summer Camp of Mathematical Modeling in China

ERIC Educational Resources Information Center

Tian, Xiaoxi; Xie, Jinxing

2013-01-01

The Summer Camp of Mathematical Modeling in China is a recently created experience designed to further Chinese students' academic pursuits in mathematical modeling. Students are given more than three months to research on a mathematical modeling project. Researchers and teams with outstanding projects are invited to the Summer Camp to present…

QR-STEM: Energy and Environment as a Context for Improving QR and STEM Understandings of 6-12 Grade Teachers II. The Quantitative Reasoning

NASA Astrophysics Data System (ADS)

Mayes, R.; Lyford, M. E.; Myers, J. D.

2009-12-01

The Quantitative Reasoning in STEM (QR STEM) project is a state level Mathematics and Science Partnership Project (MSP) with a focus on the mathematics and statistics that underlies the understanding of complex global scientific issues. This session is a companion session to the QR STEM: The Science presentation. The focus of this session is the quantitative reasoning aspects of the project. As students move from understandings that range from local to global in perspective on issues of energy and environment, there is a significant increase in the need for mathematical and statistical conceptual understanding. These understandings must be accessible to the students within the scientific context, requiring the special understandings that are endemic within quantitative reasoning. The QR STEM project brings together interdisciplinary teams of higher education faculty and middle/high school teachers to explore complex problems in energy and environment. The disciplines include life sciences, physics, chemistry, earth science, statistics, and mathematics. These interdisciplinary teams develop open ended performance tasks to implement in the classroom, based on scientific concepts that underpin energy and environment. Quantitative reasoning is broken down into three components: Quantitative Literacy, Quantitative Interpretation, and Quantitative Modeling. Quantitative Literacy is composed of arithmetic concepts such as proportional reasoning, numeracy, and descriptive statistics. Quantitative Interpretation includes algebraic and geometric concepts that underlie the ability to interpret a model of natural phenomena which is provided for the student. This model may be a table, graph, or equation from which the student is to make predictions or identify trends, or from which they would use statistics to explore correlations or patterns in data. Quantitative modeling is the ability to develop the model from data, including the ability to test hypothesis using statistical procedures. We use the term model very broadly, so it includes visual models such as box models, as well as best fit equation models and hypothesis testing. One of the powerful outcomes of the project is the conversation which takes place between science teachers and mathematics teachers. First they realize that though they are teaching concepts that cross their disciplines, the barrier of scientific language within their subjects restricts students from applying the concepts across subjects. Second the mathematics teachers discover the context of science as a means of providing real world situations that engage students in the utility of mathematics as a tool for solving problems. Third the science teachers discover the barrier to understanding science that is presented by poor quantitative reasoning ability. Finally the students are engaged in exploring energy and environment in a manner which exposes the importance of seeing a problem from multiple interdisciplinary perspectives. The outcome is a democratic citizen capable of making informed decisions, and perhaps a future scientist.

Validation Methods Research for Fault-Tolerant Avionics and Control Systems Sub-Working Group Meeting. CARE 3 peer review

NASA Technical Reports Server (NTRS)

Trivedi, K. S. (Editor); Clary, J. B. (Editor)

1980-01-01

A computer aided reliability estimation procedure (CARE 3), developed to model the behavior of ultrareliable systems required by flight-critical avionics and control systems, is evaluated. The mathematical models, numerical method, and fault-tolerant architecture modeling requirements are examined, and the testing and characterization procedures are discussed. Recommendations aimed at enhancing CARE 3 are presented; in particular, the need for a better exposition of the method and the user interface is emphasized.

Decentralized control of Markovian decision processes: Existence Sigma-admissable policies

NASA Technical Reports Server (NTRS)

Greenland, A.

1980-01-01

The problem of formulating and analyzing Markov decision models having decentralized information and decision patterns is examined. Included are basic examples as well as the mathematical preliminaries needed to understand Markov decision models and, further, to superimpose decentralized decision structures on them. The notion of a variance admissible policy for the model is introduced and it is proved that there exist (possibly nondeterministic) optional policies from the class of variance admissible policies. Directions for further research are explored.

Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century

PubMed Central

Ganusov, Vitaly V.

2016-01-01

While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest “strong inference in mathematical modeling” as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century. PMID:27499750

Enjoying mathematics or feeling competent in mathematics? Reciprocal effects on mathematics achievement and perceived math effort expenditure.

PubMed

Pinxten, Maarten; Marsh, Herbert W; De Fraine, Bieke; Van Den Noortgate, Wim; Van Damme, Jan

2014-03-01

The multidimensionality of the academic self-concept in terms of domain specificity has been well established in previous studies, whereas its multidimensionality in terms of motivational functions (the so-called affect-competence separation) needs further examination. This study aims at exploring differential effects of enjoyment and competence beliefs on two external validity criteria in the field of mathematics. Data analysed in this study were part of a large-scale longitudinal research project. Following a five-wave design, math enjoyment, math competence beliefs, math achievement, and perceived math effort expenditure measures were repeatedly collected from a cohort of 4,724 pupils in Grades 3-7. Confirmatory factor analysis (CFA) was used to test the internal factor structure of the math self-concept. Additionally, a series of nested models was tested using structural equation modelling to examine longitudinal reciprocal interrelations between math competence beliefs and math enjoyment on the one hand and math achievement and perceived math effort expenditure on the other. Our results showed that CFA models with separate factors for math enjoyment and math competence beliefs fit the data substantially better than models without it. Furthermore, differential relationships between both constructs and the two educational outcomes were observed. Math competence beliefs had positive effects on math achievement and negative effects on perceived math effort expenditure. Math enjoyment had (mild) positive effects on subsequent perceived effort expenditure and math competence beliefs. This study provides further support for the affect-competence separation. Theoretical issues regarding adequate conceptualization and practical consequences for practitioners are discussed. © 2013 The British Psychological Society.

Using Covariation Reasoning to Support Mathematical Modeling

ERIC Educational Resources Information Center

Jacobson, Erik

2014-01-01

For many students, making connections between mathematical ideas and the real world is one of the most intriguing and rewarding aspects of the study of mathematics. In the Common Core State Standards for Mathematics (CCSSI 2010), mathematical modeling is highlighted as a mathematical practice standard for all grades. To engage in mathematical…

A case study of a mathematics teacher's and science teacher's use of teacher wisdom in integrating middle school mathematics and science content

NASA Astrophysics Data System (ADS)

Saam, Julie Reinhardt

The National Science Education Standards, the National Council of Teachers of Mathematics Curriculum Standards, the Interdisciplinary Team Organization structure and the Middle School movement collectively suggest to teachers to make connections between their subject areas. This case study of a middle school mathematics teacher and science teacher utilizes the framework of teacher wisdom to bring a unique perspective to the process of developing and implementing integrated curriculum. Data collection consisted of interviews with the teachers, students, and their principal; documents such lesson plans, team meeting minutes and teacher journal entries; and field notes acquired within team meetings and classroom instruction. The interpretations of this study reveal that teacher development of integrated curriculum occurs in two ways: naturally and intentionally. The natural label used to describe when teachers comfortably share information that could serve as connections between subjects. The intentional label used to describe when the teachers purposely plan integrated lessons and units. These findings also provide an image of middle school integration. This image exhibits more than connections between subject area content; it also shows connections with away-from-school skills and events, lifeskills, and lifelong guidelines. Although these teachers found it frustrating and overwhelming to meet the many views of integration, they assembled integration curriculum that followed their philosophy of education, coincided with their personal characteristics and met the needs of their students. The interpretations of this study reveal a new model of middle school integration. Teachers can use this model as a collection of integration examples. Integration researchers can use this model as a conceptual framework to analyze the integration efforts of middle level teachers. Additional research needs to focus on: developing new modeling and evaluation tools for teachers, evaluating middle school professional development programs, investigating middle school teachers' characteristics, and continuing the study of integration's worth. The results of this study and additional research may help: (a) administrators to target specific teachers for middle school positions, (b) educators to plan and implement new programs for inservice and preservice middle school teachers, and (c) teachers to experiment with new and innovative strategies for middle school integration.

An Examination of Pre-Service Mathematics Teachers' Approaches to Construct and Solve Mathematical Modelling Problems

ERIC Educational Resources Information Center

Bukova-Guzel, Esra

2011-01-01

This study examines the approaches displayed by pre-service mathematics teachers in their experiences of constructing mathematical modelling problems and the extent to which they perform the modelling process when solving the problems they construct. This case study was carried out with 35 pre-service teachers taking the Mathematical Modelling…

Project LAUNCH: Bringing Space into Math and Science Classrooms

NASA Technical Reports Server (NTRS)

Fauerbach, M.; Henry, D. P.; Schmidt, D. L.

2005-01-01

Project LAUNCH is a K-12 teacher professional development program, which has been created in collaboration between the Whitaker Center for Science, Mathematics and Technology Education at Florida Gulf Coast University (FGCU), and the Florida Space Research Institute (FSRI). Utilizing Space as the overarching theme it is designed to improve mathematics and science teaching, using inquiry based, hands-on teaching practices, which are aligned with Florida s Sunshine State Standards. Many students are excited about space exploration and it provides a great venue to get them involved in science and mathematics. The scope of Project LAUNCH however goes beyond just providing competency in the subject area, as pedagogy is also an intricate part of the project. Participants were introduced to the Conceptual Change Model (CCM) [1] as a framework to model good teaching practices. As the CCM closely follows what scientists call the scientific process, this teaching method is also useful to actively engage institute participants ,as well as their students, in real science. Project LAUNCH specifically targets teachers in low performing, high socioeconomic schools, where the need for skilled teachers is most critical.

A review of heat transfer in human tooth--experimental characterization and mathematical modeling.

PubMed

Lin, Min; Xu, Feng; Lu, Tian Jian; Bai, Bo Feng

2010-06-01

With rapid advances in modern dentistry, high-energy output instruments (e.g., dental lasers and light polymerizing units) are increasingly employed in dental surgery for applications such as laser assisted tooth ablation, bleaching, hypersensitivity treatment and polymerization of dental restorative materials. Extreme high temperature occurs within the tooth during these treatments, which may induce tooth thermal pain (TTP) sensation. Despite the wide application of these dental treatments, the underlying mechanisms are far from clear. Therefore, there is an urgent need to better understand heat transfer (HT) process in tooth, thermally induced damage of tooth, and the corresponding TTP. This will enhance the design and optimization of clinical treatment strategies. This paper presents the state-of-the-art of the current understanding on HT in tooth, with both experimental study and mathematical modeling reviewed. Limitations of the current experimental and mathematical methodologies are discussed and potential solutions are suggested. Interpretation of TTP in terms of thermally stimulated dentinal fluid flow is also discussed. Copyright (c) 2010 Academy of Dental Materials. All rights reserved.

A mathematical model for the effects of radiation to the induced cancer in mice

NASA Astrophysics Data System (ADS)

Wada, Takahiro; Manabe, Yuichiro; Bando, Masako

We have been studying biological effects of radiation in terms of mathematical models. There are two main objects that we need to study: mutation and cancer. We proposed the Whack-A-Mole (WAM) model which takes account of the repair effects to study radiation induced mutations. We applied it to the mutation of several species including Drosophila and mice, and succeeded to reproduce the dose and dose-rate dependence of the mutation rates. Here, as a next step, we study the effects of low dose-rate radiation to an induced cancer in mice. In the experiment, they divided their mice in four groups and kept them under constant gamma-ray radiations with different dose rate for each group since the birth. On the 35th day, chemical carcinogen was given to each mouse and they observed the occurrence and the growth of cancer for one year. Our mathematical model consists of two stages. The first stage describes a multiple-step carcinogenesis and the second stage describes its growth. We assume that the carcinogenesis starts with the chemical carcinogen and that the rate of the following processes depends on the dose rate as it does in the WAM model. We found some irregularities in the data, however, the overall fit is satisfactory. This work was supported by JSPS KAKENHI Grant Number JP16H04637.

The Mathematics Attitudes and Perceptions Survey: an instrument to assess expert-like views and dispositions among undergraduate mathematics students

NASA Astrophysics Data System (ADS)

Code, Warren; Merchant, Sandra; Maciejewski, Wes; Thomas, Matthew; Lo, Joseph

2016-08-01

One goal of an undergraduate education in mathematics is to help students develop a productive disposition towards mathematics. A way of conceiving of this is as helping mathematical novices transition to more expert-like perceptions of mathematics. This conceptualization creates a need for a way to characterize students' perceptions of mathematics in authentic educational settings. This article presents a survey, the Mathematics Attitudes and Perceptions Survey (MAPS), designed to address this need. We present the development of the MAPS instrument and its validation on a large (N = 3411) set of student data. Results from various MAPS implementations corroborate results from analogous instruments in other STEM disciplines. We present these results and highlight some in particular: MAPS scores correlate with course grades; students tend to move away from expert-like orientations over a semester or year of taking a mathematics course; and interactive-engagement type lectures have less of a negative impact, but no positive impact, on students' overall orientations than traditional lecturing. We include the MAPS instrument in this article and suggest ways in which it may deepen our understanding of undergraduate mathematics education.

Mathematics as a conduit for translational research in post-traumatic osteoarthritis.

PubMed

Ayati, Bruce P; Kapitanov, Georgi I; Coleman, Mitchell C; Anderson, Donald D; Martin, James A

2017-03-01

Biomathematical models offer a powerful method of clarifying complex temporal interactions and the relationships among multiple variables in a system. We present a coupled in silico biomathematical model of articular cartilage degeneration in response to impact and/or aberrant loading such as would be associated with injury to an articular joint. The model incorporates fundamental biological and mechanical information obtained from explant and small animal studies to predict post-traumatic osteoarthritis (PTOA) progression, with an eye toward eventual application in human patients. In this sense, we refer to the mathematics as a "conduit of translation." The new in silico framework presented in this paper involves a biomathematical model for the cellular and biochemical response to strains computed using finite element analysis. The model predicts qualitative responses presently, utilizing system parameter values largely taken from the literature. To contribute to accurate predictions, models need to be accurately parameterized with values that are based on solid science. We discuss a parameter identification protocol that will enable us to make increasingly accurate predictions of PTOA progression using additional data from smaller scale explant and small animal assays as they become available. By distilling the data from the explant and animal assays into parameters for biomathematical models, mathematics can translate experimental data to clinically relevant knowledge. © 2016 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:566-572, 2017. © 2016 Orthopaedic Research Society. Published by Wiley Periodicals, Inc.

Preprocessing Inconsistent Linear System for a Meaningful Least Squares Solution

NASA Technical Reports Server (NTRS)

Sen, Syamal K.; Shaykhian, Gholam Ali

2011-01-01

Mathematical models of many physical/statistical problems are systems of linear equations. Due to measurement and possible human errors/mistakes in modeling/data, as well as due to certain assumptions to reduce complexity, inconsistency (contradiction) is injected into the model, viz. the linear system. While any inconsistent system irrespective of the degree of inconsistency has always a least-squares solution, one needs to check whether an equation is too much inconsistent or, equivalently too much contradictory. Such an equation will affect/distort the least-squares solution to such an extent that renders it unacceptable/unfit to be used in a real-world application. We propose an algorithm which (i) prunes numerically redundant linear equations from the system as these do not add any new information to the model, (ii) detects contradictory linear equations along with their degree of contradiction (inconsistency index), (iii) removes those equations presumed to be too contradictory, and then (iv) obtain the minimum norm least-squares solution of the acceptably inconsistent reduced linear system. The algorithm presented in Matlab reduces the computational and storage complexities and also improves the accuracy of the solution. It also provides the necessary warning about the existence of too much contradiction in the model. In addition, we suggest a thorough relook into the mathematical modeling to determine the reason why unacceptable contradiction has occurred thus prompting us to make necessary corrections/modifications to the models - both mathematical and, if necessary, physical.

Preprocessing in Matlab Inconsistent Linear System for a Meaningful Least Squares Solution

NASA Technical Reports Server (NTRS)

Sen, Symal K.; Shaykhian, Gholam Ali

2011-01-01

Mathematical models of many physical/statistical problems are systems of linear equations Due to measurement and possible human errors/mistakes in modeling/data, as well as due to certain assumptions to reduce complexity, inconsistency (contradiction) is injected into the model, viz. the linear system. While any inconsistent system irrespective of the degree of inconsistency has always a least-squares solution, one needs to check whether an equation is too much inconsistent or, equivalently too much contradictory. Such an equation will affect/distort the least-squares solution to such an extent that renders it unacceptable/unfit to be used in a real-world application. We propose an algorithm which (i) prunes numerically redundant linear equations from the system as these do not add any new information to the model, (ii) detects contradictory linear equations along with their degree of contradiction (inconsistency index), (iii) removes those equations presumed to be too contradictory, and then (iv) obtain the . minimum norm least-squares solution of the acceptably inconsistent reduced linear system. The algorithm presented in Matlab reduces the computational and storage complexities and also improves the accuracy of the solution. It also provides the necessary warning about the existence of too much contradiction in the model. In addition, we suggest a thorough relook into the mathematical modeling to determine the reason why unacceptable contradiction has occurred thus prompting us to make necessary corrections/modifications to the models - both mathematical and, if necessary, physical.

Mathematics education and learning disabilities in Spain.

PubMed

Casas, Ana Miranda; Castellar, Rosa García

2004-01-01

In the first part of this article, we describe the basic objectives of the math curriculum in Spain as well as the basic contents, teacher resources, and obstacles perceived in mathematics instruction. Second, we briefly describe the concept of learning disabilities (LD) as they are currently defined in Spain. As stated in the recent educational reform, a student with LD is any student with special educational needs. The emphasis is placed on the educational resources that these students need in order to achieve the curricular objectives that correspond to their age group or grade. Third, we comment specifically on the educational services model and the evaluation and instructional procedures for students with math learning disabilities. Finally, we describe some lines of research that have appeared in the last few years in Spain that have led to the development of new evaluation and intervention procedures for students with LD in computation and problem solving.

Mathematics in the lower primary years: A research-based perspective on curricula and teaching practice

NASA Astrophysics Data System (ADS)

Wright, Bob

1994-07-01

Drawing on current research the author explicates twelve assertions relating to curricula, teaching, learners and learning environments in lower primary school mathematics. Topics discussed include: unchanging and under-challenging curricula; the need for greater emphasis on developing children's verbal number strategies and number sense, and on activities specifically suited to prenumerical children; curriculum constraints on teachers; the role of problem solving and differing interpretations of problem solving; the need for a better understanding of how children learn mathematics; differences in children's knowledge; "anti-interventionism," discovery learning, constructivism, children's autonomy and developmental learning; the need for compensatory programs; and learning in collaborative settings. The author concludes that learning and teaching lower primary mathematics continues to be an important area of focus and challenge for teachers and researchers.

Lessons from the Past Look to the Future.

ERIC Educational Resources Information Center

Howden, Hilde

2000-01-01

Technological advances and many other changes in society change how and what students learn. Indicates the need to learn lessons from the past in order to be more mathematically literate and broaden the mathematics curriculum to a mathematical sciences curriculum that incorporates 21st century mathematics. (Contains 14 references.) (ASK)

Mathematics Courses for the Prospective Teacher.

ERIC Educational Resources Information Center

Kistler, Barbara C.

This paper suggests that faculty at two-year institutions need to become partners with colleges of education and K-12 teachers of mathematics in preparing future mathematics teachers. The paper presents the following: a summary of recommendations on programs for prospective teachers; a summary of recommendations about mathematics courses for…

Teaching Gifted Children Mathematics in Grades Four Through Six.

ERIC Educational Resources Information Center

Gensley, Juliana T.

Intended for teachers of gifted students in grades 4-6, the guide emphasizes the need for specialized instruction in mathematics, suggests methods for teaching mathematical facts and concepts, describes approaches and materials to develop students' understanding of mathematical principles, and explores ways to build skills and creativity. Stressed…

Utah's New Mathematics Core

ERIC Educational Resources Information Center

Utah State Office of Education, 2011

2011-01-01

Utah has adopted more rigorous mathematics standards known as the Utah Mathematics Core Standards. They are the foundation of the mathematics curriculum for the State of Utah. The standards include the skills and understanding students need to succeed in college and careers. They include rigorous content and application of knowledge and reflect…

Pose and Solve Varignon Converse Problems

ERIC Educational Resources Information Center

Contreras, José N.

2014-01-01

The activity of posing and solving problems can enrich learners' mathematical experiences because it fosters a spirit of inquisitiveness, cultivates their mathematical curiosity, and deepens their views of what it means to do mathematics. To achieve these goals, a mathematical problem needs to be at the appropriate level of difficulty,…

Ethical Dimensions of Mathematics Education

ERIC Educational Resources Information Center

Boylan, Mark

2016-01-01

The relationships between mathematics, mathematics education and issues such as social justice and equity have been addressed by the sociopolitical tradition in mathematics education. Others have introduced explicit discussion of ethics, advocating for its centrality. However, this is an area that is still under developed. There is a need for an…

Mathematical Literacy--It's Become Fundamental

ERIC Educational Resources Information Center

McCrone, Sharon Soucy; Dossey, John A.

2007-01-01

The rising tide of numbers and statistics in daily life signals a need for a fundamental broadening of the concept of literacy: mathematical literacy assuming a coequal role in the curriculum alongside language-based literacy. Mathematical literacy is not about studying higher levels of formal mathematics, but about making math relevant and…

Learning over Time: Learning Trajectories in Mathematics Education

ERIC Educational Resources Information Center

Maloney, Alan P., Ed.; Confrey, Jere, Ed.; Nguyen, Kenny H., Ed.

2014-01-01

The driving forces behind mathematics learning trajectories is the need to understand how children actually learn and make sense of mathematics--how they progress from prior knowledge, through intermediate understandings, to the mathematics target understandings--and how to use these insights to improve instruction and student learning. In this…

A New Start for Mathematics Curriculum.

ERIC Educational Resources Information Center

Tucker, Alan

Arguing that a major re-thinking of the mathematics curriculum is needed, this paper urges two-year colleges to take the lead in curriculum revision. Section I suggests that the pre-calculus orientation of high school mathematics may be inappropriate, viewing mathematics related to computers and dependent on computers for computation as more…

Investigating Task Design, Classroom Culture and Mathematics Learning: An Enactivist Approach

ERIC Educational Resources Information Center

Lozano, Maria-Dolores

2017-01-01

In this paper I introduce a methodological approach that can be useful for investigating relationships between mathematics tasks, mathematical classroom cultures and mathematics learning. This proposal responds to a need, identified in the literature, for "further research which uses alternative methods to understand student perspectives more…

Strategies for Teaching Developmental Mathematics Students at the College Level

ERIC Educational Resources Information Center

Swaincott Kautz, Natalie Lynn

2016-01-01

The purpose of this investigation was to identify strategies used by effective instructors of developmental mathematics, and to discover the perceptions developmental mathematics students have about these strategies. While there are research projects focusing solely on developmental mathematics achievement, this study fills a need by incorporating…

Topics in Mathematics.

ERIC Educational Resources Information Center

Posey, Johnsie Jo, Ed.; And Others

This manual is a collection of materials and teaching strategies to motivate the development of mathematical ideas in secondary school mathematics programs or in beginning college mathematics programs. The unit is written for the instructor with step-by-step procedures including lists of needed materials. The exercises in this unit also appear in…

Mathematical Problem Solving Ability of Eleventh Standard Students

ERIC Educational Resources Information Center

Priya, J. Johnsi

2017-01-01

There is a general assertion among mathematics instructors that learners need to acquire problem solving expertise, figure out how to communicate using mathematics knowledge and aptitude, create numerical reasoning and thinking, to see the interconnectedness amongst mathematics and other subjects. Based on this perspective, the present study aims…

Delivering Online Professional Development in Mathematics to Rural Educators

ERIC Educational Resources Information Center

Cady, Jo; Rearden, Kristin

2009-01-01

Rural school districts struggle to attract, retain, and support highly qualified mathematics teachers. A series of four online professional development courses in the form of integrated mathematics content and pedagogy courses was designed to meet the professional development needs of rural middle school mathematics teachers. Changes in teachers'…

Tracking Developmental Students into Their First College Level Mathematics Course

ERIC Educational Resources Information Center

Waycaster, Pansy

2011-01-01

A recent SACS review at the author's institution prompted an assessment of the school's developmental mathematics program. The author needed to examine the effectiveness of the developmental mathematics courses in preparing students for their first college level mathematics course. Rather than just examine success rates in developmental…

Mathematical Difficulty: Does Early Intervention Enhance Mathematical Performance?

ERIC Educational Resources Information Center

Graham, Jennifer

2008-01-01

The need to ask educators about their opinions on the subject to what extent early intervention methods enhance mathematical performance is long overdue. The purpose of this quantitative research is to examine the extent to which teachers agree that early intervention methods enhance the mathematical performance of students with mathematical…

Mathematics Teaching as Praxis

ERIC Educational Resources Information Center

Grootenboer, Peter; Edwards-Groves, Christine

2014-01-01

In this paper we argue that mathematics teaching can be conceptualised as a form of praxis. Viewing mathematics teaching as praxis foregrounds the moral nature of teaching and the educational practices that are developed in response to the educational needs in particular sites. The case for praxis in mathematics education is then made by drawing…

Effects of Gender-Based Instruction on Fifth Graders' Attitudes toward Mathematics

ERIC Educational Resources Information Center

Oswald, Deborah R.

2009-01-01

Differences in male and female brains may impact the way girls and boys process mathematics and underscores the need for research that examines modification of mathematics instruction according to gender differences. Based in constructivist theory, this mixed-methods study investigated the effect of mathematics instruction modified according to…

Tacit Beginnings Towards a Model of Scientific Thinking

NASA Astrophysics Data System (ADS)

Glass, Rory J.

2013-10-01

The purpose of this paper is to provide an examination of the role tacit knowledge plays in understanding, and to provide a model to make such knowledge identifiable. To do this I first consider the needs of society, the ubiquity of information in our world and the future demands of the science classroom. I propose the use of more implicit or tacit understandings as foundational elements for the development of student knowledge. To justify this proposition I consider a wide range of philosophical and psychological perspectives on knowledge. Then develop a Model of Scientific Knowledge, based in large part on a similar model created by Paul Ernest (Social constructivism as a philosophy of mathematics, SUNY Press, Albany, NY, 1998a; Situated cognition and the learning of mathematics, University of Oxford Department of Educational Studies, Oxford, 1998b). Finally, I consider the work that has been done by those in fields beyond education and the ways in which tacit knowledge can be used as a starting point for knowledge building.

Mathematical modeling of a single stage ultrasonically assisted distillation process.

PubMed

Mahdi, Taha; Ahmad, Arshad; Ripin, Adnan; Abdullah, Tuan Amran Tuan; Nasef, Mohamed M; Ali, Mohamad W

2015-05-01

The ability of sonication phenomena in facilitating separation of azeotropic mixtures presents a promising approach for the development of more intensified and efficient distillation systems than conventional ones. To expedite the much-needed development, a mathematical model of the system based on conservation principles, vapor-liquid equilibrium and sonochemistry was developed in this study. The model that was founded on a single stage vapor-liquid equilibrium system and enhanced with ultrasonic waves was coded using MATLAB simulator and validated with experimental data for ethanol-ethyl acetate mixture. The effects of both ultrasonic frequency and intensity on the relative volatility and azeotropic point were examined, and the optimal conditions were obtained using genetic algorithm. The experimental data validated the model with a reasonable accuracy. The results of this study revealed that the azeotropic point of the mixture can be totally eliminated with the right combination of sonication parameters and this can be utilized in facilitating design efforts towards establishing a workable ultrasonically intensified distillation system. Copyright © 2014 Elsevier B.V. All rights reserved.

Learning to teach upper primary school algebra: changes to teachers' mathematical knowledge for teaching functional thinking

NASA Astrophysics Data System (ADS)

Wilkie, Karina J.

2016-06-01

A key aspect of learning algebra in the middle years of schooling is exploring the functional relationship between two variables: noticing and generalising the relationship, and expressing it mathematically. This article describes research on the professional learning of upper primary school teachers for developing their students' functional thinking through pattern generalisation. This aspect of algebra learning has been explicitly brought to the attention of upper primary teachers in the recently introduced Australian curriculum. Ten practising teachers participated over 1 year in a design-based research project involving a sequence of geometric pattern generalisation lessons with their classes. Initial and final survey responses and teachers' interactions in regular meetings and lessons were analysed from cognitive and situated perspectives on professional learning, using a theoretical model for the different types of knowledge needed for teaching mathematics. The teachers demonstrated an increase in certain aspects of their mathematical knowledge for teaching algebra as well as some residual issues. Implications for the professional learning of practising and pre-service teachers to develop their mathematics knowledge for teaching functional thinking, and challenges with operationalising knowledge categories for field-based research are presented.

On the modelling of gyroplane flight dynamics

NASA Astrophysics Data System (ADS)

Houston, Stewart; Thomson, Douglas

2017-01-01

The study of the gyroplane, with a few exceptions, is largely neglected in the literature which is indicative of a niche configuration limited to the sport and recreational market where resources are limited. However the contemporary needs of an informed population of owners and constructors, as well as the possibility of a wider application of such low-cost rotorcraft in other roles, suggests that an examination of the mathematical modelling requirements for the study of gyroplane flight mechanics is timely. Rotorcraft mathematical modelling has become stratified in three levels, each one defining the inclusion of various layers of complexity added to embrace specific modelling features as well as an attempt to improve fidelity. This paper examines the modelling of gyroplane flight mechanics in the context of this complexity, and shows that relatively simple formulations are adequate for capturing most aspects of gyroplane trim, stability and control characteristics. In particular the conventional 6 degree-of-freedom model structure is suitable for the synthesis of models from flight test data as well as being the framework for reducing the order of the higher levels of modelling. However, a high level of modelling can be required to mimic some aspects of behaviour observed in data gathered from flight experiments and even then can fail to capture other details. These limitations are addressed in the paper. It is concluded that the mathematical modelling of gyroplanes for the simulation and analysis of trim, stability and control presents no special difficulty and the conventional techniques, methods and formulations familiar to the rotary-wing community are directly applicable.

Demographic Profile and Perceived Inset Needs of Secondary Mathematics Teachers in Limpopo Province

ERIC Educational Resources Information Center

Rakumako, Angeline; Laugksch, Rüdiger

2010-01-01

The findings of a study on the demographic profile and perceived INSET needs of secondary Mathematics teachers in Limpopo province are described. The survey instrument employed was the "Science Teacher Inventory of Needs for Limpopo province" ("STIN-LP"). Most teachers who responded to this survey teach at a rural or township…

Effect of mean diameter and polydispersity of PLG microspheres on drug release: experiment and theory.

PubMed

Berchane, N S; Carson, K H; Rice-Ficht, A C; Andrews, M J

2007-06-07

The need to tailor release rate profiles from polymeric microspheres is a significant problem. Microsphere size, which has a significant effect on drug release rate, can potentially be varied to design a controlled drug delivery system with desired release profile. In this work the effects of microspheres mean diameter, polydispersity, and polymer degradation on drug release rate from poly(lactide-co-glycolide) (PLG) microspheres are described. Piroxicam containing PLG microspheres were fabricated at 20% loading, and at three different impeller speeds. A portion of the microspheres was then sieved giving five different size distributions. In vitro release kinetics were determined for each preparation. Based on these experimental results, a suitable mathematical theory has been developed that incorporates the effect of microsphere size distribution and polymer degradation on drug release. We show from in vitro release experiments that microsphere size has a significant effect on drug release rate. The initial release rate decreased with an increase in microsphere size. In addition, the release profile changed from first order to concave-upward (sigmoidal) as the microsphere size was increased. The mathematical model gave a good fit to the experimental release data. For highly polydisperse populations (polydispersity parameter b<3), incorporating the microsphere size distribution into the mathematical model gave a better fit to the experimental results than using the representative mean diameter. The validated mathematical model can be used to predict small-molecule drug release from PLG microsphere populations.

Regression Analysis as a Cost Estimation Model for Unexploded Ordnance Cleanup at Former Military Installations

DTIC Science & Technology

2002-06-01

fits our actual data . To determine the goodness of fit, statisticians typically use the following four measures: R2 Statistic. The R2 statistic...reviewing instruction, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of...mathematical model is developed to better estimate cleanup costs using historical cost data that could be used by the Defense Department prior to placing

Mathematical problems of quantum teleportation

NASA Astrophysics Data System (ADS)

Tanaka, Yoshiharu; Asano, Masanari; Ohya, Masanori

2011-03-01

It has been considered that a maximal entangled state is needed for complete quantum teleportation. However, Kossakowski and Ohya proposed a scheme of complete teleportation for nonmaximal entangled state [1]. Basing on their scheme, we proposed a teleportation model of 2-level state with a non-maximal entangled state [2]. In the present study, we construct its expanded model, in which Alice can teleport m-level state even if non-maximal entangled state is used.

Learning to teach mathematical modelling in secondary and tertiary education

NASA Astrophysics Data System (ADS)

Ferri, Rita Borromeo

2017-07-01

Since 2003 mathematical modelling in Germany is not only a topic for scientific disciplines in university mathematics courses, but also in school starting with primary school. This paper shows what mathematical modelling means in school and how it can be taught as a basis for complex modeling problems in tertiary education.

Development of a Multidisciplinary Middle School Mathematics Infusion Model

ERIC Educational Resources Information Center

Russo, Maria; Hecht, Deborah; Burghardt, M. David; Hacker, Michael; Saxman, Laura

2011-01-01

The National Science Foundation (NSF) funded project "Mathematics, Science, and Technology Partnership" (MSTP) developed a multidisciplinary instructional model for connecting mathematics to science, technology and engineering content areas at the middle school level. Specifically, the model infused mathematics into middle school curriculum…

Frequencies as Proportions: Using a Teaching Model Based on Pirie and Kieren's Model of Mathematical Understanding

ERIC Educational Resources Information Center

Wright, Vince

2014-01-01

Pirie and Kieren (1989 "For the learning of mathematics", 9(3)7-11, 1992 "Journal of Mathematical Behavior", 11, 243-257, 1994a "Educational Studies in Mathematics", 26, 61-86, 1994b "For the Learning of Mathematics":, 14(1)39-43) created a model (P-K) that describes a dynamic and recursive process by which…

Detecting Strengths and Weaknesses in Learning Mathematics through a Model Classifying Mathematical Skills

ERIC Educational Resources Information Center

Karagiannakis, Giannis N.; Baccaglini-Frank, Anna E.; Roussos, Petros

2016-01-01

Through a review of the literature on mathematical learning disabilities (MLD) and low achievement in mathematics (LA) we have proposed a model classifying mathematical skills involved in learning mathematics into four domains (Core number, Memory, Reasoning, and Visual-spatial). In this paper we present a new experimental computer-based battery…

Teaching Mathematical Modeling in Mathematics Education

ERIC Educational Resources Information Center

Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant

2016-01-01

Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…

One Point of View: Elementary School Mathematics Specialists: Where Are They?

ERIC Educational Resources Information Center

Dossey, John A.

1984-01-01

A plea is made for the mathematics education community to support the need for elementary school mathematics specialists. Roles of such specialists in primary as well as intermediate grades are listed. (MNS)

What Is the Difference between a Puzzle and a Maths Question?

ERIC Educational Resources Information Center

Eastaway, Robert

1997-01-01

Discusses the differences between puzzles and mathematics questions. Argues that mathematics teachers need to be thoroughly grounded in the well-documented recreational side of mathematics and be encouraged to use it. (JRH)

Crash Certification by Analysis - Are We There Yet?

NASA Technical Reports Server (NTRS)

Jackson, Karen E.; Fasanella, Edwin L.; Lyle, Karen H.

2006-01-01

This paper addresses the issue of crash certification by analysis. This broad topic encompasses many ancillary issues including model validation procedures, uncertainty in test data and analysis models, probabilistic techniques for test-analysis correlation, verification of the mathematical formulation, and establishment of appropriate qualification requirements. This paper will focus on certification requirements for crashworthiness of military helicopters; capabilities of the current analysis codes used for crash modeling and simulation, including some examples of simulations from the literature to illustrate the current approach to model validation; and future directions needed to achieve "crash certification by analysis."

Teaching Mathematical Modelling for Earth Sciences via Case Studies

NASA Astrophysics Data System (ADS)

Yang, Xin-She

2010-05-01

Mathematical modelling is becoming crucially important for earth sciences because the modelling of complex systems such as geological, geophysical and environmental processes requires mathematical analysis, numerical methods and computer programming. However, a substantial fraction of earth science undergraduates and graduates may not have sufficient skills in mathematical modelling, which is due to either limited mathematical training or lack of appropriate mathematical textbooks for self-study. In this paper, we described a detailed case-study-based approach for teaching mathematical modelling. We illustrate how essential mathematical skills can be developed for students with limited training in secondary mathematics so that they are confident in dealing with real-world mathematical modelling at university level. We have chosen various topics such as Airy isostasy, greenhouse effect, sedimentation and Stokes' flow,free-air and Bouguer gravity, Brownian motion, rain-drop dynamics, impact cratering, heat conduction and cooling of the lithosphere as case studies; and we use these step-by-step case studies to teach exponentials, logarithms, spherical geometry, basic calculus, complex numbers, Fourier transforms, ordinary differential equations, vectors and matrix algebra, partial differential equations, geostatistics and basic numeric methods. Implications for teaching university mathematics for earth scientists for tomorrow's classroom will also be discussed. Refereces 1) D. L. Turcotte and G. Schubert, Geodynamics, 2nd Edition, Cambridge University Press, (2002). 2) X. S. Yang, Introductory Mathematics for Earth Scientists, Dunedin Academic Press, (2009).

Mathematics Literacy on Problem Based Learning with Indonesian Realistic Mathematics Education Approach Assisted E-Learning Edmodo

NASA Astrophysics Data System (ADS)

Wardono; Waluya, S. B.; Mariani, Scolastika; Candra D, S.

2016-02-01

This study aims to find out that there are differences in mathematical literacy ability in content Change and Relationship class VII Junior High School 19, Semarang by Problem Based Learning (PBL) model with an Indonesian Realistic Mathematics Education (called Pendidikan Matematika Realistik Indonesia or PMRI in Indonesia) approach assisted Elearning Edmodo, PBL with a PMRI approach, and expository; to know whether the group of students with learning PBL models with PMRI approach and assisted E-learning Edmodo can improve mathematics literacy; to know that the quality of learning PBL models with a PMRI approach assisted E-learning Edmodo has a good category; to describe the difficulties of students in working the problems of mathematical literacy ability oriented PISA. This research is a mixed methods study. The population was seventh grade students of Junior High School 19, Semarang Indonesia. Sample selection is done by random sampling so that the selected experimental class 1, class 2 and the control experiment. Data collected by the methods of documentation, tests and interviews. From the results of this study showed average mathematics literacy ability of students in the group PBL models with a PMRI approach assisted E-learning Edmodo better than average mathematics literacy ability of students in the group PBL models with a PMRI approach and better than average mathematics literacy ability of students in the expository models; Mathematics literacy ability in the class using the PBL model with a PMRI approach assisted E-learning Edmodo have increased and the improvement of mathematics literacy ability is higher than the improvement of mathematics literacy ability of class that uses the model of PBL learning with PMRI approach and is higher than the improvement of mathematics literacy ability of class that uses the expository models; The quality of learning using PBL models with a PMRI approach assisted E-learning Edmodo have very good category.

Automatic inference of multicellular regulatory networks using informative priors.

PubMed

Sun, Xiaoyun; Hong, Pengyu

2009-01-01

To fully understand the mechanisms governing animal development, computational models and algorithms are needed to enable quantitative studies of the underlying regulatory networks. We developed a mathematical model based on dynamic Bayesian networks to model multicellular regulatory networks that govern cell differentiation processes. A machine-learning method was developed to automatically infer such a model from heterogeneous data. We show that the model inference procedure can be greatly improved by incorporating interaction data across species. The proposed approach was applied to C. elegans vulval induction to reconstruct a model capable of simulating C. elegans vulval induction under 73 different genetic conditions.

A Review of Mathematical Models for Leukemia and Lymphoma

PubMed Central

Clapp, Geoffrey; Levy, Doron

2014-01-01

Recently, there has been significant activity in the mathematical community, aimed at developing quantitative tools for studying leukemia and lymphoma. Mathematical models have been applied to evaluate existing therapies and to suggest novel therapies. This article reviews the recent contributions of mathematical modeling to leukemia and lymphoma research. These developments suggest that mathematical modeling has great potential in this field. Collaboration between mathematicians, clinicians, and experimentalists can significantly improve leukemia and lymphoma therapy. PMID:26744598

A physiome standards-based model publication paradigm.

PubMed

Nickerson, David P; Buist, Martin L

2009-05-28

In this era of widespread broadband Internet penetration and powerful Web browsers on most desktops, a shift in the publication paradigm for physiome-style models is envisaged. No longer will model authors simply submit an essentially textural description of the development and behaviour of their model. Rather, they will submit a complete working implementation of the model encoded and annotated according to the various standards adopted by the physiome project, accompanied by a traditional human-readable summary of the key scientific goals and outcomes of the work. While the final published, peer-reviewed article will look little different to the reader, in this new paradigm, both reviewers and readers will be able to interact with, use and extend the models in ways that are not currently possible. Here, we review recent developments that are laying the foundations for this new model publication paradigm. Initial developments have focused on the publication of mathematical models of cellular electrophysiology, using technology based on a CellML- or Systems Biology Markup Language (SBML)-encoded implementation of the mathematical models. Here, we review the current state of the art and what needs to be done before such a model publication becomes commonplace.

The conceptual basis of mathematics in cardiology: (II). Calculus and differential equations.

PubMed

Bates, Jason H T; Sobel, Burton E

2003-04-01

This is the second in a series of four articles developed for the readers of Coronary Artery Disease. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas. This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to cardiovascular medicine and biology.

The conceptual basis of mathematics in cardiology III: linear systems theory and integral transforms.

PubMed

Bates, Jason H T; Sobel, Burton E

2003-05-01

This is the third in a series of four articles developed for the readers of Coronary Artery Disease. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas.This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to cardiovascular medicine and biology.

The conceptual basis of mathematics in cardiology: (I) algebra, functions and graphs.

PubMed

Bates, Jason H T; Sobel, Burton E

2003-02-01

This is the first in a series of four articles developed for the readers of. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas. This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease, abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to cardiovascular medicine and biology.

Tractable Experiment Design via Mathematical Surrogates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Williams, Brian J.

This presentation summarizes the development and implementation of quantitative design criteria motivated by targeted inference objectives for identifying new, potentially expensive computational or physical experiments. The first application is concerned with estimating features of quantities of interest arising from complex computational models, such as quantiles or failure probabilities. A sequential strategy is proposed for iterative refinement of the importance distributions used to efficiently sample the uncertain inputs to the computational model. In the second application, effective use of mathematical surrogates is investigated to help alleviate the analytical and numerical intractability often associated with Bayesian experiment design. This approach allows formore » the incorporation of prior information into the design process without the need for gross simplification of the design criterion. Illustrative examples of both design problems will be presented as an argument for the relevance of these research problems.« less

Endoscope shaft-rigidity control mechanism: "FORGUIDE".

PubMed

Loeve, Arjo J; Plettenburg, Dick H; Breedveld, Paul; Dankelman, Jenny

2012-02-01

Recent developments in flexible endoscopy and other fields of medical technology have raised the need for compact slender shafts that can be made rigid and compliant at will. A novel compact mechanism, named FORGUIDE, with this functionality was developed. The FORGUIDE shaft rigidifies due to friction between a ring of cables situated between a spring and an inflated tube. A mathematical model for the FORGUIDE mechanism working principle was made and used to obtain understanding of this mechanism, predict the maximum rigidity of a FORGUIDE shaft design, and tune its design variables. The mathematical model gave suggestions for significant performance improvement by fine-tuning the design. A prototype FORGUIDE shaft was built and put to a series of bench tests. These tests showed that the FORGUIDE mechanism provides a reliable and simple way to control the rigidity of a flexible shaft. © 2011 IEEE

Rigorous Mathematical Thinking Approach to Enhance Students’ Mathematical Creative and Critical Thinking Abilities

NASA Astrophysics Data System (ADS)

Hidayat, D.; Nurlaelah, E.; Dahlan, J. A.

2017-09-01

The ability of mathematical creative and critical thinking are two abilities that need to be developed in the learning of mathematics. Therefore, efforts need to be made in the design of learning that is capable of developing both capabilities. The purpose of this research is to examine the mathematical creative and critical thinking ability of students who get rigorous mathematical thinking (RMT) approach and students who get expository approach. This research was quasi experiment with control group pretest-posttest design. The population were all of students grade 11th in one of the senior high school in Bandung. The result showed that: the achievement of mathematical creative and critical thinking abilities of student who obtain RMT is better than students who obtain expository approach. The use of Psychological tools and mediation with criteria of intentionality, reciprocity, and mediated of meaning on RMT helps students in developing condition in critical and creative processes. This achievement contributes to the development of integrated learning design on students’ critical and creative thinking processes.

Preservice Secondary Teachers' Conceptions from a Mathematical Modeling Activity and Connections to the Common Core State Standards

ERIC Educational Resources Information Center

Stohlmann, Micah; Maiorca, Cathrine; Olson, Travis A.

2015-01-01

Mathematical modeling is an essential integrated piece of the Common Core State Standards. However, researchers have shown that mathematical modeling activities can be difficult for teachers to implement. Teachers are more likely to implement mathematical modeling activities if they have their own successful experiences with such activities. This…

Investigating and Developing Engineering Students' Mathematical Modelling and Problem-Solving Skills

ERIC Educational Resources Information Center

Wedelin, Dag; Adawi, Tom; Jahan, Tabassum; Andersson, Sven

2015-01-01

How do engineering students approach mathematical modelling problems and how can they learn to deal with such problems? In the context of a course in mathematical modelling and problem solving, and using a qualitative case study approach, we found that the students had little prior experience of mathematical modelling. They were also inexperienced…

Mathematical-Artificial Neural Network Hybrid Model to Predict Roll Force during Hot Rolling of Steel

NASA Astrophysics Data System (ADS)

Rath, S.; Sengupta, P. P.; Singh, A. P.; Marik, A. K.; Talukdar, P.

2013-07-01

Accurate prediction of roll force during hot strip rolling is essential for model based operation of hot strip mills. Traditionally, mathematical models based on theory of plastic deformation have been used for prediction of roll force. In the last decade, data driven models like artificial neural network have been tried for prediction of roll force. Pure mathematical models have accuracy limitations whereas data driven models have difficulty in convergence when applied to industrial conditions. Hybrid models by integrating the traditional mathematical formulations and data driven methods are being developed in different parts of world. This paper discusses the methodology of development of an innovative hybrid mathematical-artificial neural network model. In mathematical model, the most important factor influencing accuracy is flow stress of steel. Coefficients of standard flow stress equation, calculated by parameter estimation technique, have been used in the model. The hybrid model has been trained and validated with input and output data collected from finishing stands of Hot Strip Mill, Bokaro Steel Plant, India. It has been found that the model accuracy has been improved with use of hybrid model, over the traditional mathematical model.

Mathematics in Early Childhood: Research-Based Rationale and Practical Strategies

ERIC Educational Resources Information Center

Linder, Sandra M.; Powers-Costello, Beth; Stegelin, Dolores A.

2011-01-01

Mathematics education is a critical part of the curriculum for students worldwide. The foundation for understanding mathematical concepts related to number sense begins early in life, and early childhood classrooms can provide the seeds for mathematical skills that will be needed later in life. In this article, the authors make a case for…

An Ideology Critique of the Use-Value of Mathematics

ERIC Educational Resources Information Center

Pais, Alexandre

2013-01-01

The idea that mathematics is needed for our mundane everyday activities has raised the question of how people deal with mathematics outside the school walls. Much has been written in mathematics education research about the possibility of transferring knowledge from and into school. Whereas the majority of this literature commends the possibility…

eText, Mathematics, and Students with Visual Impairments: "What Teachers Need to Know"

ERIC Educational Resources Information Center

Bouck, Emily C.; Meyer, Nancy K.

2012-01-01

Mathematics is an important educational component for students with visual impairments, and technology to support the access to and success of students with visual impairments in mathematics is essential. However, little research exists. This particular paper explores one aspect of technology and mathematics education for students with visual…

National Mathematics Advisory Panel Reports of the Task Groups and Subcommittees

ERIC Educational Resources Information Center

US Department of Education, 2008

2008-01-01

For students to compete in the 21st-century global economy, knowledge of and proficiency in mathematics are critical. Whether headed to college or to the workforce, today's high school graduates need solid mathematics skill. The National Mathematics Advisory Panel was created in 2006 and charged with reviewing the best available scientific…

Observing and Analyzing Children's Mathematical Development, Based on Action Theory

ERIC Educational Resources Information Center

Bunck, M. J. A.; Terlien, E.; van Groenestijn, M.; Toll, S. W. M.; Van Luit, J. E. H.

2017-01-01

Children who experience difficulties with learning mathematics should be taught by teachers who focus on the child's best way of learning. Analyses of the mathematical difficulties are necessary for fine-tuning mathematics education to the needs of these children. For this reason, an instrument for Observing and Analyzing children's Mathematical…

Motivating Prospective Elementary School Teachers to Learn Mathematics by Focusing upon Children's Mathematical Thinking

ERIC Educational Resources Information Center

Philipp, Randolph A.

2008-01-01

Elementary school children in the United States are not developing acceptable levels of mathematical proficiency (National Center for Education Statistics, 1999), and a major concern of teacher educators is that teachers lack the depth and flexibility of mathematical understanding and the corresponding beliefs they need to teach for proficiency…

SEVENTH GRADE MATHEMATICS FOR THE ACADEMICALLY TALENTED, TEACHERS' GUIDE.

ERIC Educational Resources Information Center

HORN, R.A.

MATERIALS FOR BOTH ENRICHED AND ACCELERATED MATHEMATICS COURSES ARE GIVEN. THE PRESENTATION OF THE MATERIALS IS INTENDED FOR EASY ADAPTATION OF MODIFICATION TO MEET THE NEEDS OF MOST MATHEMATICS CLASSES. SUGGESTIONS AND SUPPLEMENTARY REFERENCES IN EACH UNIT ARE OFFERED AS AIDS TO THE MATHEMATICS TEACHER IN REGULAR OR ACCELERATED CLASS. UNITS…

Parent-Child Mathematical Interactions: Examining Self-Report and Direct Observation

ERIC Educational Resources Information Center

Missall, Kristen N.; Hojnoski, Robin L.; Moreano, Ginna

2017-01-01

Variability in children's early-learning home environments points to the need to better understand specific mechanisms of early mathematical development. We used a sample of 66 parent-preschool child dyads to describe parent-reported mathematical activities in the home and observed parent-child mathematical activities in a semi-structured play…

The Effects of Teacher Collaboration in Grade 9 Applied Mathematics

ERIC Educational Resources Information Center

Egodawatte, Gunawardena; McDougall, Douglas; Stoilescu, Dorian

2011-01-01

The current emphasis of many mathematics education reform documents is on the need to change the environment of mathematics classrooms from the transmission of knowledge by the teacher to the transaction of knowledge between the teacher and the students which promotes mathematical investigation and exploration. In this article, we discuss the…

Using Five-Frames in Preschool Mathematics Instruction

ERIC Educational Resources Information Center

Rizer, Jennifer

2017-01-01

Mathematics education is a critical part of instruction for students around the globe. The foundation for understanding basic mathematical concepts begins early in life. Preschool classrooms can provide the early skills in mathematical reasoning that will be needed later in life. In this study, the author sought to determine if the use of…

An Introduction to Equilibrium Thermodynamics: A Rational Approach to Its Teaching. Part 1: Notation and Mathematics.

ERIC Educational Resources Information Center

Williams, Donald F.; Glasser, David

1991-01-01

Introduces and develops mathematical notation to assist undergraduate students in overcoming conceptual difficulties involving the underlying mathematics of state functions, which tend to be different from functions encountered by students in previous mathematical courses, because of the need to manipulate special types of partial derivatives and…

Primary Teachers Notice the Impact of Language on Children's Mathematical Reasoning

ERIC Educational Resources Information Center

Bragg, Leicha A.; Herbert, Sandra; Loong, Esther Yoon-Kin; Vale, Colleen; Widjaja, Wanty

2016-01-01

Mathematical reasoning is now featured in the mathematics curriculum documents of many nations, but this necessitates changes to teaching practice and hence a need for professional learning. The development of children's mathematical reasoning requires appropriate encouragement and feedback from their teacher who can only do this if they recognise…

The Construction of Deductive Warrant Derived from Inductive Warrant in Preservice-Teacher Mathematical Argumentations

ERIC Educational Resources Information Center

Tristanti, Lia Budi; Sutawidjaja, Akbar; As'ari, Abdur Rahman; Muskar, Makbul

2016-01-01

This study discusses the construction of deductive warrant derived from inductive warrant in mathematical argumentations expressed by pre-service teacher. In completing a mathematics task, a problem solver needs argumentation to determine, reveal, and support a reasonable solution. A mathematical argumentation can be analyzed by Toulmin scheme…

The Effects of STEM PBL on Students' Mathematical and Scientific Vocabulary Knowledge

ERIC Educational Resources Information Center

Bilgin, Ali; Boedeker, Peter; Capraro, Robert M.; Capraro, Mary M.

2015-01-01

Vocabulary is at the surface level of language usage; thus, students need to develop mathematical and scientific vocabulary to be able to explicitly communicate their mathematical and scientific reasoning with others. The National Council of Teachers of Mathematics (NCTM) and the National Science Teachers Association (NSTA) have both created…

Mathematics education and students with learning disabilities: introduction to the special series.

PubMed

Rivera, D P

1997-01-01

The prevalence of students with mathematics learning disabilities has triggered an interest among special education researchers and practitioners in developing an understanding of the needs of this group of students, and in identifying effective instructional programming to foster their mathematical performance during the school years and into adulthood. Research into the characteristics of students with mathematics learning disabilities is being approached from different perspectives, including developmental, neurological and neuropsychological, and educational. This diversity helps us develop a broader understanding of students' learning needs and difficulties. Special education assessment practices encompass a variety of approaches, including norm-referenced, criterion-referenced, and nonstandardized procedures, depending on the specific assessment questions professionals seek to answer. Students' mathematical knowledge and conceptual understanding must be examined to determine their strengths and weaknesses, curriculum-based progress, and use of cognitive strategies to arrive at mathematical solutions. Research findings have identified empirically validated interventions for teaching mathematics curricula to students with mathematics learning disabilities. Research studies have been grounded in behavioral theory and cognitive psychology, with an emergent interest in the constructivist approach. Although research studies have focused primarily on computational performance, more work is being conducted in the areas of story-problem solving and technology. These areas as well as other math curricular skills require further study. Additionally, the needs of adults with math LD have spurred educators to examine the elementary and secondary math curricula and determine ways to infuse them with life skills instruction accordingly. As the field of mathematics special education continues to evolve, special educators must remain cognizant of the developments in and influences on the field of mathematics education. Reform efforts have shaped the field significantly since the 1950s, contributing to the curriculum offered in mathematics textbooks and the pedagogical practices taught in higher education courses. Mathematics educators continue to search for a better understanding of how children learn mathematics; this process is shaped by the prevailing theoretical orientations and research methodologies. This special series in mathematics special education provides readers with information about the characteristics of students with mathematics learning disabilities, assessment procedures, mathematics programming, teacher preparation, and future directions for the field. The series originated as a result of discussions with Dr. Lee Wiederholt and Dr. Judith K. Voress, who saw a need for the compilation of recent research and best practices in mathematics special education. I thank them for their support of and thoughtful insights about the development of this series. I also appreciate the support of Dr. George Hynd and his editorial assistant, Kathryn Black, in finalizing the details for publication. Finally, I am most appreciative of the authors' contributions to this series; their work continues to significantly influence the development of the field of mathematics special education and programming for students with mathematics learning disabilities.

Formation and Representation: Critical Analyses of Identity, Supply, and Demand in Science, Technology, Engineering, and Mathematics

ERIC Educational Resources Information Center

Metcalf, Heather E.

2011-01-01

Considerable research, policy, and programmatic efforts have been dedicated to addressing the participation of particular populations in STEM for decades. Each of these efforts claims equity-related goals; yet, they heavily frame the problem, through pervasive STEM pipeline model discourse, in terms of national needs, workforce supply, and…

In-Situ Optical Imaging of Carrier Transport in Multilayer Solar Cells

DTIC Science & Technology

2008-06-01

5 1. Efficiency Considerations....................................................... 5 2. Construction...improved efficiency solar cells. The need to move forward on these improvements is driven by the increasing price of oil and other traditional fuels...any improvement in material in a high efficiency multi-junction cell can be difficult to mathematically model, and much effort is involved in

Supercomputers Of The Future

NASA Technical Reports Server (NTRS)

Peterson, Victor L.; Kim, John; Holst, Terry L.; Deiwert, George S.; Cooper, David M.; Watson, Andrew B.; Bailey, F. Ron

1992-01-01

Report evaluates supercomputer needs of five key disciplines: turbulence physics, aerodynamics, aerothermodynamics, chemistry, and mathematical modeling of human vision. Predicts these fields will require computer speed greater than 10(Sup 18) floating-point operations per second (FLOP's) and memory capacity greater than 10(Sup 15) words. Also, new parallel computer architectures and new structured numerical methods will make necessary speed and capacity available.

A Long-Term Model for the Curriculum of Training for an Electric-Power Specialist

ERIC Educational Resources Information Center

Venikov, V. A.

1978-01-01

Long-term planning for professional training of electric-power specialists in Russia will have to (1) recognize the need for specialists to adapt to unforeseen developments in the field, (2) include new mathematics, physics, and computer technology, and (3) be prepared for changes in methods of production and transformation of energy. (AV)

Exploring a Professional Development Model for Teaching Culturally Relevant Mathematics

ERIC Educational Resources Information Center

Campeau, Rebecca K.

2013-01-01

An area of concern for school district administrators is the lack of training that teachers have using culturally relevant pedagogy (CRP). A lack of training may reduce a teacher's effectiveness in meeting the needs of non-White students. Obstacles to attending trainings include the beliefs and attitudes of teachers and the relevance of training…

A Model for Task Design with Focus on Exploration, Explanation, and Generalization in a Dynamic Geometry Environment

ERIC Educational Resources Information Center

Fahlgren, Maria; Brunström, Mats

2014-01-01

The increasing availability of new technologies in schools provides new possibilities for the integration of technology in mathematics education. However, research has shown that there is a need for new kinds of task that utilize the affordances provided by new technology. Numerous studies have demonstrated that dynamic geometry environments…

The Texas Projection Measure: Ignoring Complex Ecologies in a Changing World

ERIC Educational Resources Information Center

Roane, Warren

2010-01-01

The Texas Projection Measure (TPM) has grown out of the state's need to meet the requirements of No Child Left Behind (NCLB). An examination of the state's method of predicting 8th grade mathematics scores reveals that several factors have been ignored in the process of developing the model, including assumptions in its underlying statistical…

NASA Office of Aeronautics and Space Technology Summer Workshop. Volume 9: Entry technology panel

NASA Technical Reports Server (NTRS)

1975-01-01

An advanced space transportation system heavy lift orbiter, hypersonic atmospheric entry missions, development of an emergency astronaut life boat, and basic research in boundary layer transition are among the topics discussed. Emphasis is placed on the need for space testing and for better mathematical models describing the flow fields around complex structures.

Mathematical modeling the cross-contamination of food pathogens on the surface of ready-to-eat meats while slicing

USDA-ARS?s Scientific Manuscript database

The knowledge regarding food pathogens (Listeria monocytogenes, Escherichia coli O157:H7 and Salmonella spp.) surface transfer on ready-to-eat (RTE) deli meat and the slicer used for slicing different RTE products are needed to ensure RTE food safety. The objectives of this study were to investigat...

Business Partnerships to Advance STEM Education: A Model of Success for the Nation

ERIC Educational Resources Information Center

Diaz-Rubio, Ivette

2013-01-01

In order to best prepare the U.S. workforce, schools need to focus on science, technology, engineering, and mathematics (STEM) education. However, given the current educational climate of reduced school funding, high teacher turnover, and increasing student diversity, the public school system simply cannot do this alone. This is where businesses…

Competences of Mathematical Modelling of High School Students

ERIC Educational Resources Information Center

Sekerak, Josef

2010-01-01

Thanks to technological progress the world becomes more and more complicated. People stand in front of new and difficult problems that need to be solved. These are problems, the solutions of which are not universal, and cannot be learned. Many solutions require specific data that cannot be learned, as new data is part of the ongoing generation of…

Uncertainty and variability in computational and mathematical models of cardiac physiology.

PubMed

Mirams, Gary R; Pathmanathan, Pras; Gray, Richard A; Challenor, Peter; Clayton, Richard H

2016-12-01

Mathematical and computational models of cardiac physiology have been an integral component of cardiac electrophysiology since its inception, and are collectively known as the Cardiac Physiome. We identify and classify the numerous sources of variability and uncertainty in model formulation, parameters and other inputs that arise from both natural variation in experimental data and lack of knowledge. The impact of uncertainty on the outputs of Cardiac Physiome models is not well understood, and this limits their utility as clinical tools. We argue that incorporating variability and uncertainty should be a high priority for the future of the Cardiac Physiome. We suggest investigating the adoption of approaches developed in other areas of science and engineering while recognising unique challenges for the Cardiac Physiome; it is likely that novel methods will be necessary that require engagement with the mathematics and statistics community. The Cardiac Physiome effort is one of the most mature and successful applications of mathematical and computational modelling for describing and advancing the understanding of physiology. After five decades of development, physiological cardiac models are poised to realise the promise of translational research via clinical applications such as drug development and patient-specific approaches as well as ablation, cardiac resynchronisation and contractility modulation therapies. For models to be included as a vital component of the decision process in safety-critical applications, rigorous assessment of model credibility will be required. This White Paper describes one aspect of this process by identifying and classifying sources of variability and uncertainty in models as well as their implications for the application and development of cardiac models. We stress the need to understand and quantify the sources of variability and uncertainty in model inputs, and the impact of model structure and complexity and their consequences for predictive model outputs. We propose that the future of the Cardiac Physiome should include a probabilistic approach to quantify the relationship of variability and uncertainty of model inputs and outputs. © 2016 The Authors. The Journal of Physiology published by John Wiley & Sons Ltd on behalf of The Physiological Society.

Transmission Dinamics Model Of Dengue Fever

NASA Astrophysics Data System (ADS)

Debora; Rendy; Rahmi

2018-01-01

Dengue fever is an endemic disease that is transmitted through the Aedes aegypti mosquito vector. The disease is present in more than 100 countries in America, Africa, and Asia, especially tropical countries. Differential equations can be used to represent the spread of dengue virus occurring in time intervals and model in the form of mathematical models. The mathematical model in this study tries to represent the spread of dengue fever based on the data obtained and the assumptions used. The mathematical model used is a mathematical model consisting of Susceptible (S), Infected (I), Viruses (V) subpopulations. The SIV mathematical model is then analyzed to see the solution behaviour of the system.

Mathematical Modeling: Convoying Merchant Ships

ERIC Educational Resources Information Center

Mathews, Susann M.

2004-01-01

This article describes a mathematical model that connects mathematics with social studies. Students use mathematics to model independent versus convoyed ship deployments and sinkings to determine if the British should have convoyed their merchant ships during World War I. During the war, the British admiralty opposed sending merchant ships grouped…

Making the Most of Modeling Tasks

ERIC Educational Resources Information Center

Wernet, Jamie L.; Lawrence, Kevin A.; Gilbertson, Nicholas J.

2015-01-01

While there is disagreement among mathematics educators about some aspects of its meaning, mathematical modeling generally involves taking a real-world scenario and translating it into the mathematical world (Niss, Blum, and Galbraith 2007). The complete modeling process involves describing situations posed in problems with mathematical concepts,…

Dependence of the Firearm-Related Homicide Rate on Gun Availability: A Mathematical Analysis

PubMed Central

Wodarz, Dominik; Komarova, Natalia L.

2013-01-01

In the USA, the relationship between the legal availability of guns and the firearm-related homicide rate has been debated. It has been argued that unrestricted gun availability promotes the occurrence of firearm-induced homicides. It has also been pointed out that gun possession can protect potential victims when attacked. This paper provides a first mathematical analysis of this tradeoff, with the goal to steer the debate towards arguing about assumptions, statistics, and scientific methods. The model is based on a set of clearly defined assumptions, which are supported by available statistical data, and is formulated axiomatically such that results do not depend on arbitrary mathematical expressions. According to this framework, two alternative scenarios can minimize the gun-related homicide rate: a ban of private firearms possession, or a policy allowing the general population to carry guns. Importantly, the model identifies the crucial parameters that determine which policy minimizes the death rate, and thus serves as a guide for the design of future epidemiological studies. The parameters that need to be measured include the fraction of offenders that illegally possess a gun, the degree of protection provided by gun ownership, and the fraction of the population who take up their right to own a gun and carry it when attacked. Limited data available in the literature were used to demonstrate how the model can be parameterized, and this preliminary analysis suggests that a ban of private firearm possession, or possibly a partial reduction in gun availability, might lower the rate of firearm-induced homicides. This, however, should not be seen as a policy recommendation, due to the limited data available to inform and parameterize the model. However, the model clearly defines what needs to be measured, and provides a basis for a scientific discussion about assumptions and data. PMID:23923062

Computational models for the study of heart-lung interactions in mammals.

PubMed

Ben-Tal, Alona

2012-01-01

The operation and regulation of the lungs and the heart are closely related. This is evident when examining the anatomy within the thorax cavity, in the brainstem and in the aortic and carotid arteries where chemoreceptors and baroreceptors, which provide feedback affecting the regulation of both organs, are concentrated. This is also evident in phenomena such as respiratory sinus arrhythmia where the heart rate increases during inspiration and decreases during expiration, in other types of synchronization between the heart and the lungs known as cardioventilatory coupling and in the association between heart failure and sleep apnea where breathing is interrupted periodically by periods of no-breathing. The full implication and physiological significance of the cardiorespiratory coupling under normal, pathological, or extreme physiological conditions are still unknown and are subject to ongoing investigation both experimentally and theoretically using mathematical models. This article reviews mathematical models that take heart-lung interactions into account. The main ideas behind low dimensional, phenomenological models for the study of the heart-lung synchronization and sleep apnea are described first. Higher dimensions, physiology-based models are described next. These models can vary widely in detail and scope and are characterized by the way the heart-lung interaction is taken into account: via gas exchange, via the central nervous system, via the mechanical interactions, and via time delays. The article emphasizes the need for the integration of the different sources of heart-lung coupling as well as the different mathematical approaches. Copyright © 2011 Wiley Periodicals, Inc.

An improved version of the consequence analysis model for chemical emergencies, ESCAPE

NASA Astrophysics Data System (ADS)

Kukkonen, J.; Nikmo, J.; Riikonen, K.

2017-02-01

We present a refined version of a mathematical model called ESCAPE, "Expert System for Consequence Analysis and Preparing for Emergencies". The model has been designed for evaluating the releases of toxic and flammable gases into the atmosphere, their atmospheric dispersion and the effects on humans and the environment. We describe (i) the mathematical treatments of this model, (ii) a verification and evaluation of the model against selected experimental field data, and (iii) a new operational implementation of the model. The new mathematical treatments include state-of-the-art atmospheric vertical profiles and new submodels for dense gas and passive atmospheric dispersion. The model performance was first successfully verified using the data of the Thorney Island campaign, and then evaluated against the Desert Tortoise campaign. For the latter campaign, the geometric mean bias was 1.72 (this corresponds to an underprediction of approximately 70%) and 0.71 (overprediction of approximately 30%) for the concentration and the plume half-width, respectively. The geometric variance was <1.5 (this corresponds to an agreement that is better than a factor of two). These values can be considered to indicate a good agreement of predictions and data, in comparison to values evaluated for a range of other similar models. The model has also been adapted to be able to automatically use the real time predictions and forecasts of the numerical weather prediction model HIRLAM, "HIgh Resolution Limited Area Model". The operational implementation of the ESCAPE modelling system can be accessed anywhere using internet browsers, on laptop computers, tablets and mobile phones. The predicted results can be post-processed using geographic information systems. The model has already proved to be a useful tool of assessment for the needs of emergency response authorities in contingency planning.

Improving mathematical problem solving ability through problem-based learning and authentic assessment for the students of Bali State Polytechnic

NASA Astrophysics Data System (ADS)

Darma, I. K.

2018-01-01

This research is aimed at determining: 1) the differences of mathematical problem solving ability between the students facilitated with problem-based learning model and conventional learning model, 2) the differences of mathematical problem solving ability between the students facilitated with authentic and conventional assessment model, and 3) interaction effect between learning and assessment model on mathematical problem solving. The research was conducted in Bali State Polytechnic, using the 2x2 experiment factorial design. The samples of this research were 110 students. The data were collected using a theoretically and empirically-validated test. Instruments were validated by using Aiken’s approach of technique content validity and item analysis, and then analyzed using anova stylistic. The result of the analysis shows that the students facilitated with problem-based learning and authentic assessment models get the highest score average compared to the other students, both in the concept understanding and mathematical problem solving. The result of hypothesis test shows that, significantly: 1) there is difference of mathematical problem solving ability between the students facilitated with problem-based learning model and conventional learning model, 2) there is difference of mathematical problem solving ability between the students facilitated with authentic assessment model and conventional assessment model, and 3) there is interaction effect between learning model and assessment model on mathematical problem solving. In order to improve the effectiveness of mathematics learning, collaboration between problem-based learning model and authentic assessment model can be considered as one of learning models in class.

Influence of Problem-Based Learning Model of Learning to the Mathematical Communication Ability of Students of Grade XI IPA SMAN 14 Padang

NASA Astrophysics Data System (ADS)

Nisa, I. M.

2018-04-01

The ability of mathematical communication is one of the goals of learning mathematics expected to be mastered by students. However, reality in the field found that the ability of mathematical communication the students of grade XI IPA SMA Negeri 14 Padang have not developed optimally. This is evident from the low test results of communication skills mathematically done. One of the factors that causes this happens is learning that has not been fully able to facilitate students to develop mathematical communication skills well. By therefore, to improve students' mathematical communication skills required a model in the learning activities. One of the models learning that can be used is Problem Based learning model Learning (PBL). The purpose of this study is to see whether the ability the students' mathematical communication using the PBL model better than the students' mathematical communication skills of the learning using conventional learning in Class XI IPA SMAN 14 Padang. This research type is quasi experiment with design Randomized Group Only Design. Population in this research that is student of class XI IPA SMAN 14 Padang with sample class XI IPA 3 and class XI IPA 4. Data retrieval is done by using communication skill test mathematically shaped essay. To test the hypothesis used U-Mann test Whitney. Based on the results of data analysis, it can be concluded that the ability mathematical communication of students whose learning apply more PBL model better than the students' mathematical communication skills of their learning apply conventional learning in class XI IPA SMA 14 Padang at α = 0.05. This indicates that the PBL learning model effect on students' mathematical communication ability.

The Real and the Mathematical in Quantum Modeling: From Principles to Models and from Models to Principles

NASA Astrophysics Data System (ADS)

Plotnitsky, Arkady

2017-06-01

The history of mathematical modeling outside physics has been dominated by the use of classical mathematical models, C-models, primarily those of a probabilistic or statistical nature. More recently, however, quantum mathematical models, Q-models, based in the mathematical formalism of quantum theory have become more prominent in psychology, economics, and decision science. The use of Q-models in these fields remains controversial, in part because it is not entirely clear whether Q-models are necessary for dealing with the phenomena in question or whether C-models would still suffice. My aim, however, is not to assess the necessity of Q-models in these fields, but instead to reflect on what the possible applicability of Q-models may tell us about the corresponding phenomena there, vis-à-vis quantum phenomena in physics. In order to do so, I shall first discuss the key reasons for the use of Q-models in physics. In particular, I shall examine the fundamental principles that led to the development of quantum mechanics. Then I shall consider a possible role of similar principles in using Q-models outside physics. Psychology, economics, and decision science borrow already available Q-models from quantum theory, rather than derive them from their own internal principles, while quantum mechanics was derived from such principles, because there was no readily available mathematical model to handle quantum phenomena, although the mathematics ultimately used in quantum did in fact exist then. I shall argue, however, that the principle perspective on mathematical modeling outside physics might help us to understand better the role of Q-models in these fields and possibly to envision new models, conceptually analogous to but mathematically different from those of quantum theory, helpful or even necessary there or in physics itself. I shall suggest one possible type of such models, singularized probabilistic, SP, models, some of which are time-dependent, TDSP-models. The necessity of using such models may change the nature of mathematical modeling in science and, thus, the nature of science, as it happened in the case of Q-models, which not only led to a revolutionary transformation of physics but also opened new possibilities for scientific thinking and mathematical modeling beyond physics.

A Primer for Mathematical Modeling

ERIC Educational Resources Information Center

Sole, Marla

2013-01-01

With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school…

Strategies to Support Students' Mathematical Modeling

ERIC Educational Resources Information Center

Jung, Hyunyi

2015-01-01

An important question for mathematics teachers is this: "How can we help students learn mathematics to solve everyday problems, rather than teaching them only to memorize rules and practice mathematical procedures?" Teaching students using modeling activities can help them learn mathematics in real-world problem-solving situations that…

Mathematical Modeling in the High School Curriculum

ERIC Educational Resources Information Center

Hernández, Maria L.; Levy, Rachel; Felton-Koestler, Mathew D.; Zbiek, Rose Mary

2016-01-01

In 2015, mathematics leaders and instructors from the Society for Industrial and Applied Mathematics (SIAM) and the Consortium for Mathematics and Its Applications (COMAP), with input from NCTM, came together to write the "Guidelines for Assessment and Instruction in Mathematical Modeling Education" (GAIMME) report as a resource for…

Systematic Assessment Through Mathematical Model For Sustainability Reporting In Malaysia Context

NASA Astrophysics Data System (ADS)

Lanang, Wan Nurul Syahirah Wan; Turan, Faiz Mohd; Johan, Kartina

2017-08-01

Sustainability assessment have been studied and increasingly recognized as a powerful and valuable tool to measure the performance of sustainability in a company or industry. Nowadays, there are many existing tools that the users can use for sustainable development. There are various initiatives exists on tools for sustainable development, though most of the tools focused on environmental, economy and social aspects. Using the Green Project Management (GPM) P5 concept that suggests the firms not only needs to engage in mainly 3Ps principle: planet, profit, people responsible behaviours, but also, product and process need to be included in the practices, this study will introduce a new mathematical model for assessing the level of sustainability practice in the company. Based on multiple case studies, involving in-depth interviews with senior directors, feedback from experts, and previous engineering report, a systematic approach is done with the aims to obtain the respective data from the feedbacks and to be developed into a new mathematical model. By reviewing on the methodology of this research it comprises of several phases where it starts with the analyzation of the parameters and criteria selection according to the Malaysian context of industry. Moving on to the next step is data analysis involving regression and finally the normalisation process will be done to determine the result of this research either succeeded or not. Lastly, this study is expected to provide a clear guideline to any company or organization to assimilate the sustainability assessment in their development stage. In future, the better understanding towards the sustainability assessment is attained to be aligned unitedly in order to integrated the process approach into the systematic approach for the sustainability assessment.

The mechanical properties of stored red blood cells measured by a convenient microfluidic approach combining with mathematic model.

PubMed

Wang, Ying; You, Guoxing; Chen, Peipei; Li, Jianjun; Chen, Gan; Wang, Bo; Li, Penglong; Han, Dong; Zhou, Hong; Zhao, Lian

2016-03-01

The mechanical properties of red blood cells (RBCs) are critical to the rheological and hemodynamic behavior of blood. Although measurements of the mechanical properties of RBCs have been studied for many years, the existing methods, such as ektacytometry, micropipette aspiration, and microfluidic approaches, still have limitations. Mechanical changes to RBCs during storage play an important role in transfusions, and so need to be evaluated pre-transfusion, which demands a convenient and rapid detection method. We present a microfluidic approach that focuses on the mechanical properties of single cell under physiological shear flow and does not require any high-end equipment, like a high-speed camera. Using this method, the images of stretched RBCs under physical shear can be obtained. The subsequent analysis, combined with mathematic models, gives the deformability distribution, the morphology distribution, the normalized curvature, and the Young's modulus (E) of the stored RBCs. The deformability index and the morphology distribution show that the deformability of RBCs decreases significantly with storage time. The normalized curvature, which is defined as the curvature of the cell tail during stretching in flow, suggests that the surface charge of the stored RBCs decreases significantly. According to the mathematic model, which derives from the relation between shear stress and the adherent cells' extension ratio, the Young's moduli of the stored RBCs are also calculated and show significant increase with storage. Therefore, the present method is capable of representing the mechanical properties and can distinguish the mechanical changes of the RBCs during storage. The advantages of this method are the small sample needed, high-throughput, and easy-use, which make it promising for the quality monitoring of RBCs.

The Effect of Instruction through Mathematical Modelling on Modelling Skills of Prospective Elementary Mathematics Teachers

ERIC Educational Resources Information Center

Ciltas, Alper; Isik, Ahmet

2013-01-01

The aim of this study was to examine the modelling skills of prospective elementary mathematics teachers who were studying the mathematical modelling method. The research study group was composed of 35 prospective teachers. The exploratory case analysis method was used in the study. The data were obtained via semi-structured interviews and a…

Conference Board of the Mathematical Sciences Newsletter, Volume 7 Number 4.

ERIC Educational Resources Information Center

Botts, Truman, Ed.

Among the articles in this newsletter are three concerned with the decrease in federal funding of the mathematical sciences. A review of a report, Information Needs in the Mathematical Sciences, is provided in another article. (DT)

Effects of the Connected Mathematics Project 2 (CMP2) on the Mathematics Achievement of Grade 6 Students in the Mid-Atlantic Region. Final Report. NCEE 2012-4017

ERIC Educational Resources Information Center

Martin, Taylor; Brasiel, Sarah J.; Turner, Herb; Wise, John C.

2012-01-01

This study examines the effects of Connected Mathematics Project 2 (CMP2) on grade 6 student mathematics achievement and engagement using a cluster randomized controlled trial (RCT) design. It responds to a need to improve mathematics learning in the Mid-Atlantic Region (Delaware, Maryland, New Jersey, Pennsylvania, and Washington, DC). Findings…

Manipulatives Implementation For Supporting Learning Of Mathematics For Prospective Teachers

NASA Astrophysics Data System (ADS)

Sulistyaningsih, D.; Mawarsari, V. D.; Hidayah, I.; Dwijanto

2017-04-01

Manipulatives are needed by teachers to facilitate students understand of mathematics which is abstract. As a prospective mathematics teacher, the student must have good skills in making manipulatives. Aims of this study is to describe the implementation of learning courses of manipulative workshop in mathematics education courses by lecturer at Universitas Muhammadiyah Semarang which includes the preparation of learning, general professional ability, the professional capacity specifically, ability of self-development, development class managing, planning and implementation of learning, a way of delivering the material, and evaluation of learning outcomes. Data collection techniques used were questionnaires, interviews, and observation. The research instrument consisted of a questionnaire sheet, sheet observation and interview guides. Validity is determined using data triangulation and triangulation methods. Data were analyzed using an interactive model. The results showed that the average value of activities in preparation for learning, fosters capabilities of general professional, specialized professional, self-development, manage the classroom, implementing the learning, how to deliver the material, and how to evaluate learning outcomes are 79%, 73%, 67%, 75%, 83%, 72%, 64%, and 54%, respectively

Mathematics and Astronomy: Inquire Based Scientific Education at School

NASA Astrophysics Data System (ADS)

de Castro, Ana I. Gómez

2010-10-01

Mathematics is the language of science however, in secondary and high school education students are not made aware of the strong implications behind this statement. This is partially caused because mathematical training and the modelling of nature are not taught together. Astronomy provides firm scientific grounds for this joint training; the mathematics needed is simple, the data can be acquired with simple instrumentation in any place on the planet and the physics is rich with a broad range of levels. In addition, astronomy and space exploration are extremely appealing to young (14-17 years old) students helping to motivate them to study science doing science, i.e. to introduce Inquiry Based Scientific Education (IBSE). Since 1997 a global consortium is being developed to introduce IBSE techniques in secondary/high school education on a global scale: the Global Hands-On Universe association (www.globalhou.org) making use of the astronomical universe as a training lab. This contribution is a brief update on the current activities of the HOU consortium. Relevant URLS: www.globalhou.org, www.euhou.net, www.houspain.com.

From Inverse Problems in Mathematical Physiology to Quantitative Differential Diagnoses

PubMed Central

Zenker, Sven; Rubin, Jonathan; Clermont, Gilles

2007-01-01

The improved capacity to acquire quantitative data in a clinical setting has generally failed to improve outcomes in acutely ill patients, suggesting a need for advances in computer-supported data interpretation and decision making. In particular, the application of mathematical models of experimentally elucidated physiological mechanisms could augment the interpretation of quantitative, patient-specific information and help to better target therapy. Yet, such models are typically complex and nonlinear, a reality that often precludes the identification of unique parameters and states of the model that best represent available data. Hypothesizing that this non-uniqueness can convey useful information, we implemented a simplified simulation of a common differential diagnostic process (hypotension in an acute care setting), using a combination of a mathematical model of the cardiovascular system, a stochastic measurement model, and Bayesian inference techniques to quantify parameter and state uncertainty. The output of this procedure is a probability density function on the space of model parameters and initial conditions for a particular patient, based on prior population information together with patient-specific clinical observations. We show that multimodal posterior probability density functions arise naturally, even when unimodal and uninformative priors are used. The peaks of these densities correspond to clinically relevant differential diagnoses and can, in the simplified simulation setting, be constrained to a single diagnosis by assimilating additional observations from dynamical interventions (e.g., fluid challenge). We conclude that the ill-posedness of the inverse problem in quantitative physiology is not merely a technical obstacle, but rather reflects clinical reality and, when addressed adequately in the solution process, provides a novel link between mathematically described physiological knowledge and the clinical concept of differential diagnoses. We outline possible steps toward translating this computational approach to the bedside, to supplement today's evidence-based medicine with a quantitatively founded model-based medicine that integrates mechanistic knowledge with patient-specific information. PMID:17997590

Mathematical Modeling: Challenging the Figured Worlds of Elementary Mathematics

ERIC Educational Resources Information Center

Wickstrom, Megan H.

2017-01-01

This article is a report on a teacher study group that focused on three elementary teachers' perceptions of mathematical modeling in contrast to typical mathematics instruction. Through the theoretical lens of figured worlds, I discuss how mathematics instruction was conceptualized across the classrooms in terms of artifacts, discourse, and…

Mathematics Teachers' Ideas about Mathematical Models: A Diverse Landscape

ERIC Educational Resources Information Center

Bautista, Alfredo; Wilkerson-Jerde, Michelle H.; Tobin, Roger G.; Brizuela, Bárbara M.

2014-01-01

This paper describes the ideas that mathematics teachers (grades 5-9) have regarding mathematical models of real-world phenomena, and explores how teachers' ideas differ depending on their educational background. Participants were 56 United States in-service mathematics teachers. We analyzed teachers' written responses to three open-ended…

Mathematical Modelling at Secondary School: The MACSI-Clongowes Wood College Experience

ERIC Educational Resources Information Center

Charpin, J. P. F.; O'Hara, S.; Mackey, D.

2013-01-01

In Ireland, to encourage the study of STEM (science, technology, engineering and mathematics) subjects and particularly mathematics, the Mathematics Applications Consortium for Science and Industry (MACSI) and Clongowes Wood College (County Kildare, Ireland) organized a mathematical modelling workshop for senior cycle secondary school students.…

Mathematical models of thermoregulation and heat transfer in mammals. A compendium of research

NASA Technical Reports Server (NTRS)

Shitzer, A.

1972-01-01

An annotated compendium on mathematical modeling of mammal thermoregulation systems is presented. Author abstracts, tables containing the more used mathematical models, solutions to these models, and each thermoregulation mechanism considered are included.

Ocular hemodynamics and glaucoma: the role of mathematical modeling.

PubMed

Harris, Alon; Guidoboni, Giovanna; Arciero, Julia C; Amireskandari, Annahita; Tobe, Leslie A; Siesky, Brent A

2013-01-01

To discuss the role of mathematical modeling in studying ocular hemodynamics, with a focus on glaucoma. We reviewed recent literature on glaucoma, ocular blood flow, autoregulation, the optic nerve head, and the use of mathematical modeling in ocular circulation. Many studies suggest that alterations in ocular hemodynamics play a significant role in the development, progression, and incidence of glaucoma. Although there is currently a limited number of studies involving mathematical modeling of ocular blood flow, regulation, and diseases (such as glaucoma), preliminary modeling work shows the potential of mathematical models to elucidate the mechanisms that contribute most significantly to glaucoma progression. Mathematical modeling is a useful tool when used synergistically with clinical and laboratory data in the study of ocular blood flow and glaucoma. The development of models to investigate the relationship between ocular hemodynamic alterations and glaucoma progression will provide a unique and useful method for studying the pathophysiology of glaucoma.

Comparison of learning models based on mathematics logical intelligence in affective domain

NASA Astrophysics Data System (ADS)

Widayanto, Arif; Pratiwi, Hasih; Mardiyana

2018-04-01

The purpose of this study was to examine the presence or absence of different effects of multiple treatments (used learning models and logical-mathematical intelligence) on the dependent variable (affective domain of mathematics). This research was quasi experimental using 3x3 of factorial design. The population of this research was VIII grade students of junior high school in Karanganyar under the academic year 2017/2018. Data collected in this research was analyzed by two ways analysis of variance with unequal cells using 5% of significance level. The result of the research were as follows: (1) Teaching and learning with model TS lead to better achievement in affective domain than QSH, teaching and learning with model QSH lead to better achievement in affective domain than using DI; (2) Students with high mathematics logical intelligence have better achievement in affective domain than students with low mathematics logical intelligence have; (3) In teaching and learning mathematics using learning model TS, students with moderate mathematics logical intelligence have better achievement in affective domain than using DI; and (4) In teaching and learning mathematics using learning model TS, students with low mathematics logical intelligence have better achievement in affective domain than using QSH and DI.

Application of remote sensing for prediction and detection of thermal pollution

NASA Technical Reports Server (NTRS)

Veziroglu, T. N.; Lee, S. S.

1974-01-01

The first phase is described of a three year project for the development of a mathematical model for predicting thermal pollution by use of remote sensing measurements. A rigid-lid model was developed, and results were obtained for different wind conditions at Biscayne Bay in South Florida. The design of the measurement system was completed, and instruments needed for the first stage of experiment were acquired, tested, and calibrated. A preliminary research flight was conducted.

The impact of mathematical models of teaching materials on square and rectangle concepts to improve students' mathematical connection ability and mathematical disposition in middle school

NASA Astrophysics Data System (ADS)

Afrizal, Irfan Mufti; Dachlan, Jarnawi Afghani

2017-05-01

The aim of this study was to determine design of mathematical models of teaching materials to improve students' mathematical connection ability and mathematical disposition in middle school through experimental studies. The design in this study was quasi-experimental with non-equivalent control group type. This study consisted of two phases, the first phase was identify students' learning obstacle on square and rectangle concepts to obtain the appropriate design of teaching materials, beside that there were internalization of the values or characters expected to appear on students through the teaching materials. Second phase was experiments on the effectiveness and efficiency of mathematical models of teaching materials to improve students' mathematical connection ability and mathematical disposition. The result of this study are 1) Students' learning obstacle that have identified was categorized as an epistemological obstacle. 2) The improvement of students' mathematical connection ability and mathematical disposition who used mathematical teaching materials is better than the students who used conventional learning.

Dynamic hyperbolic geometry: building intuition and understanding mediated by a Euclidean model

NASA Astrophysics Data System (ADS)

Moreno-Armella, Luis; Brady, Corey; Elizondo-Ramirez, Rubén

2018-05-01

This paper explores a deep transformation in mathematical epistemology and its consequences for teaching and learning. With the advent of non-Euclidean geometries, direct, iconic correspondences between physical space and the deductive structures of mathematical inquiry were broken. For non-Euclidean ideas even to become thinkable the mathematical community needed to accumulate over twenty centuries of reflection and effort: a precious instance of distributed intelligence at the cultural level. In geometry education after this crisis, relations between intuitions and geometrical reasoning must be established philosophically, rather than taken for granted. One approach seeks intuitive supports only for Euclidean explorations, viewing non-Euclidean inquiry as fundamentally non-intuitive in nature. We argue for moving beyond such an impoverished approach, using dynamic geometry environments to develop new intuitions even in the extremely challenging setting of hyperbolic geometry. Our efforts reverse the typical direction, using formal structures as a source for a new family of intuitions that emerge from exploring a digital model of hyperbolic geometry. This digital model is elaborated within a Euclidean dynamic geometry environment, enabling a conceptual dance that re-configures Euclidean knowledge as a support for building intuitions in hyperbolic space-intuitions based not directly on physical experience but on analogies extending Euclidean concepts.

A Solution to the Cosmic Conundrum including Cosmological Constant and Dark Energy Problems

NASA Astrophysics Data System (ADS)

Singh, A.

2009-12-01

A comprehensive solution to the cosmic conundrum is presented that also resolves key paradoxes of quantum mechanics and relativity. A simple mathematical model, the Gravity Nullification model (GNM), is proposed that integrates the missing physics of the spontaneous relativistic conversion of mass to energy into the existing physics theories, specifically a simplified general theory of relativity. Mechanistic mathematical expressions are derived for a relativistic universe expansion, which predict both the observed linear Hubble expansion in the nearby universe and the accelerating expansion exhibited by the supernova observations. The integrated model addresses the key questions haunting physics and Big Bang cosmology. It also provides a fresh perspective on the misconceived birth and evolution of the universe, especially the creation and dissolution of matter. The proposed model eliminates singularities from existing models and the need for the incredible and unverifiable assumptions including the superluminous inflation scenario, multiple universes, multiple dimensions, Anthropic principle, and quantum gravity. GNM predicts the observed features of the universe without any explicit consideration of time as a governing parameter.

Space-flight simulations of calcium metabolism using a mathematical model of calcium regulation

NASA Technical Reports Server (NTRS)

Brand, S. N.

1985-01-01

The results of a series of simulation studies of calcium matabolic changes which have been recorded during human exposure to bed rest and space flight are presented. Space flight and bed rest data demonstrate losses of total body calcium during exposure to hypogravic environments. These losses are evidenced by higher than normal rates of urine calcium excretion and by negative calcium balances. In addition, intestinal absorption rates and bone mineral content are assumed to decrease. The bed rest and space flight simulations were executed on a mathematical model of the calcium metabolic system. The purpose of the simulations is to theoretically test hypotheses and predict system responses which are occurring during given experimental stresses. In this case, hypogravity occurs through the comparison of simulation and experimental data and through the analysis of model structure and system responses. The model reliably simulates the responses of selected bed rest and space flight parameters. When experimental data are available, the simulated skeletal responses and regulatory factors involved in the responses agree with space flight data collected on rodents. In addition, areas within the model that need improvement are identified.

Construction of a model demonstrating neural pathways and reflex arcs.

PubMed

Chan, V; Pisegna, J M; Rosian, R L; DiCarlo, S E

1996-12-01

Employment opportunities in the future will require higher skills and an understanding of mathematics and science. As a result of the growing number of careers that require solid science and mathematics training, the methods of science education are undergoing major reform. To adequately equip students for technologically advanced positions, new teaching methods must be developed that prepare tomorrow's workforce for the challenges of the 21st century. One such method is the use of models. By actively building and manipulating concrete models that represent scientific concepts, students are involved in the most basic level of Piaget's learning scheme: the sensorimotor stage. Models are useful in reaching all students at the foundational levels of learning, and further learning experiences are rapidly moved through higher learning levels. This success ensures greater comprehension and understanding compared with the traditional methods of rote memorization. We developed an exercise for the construction of an inexpensive, easy-to-build model demonstrating neural pathways and reflex arcs. Our exercise also includes many supplemental teaching tools. The exercise is designed to fulfill the need of sound physiological teaching materials for high school students.

Mathematical models for plant-herbivore interactions

USGS Publications Warehouse

Feng, Zhilan; DeAngelis, Donald L.

2017-01-01

Mathematical Models of Plant-Herbivore Interactions addresses mathematical models in the study of practical questions in ecology, particularly factors that affect herbivory, including plant defense, herbivore natural enemies, and adaptive herbivory, as well as the effects of these on plant community dynamics. The result of extensive research on the use of mathematical modeling to investigate the effects of plant defenses on plant-herbivore dynamics, this book describes a toxin-determined functional response model (TDFRM) that helps explains field observations of these interactions. This book is intended for graduate students and researchers interested in mathematical biology and ecology.

An overview of the CellML API and its implementation

PubMed Central

2010-01-01

Background CellML is an XML based language for representing mathematical models, in a machine-independent form which is suitable for their exchange between different authors, and for archival in a model repository. Allowing for the exchange and archival of models in a computer readable form is a key strategic goal in bioinformatics, because of the associated improvements in scientific record accuracy, the faster iterative process of scientific development, and the ability to combine models into large integrative models. However, for CellML models to be useful, tools which can process them correctly are needed. Due to some of the more complex features present in CellML models, such as imports, developing code ab initio to correctly process models can be an onerous task. For this reason, there is a clear and pressing need for an application programming interface (API), and a good implementation of that API, upon which tools can base their support for CellML. Results We developed an API which allows the information in CellML models to be retrieved and/or modified. We also developed a series of optional extension APIs, for tasks such as simplifying the handling of connections between variables, dealing with physical units, validating models, and translating models into different procedural languages. We have also provided a Free/Open Source implementation of this application programming interface, optimised to achieve good performance. Conclusions Tools have been developed using the API which are mature enough for widespread use. The API has the potential to accelerate the development of additional tools capable of processing CellML, and ultimately lead to an increased level of sharing of mathematical model descriptions. PMID:20377909

An overview of the CellML API and its implementation.

PubMed

Miller, Andrew K; Marsh, Justin; Reeve, Adam; Garny, Alan; Britten, Randall; Halstead, Matt; Cooper, Jonathan; Nickerson, David P; Nielsen, Poul F

2010-04-08

CellML is an XML based language for representing mathematical models, in a machine-independent form which is suitable for their exchange between different authors, and for archival in a model repository. Allowing for the exchange and archival of models in a computer readable form is a key strategic goal in bioinformatics, because of the associated improvements in scientific record accuracy, the faster iterative process of scientific development, and the ability to combine models into large integrative models.However, for CellML models to be useful, tools which can process them correctly are needed. Due to some of the more complex features present in CellML models, such as imports, developing code ab initio to correctly process models can be an onerous task. For this reason, there is a clear and pressing need for an application programming interface (API), and a good implementation of that API, upon which tools can base their support for CellML. We developed an API which allows the information in CellML models to be retrieved and/or modified. We also developed a series of optional extension APIs, for tasks such as simplifying the handling of connections between variables, dealing with physical units, validating models, and translating models into different procedural languages.We have also provided a Free/Open Source implementation of this application programming interface, optimised to achieve good performance. Tools have been developed using the API which are mature enough for widespread use. The API has the potential to accelerate the development of additional tools capable of processing CellML, and ultimately lead to an increased level of sharing of mathematical model descriptions.

Como Promover el Exito de las Ninas y las Minorias en las Ciencias y en las Matematicas. Para Padres/sobre Padres (How To Promote the Science and Mathematics Achievement of Females and Minorities. For Parents/about Parents).

ERIC Educational Resources Information Center

Schwartz, Wendy

Some minority and female students traditionally have not been given the help they need to enroll and succeed in mathematics and science classes. Now, however, various approaches are available to give these students the extra attention they need. Parents can help children develop an interest in science and mathematics by: (1) identifying role…

Automated Scoring of Mathematics Tasks in the Common Core Era: Enhancements to M-Rater in Support of "CBAL"™ Mathematics and the Common Core Assessments. Research Reports. ETS RR-13-26

ERIC Educational Resources Information Center

Fife, James H.

2013-01-01

The m-rater scoring engine has been used successfully for the past several years to score "CBAL"™ mathematics tasks, for the most part without the need for human scoring. During this time, various improvements to m-rater and its scoring keys have been implemented in response to specific CBAL needs. In 2012, with the general move toward…

Secondary School Advanced Mathematics, Chapter 3, Formal Geometry. Student's Text.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This text is the second of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. This volume is devoted to a rigorous development of theorems in plane geometry from 22…

Secondary School Advanced Mathematics, Chapter 8, Systems of Equations. Student's Text.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This text is the last of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. In this volume the solution of systems of linear and quadratic equations and inequalities in…

Analyses of Children's Mathematics Proficiency from ECLS-K 1998 and 2010 Cohorts: Why Early Mathematics?

ERIC Educational Resources Information Center

Lee, Joohi; Pant, Mohan D.

2017-01-01

This article presents the correlation analyses of mathematics item response theory scores from the Early Childhood Longitudinal Study, Kindergarten Class of 1998 and 2010 data, and proposes the critical need for systematic efforts to improve the quality of pre- and in-service teachers of young children in teaching mathematics.

The Intersection of Mathematics and Language in the Post-Secondary Environment: Implications for English Language Learners

ERIC Educational Resources Information Center

Choi, Jean; Milburn, Rebecca; Reynolds, Brett; Marcoccia, Philip; Silva, Patrick Justin; Panag, Sikander

2013-01-01

Given the increasing number of English Language Learners (ELLs) in post-secondary environments (Roessingh & Douglas, 2012), educational practices such as availability of language support for mathematics should be assessed to ensure that all students' needs are met. To explore the effects of language on mathematics in ELLs, mathematical test…

A Professional Development Program to Improve Math Skills among Preschool Children in Head Start

ERIC Educational Resources Information Center

Brendefur, Jonathan; Strother, Sam; Thiede, Keith; Lane, Cristianne; Surges-Prokop, Mary Jo

2013-01-01

The purpose of this study was to examine the effects on four-year-olds' knowledge of mathematics by introducing professional development and center-based mathematics activities around four mathematical domains to early educators' teaching in Head Start programs. Because of the need to provide necessary mathematical experiences to young children to…

Mathematics Education in Singapore--An Insider's Perspective

ERIC Educational Resources Information Center

Kaur, Berinderjeet

2014-01-01

Singapore's Education System has evolved over time and so has Mathematics Education in Singapore. The present day School Mathematics Curricula can best be described as one that caters for the needs of every child in school. It is based on a framework that has mathematical problem solving as its primary focus. The developments from 1946 to 2012…

The New York City Staff Development Program in Mathematics for High School Teachers and Supervisors, 1987-1988.

ERIC Educational Resources Information Center

Berney, Tomi D.; Friedman, Grace Ibanez

The state-funded New York City Staff Development Program in Mathematics was a five-workshop series serving bilingual/English-as-a-Second-Language teachers teaching mathematics, and mathematics teachers unfamiliar with the special needs of limited-English-proficient (LEP) high school students. Supervisors were also invited to participate. Workshop…

Impulsive-Analytic Disposition in Mathematical Problem Solving: A Survey and a Mathematics Test

ERIC Educational Resources Information Center

Lim, Kien H.; Wagler, Amy

2012-01-01

The Likelihood-to-Act (LtA) survey and a mathematics test were used in this study to assess students' impulsive-analytic disposition in the context of mathematical problem solving. The results obtained from these two instruments were compared to those obtained using two widely-used scales: Need for Cognition (NFC) and Barratt Impulsivity Scale…

Promoting Access to Common Core Mathematics for Students with Severe Disabilities through Mathematical Problem Solving

ERIC Educational Resources Information Center

Spooner, Fred; Saunders, Alicia; Root, Jenny; Brosh, Chelsi

2017-01-01

There is a need to teach the pivotal skill of mathematical problem solving to students with severe disabilities, moving beyond basic skills like computation to higher level thinking skills. Problem solving is emphasized as a Standard for Mathematical Practice in the Common Core State Standards across grade levels. This article describes a…