Geometry and Education in the Internet Age.

ERIC Educational Resources Information Center

Kortenkamp, Ulrich H.; Richter-Gebert, Jurgen

This paper discusses the requirements of Interactive Geometry Systems (IGSs) and how they can be fulfilled, explains how a geometry tool can benefit from the Internet, and presents Cinderella's Cafe. Cinderella's Cafe is a new IGS with a high mathematical background that uses the most general mathematical models whenever possible, is highly…

Students' Abstraction in Recognizing, Building with and Constructing a Quadrilateral

ERIC Educational Resources Information Center

Budiarto, Mega Teguh; Rahaju, Endah Budi; Hartono, Sugi

2017-01-01

This study aims to implement empirically students' abstraction with socio-cultural background of Indonesia. Abstraction is an activity that involves a vertical reorganization of previously constructed mathematics into a new mathematical structure. The principal components of the model are three dynamic nested epistemic actions: recognizing,…

Modeling hazardous mass flows Geoflows09: Mathematical and computational aspects of modeling hazardous geophysical mass flows; Seattle, Washington, 9–11 March 2009

USGS Publications Warehouse

Iverson, Richard M.; LeVeque, Randall J.

2009-01-01

A recent workshop at the University of Washington focused on mathematical and computational aspects of modeling the dynamics of dense, gravity-driven mass movements such as rock avalanches and debris flows. About 30 participants came from seven countries and brought diverse backgrounds in geophysics; geology; physics; applied and computational mathematics; and civil, mechanical, and geotechnical engineering. The workshop was cosponsored by the U.S. Geological Survey Volcano Hazards Program, by the U.S. National Science Foundation through a Vertical Integration of Research and Education (VIGRE) in the Mathematical Sciences grant to the University of Washington, and by the Pacific Institute for the Mathematical Sciences. It began with a day of lectures open to the academic community at large and concluded with 2 days of focused discussions and collaborative work among the participants.

An Evaluation of Causal Modeling Applied to Educational Productivity in Mathematics.

ERIC Educational Resources Information Center

Harnisch, Delwyn L.; Dunbar, Stephen B.

To probe a psychological theory of educational productivity, background measures along with mathematics test scores and motivational measures of over 7,000 students (9-, 13- and 17-year olds from National Assessment of Educational Progress samples) were statistically related to each other and to indicators of constructs that prior research shows…

Reduced modeling of signal transduction – a modular approach

PubMed Central

Koschorreck, Markus; Conzelmann, Holger; Ebert, Sybille; Ederer, Michael; Gilles, Ernst Dieter

2007-01-01

Background Combinatorial complexity is a challenging problem in detailed and mechanistic mathematical modeling of signal transduction. This subject has been discussed intensively and a lot of progress has been made within the last few years. A software tool (BioNetGen) was developed which allows an automatic rule-based set-up of mechanistic model equations. In many cases these models can be reduced by an exact domain-oriented lumping technique. However, the resulting models can still consist of a very large number of differential equations. Results We introduce a new reduction technique, which allows building modularized and highly reduced models. Compared to existing approaches further reduction of signal transduction networks is possible. The method also provides a new modularization criterion, which allows to dissect the model into smaller modules that are called layers and can be modeled independently. Hallmarks of the approach are conservation relations within each layer and connection of layers by signal flows instead of mass flows. The reduced model can be formulated directly without previous generation of detailed model equations. It can be understood and interpreted intuitively, as model variables are macroscopic quantities that are converted by rates following simple kinetics. The proposed technique is applicable without using complex mathematical tools and even without detailed knowledge of the mathematical background. However, we provide a detailed mathematical analysis to show performance and limitations of the method. For physiologically relevant parameter domains the transient as well as the stationary errors caused by the reduction are negligible. Conclusion The new layer based reduced modeling method allows building modularized and strongly reduced models of signal transduction networks. Reduced model equations can be directly formulated and are intuitively interpretable. Additionally, the method provides very good approximations especially for macroscopic variables. It can be combined with existing reduction methods without any difficulties. PMID:17854494

Mathematical background and attitudes toward statistics in a sample of Spanish college students.

PubMed

Carmona, José; Martínez, Rafael J; Sánchez, Manuel

2005-08-01

To examine the relation of mathematical background and initial attitudes toward statistics of Spanish college students in social sciences the Survey of Attitudes Toward Statistics was given to 827 students. Multivariate analyses tested the effects of two indicators of mathematical background (amount of exposure and achievement in previous courses) on the four subscales. Analysis suggested grades in previous courses are more related to initial attitudes toward statistics than the number of mathematics courses taken. Mathematical background was related with students' affective responses to statistics but not with their valuing of statistics. Implications of possible research are discussed.

An Application of Mathematical Groups to Structures of Human Groups. Applications of Finite Mathematics to Anthropology and Sociology. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Unit 476.

ERIC Educational Resources Information Center

Carlson, Roger

This module is designed for students with a high school algebra background. The goal is to present the elements of the group idea, primarily by way of a geometric model, and to see its application to the study of kinship relations within certain human groups. The material opens with a presentation of clans in a hypothetical society in an early…

A study on nonlinear estimation of submaximal effort tolerance based on the generalized MET concept and the 6MWT in pulmonary rehabilitation

PubMed Central

Szczegielniak, Jan; Łuniewski, Jacek; Stanisławski, Rafał; Bogacz, Katarzyna; Krajczy, Marcin; Rydel, Marek

2018-01-01

Background The six-minute walk test (6MWT) is considered to be a simple and inexpensive tool for the assessment of functional tolerance of submaximal effort. The aim of this work was 1) to background the nonlinear nature of the energy expenditure process due to physical activity, 2) to compare the results/scores of the submaximal treadmill exercise test and those of 6MWT in pulmonary patients and 3) to develop nonlinear mathematical models relating the two. Methods The study group included patients with the COPD. All patients were subjected to a submaximal exercise test and a 6MWT. To develop an optimal mathematical solution and compare the results of the exercise test and the 6MWT, the least squares and genetic algorithms were employed to estimate parameters of polynomial expansion and piecewise linear models. Results Mathematical analysis enabled to construct nonlinear models for estimating the MET result of submaximal exercise test based on average walk velocity (or distance) in the 6MWT. Conclusions Submaximal effort tolerance in COPD patients can be effectively estimated from new, rehabilitation-oriented, nonlinear models based on the generalized MET concept and the 6MWT. PMID:29425213

Introducing Seismic Tomography with Computational Modeling

NASA Astrophysics Data System (ADS)

Neves, R.; Neves, M. L.; Teodoro, V.

2011-12-01

Learning seismic tomography principles and techniques involves advanced physical and computational knowledge. In depth learning of such computational skills is a difficult cognitive process that requires a strong background in physics, mathematics and computer programming. The corresponding learning environments and pedagogic methodologies should then involve sets of computational modelling activities with computer software systems which allow students the possibility to improve their mathematical or programming knowledge and simultaneously focus on the learning of seismic wave propagation and inverse theory. To reduce the level of cognitive opacity associated with mathematical or programming knowledge, several computer modelling systems have already been developed (Neves & Teodoro, 2010). Among such systems, Modellus is particularly well suited to achieve this goal because it is a domain general environment for explorative and expressive modelling with the following main advantages: 1) an easy and intuitive creation of mathematical models using just standard mathematical notation; 2) the simultaneous exploration of images, tables, graphs and object animations; 3) the attribution of mathematical properties expressed in the models to animated objects; and finally 4) the computation and display of mathematical quantities obtained from the analysis of images and graphs. Here we describe virtual simulations and educational exercises which enable students an easy grasp of the fundamental of seismic tomography. The simulations make the lecture more interactive and allow students the possibility to overcome their lack of advanced mathematical or programming knowledge and focus on the learning of seismological concepts and processes taking advantage of basic scientific computation methods and tools.

Development Of Maneuvering Autopilot For Flight Tests

NASA Technical Reports Server (NTRS)

Menon, P. K. A.; Walker, R. A.

1992-01-01

Report describes recent efforts to develop automatic control system operating under supervision of pilot and making airplane follow prescribed trajectories during flight tests. Report represents additional progress on this project. Gives background information on technology of control of test-flight trajectories; presents mathematical models of airframe, engine and command-augmentation system; focuses on mathematical modeling of maneuvers; addresses design of autopilots for maneuvers; discusses numerical simulation and evaluation of results of simulation of eight maneuvers under control of simulated autopilot; and presents summary and discussion of future work.

From biology to mathematical models and back: teaching modeling to biology students, and biology to math and engineering students.

PubMed

Chiel, Hillel J; McManus, Jeffrey M; Shaw, Kendrick M

2010-01-01

We describe the development of a course to teach modeling and mathematical analysis skills to students of biology and to teach biology to students with strong backgrounds in mathematics, physics, or engineering. The two groups of students have different ways of learning material and often have strong negative feelings toward the area of knowledge that they find difficult. To give students a sense of mastery in each area, several complementary approaches are used in the course: 1) a "live" textbook that allows students to explore models and mathematical processes interactively; 2) benchmark problems providing key skills on which students make continuous progress; 3) assignment of students to teams of two throughout the semester; 4) regular one-on-one interactions with instructors throughout the semester; and 5) a term project in which students reconstruct, analyze, extend, and then write in detail about a recently published biological model. Based on student evaluations and comments, an attitude survey, and the quality of the students' term papers, the course has significantly increased the ability and willingness of biology students to use mathematical concepts and modeling tools to understand biological systems, and it has significantly enhanced engineering students' appreciation of biology.

Elementary Content Specialization: Models, Affordances, and Constraints

ERIC Educational Resources Information Center

Markworth, Kimberly A.; Brobst, Joseph; Ohana, Chris; Parker, Ruth

2016-01-01

Background: This study investigates the models of elementary content specialization (ECS) in elementary mathematics and science and the affordances and constraints related to ECS--both generally and in relation to specific models. Elementary content specialists are defined as full-time classroom teachers who are responsible for content instruction…

Growth curve analyses of the relationship between early maternal age and children's mathematics and reading performance.

PubMed

Torres, D Diego

2015-03-01

Regarding the methods used to examine the early maternal age-child academic outcomes relationship, the extant literature has tended to examine change using statistical analyses that fail to appreciate that individuals vary in their rates of growth. Of the one study I have been able to find that employs a true growth model to estimate this relationship, the authors only controlled for characteristics of the maternal household after family formation; confounding background factors of mothers that might select them into early childbearing, a possible source of bias, were ignored. The authors' findings nonetheless suggested an inverse relationship between early maternal age, i.e., a first birth between the ages of 13 and 17, and Canadian adolescents' mean math performance at age 10. Early maternal age was not related to the linear slope of age. To elucidate whether the early maternal age-child academic outcomes association, treated in a growth context, is consistent with this finding, the present study built on it using US data and explored children's mathematics and reading trajectories from age 5 on. Its unique contribution is that it further explicitly controlled for maternal background factors and employed a three-level growth model with repeated measures of children nested within their mothers. Though the strength of the relationship varied between mean initial academic performance and mean academic growth, results confirmed that early maternal age was negatively related to children's mathematics and reading achievement, net of post-teen first birth child-specific and maternal household factors. Once maternal background factors were included, there was no statistically significant relationship between early maternal age and either children's mean initial mathematics and reading scores or their mean mathematics and reading growth. Copyright © 2014 Elsevier Inc. All rights reserved.

Dialogic and Direct Instruction: Two Distinct Models of Mathematics Instruction and the Debate(s) Surrounding Them

ERIC Educational Resources Information Center

Munter, Charles; Stein, Mary Kay; Smith, Margaret Austin

2015-01-01

Background/Context: Which ideas should be included in the K-12 curriculum, how they are learned, and how they should be taught have been debated for decades in multiple subjects. In this article, we offer mathematics as a case in point of how new standards-related policies may offer an opportunity for reassessment and clarification of such…

Teaching Service Modelling to a Mixed Class: An Integrated Approach

ERIC Educational Resources Information Center

Deng, Jeremiah D.; Purvis, Martin K.

2015-01-01

Service modelling has become an increasingly important area in today's telecommunications and information systems practice. We have adapted a Network Design course in order to teach service modelling to a mixed class of both the telecommunication engineering and information systems backgrounds. An integrated approach engaging mathematics teaching…

Science modelling in pre-calculus: how to make mathematics problems contextually meaningful

NASA Astrophysics Data System (ADS)

Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

2011-04-01

'Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum' (National Council of Teachers of Mathematics (NCTM), Principles and Standards for School Mathematics, NCTM, Reston, VA, 2000). Commonly used pre-calculus textbooks provide a wide range of application problems. However, these problems focus students' attention on evaluating or solving pre-arranged formulas for given values. The role of scientific content is reduced to provide a background for these problems instead of being sources of data gathering for inducing mathematical tools. Students are neither required to construct mathematical models based on the contexts nor are they asked to validate or discuss the limitations of applied formulas. Using these contexts, the instructor may think that he/she is teaching problem solving, where in reality he/she is teaching algorithms of the mathematical operations (G. Kulm (ed.), New directions for mathematics assessment, in Assessing Higher Order Thinking in Mathematics, Erlbaum, Hillsdale, NJ, 1994, pp. 221-240). Without a thorough representation of the physical phenomena and the mathematical modelling processes undertaken, problem solving unintentionally appears as simple algorithmic operations. In this article, we deconstruct the representations of mathematics problems from selected pre-calculus textbooks and explicate their limitations. We argue that the structure and content of those problems limits students' coherent understanding of mathematical modelling, and this could result in weak student problem-solving skills. Simultaneously, we explore the ways to enhance representations of those mathematical problems, which we have characterized as lacking a meaningful physical context and limiting coherent student understanding. In light of our discussion, we recommend an alternative to strengthen the process of teaching mathematical modelling - utilization of computer-based science simulations. Although there are several exceptional computer-based science simulations designed for mathematics classes (see, e.g. Kinetic Book (http://www.kineticbooks.com/) or Gizmos (http://www.explorelearning.com/)), we concentrate mainly on the PhET Interactive Simulations developed at the University of Colorado at Boulder (http://phet.colorado.edu/) in generating our argument that computer simulations more accurately represent the contextual characteristics of scientific phenomena than their textual descriptions.

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

Reading Proficiency and Comparability of Mathematics and Science Scores for Students from English and Non-English Backgrounds: An International Perspective

ERIC Educational Resources Information Center

Ercikan, Kadriye; Chen, Michelle Y.; Lyons-Thomas, Juliette; Goodrich, Shawna; Sandilands, Debra; Roth, Wolff-Michael; Simon, Marielle

2015-01-01

The purpose of this research is to examine the comparability of mathematics and science scores for students from English language backgrounds (ELB) and non-English language backgrounds (NELB). We examine the relationship between English reading proficiency and performance on mathematics and science assessments in Australia, Canada, the United…

From Biology to Mathematical Models and Back: Teaching Modeling to Biology Students, and Biology to Math and Engineering Students

PubMed Central

McManus, Jeffrey M.; Shaw, Kendrick M.

2010-01-01

We describe the development of a course to teach modeling and mathematical analysis skills to students of biology and to teach biology to students with strong backgrounds in mathematics, physics, or engineering. The two groups of students have different ways of learning material and often have strong negative feelings toward the area of knowledge that they find difficult. To give students a sense of mastery in each area, several complementary approaches are used in the course: 1) a “live” textbook that allows students to explore models and mathematical processes interactively; 2) benchmark problems providing key skills on which students make continuous progress; 3) assignment of students to teams of two throughout the semester; 4) regular one-on-one interactions with instructors throughout the semester; and 5) a term project in which students reconstruct, analyze, extend, and then write in detail about a recently published biological model. Based on student evaluations and comments, an attitude survey, and the quality of the students' term papers, the course has significantly increased the ability and willingness of biology students to use mathematical concepts and modeling tools to understand biological systems, and it has significantly enhanced engineering students' appreciation of biology. PMID:20810957

Undergraduate Research: Mathematical Modeling of Mortgages

ERIC Educational Resources Information Center

Choi, Youngna; Spero, Steven

2010-01-01

In this article, we study financing in the real estate market and show how various types of mortgages can be modeled and analyzed. With only an introductory level of interest theory, finance, and calculus, we model and analyze three types of popular mortgages with real life examples that explain the background and inevitable outcome of the current…

Forest forming process and dynamic vegetation models under global change

Treesearch

A. Shvidenko; E. Gustafson

2009-01-01

The paper analyzes mathematical models that are used to project the dynamics of forest ecosystems on different spatial and temporal scales. Landscape disturbance and succession models (LDSMs) are of a particular interest for studying the forest forming process in Northern Eurasia. They have a solid empirical background and are able to model ecological processes under...

Middle Level Mathematics Teachers' Self-Efficacy Growth through Professional Development: Differences Based on Mathematical Background

ERIC Educational Resources Information Center

Stevens, Tara; Aguirre-Munoz, Zenaida; Harris, Gary; Higgins, Raegan; Liu, Xun

2013-01-01

growth of teachers with more and less mathematics background as the teachers participated in professional development across two summers. Professional development activities were associated with increases in teachers' self-efficacy; however, without considering mathematics…

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.

The Reciprocal Internal/External Frame of Reference Model Using Grades and Test Scores

ERIC Educational Resources Information Center

Möller, Jens; Zimmermann, Friederike; Köller, Olaf

2014-01-01

Background: The reciprocal I/E model (RI/EM) combines the internal/external frame of reference model (I/EM) with the reciprocal effects model (REM). The RI/EM extends the I/EM longitudinally and the REM across domains. The model predicts that, within domains, mathematics and verbal achievement (VACH) and academic self-concept have positive effects…

Distributed Algorithms for Probabilistic Solution of Computational Vision Problems.

DTIC Science & Technology

1988-03-01

34 targets. Legters and Young (1982) developed an operator-based approach r% using foreground and background models and solved a least-squares minimiza...1960), "Finite Markov Chains", Van Nostrand, , - New York. Legters , G.R., and Young, T.Y. (1982), "A Mathematical Model for Computer Image Tracking

Mathematical modeling of growth Salmonella and spoilage microorganisms in raw oysters

USDA-ARS?s Scientific Manuscript database

The main objective of this study was to develop primary and secondary models to describe the growth of Salmonella as well as background microorganisms in fresh shucked oysters. The cocktail of two Salmonella serotypes, S. Typhimurium (CICC22956) and S. Enteritidis (CICC21482), was inoculated to raw...

Unpacking the Inequality among Turkish Schools: Findings from PISA 2006

ERIC Educational Resources Information Center

Alacaci, Cengiz; Erbas, Ayhan Kursat

2010-01-01

The study investigates the effects of certain school characteristics on students' mathematics performances in Turkey in the PISA 2006 while controlling for family background and demographic characteristics. Three models of Hierarchical Linear Modeling (HLM) are constructed. The results reveal that 55% of the variance is attributable to…

Hierarchical Linear Modelling of Student and School Effects on Academic Achievement.

ERIC Educational Resources Information Center

Ma, Xin; Klinger, Don A.

2000-01-01

Used hierarchical linear modeling with data from the New Brunswick School Climate Study (Canada) to examine student background, school context, and school climate effects on Grade 6 student achievement in mathematics, science, reading, and writing. Gender, socioeconomic status, and Native ethnicity were significant predictors of academic…

CEASAW: A User-Friendly Computer Environment Analysis for the Sawmill Owner

Treesearch

Guillermo Mendoza; William Sprouse; Philip A. Araman; William G. Luppold

1991-01-01

Improved spreadsheet software capabilities have brought optimization to users with little or no background in mathematical programming. Better interface capabilities of spreadsheet models now make it possible to combine optimization models with a spreadsheet system. Sawmill production and inventory systems possess many features that make them suitable application...

Representing the Electromagnetic Field: How Maxwell's Mathematics Empowered Faraday's Field Theory

NASA Astrophysics Data System (ADS)

Tweney, Ryan D.

2011-07-01

James Clerk Maxwell `translated' Michael Faraday's experimentally-based field theory into the mathematical representation now known as `Maxwell's Equations.' Working with a variety of mathematical representations and physical models Maxwell extended the reach of Faraday's theory and brought it into consistency with other results in the physics of electricity and magnetism. Examination of Maxwell's procedures opens many issues about the role of mathematical representation in physics and the learning background required for its success. Specifically, Maxwell's training in `Cambridge University' mathematical physics emphasized the use of analogous equations across fields of physics and the repeated solving of extremely difficult problems in physics. Such training develops an array of overlearned mathematical representations supported by highly sophisticated cognitive mechanisms for the retrieval of relevant information from long term memory. For Maxwell, mathematics constituted a new form of representation in physics, enhancing the formal derivational and calculational role of mathematics and opening a cognitive means for the conduct of `experiments in the mind' and for sophisticated representations of theory.

Climate Modeling in the Calculus and Differential Equations Classroom

ERIC Educational Resources Information Center

Kose, Emek; Kunze, Jennifer

2013-01-01

Students in college-level mathematics classes can build the differential equations of an energy balance model of the Earth's climate themselves, from a basic understanding of the background science. Here we use variable albedo and qualitative analysis to find stable and unstable equilibria of such a model, providing a problem or perhaps a…

German undergraduate mathematics enrolment numbers: background and change

NASA Astrophysics Data System (ADS)

Ammann, Claudia; Frauendiener, Jörg; Holton, Derek

2010-06-01

Before we consider the German tertiary system, we review the education system and consider other relevant background details. We then concentrate on the tertiary system and observe that the mathematical enrolments are keeping up with the overall student enrolments. At the same time, the first year mathematics enrolments for women are greater than that for men, although more men are still studying mathematics at university. Finally, we note that the German economy seems to play a role in mathematics enrolments though not necessarily to its comparative detriment.

Profiling Student Use of Calculators in the Learning of High School Mathematics

ERIC Educational Resources Information Center

Crowe, Cheryll E.; Ma, Xin

2010-01-01

Using data from the 2005 National Assessment of Educational Progress, students' use of calculators in the learning of high school mathematics was profiled based on their family background, curriculum background, and advanced mathematics coursework. A statistical method new to educational research--classification and regression trees--was applied…

The Relationship among Mathematics Achievement, Affective Variables and Home Background.

ERIC Educational Resources Information Center

Wong, Ngai-ying

1992-01-01

Investigated the relationships among mathematics achievement, affect, and home background for Hong Kong students (n=1766) in grades 7-13. Achievement was most closely related to academic and nonacademic self-concepts and attitudes toward mathematics, and the latter was most influenced by self- and parental expectations. (LDR)

High-Ability Women and Men in Undergraduate Mathematics and Chemistry Courses.

ERIC Educational Resources Information Center

Bali, John; And Others

1985-01-01

Using samples of college students of very high ability and strong academic background, sex differences in performance and perceptions of performance in introductory chemistry and mathematics courses were studied. Considerable differences favoring men were found, and these appeared to be due primarily to differences in mathematics background.…

Equity in the Turkish Education System: A Multilevel Analysis of Social Background Influences on the Mathematics Performance of 15-Year-Old Students

ERIC Educational Resources Information Center

Özdemir, Caner

2016-01-01

This paper aims to discover the level of equity in the Turkish education system using maths outcomes of 15-year-old students in the Programme for International Student Assessment (PISA) exam. In order to do that, associations between various social background variables and student performance are analysed via multilevel models. Female pupils,…

Understanding, treating and avoiding hematological disease: Better medicine through mathematics?

PubMed Central

Dale, David C.; Mackey, Michael C.

2014-01-01

This paper traces the experimental, clinical and mathematical modeling efforts to understand a periodic hematological disease–cyclical neutropenia. It is primarily a highly personal account by two scientists from quite different backgrounds of the interactions over almost 40 years and their attempts to understand this intriguing disease. It’s also a story of their efforts to offer effective treatments for the patients who suffer from cyclic neutropenia and other conditions causing neutropenia and infections. PMID:25213154

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.

Segmentation of vessel-like patterns using mathematical morphology and curvature evaluation.

PubMed

Zana, F; Klein, J C

2001-01-01

This paper presents an algorithm based on mathematical morphology and curvature evaluation for the detection of vessel-like patterns in a noisy environment. Such patterns are very common in medical images. Vessel detection is interesting for the computation of parameters related to blood flow. Its tree-like geometry makes it a usable feature for registration between images that can be of a different nature. In order to define vessel-like patterns, segmentation is performed with respect to a precise model. We define a vessel as a bright pattern, piece-wise connected, and locally linear, mathematical morphology is very well adapted to this description, however other patterns fit such a morphological description. In order to differentiate vessels from analogous background patterns, a cross-curvature evaluation is performed. They are separated out as they have a specific Gaussian-like profile whose curvature varies smoothly along the vessel. The detection algorithm that derives directly from this modeling is based on four steps: (1) noise reduction; (2) linear pattern with Gaussian-like profile improvement; (3) cross-curvature evaluation; (4) linear filtering. We present its theoretical background and illustrate it on real images of various natures, then evaluate its robustness and its accuracy with respect to noise.

Contribution of spoken language and socio-economic background to adolescents' educational achievement at age 16 years.

PubMed

Spencer, Sarah; Clegg, Judy; Stackhouse, Joy; Rush, Robert

2017-03-01

Well-documented associations exist between socio-economic background and language ability in early childhood, and between educational attainment and language ability in children with clinically referred language impairment. However, very little research has looked at the associations between language ability, educational attainment and socio-economic background during adolescence, particularly in populations without language impairment. To investigate: (1) whether adolescents with higher educational outcomes overall had higher language abilities; and (2) associations between adolescent language ability, socio-economic background and educational outcomes, specifically in relation to Mathematics, English Language and English Literature GCSE grade. A total of 151 participants completed five standardized language assessments measuring vocabulary, comprehension of sentences and spoken paragraphs, and narrative skills and one nonverbal assessment when between 13 and 14 years old. These data were compared with the participants' educational achievement obtained upon leaving secondary education (16 years old). Univariate logistic regressions were employed to identify those language assessments and demographic factors that were associated with achieving a targeted A * -C grade in English Language, English Literature and Mathematics General Certificate of Secondary Education (GCSE) at 16 years. Further logistic regressions were then conducted to examine further the contribution of socio-economic background and spoken language skills in the multivariate models. Vocabulary, comprehension of sentences and spoken paragraphs, and mean length utterance in a narrative task along with socio-economic background contributed to whether participants achieved an A * -C grade in GCSE Mathematics and English Language and English Literature. Nonverbal ability contributed to English Language and Mathematics. The results of multivariate logistic regressions then found that vocabulary skills were particularly relevant to all three GCSE outcomes. Socio-economic background only remained important for English Language, once language assessment scores and demographic information were considered. Language ability, and in particular vocabulary, plays an important role for educational achievement. Results confirm a need for ongoing support for spoken language ability throughout secondary education and a potential role for speech and language therapy provision in the continuing drive to reduce the gap in educational attainment between groups from differing socio-economic backgrounds. © 2016 Royal College of Speech and Language Therapists.

What Have We Achieved in 50 Years of Equity in School Mathematics?

ERIC Educational Resources Information Center

Jorgensen, Robyn; Lowrie, Tom

2015-01-01

This paper explores the relationship between social backgrounds and geographical locations with mathematical achievement. Using the national testing system in Australia, correlations between the variables were explored and it was found that students from rural and low SES backgrounds are still being marginalised in school mathematics--in terms of…

Arithmetic Problems at School: When There Is an Apparent Contradiction between the Situation Model and the Problem Model

ERIC Educational Resources Information Center

Coquin-Viennot, Daniele; Moreau, Stephanie

2007-01-01

Background: Understanding and solving problems involves different levels of representation. On the one hand, there are logico-mathematical representations, or problem models (PMs), which contain information such as "the size of the flock changed from 31 sheep to 42" while, on the other hand, there are more qualitative representations, or…

The role of mathematics for physics teaching and understanding

NASA Astrophysics Data System (ADS)

Pospiech, Gesche; Eylon, BatSheva; Bagno, Esther; Lehavi, Yaron; Geyer, Marie-Annette

2016-05-01

-1That mathematics is the "language of physics" implies that both areas are deeply interconnected, such that often no separation between "pure" mathematics and "pure" physics is possible. To clarify their interplay a technical and a structural role of mathematics can be distinguished. A thorough understanding of this twofold role in physics is also important for shaping physics education especially with respect to teaching the nature of physics. Herewith the teachers and their pedagogical content knowledge play an important role. Therefore we develop a model of PCK concerning the interplay of mathematics and physics in order to provide a theoretical framework for the views and teaching strategies of teachers. In an exploratory study four teachers from Germany and four teachers from Israel have been interviewed concerning their views and its transfer to teaching physics. Here we describe the results from Germany. Besides general views and knowledge held by all or nearly all teachers we also observe specific individual focus depending on the teachers' background and experiences. The results fit well into the derived model of PCK.

Mathematics Performance and the Role Played by Affective and Background Factors

ERIC Educational Resources Information Center

Grootenboer, Peter; Hemmings, Brian

2007-01-01

In this article, we report on a study examining those factors which contribute to the mathematics performance of a sample of children aged between 8 and 13 years. The study was designed specifically to consider the potency of a number of mathematical affective factors, as well as background characteristics (viz., gender, ethnicity, and…

Women and Men Go to University: Mathematical Background and Gender Differences in Choice of Field in Higher Education.

ERIC Educational Resources Information Center

Ayalon, Hanna

2003-01-01

Using data on applicants to an Israeli university, researchers examined whether high school course-taking patterns affected gender segregation in higher education. Women were underrepresented among applicants to mathematics-related studies. Mathematical background in high school effectively narrowed the gender gap in applying to selective and…

Improving the Graduate School Experience for Women in Mathematics: the Edge Program

NASA Astrophysics Data System (ADS)

Bozeman, Sylvia T.; Hughes, Rhonda J.

For over a decade, Spelman College and Bryn Mawr College have collaborated on initiatives designed to increase the presence of women, with a special focus on women of color, in the upper ranks of mathematical science. The most recent initiative is the EDGE Program (Enhancing Diversity in Graduate Education), which addresses this challenge by attempting to decrease the loss of talent from U.S. graduate programs. To this end, the program provides structures that help women make successful transitions from undergraduate into graduate mathematics programs, redirect or refocus their ambitions when programs are inappropriate or unsuitable, and, ultimately, enable them to "accumulate advantages" that will empower them and foster success in their careers. A broader goal of this program is to diversify the mathematics community by creating models for mathematics programs that allow people from all backgrounds and cultures to thrive, advance, and contribute to the profession.

Visual and Vestibular Determinants of Perceived Eye-Level

NASA Technical Reports Server (NTRS)

Cohen, Malcolm Martin

2003-01-01

Both gravitational and optical sources of stimulation combine to determine the perceived elevations of visual targets. The ways in which these sources of stimulation combine with one another in operational aeronautical environments are critical for pilots to make accurate judgments of the relative altitudes of other aircraft and of their own altitude relative to the terrain. In a recent study, my colleagues and I required eighteen observers to set visual targets at their apparent horizon while they experienced various levels of G(sub z) in the human centrifuge at NASA-Ames Research Center. The targets were viewed in darkness and also against specific background optical arrays that were oriented at various angles with respect to the vertical; target settings were lowered as Gz was increased; this effect was reduced when the background optical array was visible. Also, target settings were displaced in the direction that the background optical array was pitched. Our results were attributed to the combined influences of otolith-oculomotor mechanisms that underlie the elevator illusion and visual-oculomotor mechanisms (optostatic responses) that underlie the perceptual effects of viewing pitched optical arrays that comprise the background. In this paper, I present a mathematical model that describes the independent and combined effects of G(sub z) intensity and the orientation and structure of background optical arrays; the model predicts quantitative deviations from normal accurate perceptions of target localization under a variety of conditions. Our earlier experimental results and the mathematical model are described in some detail, and the effects of viewing specific optical arrays under various gravitational-inertial conditions encountered in aeronautical environments are discussed.

Discover for Yourself: An Optimal Control Model in Insect Colonies

ERIC Educational Resources Information Center

Winkel, Brian

2013-01-01

We describe the enlightening path of self-discovery afforded to the teacher of undergraduate mathematics. This is demonstrated as we find and develop background material on an application of optimal control theory to model the evolutionary strategy of an insect colony to produce the maximum number of queen or reproducer insects in the colony at…

Development of a Conference Planning Model Using Integrated Database, Word Processing, and Spreadsheet Software.

ERIC Educational Resources Information Center

Stevens, William E.

This report presents a model for conducting a statewide conference for the approximately 900 members of the South Carolina Council of Teachers of Mathematics (SCCTM) using the AppleWorks integrated software as the basis of the implementation plan. The first and second chapters provide background information on the conference and the…

BMDExpress Data Viewer: A Visualization Tool to Analyze BMDExpress Datasets(SoTC)

EPA Science Inventory

Background: Benchmark Dose (BMD) modelling is a mathematical approach used to determine where a dose-response change begins to take place relative to controls following chemical exposure. BMDs are being increasingly applied in regulatory toxicology to estimate acceptable exposure...

BMDExpress Data Viewer: A Visualization Tool to Analyze BMDExpress Datasets (STC symposium)

EPA Science Inventory

Background: Benchmark Dose (BMD) modelling is a mathematical approach used to determine where a dose-response change begins to take place relative to controls following chemical exposure. BMDs are being increasingly applied in regulatory toxicology to estimate acceptable exposure...

Is Mathematics Education in England Working for Everyone? NFER Analysis of the PISA Performance of Disadvantaged Pupils

ERIC Educational Resources Information Center

Wheater, Rebecca; Durbin, Ben; McNamara, Stephen; Classick, Rachel

2016-01-01

The impact of socio-economic background on mathematics performance in England can be seen from the most to least disadvantaged. As socio-economic background of pupils increases, so does average mathematics performance; the gap between the most and least disadvantaged is equivalent to over three years' of schooling. However, many factors other than…

Cognitive tutor: applied research in mathematics education.

PubMed

Ritter, Steven; Anderson, John R; Koedinger, Kenneth R; Corbett, Albert

2007-04-01

For 25 years, we have been working to build cognitive models of mathematics, which have become a basis for middle- and high-school curricula. We discuss the theoretical background of this approach and evidence that the resulting curricula are more effective than other approaches to instruction. We also discuss how embedding a well specified theory in our instructional software allows us to dynamically evaluate the effectiveness of our instruction at a more detailed level than was previously possible. The current widespread use of the software is allowing us to test hypotheses across large numbers of students. We believe that this will lead to new approaches both to understanding mathematical cognition and to improving instruction.

Algebra for Enterprise Ontology: towards analysis and synthesis of enterprise models

NASA Astrophysics Data System (ADS)

Suga, Tetsuya; Iijima, Junichi

2018-03-01

Enterprise modeling methodologies have made enterprises more likely to be the object of systems engineering rather than craftsmanship. However, the current state of research in enterprise modeling methodologies lacks investigations of the mathematical background embedded in these methodologies. Abstract algebra, a broad subfield of mathematics, and the study of algebraic structures may provide interesting implications in both theory and practice. Therefore, this research gives an empirical challenge to establish an algebraic structure for one aspect model proposed in Design & Engineering Methodology for Organizations (DEMO), which is a major enterprise modeling methodology in the spotlight as a modeling principle to capture the skeleton of enterprises for developing enterprise information systems. The results show that the aspect model behaves well in the sense of algebraic operations and indeed constructs a Boolean algebra. This article also discusses comparisons with other modeling languages and suggests future work.

Using a Summer REU to Help Develop the Next Generation of Mathematical Ecologists.

PubMed

Bennie, Barbara; Eager, Eric Alan; Peirce, James P; Sandland, Gregory J

2018-04-01

Understanding the complexities of environmental issues requires individuals to bring together ideas and data from different disciplines, including ecology and mathematics. With funding from the national science foundation (NSF), scientists from the University of Wisconsin-La Crosse and the US geological survey held a research experience for undergraduates (REU) program in the summer of 2016. The goals of the program were to expose students to open problems in the area of mathematical ecology, motivate students to pursue STEM-related positions, and to prepare students for research within interdisciplinary, collaborative settings. Based on backgrounds and interests, eight students were selected to participate in one of two research projects: wind energy and wildlife conservation or the establishment and spread of waterfowl diseases. Each research program was overseen by a mathematician and a biologist. Regardless of the research focus, the program first began with formal lectures to provide students with foundational knowledge followed by student-driven research projects. Throughout this period, student teams worked in close association with their mentors to create, parameterize and evaluate ecological models to better understand their systems of interest. Students then disseminated their results at local, regional, and international meetings and through publications (one in press and one in progress). Direct and indirect measures of student development revealed that our REU program fostered a deep appreciation for and understanding of mathematical ecology. Finally, the program allowed students to gain experiences working with individuals with different backgrounds and perspectives. Taken together, this REU program allowed us to successfully excite, motivate and prepare students for future positions in the area of mathematical biology, and because of this it can be used as a model for interdisciplinary programs at other institutions.

Finite fringe hologram

NASA Technical Reports Server (NTRS)

Heflinger, L. O.

1970-01-01

In holographic interferometry a small movement of apparatus between exposures causes the background of the reconstructed scene to be covered with interference fringes approximately parallel to each other. The three-dimensional quality of the holographic image is allowable since a mathematical model will give the location of the fringes.

Review: To be or not to be an identifiable model. Is this a relevant question in animal science modelling?

PubMed

Muñoz-Tamayo, R; Puillet, L; Daniel, J B; Sauvant, D; Martin, O; Taghipoor, M; Blavy, P

2018-04-01

What is a good (useful) mathematical model in animal science? For models constructed for prediction purposes, the question of model adequacy (usefulness) has been traditionally tackled by statistical analysis applied to observed experimental data relative to model-predicted variables. However, little attention has been paid to analytic tools that exploit the mathematical properties of the model equations. For example, in the context of model calibration, before attempting a numerical estimation of the model parameters, we might want to know if we have any chance of success in estimating a unique best value of the model parameters from available measurements. This question of uniqueness is referred to as structural identifiability; a mathematical property that is defined on the sole basis of the model structure within a hypothetical ideal experiment determined by a setting of model inputs (stimuli) and observable variables (measurements). Structural identifiability analysis applied to dynamic models described by ordinary differential equations (ODEs) is a common practice in control engineering and system identification. This analysis demands mathematical technicalities that are beyond the academic background of animal science, which might explain the lack of pervasiveness of identifiability analysis in animal science modelling. To fill this gap, in this paper we address the analysis of structural identifiability from a practitioner perspective by capitalizing on the use of dedicated software tools. Our objectives are (i) to provide a comprehensive explanation of the structural identifiability notion for the community of animal science modelling, (ii) to assess the relevance of identifiability analysis in animal science modelling and (iii) to motivate the community to use identifiability analysis in the modelling practice (when the identifiability question is relevant). We focus our study on ODE models. By using illustrative examples that include published mathematical models describing lactation in cattle, we show how structural identifiability analysis can contribute to advancing mathematical modelling in animal science towards the production of useful models and, moreover, highly informative experiments via optimal experiment design. Rather than attempting to impose a systematic identifiability analysis to the modelling community during model developments, we wish to open a window towards the discovery of a powerful tool for model construction and experiment design.

Basic research for the geodynamics program

NASA Technical Reports Server (NTRS)

1991-01-01

The mathematical models of space very long base interferometry (VLBI) observables suitable for least squares covariance analysis were derived and estimatability problems inherent in the space VLBI system were explored, including a detailed rank defect analysis and sensitivity analysis. An important aim is to carry out a comparative analysis of the mathematical models of the ground-based VLBI and space VLBI observables in order to describe the background in detail. Computer programs were developed in order to check the relations, assess errors, and analyze sensitivity. In order to investigate the estimatability of different geodetic and geodynamic parameters from the space VLBI observables, the mathematical models for time delay and time delay rate observables of space VLBI were analytically derived along with the partial derivatives with respect to the parameters. Rank defect analysis was carried out both by analytical and numerical testing of linear dependencies between the columns of the normal matrix thus formed. Definite conclusions were formed about the rank defects in the system.

Do the Teacher and School Factors of the Dynamic Model Affect High- and Low-Achieving Student Groups to the Same Extent? A Cross-Country Study

ERIC Educational Resources Information Center

Vanlaar, Gudrun; Kyriakides, Leonidas; Panayiotou, Anastasia; Vandecandelaere, Machteld; McMahon, Léan; De Fraine, Bieke; Van Damme, Jan

2016-01-01

Background: The dynamic model of educational effectiveness (DMEE) is a comprehensive theoretical framework including factors that are important for school learning, based on consistent findings within educational effectiveness research. Purpose: This study investigates the impact of teacher and school factors of DMEE on mathematics and science…

Precision Cosmology: The First Half Million Years

NASA Astrophysics Data System (ADS)

Jones, Bernard J. T.

2017-06-01

Cosmology seeks to characterise our Universe in terms of models based on well-understood and tested physics. Today we know our Universe with a precision that once would have been unthinkable. This book develops the entire mathematical, physical and statistical framework within which this has been achieved. It tells the story of how we arrive at our profound conclusions, starting from the early twentieth century and following developments up to the latest data analysis of big astronomical datasets. It provides an enlightening description of the mathematical, physical and statistical basis for understanding and interpreting the results of key space- and ground-based data. Subjects covered include general relativity, cosmological models, the inhomogeneous Universe, physics of the cosmic background radiation, and methods and results of data analysis. Extensive online supplementary notes, exercises, teaching materials, and exercises in Python make this the perfect companion for researchers, teachers and students in physics, mathematics, and astrophysics.

African American Mathematics Teachers as Agents in Their African American Students' Mathematics Identity Formation

ERIC Educational Resources Information Center

Clark, Lawrence M.; Badertscher, Eden M.; Napp, Carolina

2013-01-01

Background/Context: Recent research in mathematics education has employed sociocultural and historical lenses to better understand how students experience school mathematics and come to see themselves as capable mathematics learners. This work has identified mathematics classrooms as places where power struggles related to students'…

Exploring the Earth System through online interactive models

NASA Astrophysics Data System (ADS)

Coogan, L. A.

2013-12-01

Upper level Earth Science students commonly have a strong background of mathematical training from Math courses, however their ability to use mathematical models to solve Earth Science problems is commonly limited. Their difficulty comes, in part, because of the nature of the subject matter. There is a large body of background ';conceptual' and ';observational' understanding and knowledge required in the Earth Sciences before in-depth quantification becomes useful. For example, it is difficult to answer questions about geological processes until you can identify minerals and rocks and understand the general geodynamic implications of their associations. However, science is fundamentally quantitative. To become scientists students have to translate their conceptual understanding into quantifiable models. Thus, it is desirable for students to become comfortable with using mathematical models to test hypotheses. With the aim of helping to bridging the gap between conceptual understanding and quantification I have started to build an interactive teaching website based around quantitative models of Earth System processes. The site is aimed at upper-level undergraduate students and spans a range of topics that will continue to grow as time allows. The mathematical models are all built for the students, allowing them to spend their time thinking about how the ';model world' changes in response to their manipulation of the input variables. The web site is divided into broad topics or chapters (Background, Solid Earth, Ocean and Atmosphere, Earth history) and within each chapter there are different subtopic (e.g. Solid Earth: Core, Mantle, Crust) and in each of these individual webpages. Each webpage, or topic, starts with an introduction to the topic, followed by an interactive model that the students can use sliders to control the input to and watch how the results change. This interaction between student and model is guided by a series of multiple choice questions that the student answers and immediately gets feedback whether the answer is correct or not. This way the students can ensure they understand the concepts before moving on. A discussion forum for the students to discuss the topics is in development and each page has a feedback option to allow both numerical (1-10) and written feedback on how useful the webpage was. By the end of exploring any given process students are expected to understand how the different parameters explored by the model interact to control the results. They should appreciate why the controlling equations look the way they do (all equations needed to develop the models are present in the introduction) and how these interact to control the results. While this is no substitute to students undertaking the calculations for themselves this approach allows a much wider range of topics to be explored quantitatively than if the students have to code all models themselves.

Cognitive Correlates of Performance in Advanced Mathematics

ERIC Educational Resources Information Center

Wei, Wei; Yuan, Hongbo; Chen, Chuansheng; Zhou, Xinlin

2012-01-01

Background: Much research has been devoted to understanding cognitive correlates of elementary mathematics performance, but little such research has been done for advanced mathematics (e.g., modern algebra, statistics, and mathematical logic).Aims: To promote mathematical knowledge among college students, it is necessary to understand what factors…

Models for the effects of host movement in vector-borne disease systems.

PubMed

Cosner, Chris

2015-12-01

Host and/or vector movement patterns have been shown to have significant effects in both empirical studies and mathematical models of vector-borne diseases. The processes of economic development and globalization seem likely to make host movement even more important in the future. This article is a brief survey of some of the approaches that have been used to study the effects of host movement in analytic mathematical models for vector-borne diseases. It describes the formulation and interpretation of various types of spatial models and describes a few of the conclusions that can be drawn from them. It is not intended to be comprehensive but rather to provide sufficient background material and references to the literature to serve as an entry point into this area of research for interested readers. Copyright © 2015 Elsevier Inc. All rights reserved.

Mind map learning for advanced engineering study: case study in system dynamics

NASA Astrophysics Data System (ADS)

Woradechjumroen, Denchai

2018-01-01

System Dynamics (SD) is one of the subjects that were use in learning Automatic Control Systems in dynamic and control field. Mathematical modelling and solving skills of students for engineering systems are expecting outcomes of the course which can be further used to efficiently study control systems and mechanical vibration; however, the fundamental of the SD includes strong backgrounds in Dynamics and Differential Equations, which are appropriate to the students in governmental universities that have strong skills in Mathematics and Scientifics. For private universities, students are weak in the above subjects since they obtained high vocational certificate from Technical College or Polytechnic School, which emphasize the learning contents in practice. To enhance their learning for improving their backgrounds, this paper applies mind maps based problem based learning to relate the essential relations of mathematical and physical equations. With the advantages of mind maps, each student is assigned to design individual mind maps for self-leaning development after they attend the class and learn overall picture of each chapter from the class instructor. Four problems based mind maps learning are assigned to each student. Each assignment is evaluated via mid-term and final examinations, which are issued in terms of learning concepts and applications. In the method testing, thirty students are tested and evaluated via student learning backgrounds in the past. The result shows that well-design mind maps can improve learning performance based on outcome evaluation. Especially, mind maps can reduce time-consuming and reviewing for Mathematics and Physics in SD significantly.

Examples of testing global identifiability of biological and biomedical models with the DAISY software.

PubMed

Saccomani, Maria Pia; Audoly, Stefania; Bellu, Giuseppina; D'Angiò, Leontina

2010-04-01

DAISY (Differential Algebra for Identifiability of SYstems) is a recently developed computer algebra software tool which can be used to automatically check global identifiability of (linear and) nonlinear dynamic models described by differential equations involving polynomial or rational functions. Global identifiability is a fundamental prerequisite for model identification which is important not only for biological or medical systems but also for many physical and engineering systems derived from first principles. Lack of identifiability implies that the parameter estimation techniques may not fail but any obtained numerical estimates will be meaningless. The software does not require understanding of the underlying mathematical principles and can be used by researchers in applied fields with a minimum of mathematical background. We illustrate the DAISY software by checking the a priori global identifiability of two benchmark nonlinear models taken from the literature. The analysis of these two examples includes comparison with other methods and demonstrates how identifiability analysis is simplified by this tool. Thus we illustrate the identifiability analysis of other two examples, by including discussion of some specific aspects related to the role of observability and knowledge of initial conditions in testing identifiability and to the computational complexity of the software. The main focus of this paper is not on the description of the mathematical background of the algorithm, which has been presented elsewhere, but on illustrating its use and on some of its more interesting features. DAISY is available on the web site http://www.dei.unipd.it/ approximately pia/. 2010 Elsevier Ltd. All rights reserved.

Automated Design Tools for Integrated Mixed-Signal Microsystems (NeoCAD)

DTIC Science & Technology

2005-02-01

method, Model Order Reduction (MOR) tools, system-level, mixed-signal circuit synthesis and optimization tools, and parsitic extraction tools. A unique...Mission Area: Command and Control mixed signal circuit simulation parasitic extraction time-domain simulation IC design flow model order reduction... Extraction 1.2 Overall Program Milestones CHAPTER 2 FAST TIME DOMAIN MIXED-SIGNAL CIRCUIT SIMULATION 2.1 HAARSPICE Algorithms 2.1.1 Mathematical Background

Mathematical Ability and Socio-Economic Background: IRT Modeling to Estimate Genotype by Environment Interaction.

PubMed

Schwabe, Inga; Boomsma, Dorret I; van den Berg, Stéphanie M

2017-12-01

Genotype by environment interaction in behavioral traits may be assessed by estimating the proportion of variance that is explained by genetic and environmental influences conditional on a measured moderating variable, such as a known environmental exposure. Behavioral traits of interest are often measured by questionnaires and analyzed as sum scores on the items. However, statistical results on genotype by environment interaction based on sum scores can be biased due to the properties of a scale. This article presents a method that makes it possible to analyze the actually observed (phenotypic) item data rather than a sum score by simultaneously estimating the genetic model and an item response theory (IRT) model. In the proposed model, the estimation of genotype by environment interaction is based on an alternative parametrization that is uniquely identified and therefore to be preferred over standard parametrizations. A simulation study shows good performance of our method compared to analyzing sum scores in terms of bias. Next, we analyzed data of 2,110 12-year-old Dutch twin pairs on mathematical ability. Genetic models were evaluated and genetic and environmental variance components estimated as a function of a family's socio-economic status (SES). Results suggested that common environmental influences are less important in creating individual differences in mathematical ability in families with a high SES than in creating individual differences in mathematical ability in twin pairs with a low or average SES.

Optimizing Chemotherapy Dose and Schedule by Norton-Simon Mathematical Modeling

PubMed Central

Traina, Tiffany A.; Dugan, Ute; Higgins, Brian; Kolinsky, Kenneth; Theodoulou, Maria; Hudis, Clifford A.; Norton, Larry

2011-01-01

Background To hasten and improve anticancer drug development, we created a novel approach to generating and analyzing preclinical dose-scheduling data so as to optimize benefit-to-toxicity ratios. Methods We applied mathematical methods based upon Norton-Simon growth kinetic modeling to tumor-volume data from breast cancer xenografts treated with capecitabine (Xeloda®, Roche) at the conventional schedule of 14 days of treatment followed by a 7-day rest (14 - 7). Results The model predicted that 7 days of treatment followed by a 7-day rest (7 - 7) would be superior. Subsequent preclinical studies demonstrated that this biweekly capecitabine schedule allowed for safe delivery of higher daily doses, improved tumor response, and prolonged animal survival. Conclusions We demonstrated that the application of Norton-Simon modeling to the design and analysis of preclinical data predicts an improved capecitabine dosing schedule in xenograft models. This method warrants further investigation and application in clinical drug development. PMID:20519801

The contribution of parent-child numeracy activities to young Chinese children's mathematical ability.

PubMed

Huang, Qi; Zhang, Xiao; Liu, Yingyi; Yang, Wen; Song, Zhanmei

2017-09-01

A growing body of recent research has shown that parent-child mathematical activities have a strong effect on children's mathematical learning. However, this research was conducted predominantly in Western societies and focused mainly on mothers' involvement in such activities. This study aimed to examine both mother-child and father-child numeracy activities in Hong Kong Chinese families and both parents' unique roles in predicting young Chinese children's mathematics ability. A sample of 104 Hong Kong Chinese children aged approximately 5 years and their mothers and fathers participated in this study. Mothers and fathers independently reported the frequency of their own numeracy activities with their children. Children were assessed individually using two measures of mathematical ability. Hierarchical regression models were used to investigate the contribution of parent-child numeracy activities to children's mathematical ability. Mothers' participation in number skill activities and fathers' participation in number game and application activities significantly predicted their children's mathematical performance even after controlling for background variables and children's language ability. This study extends previous research with a sample of Chinese kindergarten children and shows that parent-child numeracy activities are related to young children's mathematical ability. The findings highlight the important roles that mothers and fathers play in their young children's mathematical learning. © 2017 The British Psychological Society.

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…

Application of a Mathematical Model to Describe the Effects of Chlorpyrifos on Caenorhabditis elegans Development

PubMed Central

Boyd, Windy A.; Smith, Marjolein V.; Kissling, Grace E.; Rice, Julie R.; Snyder, Daniel W.; Portier, Christopher J.; Freedman, Jonathan H.

2009-01-01

Background The nematode Caenorhabditis elegans is being assessed as an alternative model organism as part of an interagency effort to develop better means to test potentially toxic substances. As part of this effort, assays that use the COPAS Biosort flow sorting technology to record optical measurements (time of flight (TOF) and extinction (EXT)) of individual nematodes under various chemical exposure conditions are being developed. A mathematical model has been created that uses Biosort data to quantitatively and qualitatively describe C. elegans growth, and link changes in growth rates to biological events. Chlorpyrifos, an organophosphate pesticide known to cause developmental delays and malformations in mammals, was used as a model toxicant to test the applicability of the growth model for in vivo toxicological testing. Methodology/Principal Findings L1 larval nematodes were exposed to a range of sub-lethal chlorpyrifos concentrations (0–75 µM) and measured every 12 h. In the absence of toxicant, C. elegans matured from L1s to gravid adults by 60 h. A mathematical model was used to estimate nematode size distributions at various times. Mathematical modeling of the distributions allowed the number of measured nematodes and log(EXT) and log(TOF) growth rates to be estimated. The model revealed three distinct growth phases. The points at which estimated growth rates changed (change points) were constant across the ten chlorpyrifos concentrations. Concentration response curves with respect to several model-estimated quantities (numbers of measured nematodes, mean log(TOF) and log(EXT), growth rates, and time to reach change points) showed a significant decrease in C. elegans growth with increasing chlorpyrifos concentration. Conclusions Effects of chlorpyrifos on C. elegans growth and development were mathematically modeled. Statistical tests confirmed a significant concentration effect on several model endpoints. This confirmed that chlorpyrifos affects C. elegans development in a concentration dependent manner. The most noticeable effect on growth occurred during early larval stages: L2 and L3. This study supports the utility of the C. elegans growth assay and mathematical modeling in determining the effects of potentially toxic substances in an alternative model organism using high-throughput technologies. PMID:19753116

Mathematics Achievement Levels of Black and White Youth. Report No. 165.

ERIC Educational Resources Information Center

Jones, Lyle V.; And Others

Based on data provided by the National Assessment of Educational Progress, this study examines mathematics achievement in relation to various background variables, contrasts achievement levels of black and white (females and males) youth, and evaluates group achievement differences in the light of group differences in background variables.…

Who’s Afraid of Math? Two Sources of Genetic Variance for Mathematical Anxiety

PubMed Central

Wang, Zhe; Hart, Sara Ann; Kovas, Yulia; Lukowski, Sarah; Soden, Brooke; Thompson, Lee A.; Plomin, Robert; McLoughlin, Grainne; Bartlett, Christopher W.; Lyons, Ian M.; Petrill, Stephen A.

2015-01-01

Background Emerging work suggests that academic achievement may be influenced by the management of affect as well as through efficient information processing of task demands. In particular, mathematical anxiety has attracted recent attention because of its damaging psychological effects and potential associations with mathematical problem-solving and achievement. The present study investigated the genetic and environmental factors contributing to the observed differences in the anxiety people feel when confronted with mathematical tasks. In addition, the genetic and environmental mechanisms that link mathematical anxiety with math cognition and general anxiety were also explored. Methods Univariate and multivariate quantitative genetic models were conducted in a sample of 514 12-year-old twin siblings. Results Genetic factors accounted for roughly 40% of the variation in mathematical anxiety, with the remaining being accounted for by child-specific environmental factors. Multivariate genetic analyses suggested that mathematical anxiety was influenced by the genetic and non-familial environmental risk factors associated with general anxiety and additional independent genetic influences associated with math-based problem solving. Conclusions The development of mathematical anxiety may involve not only exposure to negative experiences with mathematics, but also likely involves genetic risks related to both anxiety and math cognition. These results suggest that integrating cognitive and affective domains may be particularly important for mathematics, and may extend to other areas of academic achievement. PMID:24611799

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…

Mathematical Idea Analysis: What Embodied Cognitive Science Can Say about the Human Nature of Mathematics.

ERIC Educational Resources Information Center

Nunez, Rafael E.

This paper gives a brief introduction to a discipline called the cognitive science of mathematics. The theoretical background of the arguments is based on embodied cognition and findings in cognitive linguistics. It discusses Mathematical Idea Analysis, a set of techniques for studying implicit structures in mathematics. Particular attention is…

A Formal Theory of Perception. Technical Report No. 161.

ERIC Educational Resources Information Center

Rottmayer, William Arthur

An attempt to build a mathematical model of a device that could learn geometry is discussed. The report discusses the background and motivation of the study, the coding problem, the derivation of Suppes "Stimulus-Response Theory of Finite Automata" used in the work in learning theory, and a summary of the technical work. (DB)

Paul Pinsky, PhD | Division of Cancer Prevention

Cancer.gov

Dr. Paul Pinsky is the chief of the Early Detection Research Branch. He has a background in statistics, epidemiology and mathematical modeling. He has worked extensively with data from the Branch's two large screening trials, the Prostate, Lung, Colorectal and Ovarian (PLCO) Cancer Screening Trial and the National Lung Screening Trial (NLST). |

Confronting Color-Blind STEM Talent Development: Toward a Contextual Model for Black Student STEM Identity

ERIC Educational Resources Information Center

Collins, Kristina Henry

2018-01-01

What is Black student's science, technology, engineering, and mathematics (STEM) identity? The author addresses this question through a synthesis of the literature that includes studies that explore Black student identity. Background information regarding STEM achievement and persistence followed by empirical studies that explore STEM attitudes…

Student Math Skills Reference Manual.

ERIC Educational Resources Information Center

Wilson, Odell; And Others

This mathematics support guide is intended for use by vocational students and instructors as a review of essential mathematics concepts and for problem-solving exercises in the vocations. It is designed to accompany the "Mathematical Skills Inventory," which tests mathematics skills, attitudes, and background. A section entitled Arithmetic Skills…

Modern Versus Traditional Mathematics

ERIC Educational Resources Information Center

Roberts, A. M.

1974-01-01

The effect of different secondary school mathematics syllabi on first-year performance in college-level mathematics was studied in an attempt to evaluate the syllabus change. Students with a modern mathematics background performed sigficantly better on most first-year units. A topic-by-topic analysis of results is included. (DT)

Linear Sigma Model Toolshed for D-brane Physics

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

Hellerman, Simeon

Building on earlier work, we construct linear sigma models for strings on curved spaces in the presence of branes. Our models include an extremely general class of brane-worldvolume gauge field configurations. We explain in an accessible manner the mathematical ideas which suggest appropriate worldsheet interactions for generating a given open string background. This construction provides an explanation for the appearance of the derived category in D-brane physic complementary to that of recent work of Douglas.

Relationship between Attitude towards Technical Education and Academic Achievement in Mathematics and Science of the First and Second Year High School Students, Caritas Don Bosco School, SY 2002-2003

ERIC Educational Resources Information Center

Magno, Carlo

2003-01-01

Background: This study made use of the "Model of Academic Choice" by Meece et al. (1982). It is a general model of academic choice, expectation and value of attitude leading to achievement. The model links achievement with constructs of expectation of success on a task and the subjective value of the task influencing the attitude of…

Assessing Strategies Against Gambiense Sleeping Sickness Through Mathematical Modeling

PubMed Central

Rock, Kat S; Ndeffo-Mbah, Martial L; Castaño, Soledad; Palmer, Cody; Pandey, Abhishek; Atkins, Katherine E; Ndung’u, Joseph M; Hollingsworth, T Déirdre; Galvani, Alison; Bever, Caitlin; Chitnis, Nakul; Keeling, Matt J

2018-01-01

Abstract Background Control of gambiense sleeping sickness relies predominantly on passive and active screening of people, followed by treatment. Methods Mathematical modeling explores the potential of 3 complementary interventions in high- and low-transmission settings. Results Intervention strategies that included vector control are predicted to halt transmission most quickly. Targeted active screening, with better and more focused coverage, and enhanced passive surveillance, with improved access to diagnosis and treatment, are both estimated to avert many new infections but, when used alone, are unlikely to halt transmission before 2030 in high-risk settings. Conclusions There was general model consensus in the ranking of the 3 complementary interventions studied, although with discrepancies between the quantitative predictions due to differing epidemiological assumptions within the models. While these predictions provide generic insights into improving control, the most effective strategy in any situation depends on the specific epidemiology in the region and the associated costs. PMID:29860287

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.

Student Perceptions about Applied Mathematics.

ERIC Educational Resources Information Center

Keif, Malcolm G.; Stewart, Bob R.

Background information on the history and rationale for Tech Prep introduces the description of a study that examines the perceptions of students enrolled in Applied Mathematics 1 and Applied Mathematics 2 courses which are based on the Center for Occupational Research and Development's (CORD) applied mathematics curriculum. The primary goal is to…

Problem Posing with the Multiplication Table

ERIC Educational Resources Information Center

Dickman, Benjamin

2014-01-01

Mathematical problem posing is an important skill for teachers of mathematics, and relates readily to mathematical creativity. This article gives a bit of background information on mathematical problem posing, lists further references to connect problem posing and creativity, and then provides 20 problems based on the multiplication table to be…

Confidence in Teaching Mathematics among Malaysian Pre-Service Teachers

ERIC Educational Resources Information Center

Yunus, Aida Suraya Md.; Hamzah, Ramlah; Ismail, Habsah; Husain, Sharifah Kartini Said; Ismail, Mat Rofa

2006-01-01

This study focuses on the confidence level of mathematics education students in teaching school mathematics. Respondents were 165 final year students from four Malaysian universities. It was found that the respondents showed a strong foundation in mathematics upon entrance to the university. In spite of their strong background in school…

Exploring Relationships between Presage Variables of Florida Preservice Agricultural Education Teachers Related to Teaching Contextualized Mathematics

ERIC Educational Resources Information Center

Stripling, Christopher T.; Roberts, T. Grady

2013-01-01

The purpose of this exploratory study was to investigate the relationships between mathematics ability, personal mathematics efficacy, mathematics teaching efficacy, personal teaching efficacy, and background characteristics of preservice agricultural education teachers. Data were collected for two years at the University of Florida. Fourteen…

Identifying and Encouraging Math in Children's Out-of-School Activities in the Rural Lowcountry of South Carolina

ERIC Educational Resources Information Center

Hyatt, Sherry

2013-01-01

Research shows that children of different backgrounds and cultures learn and perform differently in mathematics despite similar intelligence levels and mathematics instruction (Alvarez & Bali, 2004). Ethnomathematics strives to explore and explain such phenomena in terms of the complex role culture plays in one's background experiences and…

Examining school effectiveness at the fourth grade: A hierarchical analysis of the Third International Mathematics and Science Study (TIMSS)

NASA Astrophysics Data System (ADS)

Stemler, Steven Edward

This study explored school effectiveness in mathematics and science at the fourth grade using data from IEA's Third International Mathematics and Science Study (TIMSS). Fourteen of the 26 countries participating in TIMSS at the fourth grade possessed sufficient between-school variability in mathematics achievement to justify the creation of explanatory models of school effectiveness while 13 countries possessed sufficient between-school variability in science achievement. Exploratory models were developed using variables drawn from student, teacher, and school questionnaires. The variables were chosen to represent the domains of student involvement, instructional methods, classroom organization, school climate, and school structure. Six explanatory models for each subject were analyzed using two-level hierarchical linear modeling (HLM) and were compared to models using only school mean SES as an explanatory variable. The amount of variability in student achievement in mathematics attributable to differences between schools ranged from 16% in Cyprus to 56% in Latvia, while the amount of between-school variance in science achievement ranged from 12% in Korea to 59% in Latvia. In general, about one-quarter of the variability in mathematics and science achievement was found to lie between schools. The research findings revealed that after adjusting for differences in student backgrounds across schools, the most effective schools in mathematics and science had students who reported seeing a positive relationship between hard work, belief in their own abilities, and achievement. In addition, more effective schools had students who reported less frequent use of computers and calculators in the classroom. These relationships were found to be stable across explanatory models, cultural contexts, and subject areas. This study has contributed a unique element to the literature by examining school effectiveness at the fourth grade across two subject areas and across 14 different countries. The results indicate that further exploration of the relationship between school effectiveness and student locus of control warrants serious consideration. Future research on school effectiveness is recommended, perhaps using trend data and looking at different grade levels.

Teacher and Classroom Characteristics and Their Relations to Mathematics Achievement of the Students in the TIMSS

ERIC Educational Resources Information Center

Akyuz, Gozde; Berberoglu, Giray

2010-01-01

Background: Teacher-related factors such as gender, experience, conceptions related to mathematics, instructional practices have effects with various magnitudes on students' mathematics achievement. Classroom related factors such as class size, class climate and limitations to teaching and their relation to mathematics achievement have also been…

Mathematics Learning Styles of Chinese Immigrant Students. Final Research Report.

ERIC Educational Resources Information Center

Tsang, Sau-Lim

Major revision in the U.S. mathematics curriculum since the 1960s have led to significant differences between the mathematics curriculum of the United States and those of many other countries. This study explored how eight Chinese immigrant students, with different cultural backgrounds, mathematics knowledge, and learning styles, learned in an…

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…

Relations between Technology, Parent Education, Self-Confidence, and Academic Aspiration of Hispanic Immigrant Students

ERIC Educational Resources Information Center

Park, Haeseong; Lawson, Daniel; Williams, Helen Easterling

2012-01-01

The purpose of this project is to test a theoretical model explaining the relationship between technology use, parent educational background, academic aspiration, and self-confidence as predictors of mathematics achievement across three immigrant groups. This study utilized data from the TIMSS 2007. To compare the effect size of technology use,…

High Achievers from Low Socioeconomic Backgrounds: The Critical Role of Disciplinary Climate and Grit

ERIC Educational Resources Information Center

Huang, Haigen; Zhu, Hao

2017-01-01

The purpose of this study was to examine whether school disciplinary climate and grit predicted low socioeconomic status (SES) students being high achievers in mathematics and science with a representative sample of 15-year-old students in the United States. Our analysis, using a two-level logistic hierarchical linear model (HLM), indicated both…

Cyberspace Math Models

DTIC Science & Technology

2013-06-01

or indicators are used as long range memory measurements. Hurst and Holder exponents are the most important and popular parameters. Traditionally...the relation between two important parameters, the Hurst exponent (measurement of global long range memory) and the Entropy (measurement of...empirical results and future study. II. BACKGROUND We recall briey the mathematical and statistical definitions and properties of the Hurst exponents

Student Background and Teacher Effects on Achievement and Attainment in Mathematics: A Longitudinal Study

ERIC Educational Resources Information Center

Muijs, Daniel; Reynolds, David

2003-01-01

In this article, we have studied the effect of student social background, classroom social context, classroom organisation, and teacher behaviours on mathematics achievement and attainment in English and Welsh primary schools. Data were collected over 2 years as part of a programme evaluation, for which we observed 138 teachers and tested and…

The Role of Family Background and School Resources on Elementary School Students' Mathematics Achievement

ERIC Educational Resources Information Center

Nonoyama-Tarumi, Yuko; Hughes, Kathleen; Willms, J. Douglas

2015-01-01

This article compares the effects of family background and school resources on fourth-grade students' math achievement, using data from the 2011 Trends in International Mathematics and Science Study (TIMSS). In order to ameliorate potential floor effects, it uses relative risk and population attributable risk to examine the effects of family…

Reorganizing Freshman Business Mathematics I: Background and Philosophy

ERIC Educational Resources Information Center

Green, Kris; Emerson, Allen

2008-01-01

This article is the first of the two-part discussion of the development of a new Freshman Business Mathematics (FBM) course at our college. Part I of the article describes the background and history behind the course, and provides a theoretical framework for the design of the course. This design involves students in learning and applying…

An Analysis of Final Course Grades in Two Different Entry Level Mathematics Courses between and among First Year College Students with Different Levels of High School Mathematics Preparation

ERIC Educational Resources Information Center

Muir, Carrie

2012-01-01

The purpose of this study was to compare the performance of first year college students with similar high school mathematics backgrounds in two introductory level college mathematics courses, "Fundamentals and Techniques of College Algebra and Quantitative Reasoning and Mathematical Skills," and to compare the performance of students…

How to mathematically optimize drug regimens using optimal control.

PubMed

Moore, Helen

2018-02-01

This article gives an overview of a technique called optimal control, which is used to optimize real-world quantities represented by mathematical models. I include background information about the historical development of the technique and applications in a variety of fields. The main focus here is the application to diseases and therapies, particularly the optimization of combination therapies, and I highlight several such examples. I also describe the basic theory of optimal control, and illustrate each of the steps with an example that optimizes the doses in a combination regimen for leukemia. References are provided for more complex cases. The article is aimed at modelers working in drug development, who have not used optimal control previously. My goal is to make this technique more accessible in the biopharma community.

Researching Race in Mathematics Education

ERIC Educational Resources Information Center

Martin, Danny Bernard

2009-01-01

Background: Within mathematics education research, policy, and practice, race remains undertheorized in relation to mathematics learning and participation. Although race is characterized in the sociological and critical theory literatures as socially and politically constructed with structural expressions, most studies of differential outcomes in…

Finite-element approach to Brownian dynamics of polymers.

PubMed

Cyron, Christian J; Wall, Wolfgang A

2009-12-01

In the last decades simulation tools for Brownian dynamics of polymers have attracted more and more interest. Such simulation tools have been applied to a large variety of problems and accelerated the scientific progress significantly. However, the currently most frequently used explicit bead models exhibit severe limitations, especially with respect to time step size, the necessity of artificial constraints and the lack of a sound mathematical foundation. Here we present a framework for simulations of Brownian polymer dynamics based on the finite-element method. This approach allows simulating a wide range of physical phenomena at a highly attractive computational cost on the basis of a far-developed mathematical background.

Mathematical algorithm development and parametric studies with the GEOFRAC three-dimensional stochastic model of natural rock fracture systems

NASA Astrophysics Data System (ADS)

Ivanova, Violeta M.; Sousa, Rita; Murrihy, Brian; Einstein, Herbert H.

2014-06-01

This paper presents results from research conducted at MIT during 2010-2012 on modeling of natural rock fracture systems with the GEOFRAC three-dimensional stochastic model. Following a background summary of discrete fracture network models and a brief introduction of GEOFRAC, the paper provides a thorough description of the newly developed mathematical and computer algorithms for fracture intensity, aperture, and intersection representation, which have been implemented in MATLAB. The new methods optimize, in particular, the representation of fracture intensity in terms of cumulative fracture area per unit volume, P32, via the Poisson-Voronoi Tessellation of planes into polygonal fracture shapes. In addition, fracture apertures now can be represented probabilistically or deterministically whereas the newly implemented intersection algorithms allow for computing discrete pathways of interconnected fractures. In conclusion, results from a statistical parametric study, which was conducted with the enhanced GEOFRAC model and the new MATLAB-based Monte Carlo simulation program FRACSIM, demonstrate how fracture intensity, size, and orientations influence fracture connectivity.

Proposing a Formalised Model for Mindful Information Systems Offshoring

NASA Astrophysics Data System (ADS)

Costello, Gabriel J.; Coughlan, Chris; Donnellan, Brian; Gadatsch, Andreas

The central thesis of this chapter is that mathematical economics can provide a novel approach to the examination of offshoring business decisions and provide an impetus for future research in the area. A growing body of research indicates that projected cost savings from IT offshoring projects are not being met. Furthermore, evidence suggests that decision-making processes have been more emotional than rational, and that many offshoring arrangements have been rushed into without adequate analysis of the true costs involved. Building on the concept of mindfulness and mindlessness introduced to the IS literature by Swanson and Ramiller, a cost equation is developed using “deductive reasoning rather than inductive study” in the tradition of mathematical economics. The model endeavours to capture a wide range of both the quantitative and qualitative parameters. Although the economic model is illustrated against the background of a European scenario, the theoretical framework is generic and applicable to organisations in any global location.

Equation Discovery for Model Identification in Respiratory Mechanics of the Mechanically Ventilated Human Lung

NASA Astrophysics Data System (ADS)

Ganzert, Steven; Guttmann, Josef; Steinmann, Daniel; Kramer, Stefan

Lung protective ventilation strategies reduce the risk of ventilator associated lung injury. To develop such strategies, knowledge about mechanical properties of the mechanically ventilated human lung is essential. This study was designed to develop an equation discovery system to identify mathematical models of the respiratory system in time-series data obtained from mechanically ventilated patients. Two techniques were combined: (i) the usage of declarative bias to reduce search space complexity and inherently providing the processing of background knowledge. (ii) A newly developed heuristic for traversing the hypothesis space with a greedy, randomized strategy analogical to the GSAT algorithm. In 96.8% of all runs the applied equation discovery system was capable to detect the well-established equation of motion model of the respiratory system in the provided data. We see the potential of this semi-automatic approach to detect more complex mathematical descriptions of the respiratory system from respiratory data.

Language and Thought in Mathematics Staff Development: A Problem Probing Protocol

ERIC Educational Resources Information Center

Kabasakalian, Rita

2007-01-01

Background/Context: The theoretical framework of the paper comes from research on problem solving, considered by many to be the essence of mathematics; research on the importance of oral language in learning mathematics; and on the importance of the teacher as the primary instrument of learning mathematics for most students. As a nation, we are…

Recommendations on the Mathematical Preparation of Teachers. CUPM Panel on Teacher Training. MAA Notes, Number 2.

ERIC Educational Resources Information Center

Mathematical Association of America, Berkeley, CA. Committee on the Undergraduate Program in Mathematics.

This document presents the latest set of recommendations on the mathematical preparation of elementary and secondary school teachers developed by the Committee on the Undergraduate Program in Mathematics (CUPM) of the Mathematical Association of America (MAA). The introduction notes the background for the recommendations, and states that they are…

2012 National Survey of Science and Mathematics Education: Status of Middle School Mathematics

ERIC Educational Resources Information Center

Fulkerson, William O.

2013-01-01

The 2012 National Survey of Science and Mathematics Education was designed to provide up-to-date information and to identify trends in the areas of teacher background and experience, curriculum and instruction, and the availability and use of instructional resources. A total of 7,752 science and mathematics teachers in schools across the United…

2012 National Survey of Science and Mathematics Education: Status of Elementary School Mathematics

ERIC Educational Resources Information Center

Malzahn, Kristen A.

2013-01-01

The 2012 National Survey of Science and Mathematics Education was designed to provide up-to-date information and to identify trends in the areas of teacher background and experience, curriculum and instruction, and the availability and use of instructional resources. A total of 7,752 science and mathematics teachers in schools across the United…

2012 National Survey of Science and Mathematics Education: Status of High School Mathematics

ERIC Educational Resources Information Center

Smith, Adrienne A.

2013-01-01

The 2012 National Survey of Science and Mathematics Education was designed to provide up-to-date information and to identify trends in the areas of teacher background and experience, curriculum and instruction, and the availability and use of instructional resources. A total of 7,752 science and mathematics teachers in schools across the United…

"Come in with an Open Mind": Changing Attitudes towards Mathematics in Primary Teacher Education

ERIC Educational Resources Information Center

Hourigan, Mairéad; Leavy, Aisling M.; Carroll, Claire

2016-01-01

Background: The relationship between attitudes and behaviour has led to a focus on the role played by attitudes in the teaching and learning of mathematics. Purpose: This paper reports on an investigation into studentteachers' self-reported attitudes towards mathematics in the context of a mathematics education programme. The programme had been…

Low Performance on Mathematical Tasks in Preschoolers: The Importance of Domain-General and Domain-Specific Abilities

ERIC Educational Resources Information Center

Costa, H. M.; Nicholson, B.; Donlan, C.; Van Herwegen, J.

2018-01-01

Background: Different domain-specific and domain-general cognitive precursors play a key role in the development of mathematical abilities. The contribution of these domains to mathematical ability changes during development. Primary school-aged children who show mathematical difficulties form a heterogeneous group, but it is not clear whether…

A Multilevel Analysis of the Role of School Quality and Family Background on Students' Mathematics Achievement in the Middle East

ERIC Educational Resources Information Center

Kareshki, Hossein; Hajinezhad, Zahra

2014-01-01

The purpose of the present study is investigating the correlation between school quality and family socioeconomic background and students' mathematics achievement in the Middle East. The countries in comparison are UAE, Syria, Qatar, Iran, Saudi Arabia, Oman, Lebanon, Jordan, and Bahrain. The study utilized data from IEA's Trends in International…

Understanding the Relationship between Parental Education and STEM Course Taking through Identity-Based and Expectancy-Value Theories of Motivation

ERIC Educational Resources Information Center

Svoboda, Ryan C.; Rozek, Christopher S.; Hyde, Janet S.; Harackiewicz, Judith M.; Destin, Mesmin

2016-01-01

High school students from lower-socioeconomic status (SES) backgrounds are less likely to enroll in advanced mathematics and science courses compared to students from higher-SES backgrounds. The current longitudinal study draws on identity-based and expectancy-value theories of motivation to explain the SES and mathematics and science…

Modelling the evolution of drug resistance in the presence of antiviral drugs

PubMed Central

Wu, Jianhong; Yan, Ping; Archibald, Chris

2007-01-01

Background The emergence of drug resistance in treated populations and the transmission of drug resistant strains to newly infected individuals are important public health concerns in the prevention and control of infectious diseases such as HIV and influenza. Mathematical modelling may help guide the design of treatment programs and also may help us better understand the potential benefits and limitations of prevention strategies. Methods To explore further the potential synergies between modelling of drug resistance in HIV and in pandemic influenza, the Public Health Agency of Canada and the Mathematics for Information Technology and Complex Systems brought together selected scientists and public health experts for a workshop in Ottawa in January 2007, to discuss the emergence and transmission of HIV antiviral drug resistance, to report on progress in the use of mathematical models to study the emergence and spread of drug resistant influenza viral strains, and to recommend future research priorities. Results General lectures and round-table discussions were organized around the issues on HIV drug resistance at the population level, HIV drug resistance in Western Canada, HIV drug resistance at the host level (with focus on optimal treatment strategies), and drug resistance for pandemic influenza planning. Conclusion Some of the issues related to drug resistance in HIV and pandemic influenza can possibly be addressed using existing mathematical models, with a special focus on linking the existing models to the data obtained through the Canadian HIV Strain and DR Surveillance Program. Preliminary statistical analysis of these data carried out at PHAC, together with the general model framework developed by Dr. Blower and her collaborators, should provide further insights into the mechanisms behind the observed trends and thus could help with the prediction and analysis of future trends in the aforementioned items. Remarkable similarity between dynamic, compartmental models for the evolution of wild and drug resistance strains of both HIV and pandemic influenza may provide sufficient common ground to create synergies between modellers working in these two areas. One of the key contributions of mathematical modeling to the control of infectious diseases is the quantification and design of optimal strategies, combining techniques of operations research with dynamic modeling would enhance the contribution of mathematical modeling to the prevention and control of infectious diseases. PMID:17953775

Secondary School Mathematics Curriculum Improvement Study Information Bulletin 7.

ERIC Educational Resources Information Center

Secondary School Mathematics Curriculum Improvement Study, New York, NY.

The background, objectives, and design of Secondary School Mathematics Curriculum Improvement Study (SSMCIS) are summarized. Details are given of the content of the text series, "Unified Modern Mathematics," in the areas of algebra, geometry, linear algebra, probability and statistics, analysis (calculus), logic, and computer…

Mathematics at Work in Alberta.

ERIC Educational Resources Information Center

Glanfield, Florence, Ed.; Tilroe, Daryle, Ed.

This document is designed to assist teachers by providing practical examples of real world applications of high school mathematics. Fifteen problems are presented that individuals in industry and business solve using mathematics. Each problem provides the contributor's name, suggested skills required to solve the problem, background information…

Teaching Mathematics Education with Cultural Competency

ERIC Educational Resources Information Center

Dornoo, Michael

2015-01-01

Students learn through connections when understanding is enhanced by a more holistic view of the content. When mathematics is presented from diverse perspectives, students with diverse backgrounds, expectations, histories, and experiences benefit greatly. In this article the author addresses the need to teach mathematics with cultural competency…

Mathematics Equity. A Resource Book.

ERIC Educational Resources Information Center

Tyree, Eddy; And Others

Provided in this document is a brief summary of current research on equity in mathematics, readings on the topic, and lists of selected programs and resource materials. Readings presented include: "Teaching Mathematics in a Multicultural Setting: Some Considerations when Teachers and Students are of Differing Cultural Backgrounds"…

Mathematical design of a novel input/instruction device using a moving acoustic emitter

NASA Astrophysics Data System (ADS)

Wang, Xianchao; Guo, Yukun; Li, Jingzhi; Liu, Hongyu

2017-10-01

This paper is concerned with the mathematical design of a novel input/instruction device using a moving emitter. The emitter acts as a point source and can be installed on a digital pen or worn on the finger of the human being who desires to interact/communicate with the computer. The input/instruction can be recognized by identifying the moving trajectory of the emitter performed by the human being from the collected wave field data. The identification process is modelled as an inverse source problem where one intends to identify the trajectory of a moving point source. There are several salient features of our study which distinguish our result from the existing ones in the literature. First, the point source is moving in an inhomogeneous background medium, which models the human body. Second, the dynamical wave field data are collected in a limited aperture. Third, the reconstruction method is independent of the background medium, and it is totally direct without any matrix inversion. Hence, it is efficient and robust with respect to the measurement noise. Both theoretical justifications and computational experiments are presented to verify our novel findings.

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.

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.

How Readability Factors Are Differentially Associated with Performance for Students of Different Backgrounds When Solving Mathematics Word Problems

ERIC Educational Resources Information Center

Walkington, Candace; Clinton, Virginia; Shivraj, Pooja

2018-01-01

The link between reading and mathematics achievement is well known, and an important question is whether readability factors in mathematics problems are differentially impacting student groups. Using 20 years of data from the National Assessment of Educational Progress and the Trends in International Mathematics and Science Study, we examine how…

System-Level Evaluation: Language and Other Background Factors Affecting Mathematics Achievement

ERIC Educational Resources Information Center

Howie, Sarah

2005-01-01

The aim of this study is to describe and to explore the main factors affecting the performance of South African pupils in the mathematics test of the Third International Mathematics and Science Study-Repeat (TIMSS-R). The first objective was to describe the performance of the pupils in the mathematics test, the pupils' proficiency in English, as…

Visuospatial Training Improves Elementary Students' Mathematics Performance

ERIC Educational Resources Information Center

Lowrie, Tom; Logan, Tracy; Ramful, Ajay

2017-01-01

Background: Although spatial ability and mathematics performance are highly correlated, there is scant research on the extent to which spatial ability training can improve mathematics performance. Aims: This study evaluated the efficacy of a visuospatial intervention programme within classrooms to determine the effect on students' (1) spatial…

Incentive Pay for Remotely Piloted Aircraft Career Fields

DTIC Science & Technology

2012-01-01

Fields C.1. Mathematical Symbols for Non-Stochastic Values and Shock Terms...78 C.2. Mathematical Symbols for Taste and Compensation . . . . . . . . . . . 79 xiii Summary Background and...manning requirement, even with the current incentive pays and reenlistment bonuses. 2 The mathematical foundations, data, and estimation methods for the

The Relationship between Elementary Teachers' Background in Mathematics, Teaching Self-Efficacy, and Teaching Outcome Expectancy When Implementing the Common Core State Standards

ERIC Educational Resources Information Center

Stuart, Jennifer Lynn

2017-01-01

The purpose of this correlation study was to identify a possible relationship between elementary teacher background in mathematics as measured by completed college math credit hours, district-provided professional development hours of training in Common Core math standards, and years of teaching experience, and teacher efficacy in math as measured…

Meta-Modeling: A Knowledge-Based Approach to Facilitating Model Construction and Reuse

NASA Technical Reports Server (NTRS)

Keller, Richard M.; Dungan, Jennifer L.

1997-01-01

In this paper, we introduce a new modeling approach called meta-modeling and illustrate its practical applicability to the construction of physically-based ecosystem process models. As a critical adjunct to modeling codes meta-modeling requires explicit specification of certain background information related to the construction and conceptual underpinnings of a model. This information formalizes the heretofore tacit relationship between the mathematical modeling code and the underlying real-world phenomena being investigated, and gives insight into the process by which the model was constructed. We show how the explicit availability of such information can make models more understandable and reusable and less subject to misinterpretation. In particular, background information enables potential users to better interpret an implemented ecosystem model without direct assistance from the model author. Additionally, we show how the discipline involved in specifying background information leads to improved management of model complexity and fewer implementation errors. We illustrate the meta-modeling approach in the context of the Scientists' Intelligent Graphical Modeling Assistant (SIGMA) a new model construction environment. As the user constructs a model using SIGMA the system adds appropriate background information that ties the executable model to the underlying physical phenomena under investigation. Not only does this information improve the understandability of the final model it also serves to reduce the overall time and programming expertise necessary to initially build and subsequently modify models. Furthermore, SIGMA's use of background knowledge helps eliminate coding errors resulting from scientific and dimensional inconsistencies that are otherwise difficult to avoid when building complex models. As a. demonstration of SIGMA's utility, the system was used to reimplement and extend a well-known forest ecosystem dynamics model: Forest-BGC.

Pupils' View of Mathematics: Initial Report for an International Comparison Project. Research Report 152.

ERIC Educational Resources Information Center

Pehkonen, Erkki

This report describes the theoretical background of an international comparison project on pupils' mathematical beliefs and outlines its realization. The first chapter briefly discusses problems with the underlying concepts of "belief" and "conception." The central concept, view of mathematics, is introduced in the second…

Creating a Critical Mass Eliminates the Effects of Stereotype Threat on Women's Mathematical Performance

ERIC Educational Resources Information Center

Pennington, Charlotte R.; Heim, Derek

2016-01-01

Background: Women in mathematical domains may become attuned to situational cues that signal a discredited social identity, contributing to their lower achievement and underrepresentation. Aim: This study examined whether heightened in-group representation alleviates the effects of stereotype threat on women's mathematical performance. It further…

Educational Neuroscience: New Horizons for Research in Mathematics Education

ERIC Educational Resources Information Center

Campbell, Stephen R.

2006-01-01

This paper outlines an initiative in mathematics education research that aims to augment qualitative methods of research into mathematical cognition and learning with quantitative methods of psychometrics and psychophysiology. Background and motivation are provided for this initiative, which is coming to be referred to as educational neuroscience.…

"Standards"-Based Mathematics Curricula and the Promotion of Quantitative Literacy in Elementary School

ERIC Educational Resources Information Center

Wilkins, Jesse L. M.

2015-01-01

Background: Prior research has shown that students taught using "Standards"-based mathematics curricula tend to outperform students on measures of mathematics achievement. However, little research has focused particularly on the promotion of student quantitative literacy (QLT). In this study, the potential influence of the…

A Reflection Framework for Teaching Mathematics

ERIC Educational Resources Information Center

Merritt, Eileen G.; Rimm-Kaufman, Sara E.; Berry, Robert Q., III; Walkowiak, Temple A.; McCracken, Erin R.

2010-01-01

Mathematics teachers confront dozens of daily decisions about how to instruct students. It is well established that high-quality instruction provides benefits for students with diverse learning and family backgrounds. However, it is often difficult for teachers to identify the critical aspects of a successful mathematics lesson as they strive to…

Mathematics Interventions for Children and Adolescents with Down Syndrome: A Research Synthesis

ERIC Educational Resources Information Center

Lemons, C. J.; Powell, S. R.; King, S. A.; Davidson, K. A.

2015-01-01

Background: Many children and adolescents with Down syndrome fail to achieve proficiency in mathematics. Researchers have suggested that tailoring interventions based on the behavioural phenotype may enhance efficacy. Method: The research questions that guided this review were (1) what types of mathematics interventions have been empirically…

An Excel-Aided Method for Teaching Calculus-Based Business Mathematics

ERIC Educational Resources Information Center

Liang, Jiajuan; Martin, Linda

2008-01-01

Calculus-based business mathematics is a required quantitative course for undergraduate business students in most AACSB accredited schools or colleges of business. Many business students, however, have relatively weak mathematical background or even display math-phobia when presented with calculus problems. Because of the popularity of Excel, its…

Secondary Mathematics Course Trajectories: Understanding Accumulated Disadvantages in Mathematics in Grades 9-12

ERIC Educational Resources Information Center

Schiller, Kathryn S.; Hunt, Donald J.

2011-01-01

Schools are institutions in which students' course taking creates series of linked learning opportunities continually shaped by not only curricular structures but demographic and academic backgrounds. In contrast to a seven-step normative course sequence reflecting the conventional hierarchical structure of mathematics, analysis of more than…

Student Achievement in College Calculus, Louisiana State University 1967-1968.

ERIC Educational Resources Information Center

Scannicchio, Thomas Henry

An investigation of freshmen achievement in an introductory calculus course was performed on the basis of high school mathematics background to find predictors of college calculus grades. Overall high school academic achievement, overall high school mathematics achievement, number of high school mathematics units, pattern of college preparatory…

Handbook for Spoken Mathematics: (Larry's Speakeasy).

ERIC Educational Resources Information Center

Chang, Lawrence A.; And Others

This handbook is directed toward those who have to deal with spoken mathematics, yet have insufficient background to know the correct verbal expression for the written symbolic one. It compiles consistent and well-defined ways of uttering mathematical expressions so listeners will receive clear, unambiguous, and well-pronounced representations.…

Who Is Afraid of Math? Two Sources of Genetic Variance for Mathematical Anxiety

ERIC Educational Resources Information Center

Wang, Zhe; Hart, Sara Ann; Kovas, Yulia; Lukowski, Sarah; Soden, Brooke; Thompson, Lee A.; Plomin, Robert; McLoughlin, Grainne; Bartlett, Christopher W.; Lyons, Ian M.; Petrill, Stephen A.

2014-01-01

Background: Emerging work suggests that academic achievement may be influenced by the management of affect as well as through efficient information processing of task demands. In particular, mathematical anxiety has attracted recent attention because of its damaging psychological effects and potential associations with mathematical problem solving…

Preparing Teachers to Lead Mathematics Discussions

ERIC Educational Resources Information Center

Boerst, Timothy A.; Sleep, Laurie; Ball, Deborah Loewenberg; Bass, Hyman

2011-01-01

Background/Context: Discussion is central to mathematics teaching and learning, as well as to mathematics as an academic discipline. Studies have shown that facilitating discussions is complex work that is not easily done or learned. To make such complex aspects of the work of teaching learnable by beginners, recent research has focused on…

Science and Mathematics Teachers' Experiences, Needs, and Expectations regarding Professional Development

ERIC Educational Resources Information Center

Chval, Kathryn; Abell, Sandra; Pareja, Enrique; Musikul, Kusalin; Ritzka, Gerard

2008-01-01

High quality teachers are essential to improving the teaching and learning of mathematics and science, necessitating effective professional development (PD) and learning environments for teachers. However, many PD programs for science and mathematics teachers fall short because they fail to consider teacher background, experience, knowledge,…

Humanities-Oriented Accents in Teaching Mathematics to Prospective Primary School Teachers

ERIC Educational Resources Information Center

Tabov, Jordan; Gortcheva, Iordanka

2016-01-01

Our research includes undergraduate students who major in primary school education. Their academic background is prevailingly in the humanities. This poses specific demands on their mathematics instruction at university. To attract them to their mathematics course and raise its effectiveness, we use a series of activities. Writing assignments…

Exploring Iconic Interpretation and Mathematics Teacher Development through Clinical Simulations

ERIC Educational Resources Information Center

Dotger, Benjamin; Masingila, Joanna; Bearkland, Mary; Dotger, Sharon

2015-01-01

Field placements serve as the traditional "clinical" experience for prospective mathematics teachers to immerse themselves in the mathematical challenges of students. This article reports data from a different type of learning experience, that of a clinical simulation with a standardized individual. We begin with a brief background on…

PISA Mathematics and Reading Performance Differences of Mainstream European and Turkish Immigrant Students

ERIC Educational Resources Information Center

Arikan, Serkan; van de Vijver, Fons J. R.; Yagmur, Kutlay

2017-01-01

Lower reading and mathematics performance of Turkish immigrant students as compared to mainstream European students could reflect differential learning outcomes, differential socioeconomic backgrounds of the groups, differential mainstream language proficiency, and/or test bias. Using PISA reading and mathematics scores of these groups, we…

Are Mathematics Problems a Problem for Women and Girls?

ERIC Educational Resources Information Center

Schonberger, Ann K.

The primary questions investigated are: Is it true that males excel in mathematical problem solving and, if so, when does this superiority develop? An examination of recent research showed that sex-related differences did exist, although small, even after controlling for mathematics background. Differences appeared in early adolescence and were…

Adaptive nonlinear control for autonomous ground vehicles

NASA Astrophysics Data System (ADS)

Black, William S.

We present the background and motivation for ground vehicle autonomy, and focus on uses for space-exploration. Using a simple design example of an autonomous ground vehicle we derive the equations of motion. After providing the mathematical background for nonlinear systems and control we present two common methods for exactly linearizing nonlinear systems, feedback linearization and backstepping. We use these in combination with three adaptive control methods: model reference adaptive control, adaptive sliding mode control, and extremum-seeking model reference adaptive control. We show the performances of each combination through several simulation results. We then consider disturbances in the system, and design nonlinear disturbance observers for both single-input-single-output and multi-input-multi-output systems. Finally, we show the performance of these observers with simulation results.

Modeling RNA interference in mammalian cells

PubMed Central

2011-01-01

Background RNA interference (RNAi) is a regulatory cellular process that controls post-transcriptional gene silencing. During RNAi double-stranded RNA (dsRNA) induces sequence-specific degradation of homologous mRNA via the generation of smaller dsRNA oligomers of length between 21-23nt (siRNAs). siRNAs are then loaded onto the RNA-Induced Silencing multiprotein Complex (RISC), which uses the siRNA antisense strand to specifically recognize mRNA species which exhibit a complementary sequence. Once the siRNA loaded-RISC binds the target mRNA, the mRNA is cleaved and degraded, and the siRNA loaded-RISC can degrade additional mRNA molecules. Despite the widespread use of siRNAs for gene silencing, and the importance of dosage for its efficiency and to avoid off target effects, none of the numerous mathematical models proposed in literature was validated to quantitatively capture the effects of RNAi on the target mRNA degradation for different concentrations of siRNAs. Here, we address this pressing open problem performing in vitro experiments of RNAi in mammalian cells and testing and comparing different mathematical models fitting experimental data to in-silico generated data. We performed in vitro experiments in human and hamster cell lines constitutively expressing respectively EGFP protein or tTA protein, measuring both mRNA levels, by quantitative Real-Time PCR, and protein levels, by FACS analysis, for a large range of concentrations of siRNA oligomers. Results We tested and validated four different mathematical models of RNA interference by quantitatively fitting models' parameters to best capture the in vitro experimental data. We show that a simple Hill kinetic model is the most efficient way to model RNA interference. Our experimental and modeling findings clearly show that the RNAi-mediated degradation of mRNA is subject to saturation effects. Conclusions Our model has a simple mathematical form, amenable to analytical investigations and a small set of parameters with an intuitive physical meaning, that makes it a unique and reliable mathematical tool. The findings here presented will be a useful instrument for better understanding RNAi biology and as modelling tool in Systems and Synthetic Biology. PMID:21272352

CE-QUAL-W2: A Numerical Two-Dimensional, Laterally Averaged Model of Hydrodynamics and Water Quality; User’s Manual.

DTIC Science & Technology

1986-08-01

publication by Ms. Jessica S. Ruff, Information Products Division, WES. This manual is published in loose-leaf format for convenience in ." ._ periodic...transfer computations. m. Variety of output options. Background 8. This manual is a product of a program of evaluation and refinement of mathematical water...zooplankton and higher order herbivores. However, these groups are presently not included in the model. Macrophyte production may also have an impact upon

A weather-driven model of malaria transmission

PubMed Central

Hoshen, Moshe B; Morse, Andrew P

2004-01-01

Background Climate is a major driving force behind malaria transmission and climate data are often used to account for the spatial, seasonal and interannual variation in malaria transmission. Methods This paper describes a mathematical-biological model of the parasite dynamics, comprising both the weather-dependent within-vector stages and the weather-independent within-host stages. Results Numerical evaluations of the model in both time and space show that it qualitatively reconstructs the prevalence of infection. Conclusion A process-based modelling structure has been developed that may be suitable for the simulation of malaria forecasts based on seasonal weather forecasts. PMID:15350206

Evidence for shared genetic risk between ADHD symptoms and reduced mathematics ability: a twin study

PubMed Central

Greven, Corina U.; Kovas, Yulia; Willcutt, Erik G.; Petrill, Stephen A.; Plomin, Robert

2013-01-01

Background Attention-deficit/hyperactivity disorder (ADHD) symptoms and mathematics ability are associated, but little is known about the genetic and environmental influences underlying this association. Methods Data came from more than 6,000 12-year-old twin pairs from the U.K. population-representative Twins Early Development Study. Parents rated each twin’s behaviour using a DSM-IV-based 18-item questionnaire of inattentive and hyperactive-impulsive ADHD symptoms. Mathematics tests based on the U.K. National Curriculum were completed by each twin. The twins also completed standardised tests of reading and general cognitive ability. Multivariate twin model fitting was applied. Results Inattentive and hyperactive-impulsive ADHD symptoms were highly heritable (67% and 73%, respectively). Mathematics ability was moderately heritable (46%). Mathematics ability and inattentiveness showed a significantly greater phenotypic correlation (rp=−0.26) and genetic correlation (rA=−0.41) than mathematics ability and hyperactivity-impulsivity (rp=−0.18; rA=−0.22). The genetic correlation between inattentiveness and mathematics ability was largely independent from hyperactivity-impulsivity, and was only partially accounted for by genetic influences related to reading and general cognitive ability. Conclusions Results revealed the novel finding that mathematics ability shows significantly stronger phenotypic and genetic associations with inattentiveness than with hyperactivity-impulsivity. Genetic associations between inattentiveness and mathematics ability could only partially be accounted for by hyperactivity-impulsivity, reading and general cognitive ability. Results suggest that mathematics ability is associated with ADHD symptoms largely because it shares genetic risk factors with inattentiveness, and provide further evidence for considering inattentiveness and hyperactivity-impulsivity separately. DNA markers for ADHD symptoms (especially inattentiveness) may also be candidate risk factors for mathematics ability and vice versa. PMID:23731013

Simulating Microbial Community Patterning Using Biocellion

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

Kang, Seung-Hwa; Kahan, Simon H.; Momeni, Babak

2014-04-17

Mathematical modeling and computer simulation are important tools for understanding complex interactions between cells and their biotic and abiotic environment: similarities and differences between modeled and observed behavior provide the basis for hypothesis forma- tion. Momeni et al. [5] investigated pattern formation in communities of yeast strains engaging in different types of ecological interactions, comparing the predictions of mathematical modeling and simulation to actual patterns observed in wet-lab experiments. However, simu- lations of millions of cells in a three-dimensional community are ex- tremely time-consuming. One simulation run in MATLAB may take a week or longer, inhibiting exploration of the vastmore » space of parameter combinations and assumptions. Improving the speed, scale, and accu- racy of such simulations facilitates hypothesis formation and expedites discovery. Biocellion is a high performance software framework for ac- celerating discrete agent-based simulation of biological systems with millions to trillions of cells. Simulations of comparable scale and accu- racy to those taking a week of computer time using MATLAB require just hours using Biocellion on a multicore workstation. Biocellion fur- ther accelerates large scale, high resolution simulations using cluster computers by partitioning the work to run on multiple compute nodes. Biocellion targets computational biologists who have mathematical modeling backgrounds and basic C++ programming skills. This chap- ter describes the necessary steps to adapt the original Momeni et al.'s model to the Biocellion framework as a case study.« less

RF tumour ablation: computer simulation and mathematical modelling of the effects of electrical and thermal conductivity.

PubMed

Lobo, S M; Liu, Z-J; Yu, N C; Humphries, S; Ahmed, M; Cosman, E R; Lenkinski, R E; Goldberg, W; Goldberg, S N

2005-05-01

This study determined the effects of thermal conductivity on RF ablation tissue heating using mathematical modelling and computer simulations of RF heating coupled to thermal transport. Computer simulation of the Bio-Heat equation coupled with temperature-dependent solutions for RF electric fields (ETherm) was used to generate temperature profiles 2 cm away from a 3 cm internally-cooled electrode. Multiple conditions of clinically relevant electrical conductivities (0.07-12 S m-1) and 'tumour' radius (5-30 mm) at a given background electrical conductivity (0.12 S m-1) were studied. Temperature response surfaces were plotted for six thermal conductivities, ranging from 0.3-2 W m-1 degrees C (the range of anticipated clinical and experimental systems). A temperature response surface was obtained for each thermal conductivity at 25 electrical conductivities and 17 radii (n=425 temperature data points). The simulated temperature response was fit to a mathematical model derived from prior phantom data. This mathematical model is of the form (T=a+bRc exp(dR) s(f) exp(g)(s)) for RF generator-energy dependent situations and (T=h+k exp(mR)+n?exp(p)(s)) for RF generator-current limited situations, where T is the temperature (degrees C) 2 cm from the electrode and a, b, c, d, f, g, h, k, m, n and p are fitting parameters. For each of the thermal conductivity temperature profiles generated, the mathematical model fit the response surface to an r2 of 0.97-0.99. Parameters a, b, c, d, f, k and m were highly correlated to thermal conductivity (r2=0.96-0.99). The monotonic progression of fitting parameters permitted their mathematical expression using simple functions. Additionally, the effect of thermal conductivity simplified the above equation to the extent that g, h, n and p were found to be invariant. Thus, representation of the temperature response surface could be accurately expressed as a function of electrical conductivity, radius and thermal conductivity. As a result, the non-linear temperature response of RF induced heating can be adequately expressed mathematically as a function of electrical conductivity, radius and thermal conductivity. Hence, thermal conductivity accounts for some of the previously unexplained variance. Furthermore, the addition of this variable into the mathematical model substantially simplifies the equations and, as such, it is expected that this will permit improved prediction of RF ablation induced temperatures in clinical practice.

A Study of the Correlation between STEM Career Knowledge, Mathematics Self-Efficacy, Career Interests, and Career Activities on the Likelihood of Pursuing a STEM Career among Middle School Students

ERIC Educational Resources Information Center

Blotnicky, Karen A.; Franz-Odendaal, Tamara; French, Frederick; Joy, Phillip

2018-01-01

Background: A sample of 1448 students in grades 7 and 9 was drawn from public schools in Atlantic Canada to explore students' knowledge of science and mathematics requirements for science, technology, engineering, and mathematics (STEM) careers. Also explored were their mathematics self-efficacy (MSE), their future career interests, their…

The Dependence on Mathematical Theory in TIMSS, PISA and TIMSS Advanced Test Items and Its Relation to Student Achievement

ERIC Educational Resources Information Center

Hole, Arne; Grønmo, Liv Sissel; Onstad, Torgeir

2018-01-01

Background: This paper discusses a framework for analyzing the dependence on mathematical theory in test items, that is, a framework for discussing to what extent knowledge of mathematical theory is helpful for the student in solving the item. The framework can be applied to any test in which some knowledge of mathematical theory may be useful,…

Elements of Mathematics, Book O: Intuitive Background. Chapter 1, Operational Systems.

ERIC Educational Resources Information Center

Exner, Robert; And Others

The sixteen chapters of this book provide the core material for the Elements of Mathematics Program, a secondary sequence developed for highly motivated students with strong verbal abilities. The sequence is based on a functional-relational approach to mathematics teaching, and emphasizes teaching by analysis of real-life situations. This text is…

How Young Children View Mathematical Representations: A Study Using Eye-Tracking Technology

ERIC Educational Resources Information Center

Bolden, David; Barmby, Patrick; Raine, Stephanie; Gardner, Matthew

2015-01-01

Background: It has been shown that mathematical representations can aid children's understanding of mathematical concepts but that children can sometimes have difficulty in interpreting them correctly. New advances in eye-tracking technology can help in this respect because it allows data to be gathered concerning children's focus of attention and…

How Important Is Where You Start? Early Mathematics Knowledge and Later School Success

ERIC Educational Resources Information Center

Claessens, Amy; Engel, Mimi

2013-01-01

Background: Children's early skills are essential for their later success in school. Recent evidence highlights the importance of early mathematics, relative to reading and socioemotional skills, for elementary school achievement. Key advocacy groups for both early childhood and mathematics education have issued position statements on the…

Provoking Contingent Moments: Knowledge for "Powerful Teaching" at the Horizon

ERIC Educational Resources Information Center

Hurst, Chris

2017-01-01

Background: Teacher knowledge continues to be a topic of debate in Australasia and in other parts of the world. There have been many attempts by mathematics educators and researchers to define the knowledge needed by teachers to teach mathematics effectively. A plethora of terms, such as mathematical content knowledge, pedagogical content…

The Effect of Integrating Lab Experiments in Electronic Circuits into Mathematic Studies--A Case Study

ERIC Educational Resources Information Center

Sabag, Nissim

2017-01-01

Background: The importance of knowledge and skills in mathematics for electrical engineering students is well known. Engineers and engineering educators agree that any engineering curriculum must include plenty of mathematics studies to enrich the engineer's toolbox. Nevertheless, little attention has been given to the possible contribution of…

Predictors of Success in Accelerated and Enrichment Summer Mathematics Courses for Academically Talented Adolescents

ERIC Educational Resources Information Center

Young, Adena E.; Worrell, Frank C.; Gabelko, Nina H.

2011-01-01

In this study, we used logistic regression to examine how well student background and prior achievement variables predicted success among students attending accelerated and enrichment mathematics courses at a summer program (N = 459). Socioeconomic status, grade point average (GPA), and mathematics diagnostic test scores significantly predicted…

The Contribution of Parent-Child Numeracy Activities to Young Chinese Children's Mathematical Ability

ERIC Educational Resources Information Center

Huang, Qi; Zhang, Xiao; Liu, Yingyi; Yang, Wen; Song, Zhanmei

2017-01-01

Background: A growing body of recent research has shown that parent-child mathematical activities have a strong effect on children's mathematical learning. However, this research was conducted predominantly in Western societies and focused mainly on mothers' involvement in such activities. Aims: This study aimed to examine both mother-child and…

Elements of Mathematics, Book O: Intuitive Background. Chapter 5, Mappings.

ERIC Educational Resources Information Center

Exner, Robert; And Others

The sixteen chapters of this book provide the core material for the Elements of Mathematics Program, a secondary sequence developed for highly motivated students with strong verbal abilities. The sequence is based on a functional-relational approach to mathematics teaching, and emphasizes teaching by analysis of real-life situations. This text is…

Using Sport to Engage and Motivate Students to Learn Mathematics

ERIC Educational Resources Information Center

Robinson, Carol L.

2012-01-01

This article describes how technology has been used to motivate the learning of mathematics for students of Sports Technology at Loughborough University. Sports applications are introduced whenever appropriate and Matlab is taught to enable the students to solve realistic problems. The mathematical background of the students is varied and the…

Role of Mathematics Learning Development Centres in HEIs

ERIC Educational Resources Information Center

Nzekwe-Excel, C.

2010-01-01

Background and Rationale: Student withdrawal and non-completion in institutions have been an issue of considerable concern. The lack of mathematical ability has been identified as a factor resulting to non-completion in higher institutions. Several students in higher education approach mathematics with a lot of anxiety. This has created the need…

Broadening Participation in Mathematics: A Study of Secondary Mathematics Teachers and Noticing for Equity

ERIC Educational Resources Information Center

Mercado, Janet

2017-01-01

Equity in mathematics teaching has gained increased attention in the last few decades. A growing field of research has provided various definitions of equity, outlined standards, and identified practices that lead to equitable learning opportunities for all students, particularly for students from non-dominant backgrounds. However, few studies…

Elements of Mathematics, Book O: Intuitive Background. Chapter 2, The Integers.

ERIC Educational Resources Information Center

Exner, Robert; And Others

The sixteen chapters of this book provide the core materials for the Elements of Mathematics Program, a secondary sequence developed for highly motivated students with strong verbal abilities. The sequence is based on a functional-relational approach to mathematics teaching, and emphasizes teaching by analysis of real-life situations. This text is…

Self-Concept Mediates the Relation between Achievement and Emotions in Mathematics

ERIC Educational Resources Information Center

Van der Beek, Jojanneke P. J.; Van der Ven, Sanne H. G.; Kroesbergen, Evelyn H.; Leseman, Paul P. M.

2017-01-01

Background: Mathematics achievement is related to positive and negative emotions. Pekrun's control-value theory of achievement emotions suggests that students' self-concept (i.e., self-appraisal of ability) may be an important mediator of the relation between mathematics achievement and emotions. Aims: The aims were (1) to investigate the…

Mathematics Instruction in Tokyo's and Hawaii's Junior High Schools. Final Report.

ERIC Educational Resources Information Center

Hawaii Univ., Honolulu. Coll. of Education.

Mathematics instruction in junior high schools in Tokyo and Hawaii was compared in order to gain knowledge of how mathematics teachers' effectiveness in the classroom may be improved. Because they were likely to influence teachers' behavior, these factors were considered: teachers' background and teaching load, allocation of time, views on…

A mathematical framework for modelling cambial surface evolution using a level set method

PubMed Central

Sellier, Damien; Plank, Michael J.; Harrington, Jonathan J.

2011-01-01

Background and Aims During their lifetime, tree stems take a series of successive nested shapes. Individual tree growth models traditionally focus on apical growth and architecture. However, cambial growth, which is distributed over a surface layer wrapping the whole organism, equally contributes to plant form and function. This study aims at providing a framework to simulate how organism shape evolves as a result of a secondary growth process that occurs at the cellular scale. Methods The development of the vascular cambium is modelled as an expanding surface using the level set method. The surface consists of multiple compartments following distinct expansion rules. Growth behaviour can be formulated as a mathematical function of surface state variables and independent variables to describe biological processes. Key Results The model was coupled to an architectural model and to a forest stand model to simulate cambium dynamics and wood formation at the scale of the organism. The model is able to simulate competition between cambia, surface irregularities and local features. Predicting the shapes associated with arbitrarily complex growth functions does not add complexity to the numerical method itself. Conclusions Despite their slenderness, it is sometimes useful to conceive of trees as expanding surfaces. The proposed mathematical framework provides a way to integrate through time and space the biological and physical mechanisms underlying cambium activity. It can be used either to test growth hypotheses or to generate detailed maps of wood internal structure. PMID:21470972

Electrical Circuits in the Mathematics/Computer Science Classroom.

ERIC Educational Resources Information Center

McMillan, Robert D.

1988-01-01

Shows how, with little or no electrical background, students can apply Boolean algebra concepts to design and build integrated electrical circuits in the classroom that will reinforce important ideas in mathematics. (PK)

An Assessment of Different Educational Background of Students Performance in Engineering Mathematics and on the Class of Award Obtained at the Higher National Diploma (HND) Level at Cape Coast Polytechnic, Ghana

ERIC Educational Resources Information Center

Asirifi, Michael Kwabena; Mensah, Kweku Abeeku; Amoako, Joseph

2015-01-01

The purpose of this research article is to find out an assessment of different educational background of students performance in engineering mathematics and on the class of award obtained at the Higher National Diploma (HND) level at Cape Coast Polytechnic. A descriptive survey was conducted on students of the Electricals/Electronics Department…

Mathematical model to estimate risk of calcium-containing renal stones

NASA Technical Reports Server (NTRS)

Pietrzyk, R. A.; Feiveson, A. H.; Whitson, P. A.

1999-01-01

BACKGROUND/AIMS: Astronauts exposed to microgravity during the course of spaceflight undergo physiologic changes that alter the urinary environment so as to increase the risk of renal stone formation. This study was undertaken to identify a simple method with which to evaluate the potential risk of renal stone development during spaceflight. METHOD: We used a large database of urinary risk factors obtained from 323 astronauts before and after spaceflight to generate a mathematical model with which to predict the urinary supersaturation of calcium stone forming salts. RESULT: This model, which involves the fewest possible analytical variables (urinary calcium, citrate, oxalate, phosphorus, and total volume), reliably and accurately predicted the urinary supersaturation of the calcium stone forming salts when compared to results obtained from a group of 6 astronauts who collected urine during flight. CONCLUSIONS: The use of this model will simplify both routine medical monitoring during spaceflight as well as the evaluation of countermeasures designed to minimize renal stone development. This model also can be used for Earth-based applications in which access to analytical resources is limited.

Assessment of numeracy in sports and exercise science students at an Australian university

NASA Astrophysics Data System (ADS)

Green, Simon; McGlynn, Susan; Stuart, Deidre; Fahey, Paul; Pettigrew, Jim; Clothier, Peter

2018-05-01

The effect of high school study of mathematics on numeracy performance of sports and exercise science (SES) students is not clear. To investigate this further, we tested the numeracy skills of 401 students enrolled in a Bachelor of Health Sciences degree in SES using a multiple-choice survey consisting of four background questions and 39 numeracy test questions. Background questions (5-point scale) focused on highest level of mathematics studied at high school, self-perception of mathematics proficiency, perceived importance of mathematics to SES and likelihood of seeking help with mathematics. Numeracy questions focused on rational number, ratios and rates, basic algebra and graph interpretation. Numeracy performance was based on answers to these questions (1 mark each) and represented by the total score (maximum = 39). Students from first (n = 212), second (n = 78) and third (n = 111) years of the SES degree completed the test. The distribution of numeracy test scores for the entire cohort was negatively skewed with a median (IQR) score of 27(11). We observed statistically significant associations between test scores and the highest level of mathematics studied (P < 0.05), being lowest in students who studied Year 10 Mathematics (20 (9)), intermediate in students who studied Year 12 General Mathematics (26 (8)) and highest in two groups of students who studied higher-level Year 12 Mathematics (31 (9), 31 (6)). There were statistically significant associations between test scores and level of self-perception of mathematics proficiency and also likelihood of seeking help with mathematics (P < 0.05) but not with perceived importance of mathematics to SES. These findings reveal that the level of mathematics studied in high school is a critical factor determining the level of numeracy performance in SES students.

An objective function exploiting suboptimal solutions in metabolic networks

PubMed Central

2013-01-01

Background Flux Balance Analysis is a theoretically elegant, computationally efficient, genome-scale approach to predicting biochemical reaction fluxes. Yet FBA models exhibit persistent mathematical degeneracy that generally limits their predictive power. Results We propose a novel objective function for cellular metabolism that accounts for and exploits degeneracy in the metabolic network to improve flux predictions. In our model, regulation drives metabolism toward a region of flux space that allows nearly optimal growth. Metabolic mutants deviate minimally from this region, a function represented mathematically as a convex cone. Near-optimal flux configurations within this region are considered equally plausible and not subject to further optimizing regulation. Consistent with relaxed regulation near optimality, we find that the size of the near-optimal region predicts flux variability under experimental perturbation. Conclusion Accounting for suboptimal solutions can improve the predictive power of metabolic FBA models. Because fluctuations of enzyme and metabolite levels are inevitable, tolerance for suboptimality may support a functionally robust metabolic network. PMID:24088221

Exploring ESL Students' Understanding of Mathematics in the Early Years: Factors That Make a Difference

ERIC Educational Resources Information Center

Miller, Jodie; Warren, Elizabeth

2014-01-01

Students living in disadvantaged contexts and whose second language is English (ESL) are at risk of not succeeding in school mathematics. It has been internationally recognised that students' socioeconomic background and their achievements in mathematics is more pronounced for Australian students (Thomson et al. 2011). This gap is even more…

A Mathematical Experience Involving Defining Processes: In-Action Definitions and Zero-Definitions

ERIC Educational Resources Information Center

Ouvrier-Buffet, Cecile

2011-01-01

In this paper, a focus is made on defining processes at stake in an unfamiliar situation coming from discrete mathematics which brings surprising mathematical results. The epistemological framework of Lakatos is questioned and used for the design and the analysis of the situation. The cognitive background of Vergnaud's approach enriches the study…

2012 National Survey of Science and Mathematics Education: Status of High School Biology

ERIC Educational Resources Information Center

Lyons, Kiira M.

2013-01-01

The 2012 National Survey of Science and Mathematics Education was designed to provide up-to-date information and to identify trends in the areas of teacher background and experience, curriculum and instruction, and the availability and use of instructional resources. A total of 7,752 science and mathematics teachers in schools across the United…

2012 National Survey of Science and Mathematics Education: Status of High School Chemistry

ERIC Educational Resources Information Center

Smith, P. Sean

2013-01-01

The 2012 National Survey of Science and Mathematics Education was designed to provide up-to-date information and to identify trends in the areas of teacher background and experience, curriculum and instruction, and the availability and use of instructional resources. A total of 7,752 science and mathematics teachers in schools across the United…

2012 National Survey of Science and Mathematics Education: Status of Elementary School Science

ERIC Educational Resources Information Center

Trygstad, Peggy J.

2013-01-01

The 2012 National Survey of Science and Mathematics Education was designed to provide up-to-date information and to identify trends in the areas of teacher background and experience, curriculum and instruction, and the availability and use of instructional resources. A total of 7,752 science and mathematics teachers in schools across the United…

Enjoying Mathematics or Feeling Competent in Mathematics? Reciprocal Effects on Mathematics Achievement and Perceived Math Effort Expenditure

ERIC Educational Resources Information Center

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

2014-01-01

Background: 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. Aim: This study aims at exploring differential effects of enjoyment…

Report of the 2012 National Survey of Science and Mathematics Education

ERIC Educational Resources Information Center

Banilower, Eric R.; Smith, P. Sean; Weiss, Iris R.; Malzahn, Kristen A.; Campbell, Kiira M.; Weis, Aaron M.

2013-01-01

The 2012 National Survey of Science and Mathematics Education was designed to provide up-to-date information and to identify trends in the areas of teacher background and experience, curriculum and instruction, and the availability and use of instructional resources. A total of 7,752 science and mathematics teachers in schools across the United…

2012 National Survey of Science and Mathematics Education: Status of Middle School Science

ERIC Educational Resources Information Center

Weis, Aaron M.

2013-01-01

The 2012 National Survey of Science and Mathematics Education was designed to provide up-to-date information and to identify trends in the areas of teacher background and experience, curriculum and instruction, and the availability and use of instructional resources. A total of 7,752 science and mathematics teachers in schools across the United…

A Case Study of Pedagogy of Mathematics Support Tutors without a Background in Mathematics Education

ERIC Educational Resources Information Center

Walsh, Richard

2017-01-01

This study investigates the pedagogical skills and knowledge of three tertiary-level mathematics support tutors in a large group classroom setting. This is achieved through the use of video analysis and a theoretical framework comprising Rowland's Knowledge Quartet and general pedagogical knowledge. The study reports on the findings in relation to…

Studies in Mathematics, Volume IV. Geometry.

ERIC Educational Resources Information Center

Kutuzov, B. V.

This book is a translation of a Russian text. The translation is exact, and the language used by the author has not been brought up to date. The volume is probably most useful as a source of supplementary materials for high school mathematics. It is also useful for teachers to broaden their mathematical background. Chapters included in the text…

Meaningful Statistics in Professional Practices as a Bridge between Mathematics and Science: An Evaluation of a Design Research Project

ERIC Educational Resources Information Center

Dierdorp, Adri; Bakker, Arthur; van Maanen, Jan A.; Eijkelhof, Harrie M. C.

2014-01-01

Background: Creating coherence between school subjects mathematics and science and making these school subjects meaningful are still topical challenges. This study investigates how students make meaningful connections between mathematics, statistics, science and applications when they engage in a specially developed unit that is based on…

Elements of Mathematics, Book O: Intuitive Background. Chapter 14, Geometry: Similitudes, Coordinates, and Trigonometry.

ERIC Educational Resources Information Center

Exner, Robert; And Others

The sixteen chapters of this book provide the core material for the Elements of Mathematics Program, a secondary sequence developed for highly motivated students with strong verbal abilities. The sequence is based on a functional-relational approach to mathematics teaching, and emphasizes teaching by analysis of real-life situations. This text is…

Polytechnic Engineering Mathematics: Assessing Its Relevance to the Productivity of Industries in Uganda

ERIC Educational Resources Information Center

Jehopio, Peter J.; Wesonga, Ronald

2017-01-01

Background: The main objective of the study was to examine the relevance of engineering mathematics to the emerging industries. The level of abstraction, the standard of rigor, and the depth of theoretical treatment are necessary skills expected of a graduate engineering technician to be derived from mathematical knowledge. The question of whether…

2012 National Survey of Science and Mathematics Education: Status of High School Physics

ERIC Educational Resources Information Center

Banilower, Eric R.

2013-01-01

The 2012 National Survey of Science and Mathematics Education was designed to provide up-to-date information and to identify trends in the areas of teacher background and experience, curriculum and instruction, and the availability and use of instructional resources. A total of 7,752 science and mathematics teachers in schools across the United…

Judged Similarity of Aptitude and Achievement Tests in Mathematics.

ERIC Educational Resources Information Center

Donlon, Thomas F.

This study attempts to establish the ability of a panel of five judges with varied mathematics background to distinguish between two types of mathematical tests by separating their component items when they are presented in a mixed pool of aptitude and achievement tests. Typically, the two tests show high correlation. The judges showed about 70%…

The Math Wars: Tensions in the Development of School Mathematics Curricula

ERIC Educational Resources Information Center

Wright, Pete

2012-01-01

The Math Wars have been raging since the 1990's in the United States, where the world of mathematics education has become polarised into two camps: the reformers and the traditionalists. In this article I explore the background to the Math Wars, with specific reference to conflicting ideologies of mathematics education. I draw parallels with…

Understanding and Supporting Teacher Horizon Knowledge around Limits: A Framework for Evaluating Textbooks for Teachers

ERIC Educational Resources Information Center

Kajander, Ann; Lovric, Miroslav

2017-01-01

As part of recent scrutiny of teacher capacity, the question of teachers' content knowledge of higher level mathematics emerges as important to the field of mathematics education. Elementary teachers in North America and some other countries tend to be subject generalists, yet it appears that some higher level mathematics background may be…

Strong Is the Silence: Challenging Interlocking Systems of Privilege and Oppression in Mathematics Teacher Education

ERIC Educational Resources Information Center

Herbel-Eisenmann, Beth; Bartell, Tonya Gau; Breyfogle, M. Lynn; Bieda, Kristen; Crespo, Sandra; Dominguez, Higinio; Drake, Corey

2013-01-01

In this essay, the authors provide a rationale for the need to break the silence of privilege and oppression in mathematics education. They begin by providing a brief rationale from their personal and professional perspectives, which includes background about planning and executing the Privilege and Oppression in the Mathematics Preparation of…

Factors Related to White, Black, and Hispanic Women's Mathematics Attainments: A Descriptive Study.

ERIC Educational Resources Information Center

Rothschild, Susan J. S.; Lichtman, Marilyn

Virtually no research conducted on women and mathematics is longitudinal in scope, generalizable in extent, and ethnic-race specific in nature. This descriptive study begins to fill the gap by examining the effects of background, school, and social-psychological factors on Hispanic, black, and white women's mathematics attainments. Data for the…

If One Goes up the Other Must Come Down: Examining Ipsative Relationships between Math and English Self-concept Trajectories across High School

ERIC Educational Resources Information Center

Parker, Philip D.; Marsh, Herbert W.; Morin, Alexandre J. S.; Seaton, Marjorie; Van Zanden, Brooke

2015-01-01

Background: The Internal-External frame of reference (IE) model suggests that as self-concept in one domain goes up (e.g., English) self-concept in other domains (e.g., mathematics) should go down (ipsative self-concept hypothesis). Aims: To our knowledge this assumption has not been tested. Testing this effect also provides a context for…

Cosmic clustering

DOE PAGES

Anninos, Dionysios; Denef, Frederik

2016-06-30

We show that the late time Hartle-Hawking wave function for a free massless scalar in a fixed de Sitter background encodes a sharp ultrametric structure for the standard Euclidean distance on the space of field configurations. This implies a hierarchical, tree-like organization of the state space, reflecting its genesis as a branched diffusion process. In conclusion, an equivalent mathematical structure organizes the state space of the Sherrington-Kirkpatrick model of a spin glass.

Detecting the Stochastic Gravitational-Wave Background

NASA Astrophysics Data System (ADS)

Colacino, Carlo Nicola

2017-12-01

The stochastic gravitational-wave background (SGWB) is by far the most difficult source of gravitational radiation detect. At the same time, it is the most interesting and intriguing one. This book describes the initial detection of the SGWB and describes the underlying mathematics behind one of the most amazing discoveries of the 21st century. On the experimental side it would mean that interferometric gravitational wave detectors work even better than expected. On the observational side, such a detection could give us information about the very early Universe, information that could not be obtained otherwise. Even negative results and improved upper bounds could put constraints on many cosmological and particle physics models.

FNAS/summer faculty fellowship research continuation program. Task 6: Integrated model development for liquid fueled rocket propulsion systems. Task 9: Aspects of model-based rocket engine condition monitoring and control

NASA Technical Reports Server (NTRS)

Santi, L. Michael; Helmicki, Arthur J.

1993-01-01

The objective of Phase I of this research effort was to develop an advanced mathematical-empirical model of SSME steady-state performance. Task 6 of Phase I is to develop component specific modification strategy for baseline case influence coefficient matrices. This report describes the background of SSME performance characteristics and provides a description of the control variable basis of three different gains models. The procedure used to establish influence coefficients for each of these three models is also described. Gains model analysis results are compared to Rocketdyne's power balance model (PBM).

A refined methodology for modeling volume quantification performance in CT

NASA Astrophysics Data System (ADS)

Chen, Baiyu; Wilson, Joshua; Samei, Ehsan

2014-03-01

The utility of CT lung nodule volume quantification technique depends on the precision of the quantification. To enable the evaluation of quantification precision, we previously developed a mathematical model that related precision to image resolution and noise properties in uniform backgrounds in terms of an estimability index (e'). The e' was shown to predict empirical precision across 54 imaging and reconstruction protocols, but with different correlation qualities for FBP and iterative reconstruction (IR) due to the non-linearity of IR impacted by anatomical structure. To better account for the non-linearity of IR, this study aimed to refine the noise characterization of the model in the presence of textured backgrounds. Repeated scans of an anthropomorphic lung phantom were acquired. Subtracted images were used to measure the image quantum noise, which was then used to adjust the noise component of the e' calculation measured from a uniform region. In addition to the model refinement, the validation of the model was further extended to 2 nodule sizes (5 and 10 mm) and 2 segmentation algorithms. Results showed that the magnitude of IR's quantum noise was significantly higher in structured backgrounds than in uniform backgrounds (ASiR, 30-50%; MBIR, 100-200%). With the refined model, the correlation between e' values and empirical precision no longer depended on reconstruction algorithm. In conclusion, the model with refined noise characterization relfected the nonlinearity of iterative reconstruction in structured background, and further showed successful prediction of quantification precision across a variety of nodule sizes, dose levels, slice thickness, reconstruction algorithms, and segmentation software.

Research on air and missile defense task allocation based on extended contract net protocol

NASA Astrophysics Data System (ADS)

Zhang, Yunzhi; Wang, Gang

2017-10-01

Based on the background of air and missile defense distributed element corporative engagement, the interception task allocation problem of multiple weapon units with multiple targets under network condition is analyzed. Firstly, a mathematical model of task allocation is established by combat task decomposition. Secondly, the initialization assignment based on auction contract and the adjustment allocation scheme based on swap contract were introduced to the task allocation. Finally, through the simulation calculation of typical situation, the model can be used to solve the task allocation problem in complex combat environment.

Mathematics at A-Level. A Discussion Paper on the Applied Content. No. 93.

ERIC Educational Resources Information Center

Mathematical Association, Leicester (England).

In September 1979, the Mathematical Association in England held a weekend seminar on the scope of Applied Mathematics at A-level, and a subcommittee was established to consider the topic at more length. This paper is the first product of the subcommittee's deliberations. Sections 1 and 2 describe the background to current A-level courses: (1) who…

Defining Mathematics Competency in the Service of Cognitively Based Assessment for Grades 6 through 8. Research Report. ETS RR-09-42

ERIC Educational Resources Information Center

Graf, Edith Aurora

2009-01-01

This report makes recommendations for the development of middle-school assessment in mathematics, based on a synthesis of scientific findings in cognitive psychology and mathematics education. The focus is on background research, rather than test specifications or example tasks. Readers interested in early development and pilot efforts associated…

Investigating Relationships between the Usage of Mathematics Learning Support and Performance of At-Risk Students

ERIC Educational Resources Information Center

Berry, Emma; Mac An Bhaird, Ciarán; O'Shea, Ann

2015-01-01

The provision of some level of Mathematics Learning Support is now commonplace in the majority of Higher Education Institutions in the UK and Ireland. Most of these supports were initially established with the aim of trying to address the problem of large numbers of first-year students with weak mathematical backgrounds. The centres provide…

How Should Fifth-Grade Mathematics Teachers Start the School Year?: Relations between Teacher-Student Interactions and Mathematics Instruction over One Year

ERIC Educational Resources Information Center

Banse, Holland W.; Curby, Timothy W.; Palacios, Natalia A.; Rimm-Kaufman, Sara E.

2018-01-01

Background: Teaching is comprised of interconnected practices. Some practices are domain neutral (DN), or independent of a content area. Examples of DN practices include emotional and instructional support and classroom organization. Others are domain specific (DS), or content dependent. Within a mathematics context, examples of DS practices…

The systems biology simulation core algorithm

PubMed Central

2013-01-01

Background With the increasing availability of high dimensional time course data for metabolites, genes, and fluxes, the mathematical description of dynamical systems has become an essential aspect of research in systems biology. Models are often encoded in formats such as SBML, whose structure is very complex and difficult to evaluate due to many special cases. Results This article describes an efficient algorithm to solve SBML models that are interpreted in terms of ordinary differential equations. We begin our consideration with a formal representation of the mathematical form of the models and explain all parts of the algorithm in detail, including several preprocessing steps. We provide a flexible reference implementation as part of the Systems Biology Simulation Core Library, a community-driven project providing a large collection of numerical solvers and a sophisticated interface hierarchy for the definition of custom differential equation systems. To demonstrate the capabilities of the new algorithm, it has been tested with the entire SBML Test Suite and all models of BioModels Database. Conclusions The formal description of the mathematics behind the SBML format facilitates the implementation of the algorithm within specifically tailored programs. The reference implementation can be used as a simulation backend for Java™-based programs. Source code, binaries, and documentation can be freely obtained under the terms of the LGPL version 3 from http://simulation-core.sourceforge.net. Feature requests, bug reports, contributions, or any further discussion can be directed to the mailing list simulation-core-development@lists.sourceforge.net. PMID:23826941

Mathematical Modeling of E6-p53 interactions in Cervical Cancer

PubMed

Khattak, Faryal; Haseeb, Muhammad; Fazal, Sahar; Bhatti, A I; Ullah, Mukhtar

2017-04-01

Background: Cervical cancer is the third most common cancer in women throughout the world. The human papillomavirus (HPV) E6 viral protein plays an essential role in proteasomal degradation of the cancer suppressant protein p53. As a result, p53 negative regulation and apoptosis relevant activities are abrogated, facilitating development of cervical cancer. Methods: A mathematical model of E6-p53 interactions was developed using mathematical laws. In-silico simulations were carried out on CellDesigner and as a test case the small molecule drug RITA was considered for its ability to rescue the functions of tumor suppressor p53 by inhibiting E6 mediated proteasomal degradation. Results: Using a computational model we scrutinized how p53 responds to RITA, and chemical reactions of this small molecule drug were incorporated to perceive the full effects. The evolved strategy allowed the p53 response and rescue of its tumor suppressor function to be delineated, RITA being found to block p53 interactions with E6 associated proteins. Conclusion: We could develop a model of E6-p53 interactions with incorporation of actions of the small molecule drug RITA. Suppression of E6 associated proteins by RITA induces accumulation of tumor suppressant p53. Using CellDesigner to encode the model ensured that it can be easily modified and extended as more data become available. This strategy should play an effective role in the development of therapies against cancer. Creative Commons Attribution License

Mathematical Modeling of E6-p53 interactions in Cervical Cancer

PubMed Central

Khattak, Faryal; Haseeb, Muhammad; Fazal, Sahar; Bhatti, AI; Ullah, Mukhtar

2017-01-01

Background: Cervical cancer is the third most common cancer in women throughout the world. The human papillomavirus (HPV) E6 viral protein plays an essential role in proteasomal degradation of the cancer suppressant protein p53. As a result, p53 negative regulation and apoptosis relevant activities are abrogated, facilitating development of cervical cancer. Methods: A mathematical model of E6-p53 interactions was developed using mathematical laws. In-silico simulations were carried out on CellDesigner and as a test case the small molecule drug RITA was considered for its ability to rescue the functions of tumor suppressor p53 by inhibiting E6 mediated proteasomal degradation. Results: Using a computational model we scrutinized how p53 responds to RITA, and chemical reactions of this small molecule drug were incorporated to perceive the full effects. The evolved strategy allowed the p53 response and rescue of its tumor suppressor function to be delineated, RITA being found to block p53 interactions with E6 associated proteins. Conclusion: We could develop a model of E6-p53 interactions with incorporation of actions of the small molecule drug RITA. Suppression of E6 associated proteins by RITA induces accumulation of tumor suppressant p53. Using CellDesigner to encode the model ensured that it can be easily modified and extended as more data become available. This strategy should play an effective role in the development of therapies against cancer. PMID:28547941

Mathematical modeling of laser lipolysis

PubMed Central

Mordon, Serge R; Wassmer, Benjamin; Reynaud, Jean Pascal; Zemmouri, Jaouad

2008-01-01

Background and Objectives Liposuction continues to be one of the most popular procedures performed in cosmetic surgery. As the public's demand for body contouring continues, laser lipolysis has been proposed to improve results, minimize risk, optimize patient comfort, and reduce the recovery period. Mathematical modeling of laser lipolysis could provide a better understanding of the laser lipolysis process and could determine the optimal dosage as a function of fat volume to be removed. Study design/Materials and Methods An Optical-Thermal-Damage Model was formulated using finite-element modeling software (Femlab 3.1, Comsol Inc). The general model simulated light distribution using the diffusion approximation of the transport theory, temperature rise using the bioheat equation and laser-induced injury using the Arrhenius damage model. Biological tissue was represented by two homogenous regions (dermis and fat layer) with a nonlinear air-tissue boundary condition including free convection. Video recordings were used to gain a better understanding of the back and forth movement of the cannula during laser lipolysis in order to consider them in our mathematical model. Infrared video recordings were also performed in order to compare the actual surface temperatures to our calculations. The reduction in fat volume was determined as a function of the total applied energy and subsequently compared to clinical data reported in the literature. Results In patients, when using cooled tumescent anesthesia, 1064 nm Nd:YAG laser or 980 nm diode laser: (6 W, back and forth motion: 100 mm/s) give similar skin surface temperature (max: 41°C). These measurements are in accordance with those obtained by mathematical modeling performed with a 1 mm cannula inserted inside the hypodermis layer at 0.8 cm below the surface. Similarly, the fat volume reduction observed in patients at 6-month follow up can be determined by mathematical modeling. This fat reduction depends on the applied energy, typically 5 cm3 for 3000 J. At last, skin retraction was observed in patients at 6-month follow up. This observation can be easily explained by mathematical modeling showing that the temperature increase inside the lower dermis is sufficient (48–50°C) to induce skin tightening Discussion and Conclusion Laser lipolysis can be described by a theoretical model. Fat volume reduction observed in patients is in accordance with model calculations. Due to heat diffusion, temperature elevation is also produced inside the lower reticular dermis. This interesting observation can explain remodeling of the collagenous tissue, with clinically evident skin tightening. In conclusion, while the heat generated by interstitial laser irradiation provides stimulate lipolysis of the fat cells, the collagen and elastin are also stimulated resulting in a tightening in the skin. This mathematical model should serve as a useful tool to simulate and better understand the mechanism of action of the laser lipolysis PMID:18312643

Identification and agreement of first turn point by mathematical analysis applied to heart rate, carbon dioxide output and electromyography

PubMed Central

Zamunér, Antonio R.; Catai, Aparecida M.; Martins, Luiz E. B.; Sakabe, Daniel I.; Silva, Ester Da

2013-01-01

Background The second heart rate (HR) turn point has been extensively studied, however there are few studies determining the first HR turn point. Also, the use of mathematical and statistical models for determining changes in dynamic characteristics of physiological variables during an incremental cardiopulmonary test has been suggested. Objectives To determine the first turn point by analysis of HR, surface electromyography (sEMG), and carbon dioxide output () using two mathematical models and to compare the results to those of the visual method. Method Ten sedentary middle-aged men (53.9±3.2 years old) were submitted to cardiopulmonary exercise testing on an electromagnetic cycle ergometer until exhaustion. Ventilatory variables, HR, and sEMG of the vastus lateralis were obtained in real time. Three methods were used to determine the first turn point: 1) visual analysis based on loss of parallelism between and oxygen uptake (); 2) the linear-linear model, based on fitting the curves to the set of data (Lin-Lin ); 3) a bi-segmental linear regression of Hinkley' s algorithm applied to HR (HMM-HR), (HMM- ), and sEMG data (HMM-RMS). Results There were no differences between workload, HR, and ventilatory variable values at the first ventilatory turn point as determined by the five studied parameters (p>0.05). The Bland-Altman plot showed an even distribution of the visual analysis method with Lin-Lin , HMM-HR, HMM-CO2, and HMM-RMS. Conclusion The proposed mathematical models were effective in determining the first turn point since they detected the linear pattern change and the deflection point of , HR responses, and sEMG. PMID:24346296

Reflection Matrix Method for Controlling Light After Reflection From a Diffuse Scattering Surface

DTIC Science & Technology

2016-12-22

reflective inverse diffusion, which was a proof-of-concept experiment that used phase modulation to shape the wavefront of a laser causing it to refocus...after reflection from a rough surface. By refocusing the light, reflective inverse diffusion has the potential to eliminate the complex radiometric model...photography. However, the initial reflective inverse diffusion experiments provided no mathematical background and were conducted under the premise that the

Dynamics of Zika virus outbreaks: an overview of mathematical modeling approaches

PubMed Central

Wiratsudakul, Anuwat; Suparit, Parinya

2018-01-01

Background The Zika virus was first discovered in 1947. It was neglected until a major outbreak occurred on Yap Island, Micronesia, in 2007. Teratogenic effects resulting in microcephaly in newborn infants is the greatest public health threat. In 2016, the Zika virus epidemic was declared as a Public Health Emergency of International Concern (PHEIC). Consequently, mathematical models were constructed to explicitly elucidate related transmission dynamics. Survey Methodology In this review article, two steps of journal article searching were performed. First, we attempted to identify mathematical models previously applied to the study of vector-borne diseases using the search terms “dynamics,” “mathematical model,” “modeling,” and “vector-borne” together with the names of vector-borne diseases including chikungunya, dengue, malaria, West Nile, and Zika. Then the identified types of model were further investigated. Second, we narrowed down our survey to focus on only Zika virus research. The terms we searched for were “compartmental,” “spatial,” “metapopulation,” “network,” “individual-based,” “agent-based” AND “Zika.” All relevant studies were included regardless of the year of publication. We have collected research articles that were published before August 2017 based on our search criteria. In this publication survey, we explored the Google Scholar and PubMed databases. Results We found five basic model architectures previously applied to vector-borne virus studies, particularly in Zika virus simulations. These include compartmental, spatial, metapopulation, network, and individual-based models. We found that Zika models carried out for early epidemics were mostly fit into compartmental structures and were less complicated compared to the more recent ones. Simple models are still commonly used for the timely assessment of epidemics. Nevertheless, due to the availability of large-scale real-world data and computational power, recently there has been growing interest in more complex modeling frameworks. Discussion Mathematical models are employed to explore and predict how an infectious disease spreads in the real world, evaluate the disease importation risk, and assess the effectiveness of intervention strategies. As the trends in modeling of infectious diseases have been shifting towards data-driven approaches, simple and complex models should be exploited differently. Simple models can be produced in a timely fashion to provide an estimation of the possible impacts. In contrast, complex models integrating real-world data require more time to develop but are far more realistic. The preparation of complicated modeling frameworks prior to the outbreaks is recommended, including the case of future Zika epidemic preparation. PMID:29593941

Chances of success in and engagement with mathematics for students who enter university with a weak mathematics background

NASA Astrophysics Data System (ADS)

Varsavsky, Cristina

2010-12-01

An increasing number of Australian students elect not to undertake studies in mathematical methods in the final years of their secondary schooling. Some higher education providers now offer pathways for these students to pursue mathematics studies up to a major specialization within the bachelor of science programme. This article analyses the performance in and engagement with mathematics of the students who elect to take up this option. Findings indicate that these are not very different when compared to students who enter university with an intermediate mathematics preparation. The biggest contrast in performance and engagement is with those students who have studied mathematics in senior secondary school to an advanced level.

HIV Treatment as Prevention: Systematic Comparison of Mathematical Models of the Potential Impact of Antiretroviral Therapy on HIV Incidence in South Africa

PubMed Central

Eaton, Jeffrey W.; Johnson, Leigh F.; Salomon, Joshua A.; Bärnighausen, Till; Bendavid, Eran; Bershteyn, Anna; Bloom, David E.; Cambiano, Valentina; Fraser, Christophe; Hontelez, Jan A. C.; Humair, Salal; Klein, Daniel J.; Long, Elisa F.; Phillips, Andrew N.; Pretorius, Carel; Stover, John; Wenger, Edward A.; Williams, Brian G.; Hallett, Timothy B.

2012-01-01

Background Many mathematical models have investigated the impact of expanding access to antiretroviral therapy (ART) on new HIV infections. Comparing results and conclusions across models is challenging because models have addressed slightly different questions and have reported different outcome metrics. This study compares the predictions of several mathematical models simulating the same ART intervention programmes to determine the extent to which models agree about the epidemiological impact of expanded ART. Methods and Findings Twelve independent mathematical models evaluated a set of standardised ART intervention scenarios in South Africa and reported a common set of outputs. Intervention scenarios systematically varied the CD4 count threshold for treatment eligibility, access to treatment, and programme retention. For a scenario in which 80% of HIV-infected individuals start treatment on average 1 y after their CD4 count drops below 350 cells/µl and 85% remain on treatment after 3 y, the models projected that HIV incidence would be 35% to 54% lower 8 y after the introduction of ART, compared to a counterfactual scenario in which there is no ART. More variation existed in the estimated long-term (38 y) reductions in incidence. The impact of optimistic interventions including immediate ART initiation varied widely across models, maintaining substantial uncertainty about the theoretical prospect for elimination of HIV from the population using ART alone over the next four decades. The number of person-years of ART per infection averted over 8 y ranged between 5.8 and 18.7. Considering the actual scale-up of ART in South Africa, seven models estimated that current HIV incidence is 17% to 32% lower than it would have been in the absence of ART. Differences between model assumptions about CD4 decline and HIV transmissibility over the course of infection explained only a modest amount of the variation in model results. Conclusions Mathematical models evaluating the impact of ART vary substantially in structure, complexity, and parameter choices, but all suggest that ART, at high levels of access and with high adherence, has the potential to substantially reduce new HIV infections. There was broad agreement regarding the short-term epidemiologic impact of ambitious treatment scale-up, but more variation in longer term projections and in the efficiency with which treatment can reduce new infections. Differences between model predictions could not be explained by differences in model structure or parameterization that were hypothesized to affect intervention impact. Please see later in the article for the Editors' Summary PMID:22802730

Mathematical Modeling of HIV Prevention Measures Including Pre-Exposure Prophylaxis on HIV Incidence in South Korea

PubMed Central

Kim, Sun Bean; Yoon, Myoungho; Ku, Nam Su; Kim, Min Hyung; Song, Je Eun; Ahn, Jin Young; Jeong, Su Jin; Kim, Changsoo; Kwon, Hee-Dae; Lee, Jeehyun; Smith, Davey M.; Choi, Jun Yong

2014-01-01

Background Multiple prevention measures have the possibility of impacting HIV incidence in South Korea, including early diagnosis, early treatment, and pre-exposure prophylaxis (PrEP). We investigated how each of these interventions could impact the local HIV epidemic, especially among men who have sex with men (MSM), who have become the major risk group in South Korea. A mathematical model was used to estimate the effects of each these interventions on the HIV epidemic in South Korea over the next 40 years, as compared to the current situation. Methods We constructed a mathematical model of HIV infection among MSM in South Korea, dividing the MSM population into seven groups, and simulated the effects of early antiretroviral therapy (ART), early diagnosis, PrEP, and combination interventions on the incidence and prevalence of HIV infection, as compared to the current situation that would be expected without any new prevention measures. Results Overall, the model suggested that the most effective prevention measure would be PrEP. Even though PrEP effectiveness could be lessened by increased unsafe sex behavior, PrEP use was still more beneficial than the current situation. In the model, early diagnosis of HIV infection was also effectively decreased HIV incidence. However, early ART did not show considerable effectiveness. As expected, it would be most effective if all interventions (PrEP, early diagnosis and early treatment) were implemented together. Conclusions This model suggests that PrEP and early diagnosis could be a very effective way to reduce HIV incidence in South Korea among MSM. PMID:24662776

Intensity level for exercise training in fibromyalgia by using mathematical models

PubMed Central

2010-01-01

Background It has not been assessed before whether mathematical models described in the literature for prescriptions of exercise can be used for fibromyalgia syndrome patients. The objective of this paper was to determine how age-predicted heart rate formulas can be used with fibromyalgia syndrome populations as well as to find out which mathematical models are more accurate to control exercise intensity. Methods A total of 60 women aged 18-65 years with fibromyalgia syndrome were included; 32 were randomized to walking training at anaerobic threshold. Age-predicted formulas to maximum heart rate ("220 minus age" and "208 minus 0.7 × age") were correlated with achieved maximum heart rate (HRMax) obtained by spiroergometry. Subsequently, six mathematical models using heart rate reserve (HRR) and age-predicted HRMax formulas were studied to estimate the intensity level of exercise training corresponding to heart rate at anaerobic threshold (HRAT) obtained by spiroergometry. Linear and nonlinear regression models were used for correlations and residues analysis for the adequacy of the models. Results Age-predicted HRMax and HRAT formulas had a good correlation with achieved heart rate obtained in spiroergometry (r = 0.642; p < 0.05). For exercise prescription in the anaerobic threshold intensity, the percentages were 52.2-60.6% HRR and 75.5-80.9% HRMax. Formulas using HRR and the achieved HRMax showed better correlation. Furthermore, the percentages of HRMax and HRR were significantly higher for the trained individuals (p < 0.05). Conclusion Age-predicted formulas can be used for estimating HRMax and for exercise prescriptions in women with fibromyalgia syndrome. Karnoven's formula using heart rate achieved in ergometric test showed a better correlation. For the prescription of exercises in the threshold intensity, 52% to 60% HRR or 75% to 80% HRMax must be used in sedentary women with fibromyalgia syndrome and these values are higher and must be corrected for trained patients. PMID:20307323

Mathematics Readiness of First-Year University Students

ERIC Educational Resources Information Center

Atuahene, Francis; Russell, Tammy A.

2016-01-01

The majority of high school students, particularly underrepresented minorities (URMs) from low socioeconomic backgrounds are graduating from high school less prepared academically for advanced-level college mathematics. Using 2009 and 2010 course enrollment data, several statistical analyses (multiple linear regression, Cochran Mantel Haenszel…

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

Potomkin, Mykhailo; Kaiser, Andreas; Berlyand, Leonid

We consider active particles swimming in a convergent fluid flow in a trapezoid nozzle with no-slip walls. We use mathematical modeling to analyze trajectories of these particles inside the nozzle. By extensive Monte Carlo simulations, we show that trajectories are strongly affected by the background fluid flow and geometry of the nozzle leading to wall accumulation and upstream motion (rheotaxis). In particular, we describe the non-trivial focusing of active rods depending on physical and geometrical parameters. It is also established that the convergent component of the background flow leads to stability of both downstream and upstream swimming at the centerline.more » The stability of downstream swimming enhances focusing, and the stability of upstream swimming enables rheotaxis in the bulk.« less

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

A Comparative Analysis of the Relationship among Quality Instruction, Teacher Self-Efficacy, Student Background, and Mathematics Achievement in South Korea and the United States

ERIC Educational Resources Information Center

Son, Ji-Won; Han, Seong Won; Kang, Chungseo; Kwon, Oh Nam

2016-01-01

The purpose of this study is to compare and contrast student, teacher, and school factors that are associated with student mathematics achievement in South Korea and the United States. Using the data from the Trends in International Mathematics and Science Study (TIMSS) 2011, this study examines factors that are linked to teachers who deliver…

The Use of Graphing Technology to Promote Transfer of Learning: the Interpretation of Graphs in Physics.

NASA Astrophysics Data System (ADS)

Nichols, Jeri Ann

This study examined the relationship between mathematics background and performance on graph-related problems in physics before and after instruction on the graphical analysis of motion and several microcomputer-based laboratory experiences. Students identified as either having or not having a graphing technology enhanced precalculus mathematics background were further categorized into one of four groups according to mathematics placement at the university. The performances of these groups were compared to identity differences. Pre- and Post-test data were collected from 589 students and 312 students during Autumn Quarter 1990 and Winter Quarter 1991 respectively. Background information was collected from each student. Significant differences were found between students with the technology enhanced mathematics background and those without when considering the entire populations both quarters. The students with the technology background were favored Autumn quarter and students without the technology background were favored Winter quarter. However, the entire population included an underrepresentation of students at the highest and lowest placements; hence, these were eliminated from the analyses. No significant differences were found between the technology/no technology groups after the elimination of the underrepresented groups. All categories of students increased their mean scores from pretest to post-test; the average increase was 8.23 points Autumn Quarter and 11.41 points Winter Quarter. Males consistently outperformed females on both the pretest and the post-test Autumn 1990. All students found questions involving the concept of acceleration more difficult than questions involving velocity or distance. Questions requiring students to create graphs were more difficult than questions requiring students to interpret graphs. Further research involving a qualitative component is recommended to identify the specific skills students use when solving graph-related physics problems. In addition, it is recommended that a similar study be conducted to include a control group not participating in the microcomputer -based laboratory experiments.

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…

Collaborative and Cooperative Learning in Malaysian Mathematics Education

ERIC Educational Resources Information Center

Hossain, Md. Anowar; Tarmizi, Rohani Ahmad; Ayud, Ahmad Fauzi Mohd

2012-01-01

Collaborative and cooperative learning studies are well recognized in Malaysian mathematics education research. Cooperative learning is used to serve various ability students taking into consideration of their level of understanding, learning styles, sociological backgrounds that develop students' academic achievement and skills, and breeze the…

On Automatic Assessment and Conceptual Understanding

ERIC Educational Resources Information Center

Rasila, Antti; Malinen, Jarmo; Tiitu, Hannu

2015-01-01

We consider two complementary aspects of mathematical skills, i.e. "procedural fluency" and "conceptual understanding," from a point of view that is related to modern e-learning environments and computer-based assessment. Pedagogical background of teaching mathematics is discussed, and it is proposed that the traditional book…

Ideas: NCTM Standards-Based Instruction, Grades K-4.

ERIC Educational Resources Information Center

Hynes, Michael C., Ed.

This document is a collection of activity-based mathematics lessons for grades K-4 from the "Ideas" department in "Arithmetic Teacher: Mathematics Education through the Middle Grades." Each lesson includes background information, objectives, directions, extensions, and student worksheets. A matrix is included which correlates…

Ideas: NCTM Standards-Based Instruction, Grades 5-8.

ERIC Educational Resources Information Center

Hynes, Michael C., Ed.

This document is a collection of activity-based mathematics lessons for grades 5-8 from the "Ideas" department in "Arithmetic Teacher: Mathematics Education through the Middle Grades." Each lesson includes background information, objectives, directions, extensions, and student worksheets. A matrix is included which correlates…

Trigonometry Learning

ERIC Educational Resources Information Center

Gur, Hulya

2009-01-01

Background: Trigonometry is an area of mathematics that students believe to be particularly difficult and abstract compared with the other subjects of mathematics. Trigonometry is often introduced early in year 8 with most textbooks traditionally starting with naming sides of right-angled triangles. Students need to see and understand why their…

An appraisal of an online tutorial system for the teaching and learning of engineering physics in conjunction with contextual physics and mathematics, and relevant mathematics

NASA Astrophysics Data System (ADS)

Bhathal, Ragbir

2016-09-01

The number of students entering engineering schools in Australian universities has increased tremendously over the last few years because of the Australian Federal Government's policy of increasing the participation rates of Higher School Certificate students and students from low social economic status backgrounds in the tertiary sector. They now come with a diverse background of skills, motivations and prior knowledge. It is imperative that new methods of teaching and learning be developed. This paper describes an online tutorial system used in conjunction with contextual physics and mathematics, and the revision of the relevant mathematical knowledge at the appropriate time before a new topic is introduced in the teaching and learning of engineering physics. Taken as a whole, this study shows that students not only improved their final examination results but there was also an increase in the retention rate of first-year engineering students which has financial implications for the university.

How much crosstalk can be allowed in a stereoscopic system at various grey levels?

NASA Astrophysics Data System (ADS)

Shestak, Sergey; Kim, Daesik; Kim, Yongie

2012-03-01

We have calculated a perceptual threshold of stereoscopic crosstalk on the basis of mathematical model of human vision sensitivity. Instead of linear model of just noticeable difference (JND) known as Weber's law we applied nonlinear Barten's model. The predicted crosstalk threshold varies with the background luminance. The calculated values of threshold are in a reasonable agreement with known experimental data. We calculated perceptual threshold of crosstalk for various combinations of the applied grey level. This result can be applied for the assessment of grey-to-grey crosstalk compensation. Further computational analysis of the applied model predicts the increase of the displayable image contrast with reduction of the maximum displayable luminance.

Artificial emotion triggered stochastic behavior transitions with motivational gain effects for multi-objective robot tasks

NASA Astrophysics Data System (ADS)

Dağlarli, Evren; Temeltaş, Hakan

2007-04-01

This paper presents artificial emotional system based autonomous robot control architecture. Hidden Markov model developed as mathematical background for stochastic emotional and behavior transitions. Motivation module of architecture considered as behavioral gain effect generator for achieving multi-objective robot tasks. According to emotional and behavioral state transition probabilities, artificial emotions determine sequences of behaviors. Also motivational gain effects of proposed architecture can be observed on the executing behaviors during simulation.

Spatial predictive mapping using artificial neural networks

NASA Astrophysics Data System (ADS)

Noack, S.; Knobloch, A.; Etzold, S. H.; Barth, A.; Kallmeier, E.

2014-11-01

The modelling or prediction of complex geospatial phenomena (like formation of geo-hazards) is one of the most important tasks for geoscientists. But in practice it faces various difficulties, caused mainly by the complexity of relationships between the phenomena itself and the controlling parameters, as well by limitations of our knowledge about the nature of physical/ mathematical relationships and by restrictions regarding accuracy and availability of data. In this situation methods of artificial intelligence, like artificial neural networks (ANN) offer a meaningful alternative modelling approach compared to the exact mathematical modelling. In the past, the application of ANN technologies in geosciences was primarily limited due to difficulties to integrate it into geo-data processing algorithms. In consideration of this background, the software advangeo® was developed to provide a normal GIS user with a powerful tool to use ANNs for prediction mapping and data preparation within his standard ESRI ArcGIS environment. In many case studies, such as land use planning, geo-hazards analysis and prevention, mineral potential mapping, agriculture & forestry advangeo® has shown its capabilities and strengths. The approach is able to add considerable value to existing data.

Preserving Simplecticity in the Numerical Integration of Linear Beam Optics

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

Allen, Christopher K.

2017-07-01

Presented are mathematical tools and methods for the development of numerical integration techniques that preserve the symplectic condition inherent to mechanics. The intended audience is for beam physicists with backgrounds in numerical modeling and simulation with particular attention to beam optics applications. The paper focuses on Lie methods that are inherently symplectic regardless of the integration accuracy order. Section 2 provides the mathematically tools used in the sequel and necessary for the reader to extend the covered techniques. Section 3 places those tools in the context of charged-particle beam optics; in particular linear beam optics is presented in terms ofmore » a Lie algebraic matrix representation. Section 4 presents numerical stepping techniques with particular emphasis on a third-order leapfrog method. Section 5 discusses the modeling of field imperfections with particular attention to the fringe fields of quadrupole focusing magnets. The direct computation of a third order transfer matrix for a fringe field is shown.« less

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…

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…

Low contrast detection in abdominal CT: comparing single-slice and multi-slice tasks

NASA Astrophysics Data System (ADS)

Ba, Alexandre; Racine, Damien; Viry, Anaïs.; Verdun, Francis R.; Schmidt, Sabine; Bochud, François O.

2017-03-01

Image quality assessment is crucial for the optimization of computed tomography (CT) protocols. Human and mathematical model observers are increasingly used for the detection of low contrast signal in abdominal CT, but are frequently limited to the use of a single image slice. Another limitation is that most of them only consider the detection of a signal embedded in a uniform background phantom. The purpose of this paper was to test if human observer performance is significantly different in CT images read in single or multiple slice modes and if these differences are the same for anatomical and uniform clinical images. We investigated detection performance and scrolling trends of human observers of a simulated liver lesion embedded in anatomical and uniform CT backgrounds. Results show that observers don't take significantly benefit of additional information provided in multi-slice reading mode. Regarding the background, performances are moderately higher for uniform than for anatomical images. Our results suggest that for low contrast detection in abdominal CT, the use of multi-slice model observers would probably only add a marginal benefit. On the other hand, the quality of a CT image is more accurately estimated with clinical anatomical backgrounds.

Modeling combination HCV prevention among HIV-infected men who have sex with men and people who inject drugs

PubMed Central

Martin, Natasha K.; Skaathun, Britt; Vickerman, Peter; Stuart, David

2017-01-01

Background People who inject drugs (PWID) and HIV-infected men who have sex with men (MSM) are key risk groups for hepatitis C virus (HCV) transmission. Mathematical modeling studies can help elucidate what level and combination of prevention intervention scale-up is required to control or eliminate epidemics among these key populations. Methods We discuss the evidence surrounding HCV prevention interventions and provide an overview of the mathematical modeling literature projecting the impact of scaled-up HCV prevention among PWID and HIV-infected MSM. Results Harm reduction interventions such as opiate substitution therapy and needle and syringe programs are effective in reducing HCV incidence among PWID. Modeling and limited empirical data indicate HCV treatment could additionally be used for prevention. No studies have evaluated the effectiveness of behavior change interventions to reduce HCV incidence among MSM, but existing interventions to reduce HIV risk could be effective. Mathematical modeling and empirical data indicates that scale-up of harm reduction could reduce HCV transmission, but in isolation is unlikely to eliminate HCV among PWID. By contrast, elimination is possibly achievable through combination scale-up of harm reduction and HCV treatment. Similarly, among HIV-infected MSM, eliminating the emerging epidemics will likely require HCV treatment scale-up in combination with additional interventions to reduce HCV-related risk behaviors. Conclusions Elimination of HCV will likely require combination prevention efforts among both PWID and HIV-infected MSM populations. Further empirical research is required to validate HCV treatment as prevention among these populations, and to identify effective behavioral interventions to reduce HCV incidence among MSM. PMID:28534885

Stretch-dependent changes in surface profiles of the human crystalline lens during accommodation: A finite element study

PubMed Central

Pour, Hooman Mohammad; Kanapathipillai, Sangarapillai; Zarrabi, Khosrow; Manns, Fabrice; Ho, Arthur

2015-01-01

Background A nonlinear isotropic finite element (FE) model of a 29 year old human crystalline lens was constructed to study the effects of various geometrical parameters on lens accommodation. Methods The model simulates dis-accommodation by stretching of the lens and predicts the change in the lens capsule, cortex and nucleus surface profiles at select states of stretching/accommodation. Multiple regression analysis (MRA) is used to develop a stretch-dependent mathematical model relating the lens sagittal height to the radial position of the lens surface as a function of dis-accommodative stretch. A load analysis is performed to compare the FE results to empirical results from lens stretcher studies. Using the predicted geometrical changes, the optical response of the whole eye during accommodation was analysed by ray-tracing. Results Aspects of lens shape change relative to stretch were evaluated including change in diameter (d), central thickness (T) and accommodation (A). Maximum accommodation achieved was 10.29 D. From the MRA, the stretch-dependent mathematical model of the lens shape related lens curvatures as a function of lens ciliary stretch well (maximum mean-square residual error 2.5×10−3 µm, p<0.001). The results are compared with those from in vitro studies. Conclusions The FE and ray-tracing predictions are consistent with EVAS studies in terms of load and power change versus change in thickness. The mathematical stretch-dependent model of accommodation presented may have utility in investigating lens behaviour at states other than the relaxed or fully-accommodated states. PMID:25727940

Factors Affecting Turkish Students' Achievement in Mathematics

ERIC Educational Resources Information Center

Demir, Ibrahim; Kilic, Serpil; Depren, Ozer

2009-01-01

Following past researches, student background, learning strategies, self-related cognitions in mathematics and school climate variables were important for achievement. The purpose of this study was to identify a number of factors that represent the relationship among sets of interrelated variables using principal component factor analysis and…

The Power of the Raised Eyebrow.

ERIC Educational Resources Information Center

Burton, Grace M.

This paper begins by emphasizing the school counselor's role in insuring equal educational opportunities for all students. The problem of girls' low enrollment in secondary school mathematics classes and the implications of an inadequate mathematics background are discussed. Specific steps to encourage young women to continue their study of…

Instructional Gaming: Using Technology to Support Early Mathematical Proficiency

ERIC Educational Resources Information Center

Nelson-Walker, Nancy J.; Doabler, Christian T.; Fien, Hank; Gause, Marshall; Baker, Scott K.; Clarke, Ben

2013-01-01

Widespread concern has been expressed about the persistent low mathematics achievement of students in the US, particularly for students from low-income and minority backgrounds and students with disabilities. Instructional gaming technology, when designed and fictionalized well, has the potential to improve the motivation and mathematics…

Creating Constructivist Environments and Constructing Creative Mathematics.

ERIC Educational Resources Information Center

Pirie, Susan; Kieren, Thomas

1992-01-01

Proposes and describes four teachers' beliefs necessary in creating constructivist classroom environments. Presents the background, description, and analysis of seven teaching episodes that examine the mathematical understanding actions of pupils in classrooms in which teachers exhibit these beliefs in an effort to verify the necessity of the…

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.

The Role of Mediators in the Development of Longitudinal Mathematics Achievement Associations

PubMed Central

Watts, Tyler W.; Duncan, Greg J.; Chen, Meichu; Claessens, Amy; Davis-Kean, Pamela E.; Duckworth, Kathryn; Engel, Mimi; Siegler, Robert; Susperreguy, Maria Ines

2016-01-01

Despite research demonstrating a strong association between early and later mathematics achievement, few studies have investigated mediators of this association. Using longitudinal data (n=1362), we tested the extent to which mathematics self-concepts, school placement, executive functioning, and proficiency in fractions and division account for the association between mathematics achievement in first grade and at age 15. As hypothesized, a strong longitudinal association between first grade and adolescent mathematics achievement was present (β= .36) even after controlling for a host of background characteristics, including cognitive skills and reading ability. The mediators accounted for 39% of this association, with mathematics self-concept, gifted and talented placement, and knowledge of fractions and division, serving as significant mediators. PMID:26332124

Generalist Genes and Learning Disabilities: A Multivariate Genetic Analysis of Low Performance in Reading, Mathematics, Language and General Cognitive Ability in a Sample of 8000 12-Year-Old Twins

ERIC Educational Resources Information Center

Haworth, Claire M. A.; Kovas, Yulia; Harlaar, Nicole; Hayiou-Thomas, Marianna E.; Petrill, Stephen A.; Dale, Philip S.; Plomin, Robert

2009-01-01

Background: Our previous investigation found that the same genes influence poor reading and mathematics performance in 10-year-olds. Here we assess whether this finding extends to language and general cognitive disabilities, as well as replicating the earlier finding for reading and mathematics in an older and larger sample. Methods: Using a…

The mathematics of tanning

PubMed Central

Thingnes, Josef; Øyehaug, Leiv; Hovig, Eivind; Omholt, Stig W

2009-01-01

Background The pigment melanin is produced by specialized cells, called melanocytes. In healthy skin, melanocytes are sparsely spread among the other cell types in the basal layer of the epidermis. Sun tanning results from an UV-induced increase in the release of melanin to neighbouring keratinocytes, the major cell type component of the epidermis as well as redistribution of melanin among these cells. Here we provide a mathematical conceptualization of our current knowledge of the tanning response, in terms of a dynamic model. The resolution level of the model is tuned to available data, and its primary focus is to describe the tanning response following UV exposure. Results The model appears capable of accounting for available experimental data on the tanning response in different skin and photo types. It predicts that the thickness of the epidermal layer and how far the melanocyte dendrites grow out in the epidermal layers after UV exposure influence the tanning response substantially. Conclusion Despite the paucity of experimental validation data the model is constrained enough to serve as a foundation for the establishment of a theoretical-experimental research programme aimed at elucidating the more fine-grained regulatory anatomy underlying the tanning response. PMID:19505344

Epigenetic chromatin silencing: bistability and front propagation

NASA Astrophysics Data System (ADS)

Sedighi, Mohammad; Sengupta, Anirvan M.

2007-12-01

The role of post-translational modification of histones in eukaryotic gene regulation is well recognized. Epigenetic silencing of genes via heritable chromatin modifications plays a major role in cell fate specification in higher organisms. We formulate a coarse-grained model of chromatin silencing in yeast and study the conditions under which the system becomes bistable, allowing for different epigenetic states. We also study the dynamics of the boundary between the two locally stable states of chromatin: silenced and unsilenced. The model could be of use in guiding the discussion on chromatin silencing in general. In the context of silencing in budding yeast, it helps us understand the phenotype of various mutants, some of which may be non-trivial to see without the help of a mathematical model. One such example is a mutation that reduces the rate of background acetylation of particular histone side chains that competes with the deacetylation by Sir2p. The resulting negative feedback due to a Sir protein depletion effect gives rise to interesting counter-intuitive consequences. Our mathematical analysis brings forth the different dynamical behaviors possible within the same molecular model and guides the formulation of more refined hypotheses that could be addressed experimentally.

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…

A True-Color Sensor and Suitable Evaluation Algorithm for Plant Recognition

PubMed Central

Schmittmann, Oliver; Schulze Lammers, Peter

2017-01-01

Plant-specific herbicide application requires sensor systems for plant recognition and differentiation. A literature review reveals a lack of sensor systems capable of recognizing small weeds in early stages of development (in the two- or four-leaf stage) and crop plants, of making spraying decisions in real time and, in addition, are that are inexpensive and ready for practical use in sprayers. The system described in this work is based on free cascadable and programmable true-color sensors for real-time recognition and identification of individual weed and crop plants. The application of this type of sensor is suitable for municipal areas and farmland with and without crops to perform the site-specific application of herbicides. Initially, databases with reflection properties of plants, natural and artificial backgrounds were created. Crop and weed plants should be recognized by the use of mathematical algorithms and decision models based on these data. They include the characteristic color spectrum, as well as the reflectance characteristics of unvegetated areas and areas with organic material. The CIE-Lab color-space was chosen for color matching because it contains information not only about coloration (a- and b-channel), but also about luminance (L-channel), thus increasing accuracy. Four different decision making algorithms based on different parameters are explained: (i) color similarity (ΔE); (ii) color similarity split in ΔL, Δa and Δb; (iii) a virtual channel ‘d’ and (iv) statistical distribution of the differences of reflection backgrounds and plants. Afterwards, the detection success of the recognition system is described. Furthermore, the minimum weed/plant coverage of the measuring spot was calculated by a mathematical model. Plants with a size of 1–5% of the spot can be recognized, and weeds in the two-leaf stage can be identified with a measuring spot size of 5 cm. By choosing a decision model previously, the detection quality can be increased. Depending on the characteristics of the background, different models are suitable. Finally, the results of field trials on municipal areas (with models of plants), winter wheat fields (with artificial plants) and grassland (with dock) are shown. In each experimental variant, objects and weeds could be recognized. PMID:28786922

A True-Color Sensor and Suitable Evaluation Algorithm for Plant Recognition.

PubMed

Schmittmann, Oliver; Schulze Lammers, Peter

2017-08-08

Plant-specific herbicide application requires sensor systems for plant recognition and differentiation. A literature review reveals a lack of sensor systems capable of recognizing small weeds in early stages of development (in the two- or four-leaf stage) and crop plants, of making spraying decisions in real time and, in addition, are that are inexpensive and ready for practical use in sprayers. The system described in this work is based on free cascadable and programmable true-color sensors for real-time recognition and identification of individual weed and crop plants. The application of this type of sensor is suitable for municipal areas and farmland with and without crops to perform the site-specific application of herbicides. Initially, databases with reflection properties of plants, natural and artificial backgrounds were created. Crop and weed plants should be recognized by the use of mathematical algorithms and decision models based on these data. They include the characteristic color spectrum, as well as the reflectance characteristics of unvegetated areas and areas with organic material. The CIE-Lab color-space was chosen for color matching because it contains information not only about coloration (a- and b-channel), but also about luminance (L-channel), thus increasing accuracy. Four different decision making algorithms based on different parameters are explained: (i) color similarity (ΔE); (ii) color similarity split in ΔL, Δa and Δb; (iii) a virtual channel 'd' and (iv) statistical distribution of the differences of reflection backgrounds and plants. Afterwards, the detection success of the recognition system is described. Furthermore, the minimum weed/plant coverage of the measuring spot was calculated by a mathematical model. Plants with a size of 1-5% of the spot can be recognized, and weeds in the two-leaf stage can be identified with a measuring spot size of 5 cm. By choosing a decision model previously, the detection quality can be increased. Depending on the characteristics of the background, different models are suitable. Finally, the results of field trials on municipal areas (with models of plants), winter wheat fields (with artificial plants) and grassland (with dock) are shown. In each experimental variant, objects and weeds could be recognized.

A Chinese young adult non-scientist's epistemologies and her understandings of the concept of speed

NASA Astrophysics Data System (ADS)

Cao, Ying; Brizuela, Barbara M.

2015-08-01

Past research has investigated students' epistemologies while they were taking courses that required an integrated understanding of mathematical and scientific concepts. However, past studies have not investigated students who are not currently enrolled in such classes. Additionally, past studies have primarily focused on individuals who are native English speakers from Western cultures. In this paper, we aim to investigate whether Hammer and his colleagues' claims concerning learners' epistemologies could be extended to individuals who lack advanced mathematics and science training, have had different cultural and learning experiences, and have grown up speaking and learning in another language. To this end, we interviewed a participant with these characteristics about her understandings of the concept of speed. Our findings show that previous theoretical frameworks can be used to explain the epistemologies of the individual examined in this study. The case suggests that these theories may be relevant regardless of the learner's mathematics and science background, language, educational experience, and cultural background. In the future, more cases should be examined with learners from different academic backgrounds and cultures to further support this finding.

Research in Mathematics Education

ERIC Educational Resources Information Center

Schoenfeld, Alan H.

2016-01-01

As one of the three Rs, "'rithmetic" has always been central to education and education research. By virtue of that centrality, research in mathematics education has often reflected and at times led trends in education research. This chapter provides some deep background on epistemological and other issues that shape current research,…

The Promise of Differentiated Instruction for Enhancing the Mathematical Understandings of College Students

ERIC Educational Resources Information Center

Chamberlin, Michelle; Powers, Robert

2010-01-01

Mathematics instructors must respond to diverse needs of individual students, including different abilities, interests, learning styles and cultural backgrounds. To do so, grade kindergarten-12 teachers have been using differentiated instruction, a process of proactively modifying instruction based on students' needs. It is supported by literature…

Family Child Care Learning Environments: Caregiver Knowledge and Practices Related to Early Literacy and Mathematics

ERIC Educational Resources Information Center

Phillips, Beth M.; Morse, Erika E.

2011-01-01

This paper presents findings from a stratified-random survey of family child care providers' backgrounds, caregiving environments, practices, attitudes, and knowledge related to language, literacy, and mathematics development for preschool children. Descriptive results are consistent with prior studies suggesting that home-based providers are…

Speaking Up and Speaking Out about Gender in Mathematics

ERIC Educational Resources Information Center

Rubel, Laurie H.

2016-01-01

Diversity and equity are stated priority areas across the field of mathematics education, from the ivory towers of the academy, across teacher education programs, to school districts, schools, and individual classrooms. The talk surrounding diversity and equity is usually framed around categories of race, cultural background, language, disability…

Pathways to Arithmetic Fact Retrieval and Percentage Calculation in Adolescents

ERIC Educational Resources Information Center

Träff, Ulf; Skagerlund, Kenny; Olsson, Linda; Östergren, Rickard

2017-01-01

Background: Developing sufficient mathematical skills is a prerequisite to function adequately in society today. Given this, an important task is to increase our understanding regarding the cognitive mechanisms underlying young people's acquisition of early number skills and formal mathematical knowledge. Aims: The purpose was to examine whether…

The Development of Executive Functions and Early Mathematics: A Dynamic Relationship

ERIC Educational Resources Information Center

Van der Ven, Sanne H. G.; Kroesbergen, Evelyn H.; Boom, Jan; Leseman, Paul P. M.

2012-01-01

Background: The relationship between executive functions and mathematical skills has been studied extensively, but results are inconclusive, and how this relationship evolves longitudinally is largely unknown. Aim: The aim was to investigate the factor structure of executive functions in inhibition, shifting, and updating; the longitudinal…

Integrative Pre-Service Elementary Teacher Training: The Role of Interdisciplinary Collaborative Mathematics

ERIC Educational Resources Information Center

Chiatula, Victoria Oliaku

2015-01-01

This primer summarizes interdisciplinary collaborative mathematics as an integrative approach to train pre-service elementary teachers to teach math utilizing Junior Achievement USA (JA) educational programs within an elementary Math Methods course. The primer provides a JA historical background/program overview, summarizes the interdisciplinary…

Trajectories of Mathematics and Technology Education Pointing to Engineering Design

ERIC Educational Resources Information Center

Daugherty, Jenny L.; Reese, George C.; Merrill, Chris

2010-01-01

A brief examination and comparison of mathematics and technology education provides the background for a discussion of integration. In particular, members of each field have responded to the increasing pressures to better prepare students for the technologically rich, globally competitive future. Approaches based within each discipline are varied…

Rockets: An Educator's Guide with Activities in Science, Mathematics, and Technology.

ERIC Educational Resources Information Center

National Aeronautics and Space Administration, Washington, DC.

This educational guide discusses rockets and includes activities in science, mathematics, and technology. It begins with background information on the history of rocketry, scientific principles, and practical rocketry. The sections on scientific principles and practical rocketry focus on Sir Isaac Newton's Three Laws of Motion. These laws explain…

Generalized image contrast enhancement technique based on Heinemann contrast discrimination model

NASA Astrophysics Data System (ADS)

Liu, Hong; Nodine, Calvin F.

1994-03-01

This paper presents a generalized image contrast enhancement technique which equalizes perceived brightness based on the Heinemann contrast discrimination model. This is a modified algorithm which presents an improvement over the previous study by Mokrane in its mathematically proven existence of a unique solution and in its easily tunable parameterization. The model uses a log-log representation of contrast luminosity between targets and the surround in a fixed luminosity background setting. The algorithm consists of two nonlinear gray-scale mapping functions which have seven parameters, two of which are adjustable Heinemann constants. Another parameter is the background gray level. The remaining four parameters are nonlinear functions of gray scale distribution of the image, and can be uniquely determined once the previous three are given. Tests have been carried out to examine the effectiveness of the algorithm for increasing the overall contrast of images. It can be demonstrated that the generalized algorithm provides better contrast enhancement than histogram equalization. In fact, the histogram equalization technique is a special case of the proposed mapping.

Spinning projectile's attitude measurement with LW infrared radiation under sea-sky background

NASA Astrophysics Data System (ADS)

Xu, Miaomiao; Bu, Xiongzhu; Yu, Jing; He, Zilu

2018-05-01

With the further development of infrared radiation research in sea-sky background and the requirement of spinning projectile's attitude measurement, the sea-sky infrared radiation field is used to carry out spinning projectile's attitude angle instead of inertial sensors. Firstly, the generation mechanism of sea-sky infrared radiation is analysed. The mathematical model of sea-sky infrared radiation is deduced in LW (long wave) infrared 8 ∼ 14 μm band by calculating the sea surface and sky infrared radiation. Secondly, according to the movement characteristics of spinning projectile, the attitude measurement model of infrared sensors on projectile's three axis is established. And the feasibility of the model is analysed by simulation. Finally, the projectile's attitude calculation algorithm is designed to improve the attitude angle estimation accuracy. The results of semi-physical experiments show that the segmented interactive algorithm estimation error of pitch and roll angle is within ±1.5°. The attitude measurement method is effective and feasible, and provides accurate measurement basis for the guidance of spinning projectile.

Sex-related Differences in the Determinants and Process of Science and Mathematics Choice in Pre-university Education

NASA Astrophysics Data System (ADS)

van Langen, Annemarie; Rekers-Mombarg, Lyset; Dekkers, Hetty

2006-01-01

The more science and mathematics subjects that pupils in pre-university education include in their final examination package, the more future academic routes are available to them. Equality of educational opportunity is thus threatened when groups of pupils, distinguished by sex and family background but otherwise of equal capacities and achievement, are found to differ in their choices. This proposition is examined using data from a large Dutch cohort. Multilevel analyses show that the choice of science and mathematics subjects by girls is influenced by their family background while the choice by boys is not. The influence of various pupil and family variables on the subject selection process is explored via path analyses. The results confirm the importance of viewing subject choice as a chronological process that progresses differently for boys and girls.

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…

Multiplicity Counting

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

Geist, William H.

2015-12-01

This set of slides begins by giving background and a review of neutron counting; three attributes of a verification item are discussed: 240Pu eff mass; α, the ratio of (α,n) neutrons to spontaneous fission neutrons; and leakage multiplication. It then takes up neutron detector systems – theory & concepts (coincidence counting, moderation, die-away time); detector systems – some important details (deadtime, corrections); introduction to multiplicity counting; multiplicity electronics and example distributions; singles, doubles, and triples from measured multiplicity distributions; and the point model: multiplicity mathematics.

Examining the career development of Mexican American middle school students: A test of social cognitive career theory

NASA Astrophysics Data System (ADS)

Navarro, Rachel Leah

This study tested portions of Lent, Brown, and Hackett's (1994) Social Cognitive Career Theory (SCCT) in the domain of mathematics and science with a sample of Mexican American middle school students. Results supported a modified path model. This study's findings supported several SCCT propositions regarding the positive relationships among background contextual affordances, learning experiences, self-efficacy, outcome expectations, interests, and goals. However, findings suggested that the influence of person inputs (i.e., gender and generational status) and some background contextual affordances (i.e., acculturation level) on learning experiences may be not be direct; instead, an indirect effect via a relationship with other background contextual affordances (i.e., perceived social support and social class) was found. Furthermore, results supported direct effects of gender on self-efficacy and learning experiences on goal intentions---two relationships not posited in SCCT. Implications for future research and counseling with Mexican American adolescents are discussed.

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…

Using a Mathematical Model to Analyze the Role of Probiotics and Inflammation in Necrotizing Enterocolitis

PubMed Central

Arciero, Julia C.; Ermentrout, G. Bard; Upperman, Jeffrey S.; Vodovotz, Yoram; Rubin, Jonathan E.

2010-01-01

Background Necrotizing enterocolitis (NEC) is a severe disease of the gastrointestinal tract of pre-term babies and is thought to be related to the physiological immaturity of the intestine and altered levels of normal flora in the gut. Understanding the factors that contribute to the pathology of NEC may lead to the development of treatment strategies aimed at re-establishing the integrity of the epithelial wall and preventing the propagation of inflammation in NEC. Several studies have shown a reduced incidence and severity of NEC in neonates treated with probiotics (beneficial bacteria species). Methodology/Principal Findings The objective of this study is to use a mathematical model to predict the conditions under which probiotics may be successful in promoting the health of infants suffering from NEC. An ordinary differential equation model is developed that tracks the populations of pathogenic and probiotic bacteria in the intestinal lumen and in the blood/tissue region. The permeability of the intestinal epithelial layer is treated as a variable, and the role of the inflammatory response is included. The model predicts that in the presence of probiotics health is restored in many cases that would have been otherwise pathogenic. The timing of probiotic administration is also shown to determine whether or not health is restored. Finally, the model predicts that probiotics may be harmful to the NEC patient under very specific conditions, perhaps explaining the detrimental effects of probiotics observed in some clinical studies. Conclusions/Significance The reduced, experimentally motivated mathematical model that we have developed suggests how a certain general set of characteristics of probiotics can lead to beneficial or detrimental outcomes for infants suffering from NEC, depending on the influences of probiotics on defined features of the inflammatory response. PMID:20419099

Spatiotemporal models for the simulation of infrared backgrounds

NASA Astrophysics Data System (ADS)

Wilkes, Don M.; Cadzow, James A.; Peters, R. Alan, II; Li, Xingkang

1992-09-01

It is highly desirable for designers of automatic target recognizers (ATRs) to be able to test their algorithms on targets superimposed on a wide variety of background imagery. Background imagery in the infrared spectrum is expensive to gather from real sources, consequently, there is a need for accurate models for producing synthetic IR background imagery. We have developed a model for such imagery that will do the following: Given a real, infrared background image, generate another image, distinctly different from the one given, that has the same general visual characteristics as well as the first and second-order statistics of the original image. The proposed model consists of a finite impulse response (FIR) kernel convolved with an excitation function, and histogram modification applied to the final solution. A procedure for deriving the FIR kernel using a signal enhancement algorithm has been developed, and the histogram modification step is a simple memoryless nonlinear mapping that imposes the first order statistics of the original image onto the synthetic one, thus the overall model is a linear system cascaded with a memoryless nonlinearity. It has been found that the excitation function relates to the placement of features in the image, the FIR kernel controls the sharpness of the edges and the global spectrum of the image, and the histogram controls the basic coloration of the image. A drawback to this method of simulating IR backgrounds is that a database of actual background images must be collected in order to produce accurate FIR and histogram models. If this database must include images of all types of backgrounds obtained at all times of the day and all times of the year, the size of the database would be prohibitive. In this paper we propose improvements to the model described above that enable time-dependent modeling of the IR background. This approach can greatly reduce the number of actual IR backgrounds that are required to produce a sufficiently accurate mathematical model for synthesizing a similar IR background for different times of the day. Original and synthetic IR backgrounds will be presented. Previous research in simulating IR backgrounds was performed by Strenzwilk, et al., Botkin, et al., and Rapp. The most recent work of Strenzwilk, et al. was based on the use of one-dimensional ARMA models for synthesizing the images. Their results were able to retain the global statistical and spectral behavior of the original image, but the synthetic image was not visually very similar to the original. The research presented in this paper is the result of an attempt to improve upon their results, and represents a significant improvement in quality over previously obtained results.

Neurocognitive mechanisms of mathematical giftedness: A literature review.

PubMed

Zhang, Li; Gan, John Q; Wang, Haixian

2017-01-01

Mathematically gifted children/adolescents have demonstrated exceptional abilities and traits in logical reasoning, mental imagery, and creative thinking. In the field of cognitive neuroscience, the past studies on mathematically gifted brains have concentrated on investigating event-related brain activation regions, cerebral laterality of cognitive functions, functional specialization that is uniquely dedicated for specific cognitive purposes, and functional interactions among discrete brain regions. From structural and functional perspectives, these studies have witnessed both "general" and "unique" neural characteristics of mathematically gifted brains. In this article, the theoretical background, empirical studies, and neurocognitive mechanisms of mathematically gifted children/adolescents are reviewed. Based on the integration of the findings, some potential directions for the future research are identified and discussed.

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.

Focusing of active particles in a converging flow

DOE PAGES

Potomkin, Mykhailo; Kaiser, Andreas; Berlyand, Leonid; ...

2017-10-20

We consider active particles swimming in a convergent fluid flow in a trapezoid nozzle with no-slip walls. We use mathematical modeling to analyze trajectories of these particles inside the nozzle. By extensive Monte Carlo simulations, we show that trajectories are strongly affected by the background fluid flow and geometry of the nozzle leading to wall accumulation and upstream motion (rheotaxis). In particular, we describe the non-trivial focusing of active rods depending on physical and geometrical parameters. It is also established that the convergent component of the background flow leads to stability of both downstream and upstream swimming at the centerline.more » The stability of downstream swimming enhances focusing, and the stability of upstream swimming enables rheotaxis in the bulk.« less

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…

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…

Mathematical subtleties and scientific knowledge: Francis Bacon and mathematics, at the crossing of two traditions.

PubMed

Mori, Giuliano

2017-03-01

This article engages the much-debated role of mathematics in Bacon's philosophy and inductive method at large. The many references to mathematics in Bacon's works are considered in the context of the humanist reform of the curriculum studiorum and, in particular, through a comparison with the kinds of natural and intellectual subtlety as they are defined by many sixteenth-century authors, including Cardano, Scaliger and Montaigne. Additionally, this article gives a nuanced background to the 'subtlety' commonly thought to have been eschewed by Bacon and by Bacon's self-proclaimed followers in the Royal Society of London. The aim of this article is ultimately to demonstrate that Bacon did not reject the use of mathematics in natural philosophy altogether. Instead, he hoped that following the Great Instauration a kind of non-abstract mathematics could be founded: a kind of mathematics which was to serve natural philosophy by enabling men to grasp the intrinsic subtlety of nature. Rather than mathematizing nature, it was mathematics that needed to be 'naturalized'.

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…

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.

Are Alternative Strategies Required to Accelerate the Global Elimination of Lymphatic Filariasis? Insights From Mathematical Models

PubMed Central

Stolk, Wilma A; Prada, Joaquin M; Smith, Morgan E; Kontoroupis, Periklis; de Vos, Anneke S; Touloupou, Panayiota; Irvine, Michael A; Brown, Paul; Subramanian, Swaminathan; Kloek, Marielle; Michael, E; Hollingsworth, T Deirdre; de Vlas, Sake J

2018-01-01

Abstract Background With the 2020 target year for elimination of lymphatic filariasis (LF) approaching, there is an urgent need to assess how long mass drug administration (MDA) programs with annual ivermectin + albendazole (IA) or diethylcarbamazine + albendazole (DA) would still have to be continued, and how elimination can be accelerated. We addressed this using mathematical modeling. Methods We used 3 structurally different mathematical models for LF transmission (EPIFIL, LYMFASIM, TRANSFIL) to simulate trends in microfilariae (mf) prevalence for a range of endemic settings, both for the current annual MDA strategy and alternative strategies, assessing the required duration to bring mf prevalence below the critical threshold of 1%. Results Three annual MDA rounds with IA or DA and good coverage (≥65%) are sufficient to reach the threshold in settings that are currently at mf prevalence <4%, but the required duration increases with increasing mf prevalence. Switching to biannual MDA or employing triple-drug therapy (ivermectin, diethylcarbamazine, and albendazole [IDA]) could reduce program duration by about one-third. Optimization of coverage reduces the time to elimination and is particularly important for settings with a history of poorly implemented MDA (low coverage, high systematic noncompliance). Conclusions Modeling suggests that, in several settings, current annual MDA strategies will be insufficient to achieve the 2020 LF elimination targets, and programs could consider policy adjustment to accelerate, guided by recent monitoring and evaluation data. Biannual treatment and IDA hold promise in reducing program duration, provided that coverage is good, but their efficacy remains to be confirmed by more extensive field studies. PMID:29860286

Outcomes in a Randomised Controlled Trial of Mathematics Tutoring

ERIC Educational Resources Information Center

Topping, K. J.; Miller, D.; Murray, P.; Henderson, S.; Fortuna, C.; Conlin, N.

2011-01-01

Background: Large-scale randomised controlled trials (RCT) are relatively rare in education. The present study was an attempt to scale up previous small peer tutoring projects, while investing only modestly in continuing professional development for teachers. Purpose: A two-year RCT of peer tutoring in mathematics was undertaken in one local…

Examining Organizational Practices That Predict Persistence among High-Achieving Black Males in High School

ERIC Educational Resources Information Center

Anderson, Kenneth Alonzo

2016-01-01

Background/Context: This article summarizes an increasing trend of antideficit Black male research in mathematics and highlights opportunities to add to the research. A review of the literature shows that antideficit researchers often examine relationships between individual traits and persistence of high-achieving Black males in mathematics.…

Developmental Dynamics between Mathematical Performance, Task Motivation, and Teachers' Goals during the Transition to Primary School

ERIC Educational Resources Information Center

Aunola, Kaisa; Leskinen, Esko; Nurmi, Jari-Erik

2006-01-01

Background: It has been suggested that children's learning motivation and interest in a particular subject play an important role in their school performance, particularly in mathematics. However, few cross-lagged longitudinal studies have been carried out to investigate the prospective relationships between academic achievement and task…

Is There Room in Math Reform for Preservice Teachers to Use Reading Strategies? National Implications

ERIC Educational Resources Information Center

Franz, Dana Pomykal; Hopper, Peggy F.

2007-01-01

Background: Research is proposed for preservice secondary mathematics teachers to develop and use reading strategies in math classrooms. Purpose: to determine if increased instruction on using specific reading strategies in secondary mathematics classrooms significantly impacts a) the type of reading-specific instructional strategies used, b)…

Exploring the Associations among Nutrition, Science, and Mathematics Knowledge for an Integrative, Food-Based Curriculum

ERIC Educational Resources Information Center

Stage, Virginia C.; Kolasa, Kathryn M.; Díaz, Sebastián R.; Duffrin, Melani W.

2018-01-01

Background: Explore associations between nutrition, science, and mathematics knowledge to provide evidence that integrating food/nutrition education in the fourth-grade curriculum may support gains in academic knowledge. Methods: Secondary analysis of a quasi-experimental study. Sample included 438 students in 34 fourth-grade classrooms across…

Track Placement and the Motivational Predictors of Math Course Enrollment

ERIC Educational Resources Information Center

Reyes, Marcela; Domina, Thurston

2017-01-01

Background: Virtually all high schools offer a range of courses to allow students to enroll in four years of high school mathematics. However, only two thirds of U.S. high school graduates took mathematics courses each school year. Purpose/Research Question: This study addresses three research questions: First, how do students' math course…

Looking within and beyond the Geometry Curriculum: Connecting Spatial Reasoning to Mathematics Learning

ERIC Educational Resources Information Center

Mulligan, Joanne

2015-01-01

This commentary adopts a broad perspective in considering the contributions of papers from cross- and interdisciplinary fields of mathematics education, psychology, child development and neuroscience. The discussion aims to complement the commentary by Dindyal, focused on background research on geometry and implications for pedagogy and curricula.…

Dragging in a Dynamic Geometry Environment through the Lens of Variation

ERIC Educational Resources Information Center

Leung, Allen

2008-01-01

What makes Dynamic Geometry Environment (DGE) a powerful mathematical knowledge acquisition microworld is its ability to visually make explicit the implicit dynamism of thinking about mathematical geometrical concepts. One of DGE's powers is to equip us with the ability to retain the background of a geometrical configuration while we can…

Secondary School Science and Mathematics Teachers, Characteristics and Service Loads.

ERIC Educational Resources Information Center

Mills, Thomas J.

Determined were the educational and professional backgrounds, and some aspects of the operational environment of teachers of secondary school science and mathematics (Grades 7-12) in the public and private schools of the United States during the school year 1960-61. A stratified random sampling method was used to ensure proportional representation…

Evidence for Shared Genetic Risk between ADHD Symptoms and Reduced Mathematics Ability: A Twin Study

ERIC Educational Resources Information Center

Greven, Corina U.; Kovas, Yulia; Willcutt, Erik G.; Petrill, Stephen A.; Plomin, Robert

2013-01-01

Background: Attention-deficit/hyperactivity disorder (ADHD) symptoms and mathematics ability are associated, but little is known about the genetic and environmental influences underlying this association. Methods: Data came from more than 6,000 twelve-year-old twin pairs from the UK population-representative Twins Early Development Study. Parents…

Students' Attention When Using Touchscreens and Pen Tablets in a Mathematics Classroom

ERIC Educational Resources Information Center

Chen, Cheng-Huan; Chiu, Chiung-Hui; Lin, Chia-Ping; Chou, Ying-Chun

2017-01-01

Aim/Purpose: The present study investigated and compared students' attention in terms of time-on-task and number of distractors between using a touchscreen and a pen tablet in mathematical problem solving activities with virtual manipulatives. Background: Although there is an increasing use of these input devices in educational practice, little…

Learning Mathematics: Perspectives of Australian Aboriginal Children and Their Teachers

ERIC Educational Resources Information Center

Howard, Peter; Perry, Bob

2005-01-01

Two key stakeholders in enhancing and building Aboriginal children's capacity to learn mathematics are teachers and the Aboriginal children themselves. In Australian schools it is often the case that the two groups come from different cultural backgrounds with very differing life experiences. This paper reports on an ethnographic study and focuses…

Navigation. Northern New England Marine Education Project.

ERIC Educational Resources Information Center

Maine Univ., Orono. Coll. of Education.

This guide provides student practice problems which use the procedures of ship navigators to reinforce the skills of mathematics learned in the secondary school and which seek to provide examples of the application of mathematical concepts. Along with the practice problems, teacher background material is provided briefly in the body of the unit.…

Longitudinal Study of Low and High Achievers in Early Mathematics

ERIC Educational Resources Information Center

Navarro, Jose I.; Aguilar, Manuel; Marchena, Esperanza; Ruiz, Gonzalo; Menacho, Inmaculada; Van Luit, Johannes E. H.

2012-01-01

Background: Longitudinal studies allow us to identify, which specific maths skills are weak in young children, and whether there is a continuing weakness in these areas throughout their school years. Aims: This 2-year study investigated whether certain socio-demographic variables affect early mathematical competency in children aged 5-7 years.…

Mathematics Technical Report: Exercise Volume. National Assessment of Educational Progress. Report No. 04-MA-20.

ERIC Educational Resources Information Center

Education Commission of the States, Denver, CO. National Assessment of Educational Progress.

Included in Chapter 1 of this report are background information on the 1972-73 mathematics assessment; details of the computational formulas used in reporting results; and explanations of the technical documentation, exercise presentation, documentation pages, scoring guides, and data tables for released and unreleased exercises. The remainder of…

Race, Ideology, and Academic Ability: A Relational Analysis of Racial Narratives in Mathematics

ERIC Educational Resources Information Center

Shah, Niral

2017-01-01

Background/Context: There is evidence that race affects students' learning experiences in mathematics, a subject typically thought of as "race-neutral" and "culture-free." Research in psychology and sociology has shown that racial narratives (e.g., "Asians are good at math") are pervasive in U.S. culture and play a…

The Effectiveness of Support for Students with Non-Traditional Mathematics Backgrounds

ERIC Educational Resources Information Center

Symonds, R. J.; Lawson, D. A.; Robinson, C. L.

2007-01-01

This article describes an initiative introduced at Loughborough University by SIGMA, a Centre for Excellence in Teaching and Learning (CETL), to support physics students who were mathematically less well-prepared than their counterparts. The article outlines how students were identified as being less well-prepared. These students were taught in a…

End-of-High-School Mathematics Attainment: How Did Students Get There?

ERIC Educational Resources Information Center

Newton, Xiaoxia A.

2010-01-01

Background: Many studies have looked at students' mathematics achievement in the middle and high school years and the kinds of factors that are associated with their achievement. Within this domain, however, most research utilized cross-sectional data. Cross-sectional designs have both statistical and conceptual limitations. Few studies used…

A Mathematics Entrance Exam for General (Non-Majors) Physics

ERIC Educational Resources Information Center

Chediak, Alex

2010-01-01

In a previous issue of "The Physics Teacher", John Hubisz explained how a mathematics background check has been used at three different colleges to determine the appropriate physics sequence for incoming students. Based on their performance, students are placed into either calculus-based physics (CBP), algebra-trig physics (ATP), or a year of…

Student Perception of the Effectiveness of Mathematics Support at Cardiff University

ERIC Educational Resources Information Center

Gillard, Jonathan; Robathan, Kirsty; Wilson, Robert

2012-01-01

Much work is currently being undertaken to investigate the effectiveness of informal, "drop-in" mathematics support services. This can be a difficult task; students are individuals with different expectations and backgrounds, and support that is effective for one student, may be less effective in relation to another. This article…

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…

Coaching in Early Mathematics.

PubMed

Germeroth, Carrie; Sarama, Julie

2017-01-01

Falling scores in math have prompted a renewed interest in math instruction at early ages. By their own admission, early childhood educators are generally underprepared and not always comfortable teaching math. Professional development (PD) in early mathematics is widely considered a main way to increase teachers' skills and efficacy (e.g., Guskey, 2000; Hyson & Woods, 2014; Munby, Russell, & Martin, 2001; Piasta, Logan, Pelatti, Capps, & Petrill, 2015; Richardson & Placier, 2001; Sarama, Clements, Wolfe, & Spitler, 2016; Sarama & DiBiase, 2004; Zaslow, 2014). However, it has been documented that stand-alone PD is not as effective in changing practice (e.g., Biancarosa & Bryk, 2011; Garet et al., 2008; Guskey, 2000; Hyson & Woods, 2014; Institute of Medicine and National Research Council, 2015; Joyce & Showers, 2002; Zaslow, 2014). Site-embedded ongoing support in the form of coaching or mentoring has been shown to be critical for successful implementation (Neuman & Cunningham, 2009; Powell, Diamond, Burchinal, & Koehler, 2010). In this chapter, we describe coaching models and abstract characteristics of effective coaching from the research. With this background, we provide an in-depth view of the coaching aspect of two large empirical studies in early mathematics. We introduce the theoretical framework from which the coaching models for these projects were developed and describe the research on which they were based. We then summarize how the planned models were instantiated and challenges to their implementation within each project. In the final section, we summarize what we have learned and described implications and challenges for the field. © 2017 Elsevier Inc. All rights reserved.

Test anxiety in mathematics among early undergraduate students in a British university in Malaysia

NASA Astrophysics Data System (ADS)

Karjanto, Natanael; Yong, Su Ting

2013-03-01

The level of test anxiety in mathematics subjects among early undergraduate students at the University of Nottingham Malaysia Campus is studied in this article. The sample consists of 206 students taking several mathematics modules who completed the questionnaires on test anxiety just before they entered the venue for midterm examinations. The sample data include the differences in the context of academic levels, gender groups and nationality backgrounds. The level of test anxiety in mathematics is measured using seven Likert questionnaire statements adapted from the Test Anxiety Inventory describing one's emotional feeling before the start of an examination. In general, the result shows that the students who had a lower score expectation were more anxious than those who had a higher score expectation, but that they obtained a better score than the expected score. In the context of academic levels, gender groups and nationality backgrounds, there were no significant correlations between the level of test anxiety and the students' academic performance. The effect size of the correlation values ranged from extremely small to moderate.

Family Background, Entry Selectivity and Opportunities to Learn: What Matters in Primary Teacher Education? An International Comparison of Fifteen Countries

ERIC Educational Resources Information Center

Blomeke, Sigrid; Suhl, Ute; Kaiser, Gabriele; Dohrmann, Martina

2012-01-01

First findings of IEA's "Teacher Education and Development Study in Mathematics (TEDS-M)" had revealed differences in the demographic background, opportunities to learn (OTL), and outcomes of teacher education between student teachers from different countries. Two hypotheses are examined: OTL and teacher background are significant predictors of…

Pre-Service Teachers' Developing Conceptions about the Nature and Pedagogy of Mathematical Modeling in the Context of a Mathematical Modeling Course

ERIC Educational Resources Information Center

Cetinkaya, Bulent; Kertil, Mahmut; Erbas, Ayhan Kursat; Korkmaz, Himmet; Alacaci, Cengiz; Cakiroglu, Erdinc

2016-01-01

Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers' developing conceptions about (a) the nature of mathematical modeling in simulations of "real life" problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike…

Evolution of Mathematics Teachers' Pedagogical Knowledge When They Are Teaching through Modeling

ERIC Educational Resources Information Center

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

2017-01-01

Use of mathematical modeling in mathematics education has been receiving significant attention as a way to develop students' mathematical knowledge and skills. As effective use of modeling in classes depends on the competencies of teachers we need to know more about the nature of teachers' knowledge to use modeling in mathematics education and how…

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…

A review on principles, theory and practices of 2D-QSAR.

PubMed

Roy, Kunal; Das, Rudra Narayan

2014-01-01

The central axiom of science purports the explanation of every natural phenomenon using all possible logics coming from pure as well as mixed scientific background. The quantitative structure-activity relationship (QSAR) analysis is a study correlating the behavioral manifestation of compounds with their structures employing the interdisciplinary knowledge of chemistry, mathematics, biology as well as physics. Several studies have attempted to mathematically correlate the chemistry and property (physicochemical/ biological/toxicological) of molecules using various computationally or experimentally derived quantitative parameters termed as descriptors. The dimensionality of the descriptors depends on the type of algorithm employed and defines the nature of QSAR analysis. The most interesting feature of predictive QSAR models is that the behavior of any new or even hypothesized molecule can be predicted by the use of the mathematical equations. The phrase "2D-QSAR" signifies development of QSAR models using 2D-descriptors. Such predictor variables are the most widely practised ones because of their simple and direct mathematical algorithmic nature involving no time consuming energy computations and having reproducible operability. 2D-descriptors have a deluge of contributions in extracting chemical attributes and they are also capable of representing the 3D molecular features to some extent; although in no case they should be considered as the ultimate one, since they often suffer from the problems of intercorrelation, insufficient chemical information as well as lack of interpretation. However, by following rational approaches, novel 2D-descriptors may be developed to obviate various existing problems giving potential 2D-QSAR equations, thereby solving the innumerable chemical mysteries still unexplored.

Structural analysis of eyespots: dynamics of morphogenic signals that govern elemental positions in butterfly wings

PubMed Central

2012-01-01

Background To explain eyespot colour-pattern determination in butterfly wings, the induction model has been discussed based on colour-pattern analyses of various butterfly eyespots. However, a detailed structural analysis of eyespots that can serve as a foundation for future studies is still lacking. In this study, fundamental structural rules related to butterfly eyespots are proposed, and the induction model is elaborated in terms of the possible dynamics of morphogenic signals involved in the development of eyespots and parafocal elements (PFEs) based on colour-pattern analysis of the nymphalid butterfly Junonia almana. Results In a well-developed eyespot, the inner black core ring is much wider than the outer black ring; this is termed the inside-wide rule. It appears that signals are wider near the focus of the eyespot and become narrower as they expand. Although fundamental signal dynamics are likely to be based on a reaction-diffusion mechanism, they were described well mathematically as a type of simple uniformly decelerated motion in which signals associated with the outer and inner black rings of eyespots and PFEs are released at different time points, durations, intervals, and initial velocities into a two-dimensional field of fundamentally uniform or graded resistance; this produces eyespots and PFEs that are diverse in size and structure. The inside-wide rule, eyespot distortion, structural differences between small and large eyespots, and structural changes in eyespots and PFEs in response to physiological treatments were explained well using mathematical simulations. Natural colour patterns and previous experimental findings that are not easily explained by the conventional gradient model were also explained reasonably well by the formal mathematical simulations performed in this study. Conclusions In a mode free from speculative molecular interactions, the present study clarifies fundamental structural rules related to butterfly eyespots, delineates a theoretical basis for the induction model, and proposes a mathematically simple mode of long-range signalling that may reflect developmental mechanisms associated with butterfly eyespots. PMID:22409965

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…

Quantum Finance

NASA Astrophysics Data System (ADS)

Baaquie, Belal E.

2007-09-01

Foreword; Preface; Acknowledgements; 1. Synopsis; Part I. Fundamental Concepts of Finance: 2. Introduction to finance; 3. Derivative securities; Part II. Systems with Finite Number of Degrees of Freedom: 4. Hamiltonians and stock options; 5. Path integrals and stock options; 6. Stochastic interest rates' Hamiltonians and path integrals; Part III. Quantum Field Theory of Interest Rates Models: 7. Quantum field theory of forward interest rates; 8. Empirical forward interest rates and field theory models; 9. Field theory of Treasury Bonds' derivatives and hedging; 10. Field theory Hamiltonian of forward interest rates; 11. Conclusions; Appendix A: mathematical background; Brief glossary of financial terms; Brief glossary of physics terms; List of main symbols; References; Index.

Increasing Access for Economically Disadvantaged Students: The NSF/CSEM & S-STEM Programs at Louisiana State University

NASA Astrophysics Data System (ADS)

Wilson, Zakiya S.; Iyengar, Sitharama S.; Pang, Su-Seng; Warner, Isiah M.; Luces, Candace A.

2012-10-01

Increasing college degree attainment for students from disadvantaged backgrounds is a prominent component of numerous state and federal legislation focused on higher education. In 1999, the National Science Foundation (NSF) instituted the "Computer Science, Engineering, and Mathematics Scholarships" (CSEMS) program; this initiative was designed to provide greater access and support to academically talented students from economically disadvantaged backgrounds. Originally intended to provide financial support to lower income students, this NSF program also advocated that additional professional development and advising would be strategies to increase undergraduate persistence to graduation. This innovative program for economically disadvantaged students was extended in 2004 to include students from other disciplines including the physical and life sciences as well as the technology fields, and the new name of the program was Scholarships for Science, Technology, Engineering and Mathematics (S-STEM). The implementation of these two programs in Louisiana State University (LSU) has shown significant and measurable success since 2000, making LSU a Model University in providing support to economically disadvantaged students within the STEM disciplines. The achievement of these programs is evidenced by the graduation rates of its participants. This report provides details on the educational model employed through the CSEMS/S-STEM projects at LSU and provides a path to success for increasing student retention rates in STEM disciplines. While the LSU's experience is presented as a case study, the potential relevance of this innovative mentoring program in conjunction with the financial support system is discussed in detail.

Collaborative Emission Reduction Model Based on Multi-Objective Optimization for Greenhouse Gases and Air Pollutants.

PubMed

Meng, Qing-chun; Rong, Xiao-xia; Zhang, Yi-min; Wan, Xiao-le; Liu, Yuan-yuan; Wang, Yu-zhi

2016-01-01

CO2 emission influences not only global climate change but also international economic and political situations. Thus, reducing the emission of CO2, a major greenhouse gas, has become a major issue in China and around the world as regards preserving the environmental ecology. Energy consumption from coal, oil, and natural gas is primarily responsible for the production of greenhouse gases and air pollutants such as SO2 and NOX, which are the main air pollutants in China. In this study, a mathematical multi-objective optimization method was adopted to analyze the collaborative emission reduction of three kinds of gases on the basis of their common restraints in different ways of energy consumption to develop an economic, clean, and efficient scheme for energy distribution. The first part introduces the background research, the collaborative emission reduction for three kinds of gases, the multi-objective optimization, the main mathematical modeling, and the optimization method. The second part discusses the four mathematical tools utilized in this study, which include the Granger causality test to analyze the causality between air quality and pollutant emission, a function analysis to determine the quantitative relation between energy consumption and pollutant emission, a multi-objective optimization to set up the collaborative optimization model that considers energy consumption, and an optimality condition analysis for the multi-objective optimization model to design the optimal-pole algorithm and obtain an efficient collaborative reduction scheme. In the empirical analysis, the data of pollutant emission and final consumption of energies of Tianjin in 1996-2012 was employed to verify the effectiveness of the model and analyze the efficient solution and the corresponding dominant set. In the last part, several suggestions for collaborative reduction are recommended and the drawn conclusions are stated.

Collaborative Emission Reduction Model Based on Multi-Objective Optimization for Greenhouse Gases and Air Pollutants

PubMed Central

Zhang, Yi-min; Wan, Xiao-le; Liu, Yuan-yuan; Wang, Yu-zhi

2016-01-01

CO2 emission influences not only global climate change but also international economic and political situations. Thus, reducing the emission of CO2, a major greenhouse gas, has become a major issue in China and around the world as regards preserving the environmental ecology. Energy consumption from coal, oil, and natural gas is primarily responsible for the production of greenhouse gases and air pollutants such as SO2 and NOX, which are the main air pollutants in China. In this study, a mathematical multi-objective optimization method was adopted to analyze the collaborative emission reduction of three kinds of gases on the basis of their common restraints in different ways of energy consumption to develop an economic, clean, and efficient scheme for energy distribution. The first part introduces the background research, the collaborative emission reduction for three kinds of gases, the multi-objective optimization, the main mathematical modeling, and the optimization method. The second part discusses the four mathematical tools utilized in this study, which include the Granger causality test to analyze the causality between air quality and pollutant emission, a function analysis to determine the quantitative relation between energy consumption and pollutant emission, a multi-objective optimization to set up the collaborative optimization model that considers energy consumption, and an optimality condition analysis for the multi-objective optimization model to design the optimal-pole algorithm and obtain an efficient collaborative reduction scheme. In the empirical analysis, the data of pollutant emission and final consumption of energies of Tianjin in 1996–2012 was employed to verify the effectiveness of the model and analyze the efficient solution and the corresponding dominant set. In the last part, several suggestions for collaborative reduction are recommended and the drawn conclusions are stated. PMID:27010658

Sustained virological response with intravenous silibinin: individualized IFN-free therapy via real-time modeling of HCV kinetics

PubMed Central

Dahari, Harel; Shteingart, Shimon; Gafanovich, Inna; Cotler, Scott J.; D'Amato, Massimo; Pohl, Ralf T.; Weiss, Gali; Ashkenazi, Yaakov Jack; Tichler, Thomas; Goldin, Eran; Lurie, Yoav

2014-01-01

Background & Aims Intravenous silibinin (SIL) is a potent antiviral agent against hepatitis C virus (HCV) genotype-1. In this proof of concept case-study we tested: (i) whether interferon-alfa (IFN)-free treatment with SIL plus ribavirin (RBV) can achieve sustained virological response (SVR), (ii) whether SIL is safe and feasible for prolonged duration of treatment, and (iii) whether mathematical modeling of early on-treatment HCV kinetics can guide duration of therapy to achieve SVR. Methods A 44 year-old female HCV-(genotype-1)-infected patient who developed severe psychiatric adverse events to a previous course of pegIFN+RBV, initiated combination treatment with 1200 mg/day of SIL, 1200 mg/day of RBV and 6000 u/day vitamin D. Blood samples were collected frequently till week 4, thereafter every 1 to 12 weeks until the end of therapy. The standard-biphasic-mathematical model was used to predict the duration of therapy to achieve SVR. Results Based on modeling the observed viral kinetics during the first 3 weeks of treatment, SVR was predicted to be achieved within 34 weeks of therapy. Provided with this information, the patient agreed to complete 34 weeks of treatment. IFN-free treatment with SIL+RBV was feasible, safe, and achieved SVR (week-33). Conclusions We report, for the first time, the use of real-time mathematical modeling of HCV kinetics to individualize duration of IFN-free therapy and to empower a patient to participate in shared decision making regarding length of treatment. SIL-based individualized therapy provides a treatment option for patients who do not respond to or cannot receive other HCV agents and should be further validated. PMID:25251042

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…

Mathematical Modeling with Middle School Students: The Robot Art Model-Eliciting Activity

ERIC Educational Resources Information Center

Stohlmann, Micah S.

2017-01-01

Internationally mathematical modeling is garnering more attention for the benefits associated with it. Mathematical modeling can develop students' communication skills and the ability to demonstrate understanding through different representations. With the increased attention on mathematical modeling, there is a need for more curricula to be…

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)…

Tumor Volume Estimation and Quasi-Continuous Administration for Most Effective Bevacizumab Therapy

PubMed Central

Sápi, Johanna; Kovács, Levente; Drexler, Dániel András; Kocsis, Pál; Gajári, Dávid; Sápi, Zoltán

2015-01-01

Background Bevacizumab is an exogenous inhibitor which inhibits the biological activity of human VEGF. Several studies have investigated the effectiveness of bevacizumab therapy according to different cancer types but these days there is an intense debate on its utility. We have investigated different methods to find the best tumor volume estimation since it creates the possibility for precise and effective drug administration with a much lower dose than in the protocol. Materials and Methods We have examined C38 mouse colon adenocarcinoma and HT-29 human colorectal adenocarcinoma. In both cases, three groups were compared in the experiments. The first group did not receive therapy, the second group received one 200 μg bevacizumab dose for a treatment period (protocol-based therapy), and the third group received 1.1 μg bevacizumab every day (quasi-continuous therapy). Tumor volume measurement was performed by digital caliper and small animal MRI. The mathematical relationship between MRI-measured tumor volume and mass was investigated to estimate accurate tumor volume using caliper-measured data. A two-dimensional mathematical model was applied for tumor volume evaluation, and tumor- and therapy-specific constants were calculated for the three different groups. The effectiveness of bevacizumab administration was examined by statistical analysis. Results In the case of C38 adenocarcinoma, protocol-based treatment did not result in significantly smaller tumor volume compared to the no treatment group; however, there was a significant difference between untreated mice and mice who received quasi-continuous therapy (p = 0.002). In the case of HT-29 adenocarcinoma, the daily treatment with one-twelfth total dose resulted in significantly smaller tumors than the protocol-based treatment (p = 0.038). When the tumor has a symmetrical, solid closed shape (typically without treatment), volume can be evaluated accurately from caliper-measured data with the applied two-dimensional mathematical model. Conclusion Our results provide a theoretical background for a much more effective bevacizumab treatment using optimized administration. PMID:26540189

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.

Aerodynamics and mathematics in National Socialist Germany and Fascist Italy: a comparison of research institutes.

PubMed

Epple, Moritz; Karachalios, Andreas; Remmert, Volker R

2005-01-01

The article is concerned with the mathematical sciences in National Socialist Germany and Fascist Italy, with special attention to research important to the war effort. It focuses on three institutional developments: the expansion of the Kaiser Wilhelm Institute for Fluid Dynamics in Göttingen, the foundation of the Reich Institute for Mathematics in Oberwolfach (Black Forest), and the work of the Istituto Nazionale per le Applicazioni del Calcolo in Rome. All three developments are embedded in the general political background, thus providing a basis for comparative conclusions about the conditions of the mathematical sciences and military-related research in Germany and Italy. It turns out that in both countries, the increasing demand for mathematical knowledge in modern warfare led to the establishment of "extra-university" national institutions specifically devoted to mathematical research.

The Role of Mediators in the Development of Longitudinal Mathematics Achievement Associations.

PubMed

Watts, Tyler W; Duncan, Greg J; Chen, Meichu; Claessens, Amy; Davis-Kean, Pamela E; Duckworth, Kathryn; Engel, Mimi; Siegler, Robert; Susperreguy, Maria I

2015-01-01

Despite research demonstrating a strong association between early and later mathematics achievement, few studies have investigated mediators of this association. Using longitudinal data (n = 1,362), this study tested the extent to which mathematics self-concepts, school placement, executive functioning, and proficiency in fractions and division account for the association between mathematics achievement in first grade and at age 15. As hypothesized, a strong longitudinal association between first-grade and adolescent mathematics achievement was present (β = .36) even after controlling for a host of background characteristics, including cognitive skills and reading ability. The mediators accounted for 39% of this association, with mathematics self-concept, gifted and talented placement, and knowledge of fractions and division serving as significant mediators. © 2015 The Authors. Child Development © 2015 Society for Research in Child Development, Inc.

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.…

Computational control of flexible aerospace systems

NASA Technical Reports Server (NTRS)

Sharpe, Lonnie, Jr.; Shen, Ji Yao

1994-01-01

The main objective of this project is to establish a distributed parameter modeling technique for structural analysis, parameter estimation, vibration suppression and control synthesis of large flexible aerospace structures. This report concentrates on the research outputs produced in the last two years. The main accomplishments can be summarized as follows. A new version of the PDEMOD Code had been completed based on several incomplete versions. The verification of the code had been conducted by comparing the results with those examples for which the exact theoretical solutions can be obtained. The theoretical background of the package and the verification examples has been reported in a technical paper submitted to the Joint Applied Mechanics & Material Conference, ASME. A brief USER'S MANUAL had been compiled, which includes three parts: (1) Input data preparation; (2) Explanation of the Subroutines; and (3) Specification of control variables. Meanwhile, a theoretical investigation of the NASA MSFC two-dimensional ground-based manipulator facility by using distributed parameter modeling technique has been conducted. A new mathematical treatment for dynamic analysis and control of large flexible manipulator systems has been conceived, which may provide an embryonic form of a more sophisticated mathematical model for future modified versions of the PDEMOD Codes.

A Mathematical Model of Sentimental Dynamics Accounting for Marital Dissolution

PubMed Central

Rey, José-Manuel

2010-01-01

Background Marital dissolution is ubiquitous in western societies. It poses major scientific and sociological problems both in theoretical and therapeutic terms. Scholars and therapists agree on the existence of a sort of second law of thermodynamics for sentimental relationships. Effort is required to sustain them. Love is not enough. Methodology/Principal Findings Building on a simple version of the second law we use optimal control theory as a novel approach to model sentimental dynamics. Our analysis is consistent with sociological data. We show that, when both partners have similar emotional attributes, there is an optimal effort policy yielding a durable happy union. This policy is prey to structural destabilization resulting from a combination of two factors: there is an effort gap because the optimal policy always entails discomfort and there is a tendency to lower effort to non-sustaining levels due to the instability of the dynamics. Conclusions/Significance These mathematical facts implied by the model unveil an underlying mechanism that may explain couple disruption in real scenarios. Within this framework the apparent paradox that a union consistently planned to last forever will probably break up is explained as a mechanistic consequence of the second law. PMID:20360987

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.

Radiofrequency ablation: importance of background tissue electrical conductivity--an agar phantom and computer modeling study.

PubMed

Solazzo, Stephanie A; Liu, Zhengjun; Lobo, S Melvyn; Ahmed, Muneeb; Hines-Peralta, Andrew U; Lenkinski, Robert E; Goldberg, S Nahum

2005-08-01

To determine whether radiofrequency (RF)-induced heating can be correlated with background electrical conductivity in a controlled experimental phantom environment mimicking different background tissue electrical conductivities and to determine the potential electrical and physical basis for such a correlation by using computer modeling. The effect of background tissue electrical conductivity on RF-induced heating was studied in a controlled system of 80 two-compartment agar phantoms (with inner wells of 0.3%, 1.0%, or 36.0% NaCl) with background conductivity that varied from 0.6% to 5.0% NaCl. Mathematical modeling of the relationship between electrical conductivity and temperatures 2 cm from the electrode (T2cm) was performed. Next, computer simulation of RF heating by using two-dimensional finite-element analysis (ETherm) was performed with parameters selected to approximate the agar phantoms. Resultant heating, in terms of both the T2cm and the distance of defined thermal isotherms from the electrode surface, was calculated and compared with the phantom data. Additionally, electrical and thermal profiles were determined by using the computer modeling data and correlated by using linear regression analysis. For each inner compartment NaCl concentration, a negative exponential relationship was established between increased background NaCl concentration and the T2cm (R2= 0.64-0.78). Similar negative exponential relationships (r2 > 0.97%) were observed for the computer modeling. Correlation values (R2) between the computer and experimental data were 0.9, 0.9, and 0.55 for the 0.3%, 1.0%, and 36.0% inner NaCl concentrations, respectively. Plotting of the electrical field generated around the RF electrode identified the potential for a dramatic local change in electrical field distribution (ie, a second electrical peak ["E-peak"]) occurring at the interface between the two compartments of varied electrical background conductivity. Linear correlations between the E-peak and heating at T2cm (R2= 0.98-1.00) and the 50 degrees C isotherm (R2= 0.99-1.00) were established. These results demonstrate the strong relationship between background tissue conductivity and RF heating and further explain electrical phenomena that occur in a two-compartment system.

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;…

Using Confirmatory Factor Analysis to Validate the Chamberlin Affective Instrument for Mathematical Problem Solving with Academically Advanced Students

ERIC Educational Resources Information Center

Chamberlin, Scott A.; Moore, Alan D.; Parks, Kelly

2017-01-01

Background: Student affect plays a considerable role in mathematical problem solving performance, yet is rarely formally assessed. In this manuscript, an instrument and its properties are discussed to enable educational psychologists the opportunity to assess student affect. Aims: The study was conducted to norm the CAIMPS (instrument) with gifted…

Mathematical description and program documentation for CLASSY, an adaptive maximum likelihood clustering method

NASA Technical Reports Server (NTRS)

Lennington, R. K.; Rassbach, M. E.

1979-01-01

Discussed in this report is the clustering algorithm CLASSY, including detailed descriptions of its general structure and mathematical background and of the various major subroutines. The report provides a development of the logic and equations used with specific reference to program variables. Some comments on timing and proposed optimization techniques are included.

SKOPE-IT (Shareable Knowledge Objects as Portable Intelligent Tutors): Overlaying Natural Language Tutoring on an Adaptive Learning System for Mathematics

ERIC Educational Resources Information Center

Nye, Benjamin D.; Pavlik, Philip I., Jr.; Windsor, Alistair; Olney, Andrew M.; Hajeer, Mustafa; Hu, Xiangen

2018-01-01

Background: This study investigated learning outcomes and user perceptions from interactions with a hybrid intelligent tutoring system created by combining the AutoTutor conversational tutoring system with the Assessment and Learning in Knowledge Spaces (ALEKS) adaptive learning system for mathematics. This hybrid intelligent tutoring system (ITS)…

Worldviews, Religions, and Beliefs about Teaching and Learning: Perception of Mathematics Teachers with Different Religious Backgrounds

ERIC Educational Resources Information Center

Chan, Yip-Cheung; Wong, Ngai-Ying

2014-01-01

Beliefs about mathematics education and their influences on teaching practices have been widely investigated in recent decades. There have been numerous empirical studies on the influences of religions on teachers' and students' beliefs about subjects such as sciences and language. However, the influences of worldviews in general and…

The Negative Numbers. A Source-Work Collection for In-Service and Pre-Service Teacher Courses.

ERIC Educational Resources Information Center

Arcavi, A.; Bruckheimer, M.

These materials on negative numbers are designed for use in workshops for pre- and in-service teacher training, especially for teachers in junior high schools. The general aims are: to improve teachers' mathematical knowledge of topics, to enrich teachers' mathematical background, to allow opportunity to discuss relevant didactics, and to create a…

Conceptualizing the African American Mathematics Teacher as a Key Figure in the African American Education Historical Narrative

ERIC Educational Resources Information Center

Clark, Lawrence M.; Jones Frank, Toya; Davis, Julius

2013-01-01

Background/Context: Historians and researchers have documented and explored the work and role of African American teachers in the U.S. educational system, yet there has been limited attention to the specific work, role, and experiences of African American mathematics teachers. To meaningfully and responsibly conceptualize the role of African…

The Irrational Numbers. A Source-Work Collection for In-Service and Pre-Service Teacher Courses.

ERIC Educational Resources Information Center

Arcavi, A.; Bruckheimer, M.

These materials on irrational numbers are designed for use in workshops for pre- and in-service teacher training, especially for teachers in junior high schools. The general aims are: to improve teachers' mathematical knowledge of topics, to enrich teachers' mathematical background, to allow opportunity to discuss relevant didactics, and to create…

Sound Off: The Myth of Differentiation in Mathematics--Providing Maximum Growth

ERIC Educational Resources Information Center

O'Roark, Jason Lee

2013-01-01

After serving as a high school math teacher in Maryland for three years, the author moved to teaching sixth-grade math. His high school background led him to differentiate differently than his colleagues. The article discusses his observations and his conclusions and offers a plan to implement changes in the way mathematics is taught through…

The Cognitive Underpinnings of Emerging Mathematical Skills: Executive Functioning, Patterns, Numeracy, and Arithmetic

ERIC Educational Resources Information Center

Lee, Kerry; Ng, Swee Fong; Pe, Madeline Lee; Ang, Su Yin; Hasshim, Muhammad Nabil Azhar Mohd; Bull, Rebecca

2012-01-01

Background: Exposure to mathematical pattern tasks is often deemed important for developing children's algebraic thinking skills. Yet, there is a dearth of evidence on the cognitive underpinnings of pattern tasks and how early competencies on these tasks are related to later development. Aims: We examined the domain-specific and domain-general…

Case Studies of a Robot-Based Game to Shape Interests and Hone Proportional Reasoning Skills

ERIC Educational Resources Information Center

Alfieri, Louis; Higashi, Ross; Shoop, Robin; Schunn, Christian D.

2015-01-01

Background: Robot-math is a term used to describe mathematics instruction centered on engineering, particularly robotics. This type of instruction seeks first to make the mathematics skills useful for robotics-centered challenges, and then to help students extend (transfer) those skills. A robot-math intervention was designed to target the…

CHARACTERISTICS OF THE TECHNICAL EDUCATION STUDENT.

ERIC Educational Resources Information Center

MILLER, AARON J.

THE POST-HIGH SCHOOL TRAINEE SHOULD BE A HIGH SCHOOL GRADUATE OR THE EQUIVALENT. A FAIR DEGREE OF PROFICIENCY IN MATHEMATICS AND SCIENCE IS REQUIRED. IT IS REASONABLE TO EXPECT THE COMPLETION OF 2 YEARS OF HIGH SCHOOL MATHEMATICS AND 1 YEAR OF HIGH SCHOOL SCIENCE. SOME BACKGROUND IN DRAFTING AND SHOP IS DESIRABLE. THE STUDENT SHOULD BE AVERAGE OR…

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.

Use of prior knowledge for the analysis of high-throughput transcriptomics and metabolomics data

PubMed Central

2014-01-01

Background High-throughput omics technologies have enabled the measurement of many genes or metabolites simultaneously. The resulting high dimensional experimental data poses significant challenges to transcriptomics and metabolomics data analysis methods, which may lead to spurious instead of biologically relevant results. One strategy to improve the results is the incorporation of prior biological knowledge in the analysis. This strategy is used to reduce the solution space and/or to focus the analysis on biological meaningful regions. In this article, we review a selection of these methods used in transcriptomics and metabolomics. We combine the reviewed methods in three groups based on the underlying mathematical model: exploratory methods, supervised methods and estimation of the covariance matrix. We discuss which prior knowledge has been used, how it is incorporated and how it modifies the mathematical properties of the underlying methods. PMID:25033193

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)

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.

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…

Pre-service science teachers' perceptions of mathematics courses in a science teacher education programme

NASA Astrophysics Data System (ADS)

Incikabi, Lutfi; Serin, Mehmet Koray

2017-08-01

Most science departments offer compulsory mathematics courses to their students with the expectation that students can apply their experience from the mathematics courses to other fields of study, including science. The current study first aims to investigate the views of pre-service science teachers of science-teaching preparation degrees and their expectations regarding the difficulty level of mathematics courses in science-teaching education programmes. Second, the study investigates changes and the reasons behind the changes in their interest regarding mathematics after completing these courses. Third, the current study seeks to reveal undergraduate science teachers' opinions regarding the contribution of undergraduate mathematics courses to their professional development. Being qualitative in nature, this study was a case study. According to the results, almost all of the students considered that undergraduate mathematics courses were 'difficult' because of the complex and intensive content of the courses and their poor background mathematical knowledge. Moreover, the majority of science undergraduates mentioned that mathematics would contribute to their professional development as a science teacher. On the other hand, they declared a negative change in their attitude towards mathematics after completing the mathematics courses due to continuous failure at mathematics and their teachers' lack of knowledge in terms of teaching mathematics.

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

A case study of pedagogy of mathematics support tutors without a background in mathematics education

NASA Astrophysics Data System (ADS)

Walsh, Richard

2017-01-01

This study investigates the pedagogical skills and knowledge of three tertiary-level mathematics support tutors in a large group classroom setting. This is achieved through the use of video analysis and a theoretical framework comprising Rowland's Knowledge Quartet and general pedagogical knowledge. The study reports on the findings in relation to these tutors' provision of mathematics support to first and second year undergraduate engineering students and second year undergraduate science students. It was found that tutors are lacking in various pedagogical skills which are needed for high-quality learning amongst service mathematics students (e.g. engineering/science/technology students), a demographic which have low levels of mathematics upon entering university. Tutors teach their support classes in a very fast didactic way with minimal opportunities for students to ask questions or to attempt problems. It was also found that this teaching method is even more so exaggerated in mandatory departmental mathematics tutorials that students take as part of their mathematics studies at tertiary level. The implications of the findings on mathematics tutor training at tertiary level are also discussed.

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…

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…

Application of the bridged crack model for evaluation of materials repairing and self-healing

NASA Astrophysics Data System (ADS)

Perelmuter, M.

2017-12-01

The bridged crack model is used for analysis of repairing and self-healing of cracked structures. Material repairing is treated as insertions of external ligaments into cracks or placement of the reinforcing patches over cracks. Bonds destruction and regeneration at the crack bridged zone is evaluated by the thermo-fluctuation kinetic theory. The healing time is dependent on the chemical reaction rate of the healing agent, the crack size and the external loads. The decreasing of the stress intensity factors is used as the measure of the repairing and healing effects. The mathematical background of the problem solution is based on the methods of the singular integral-differential equations. The model can be used for the evaluation of composite materials durability.

Modeling and validation of photometric characteristics of space targets oriented to space-based observation.

PubMed

Wang, Hongyuan; Zhang, Wei; Dong, Aotuo

2012-11-10

A modeling and validation method of photometric characteristics of the space target was presented in order to track and identify different satellites effectively. The background radiation characteristics models of the target were built based on blackbody radiation theory. The geometry characteristics of the target were illustrated by the surface equations based on its body coordinate system. The material characteristics of the target surface were described by a bidirectional reflectance distribution function model, which considers the character of surface Gauss statistics and microscale self-shadow and is obtained by measurement and modeling in advance. The contributing surfaces of the target to observation system were determined by coordinate transformation according to the relative position of the space-based target, the background radiation sources, and the observation platform. Then a mathematical model on photometric characteristics of the space target was built by summing reflection components of all the surfaces. Photometric characteristics simulation of the space-based target was achieved according to its given geometrical dimensions, physical parameters, and orbital parameters. Experimental validation was made based on the scale model of the satellite. The calculated results fit well with the measured results, which indicates the modeling method of photometric characteristics of the space target is correct.

Calculus of Elementary Functions, Part I. Teacher's Commentary. Revised Edition.

ERIC Educational Resources Information Center

Herriot, Sarah T.; And Others

This course is intended for students who have a thorough knowledge of college preparatory mathematics including algebra, axiomatic geometry, trigonometry, and analytic geometry. It does not assume they have acquired a background of elementary functions. This teacher's guide contains background information, suggested instructional procedures, and…

Equity and spatial reasoning: reducing the mathematical achievement gap in gender and social disadvantage

NASA Astrophysics Data System (ADS)

Lowrie, Tom; Jorgensen, Robyn

2018-03-01

Since the early 70s, there has been recognition that there are specific differences in achievement based on variables, such as gender and socio-economic background, in terms of mathematics performance. However, these differences are not unilateral but rather quite specific and relate strongly to spatial reasoning. This early work has paved the way for thinking critically about who achieves in mathematics and why. This project innovatively combines the strengths of the two Chief Investigators—Lowrie's work in spatial reasoning and Jorgensen's work in equity. The assumptions, the approach and theoretical framing used in the study unite quite disparate areas of mathematics education into a cogent research program that seeks to challenge some of the long-held views in the field of mathematics education.

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…

Mouse Hair Cycle Expression Dynamics Modeled as Coupled Mesenchymal and Epithelial Oscillators

PubMed Central

Tasseff, Ryan; Bheda-Malge, Anjali; DiColandrea, Teresa; Bascom, Charles C.; Isfort, Robert J.; Gelinas, Richard

2014-01-01

The hair cycle is a dynamic process where follicles repeatedly move through phases of growth, retraction, and relative quiescence. This process is an example of temporal and spatial biological complexity. Understanding of the hair cycle and its regulation would shed light on many other complex systems relevant to biological and medical research. Currently, a systematic characterization of gene expression and summarization within the context of a mathematical model is not yet available. Given the cyclic nature of the hair cycle, we felt it was important to consider a subset of genes with periodic expression. To this end, we combined several mathematical approaches with high-throughput, whole mouse skin, mRNA expression data to characterize aspects of the dynamics and the possible cell populations corresponding to potentially periodic patterns. In particular two gene clusters, demonstrating properties of out-of-phase synchronized expression, were identified. A mean field, phase coupled oscillator model was shown to quantitatively recapitulate the synchronization observed in the data. Furthermore, we found only one configuration of positive-negative coupling to be dynamically stable, which provided insight on general features of the regulation. Subsequent bifurcation analysis was able to identify and describe alternate states based on perturbation of system parameters. A 2-population mixture model and cell type enrichment was used to associate the two gene clusters to features of background mesenchymal populations and rapidly expanding follicular epithelial cells. Distinct timing and localization of expression was also shown by RNA and protein imaging for representative genes. Taken together, the evidence suggests that synchronization between expanding epithelial and background mesenchymal cells may be maintained, in part, by inhibitory regulation, and potential mediators of this regulation were identified. Furthermore, the model suggests that impairing this negative regulation will drive a bifurcation which may represent transition into a pathological state such as hair miniaturization. PMID:25375120

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…

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.

Developing an Instrument for Measuring Teachers' Mathematics Content Knowledge on Ratio and Proportion: A Case of Indonesian Primary Teachers

ERIC Educational Resources Information Center

Ekawati, Rooselyna; Lin, Fou-Lai; Yang, Kai-Lin

2015-01-01

In this study, we developed an instrument for assessing teachers' mathematics content knowledge (MCK) on ratio and proportion and examined the profile of Indonesian primary teacher's MCK on this topic. The MCK items were administered to 271 Indonesian in-service primary teachers with a variety of educational backgrounds and teaching experiences.…

Enhancing Interdisciplinary Mathematics and Biology Education: A Microarray Data Analysis Course Bridging These Disciplines

ERIC Educational Resources Information Center

Tra, Yolande V.; Evans, Irene M.

2010-01-01

"BIO2010" put forth the goal of improving the mathematical educational background of biology students. The analysis and interpretation of microarray high-dimensional data can be very challenging and is best done by a statistician and a biologist working and teaching in a collaborative manner. We set up such a collaboration and designed a course on…

Family Backgrounds of Young Asian Americans Who Reason Extremely Well Mathematically.

ERIC Educational Resources Information Center

Moore, Sara Delano; Stanley, Julian C.

From a group of 292 youth (269 male, 23 female) who scored 700-800 on the mathematical portion of the College Board's Scholastic Aptitude Test (SAT-M) before age 13, the subscale of 68 students who were of Asian descent (55 males, 13 females) were asked to complete a questionnaire concerning their parents' and grandparents' educational and…

The Effects of Using Exploratory Computerized Environments in Grades 1 to 8 Mathematics: A Meta-Analysis of Research

ERIC Educational Resources Information Center

Sokolowski, Andrzej; Li, Yeping; Willson, Victor

2015-01-01

Background: The process of problem solving is difficult for students; thus, mathematics educators have made multiple attempts to seek ways of making this process more accessible to learners. The purpose of this study was to examine the effect size statistic of utilizing exploratory computerized environments (ECEs) to support the process of word…

Visual Working Memory and Number Sense: Testing the Double Deficit Hypothesis in Mathematics

ERIC Educational Resources Information Center

Toll, Sylke W. M.; Kroesbergen, Evelyn H.; Van Luit, Johannes E. H.

2016-01-01

Background: Evidence exists that there are two main underlying cognitive factors in mathematical difficulties: working memory and number sense. It is suggested that real math difficulties appear when both working memory and number sense are weak, here referred to as the double deficit (DD) hypothesis. Aims: The aim of this study was to test the DD…

2012 National Survey of Science and Mathematics Education: Compendium of Tables for High School Biology

ERIC Educational Resources Information Center

Horizon Research, Inc., 2013

2013-01-01

The 2012 National Survey of Science and Mathematics Education was designed to provide up-to-date information and to identify trends in the areas of teacher background and experience, curriculum and instruction, and the availability and use of instructional resources. This compendium, one of a series, details the results of a survey of high school…

2012 National Survey of Science and Mathematics Education: Compendium of Tables for High School Physics

ERIC Educational Resources Information Center

Horizon Research, Inc., 2013

2013-01-01

The 2012 National Survey of Science and Mathematics Education was designed to provide up-to-date information and to identify trends in the areas of teacher background and experience, curriculum and instruction, and the availability and use of instructional resources. This compendium, one of a series, details the results of a survey of high school…

Concepts of Mathematics for Students of Physics and Engineering: A Dictionary

NASA Technical Reports Server (NTRS)

Kolecki, Joseph C.

2003-01-01

A physicist with an engineering background, the author presents a mathematical dictionary containing material encountered over many years of study and professional work at NASA. This work is a compilation of the author's experience and progress in the field of study represented and consists of personal notes and observations that can be used by students in physics and engineering.

Students' Agency in an In-Class Computer-Centered Developmental Mathematics Classroom: The Best Laid Plans of Math and (Wo)men

ERIC Educational Resources Information Center

Aly, Geillan Dahab

2016-01-01

Community colleges are tasked with helping all students regardless of their academic background to receive a degree, certificate, or other form of education. Many of these students need support in learning the mathematical content necessary to take college-level courses. Since a large proportion of students in these developmental classes are…

Cognitive Backgrounds of Problem Solving: A Comparison of Open-Ended vs. Closed Mathematics Problems

ERIC Educational Resources Information Center

Bahar, Abdulkadir; Maker, C. June

2015-01-01

Problem solving has been a core theme in education for several decades. Educators and policy makers agree on the importance of the role of problem solving skills for school and real life success. A primary purpose of this study was to investigate the influence of cognitive abilities on mathematical problem solving performance of elementary…

Equity in Mathematics and Science Outcomes: Characteristics Associated with High and Low Achievement on PISA 2006 in Ireland

ERIC Educational Resources Information Center

Gilleece, Lorraine; Cosgrove, Jude; Sofroniou, Nick

2010-01-01

Equity in education is a key concern internationally; however, it is rare that this issue is examined separately for low- and high-achieving students and concurrently across different subject domains. This study examines student and school background characteristics associated with low and high achievement in mathematics and science on the…

Revisiting Mathematical Problem Solving and Posing in the Digital Era: Toward Pedagogically Sound Uses of Modern Technology

ERIC Educational Resources Information Center

Abramovich, S.

2014-01-01

The availability of sophisticated computer programs such as "Wolfram Alpha" has made many problems found in the secondary mathematics curriculum somewhat obsolete for they can be easily solved by the software. Against this background, an interplay between the power of a modern tool of technology and educational constraints it presents is…

Leader Perceptions and Student Achievement: An Examination of Reading and Mathematics International Test Results in Korea and the USA

ERIC Educational Resources Information Center

Shin, Seon-Hi; Slater, Charles L.; Ortiz, Steve

2017-01-01

Purpose: The purpose of this paper is to examine what factors affect student achievement in reading and mathematics. The research questions addressed the perceptions of school principals and background characteristics related to student achievement in Korea and the USA with respect to differences among students in low, middle and high quantiles.…

Generalized image contrast enhancement technique based on the Heinemann contrast discrimination model

NASA Astrophysics Data System (ADS)

Liu, Hong; Nodine, Calvin F.

1996-07-01

This paper presents a generalized image contrast enhancement technique, which equalizes the perceived brightness distribution based on the Heinemann contrast discrimination model. It is based on the mathematically proven existence of a unique solution to a nonlinear equation, and is formulated with easily tunable parameters. The model uses a two-step log-log representation of luminance contrast between targets and surround in a luminous background setting. The algorithm consists of two nonlinear gray scale mapping functions that have seven parameters, two of which are adjustable Heinemann constants. Another parameter is the background gray level. The remaining four parameters are nonlinear functions of the gray-level distribution of the given image, and can be uniquely determined once the previous three are set. Tests have been carried out to demonstrate the effectiveness of the algorithm for increasing the overall contrast of radiology images. The traditional histogram equalization can be reinterpreted as an image enhancement technique based on the knowledge of human contrast perception. In fact, it is a special case of the proposed algorithm.

The way adults with orientation to mathematics teaching cope with the solution of everyday real-world problems

NASA Astrophysics Data System (ADS)

Gazit, Avikam; Patkin, Dorit

2012-03-01

The article aims to check the way adults, some who are practicing mathematics teachers at elementary school, some who are academicians making a career change to mathematics teachers at junior high school and the rest who are pre-service mathematics teachers at elementary school, cope with the solution of everyday real-world problems of buying and selling. The findings show that even adults with mathematical background tend to make mistakes in solving everyday real-world problems. Only about 70% of the adults who have an orientation to mathematics solved the sample problem correctly. The lowest percentage of success was demonstrated by the academicians making a career change to junior high school mathematics teachers whereas the highest percentage of success was manifested by pre-service elementary school mathematics teachers. Moreover, the findings illustrate that life experience of the practicing mathematics teachers and, mainly, of the academicians making a career change, who were older than the pre-service teachers, did not facilitate the solution of such a real-world problem. Perhaps the reason resides in the process of mathematics teaching at school, which does not put an emphasis on the solution of everyday real-world problems.

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

Higher spin gravitational couplings: Ghosts in the Yang-Mills detour complex

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

Gover, A. R.; Hallowell, K.; Waldron, A.

2007-01-15

Gravitational interactions of higher spin fields are generically plagued by inconsistencies. There exists however, a simple framework that couples higher spins to a broad class of gravitational backgrounds (including Ricci flat and Einstein) consistently at the classical level. The model is the simplest example of a Yang-Mills detour complex and has broad mathematical applications, especially to conformal geometry. Even the simplest version of the theory, which couples gravitons, vectors and scalar fields in a flat background is rather rich, providing an explicit setting for detailed analysis of ghost excitations. Its asymptotic scattering states consist of a physical massless graviton, scalar,more » and massive vector along with a degenerate pair of zero norm photon excitations. Coherent states of the unstable sector do have positive norms, but their evolution is no longer unitary and amplitudes grow with time. The class of models proposed is extremely general and of considerable interest for ghost condensation and invariant theory.« less

Asian American women in science, engineering, and mathematics: Background contextual and college environment influences on self-efficacy and academic achievement

NASA Astrophysics Data System (ADS)

Vogt, Kristen E.

2005-07-01

The purpose of this research study was to examine, for undergraduate women of various Asian American ethnic backgrounds, the influence of background contextual and college environment factors on their sense of academic self-efficacy and achievement in science, technology, engineering, and mathematics (STEM) majors. Social cognitive career theory and its critiques provided a theoretical foundation for relationships from past performance, socioeconomic status, acculturation, and college environment variables (compositional diversity, racial climate, gendered climate, academic peer support), to academic self-efficacy and achievement. Data were collected through an online survey. Instrumentation included the scales of Language, Identity, and Behavioral Acculturation; Gender Discrimination; Faculty and Classroom Behavior; Interactions with Peers; and Academic Milestones Self-efficacy. The participants were 228 Asian American undergraduate women in STEM at a large public, doctoral research extensive university on the east coast; the response rate was 51%. In three MANOVAs for nine social cognitive career variables, four ethnic groups (East, South, Southeast, and Multi-ethnic Asian American) significantly differed only on socioeconomic status. In path analysis, the initial model was not a good fit and was rejected. The model was respecified through statistical and theoretical evaluation, tested in exploratory analysis, and considered a good fit. The respecified model explained 36% of semester GPA (achievement) and 28% of academic self-efficacy. The academic achievement of Asian American women in STEM was related to past performance, background contextual factors, academic self-efficacy, academic peer support, and gendered climate. The strongest direct influence on achievement was academic self-efficacy followed by past performance. The total effect of Asian acculturation on achievement was negative and the total effect of American acculturation on achievement was not significant; academic self-efficacy mediated these complex relationships. The total effects of racial and gendered compositional diversity and racial climate on both academic self-efficacy and achievement were not significant. Students in majors with more female peers reported less academic peer support. In this study, when culturally specific variables embellished social cognitive career theory, the theory exhibited cultural validity for undergraduate Asian American women in STEM. The nature of the relationships among culturally specific variables and college environment variables, however, requires further study.

Evaluation and clinical significance of the stomach age model for evaluating aging of the stomach-a multicenter study in China

PubMed Central

2014-01-01

Background A higher prevalence of chronic atrophic gastritis (CAG) occurs in younger adults in Asia. We used Stomach Age to examine the different mechanisms of CAG between younger adults and elderly individuals, and established a simple model of cancer risk that can be applied to CAG surveillance. Methods Stomach Age was determined by FISH examination of telomere length in stomach biopsies. Δψm was also determined by flow cytometry. Sixty volunteers were used to confirm the linear relationship between telomere length and age while 120 subjects were used to build a mathematical model by a multivariate analysis. Overall, 146 subjects were used to evaluate the validity of the model, and 1,007 subjects were used to evaluate the relationship between prognosis and Δage (calculated from the mathematical model). ROC curves were used to evaluate the relationship between prognosis and Δage and to determine the cut-off point for Δage. Results We established that a tight linear relationship between the telomere length and the age. The telomere length was obvious different between patients with and without CAG even in the same age. Δψm decreased in individuals whose Stomach Age was greater than real age, especially in younger adults. A mathematical model of Stomach Age (real age + Δage) was successfully constructed which was easy to apply in clinical work. A higher Δage was correlated with a worse outcome. The criterion of Δage >3.11 should be considered as the cut-off to select the subgroup of patients who require endoscopic surveillance. Conclusion Variation in Stomach Age between individuals of the same biological age was confirmed. Attention should be paid to those with a greater Stomach Age, especially in younger adults. The Δage in the Simple Model can be used as a criterion to select CAG patients for gastric cancer surveillance. PMID:25057261

Non-stationary background intensity and Caribbean seismic events

NASA Astrophysics Data System (ADS)

Valmy, Larissa; Vaillant, Jean

2014-05-01

We consider seismic risk calculation based on models with non-stationary background intensity. The aim is to improve predictive strategies in the framework of seismic risk assessment from models describing at best the seismic activity in the Caribbean arc. Appropriate statistical methods are required for analyzing the volumes of data collected. The focus is on calculating earthquakes occurrences probability and analyzing spatiotemporal evolution of these probabilities. The main modeling tool is the point process theory in order to take into account past history prior to a given date. Thus, the seismic event conditional intensity is expressed by means of the background intensity and the self exciting component. This intensity can be interpreted as the expected event rate per time and / or surface unit. The most popular intensity model in seismology is the ETAS (Epidemic Type Aftershock Sequence) model introduced and then generalized by Ogata [2, 3]. We extended this model and performed a comparison of different probability density functions for the triggered event times [4]. We illustrate our model by considering the CDSA (Centre de Données Sismiques des Antilles) catalog [1] which contains more than 7000 seismic events occurred in the Lesser Antilles arc. Statistical tools for testing the background intensity stationarity and for dynamical segmentation are presented. [1] Bengoubou-Valérius M., Bazin S., Bertil D., Beauducel F. and Bosson A. (2008). CDSA: a new seismological data center for the French Lesser Antilles, Seismol. Res. Lett., 79 (1), 90-102. [2] Ogata Y. (1998). Space-time point-process models for earthquake occurrences, Annals of the Institute of Statistical Mathematics, 50 (2), 379-402. [3] Ogata, Y. (2011). Significant improvements of the space-time ETAS model for forecasting of accurate baseline seismicity, Earth, Planets and Space, 63 (3), 217-229. [4] Valmy L. and Vaillant J. (2013). Statistical models in seismology: Lesser Antilles arc case, Bull. Soc. géol. France, 2013, 184 (1), 61-67.

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.

Demand modelling of passenger air travel: An analysis and extension. Volume 1: Background and summary

NASA Technical Reports Server (NTRS)

Jacobson, I. D.

1978-01-01

The framework for a model of travel demand which will be useful in predicting the total market for air travel between two cities is discussed. Variables to be used in determining the need for air transportation where none currently exists and the effect of changes in system characteristics on attracting latent demand are identified. Existing models are examined in order to provide insight into their strong points and shortcomings. Much of the existing behavioral research in travel demand is incorporated to allow the inclusion of non-economic factors, such as convenience. The model developed 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.

Evaluation of Multiclass Model Observers in PET LROC Studies

NASA Astrophysics Data System (ADS)

Gifford, H. C.; Kinahan, P. E.; Lartizien, C.; King, M. A.

2007-02-01

A localization ROC (LROC) study was conducted to evaluate nonprewhitening matched-filter (NPW) and channelized NPW (CNPW) versions of a multiclass model observer as predictors of human tumor-detection performance with PET images. Target localization is explicitly performed by these model observers. Tumors were placed in the liver, lungs, and background soft tissue of a mathematical phantom, and the data simulation modeled a full-3D acquisition mode. Reconstructions were performed with the FORE+AWOSEM algorithm. The LROC study measured observer performance with 2D images consisting of either coronal, sagittal, or transverse views of the same set of cases. Versions of the CNPW observer based on two previously published difference-of-Gaussian channel models demonstrated good quantitative agreement with human observers. One interpretation of these results treats the CNPW observer as a channelized Hotelling observer with implicit internal noise

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,…

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.

How Uncertain is Uncertainty?

NASA Astrophysics Data System (ADS)

Vámos, Tibor

The gist of the paper is the fundamental uncertain nature of all kinds of uncertainties and consequently a critical epistemic review of historical and recent approaches, computational methods, algorithms. The review follows the development of the notion from the beginnings of thinking, via the Aristotelian and Skeptic view, the medieval nominalism and the influential pioneering metaphors of ancient India and Persia to the birth of modern mathematical disciplinary reasoning. Discussing the models of uncertainty, e.g. the statistical, other physical and psychological background we reach a pragmatic model related estimation perspective, a balanced application orientation for different problem areas. Data mining, game theories and recent advances in approximation algorithms are discussed in this spirit of modest reasoning.

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…

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…

The Combination of Just-in-Time Teaching and Wikispaces in Physics Classrooms

NASA Astrophysics Data System (ADS)

Mohottala, Hashini E.

2013-01-01

The general student population enrolled in today's physics classrooms is diverse. They come from a variety of different educational backgrounds. Some demonstrate a good knowledge of natural laws of physics with a better understanding of mathematical concepts, while others show a fair knowledge in fundamentals of physics with a minimum knowledge in mathematics. There are few who have not been exposed to physics or mathematics in their high schools (or at least they claim it to be the case). In addition, now we have "nontraditional" students: working part-time students, older students, commuting students, and, occasionally, military veterans. Regardless of the background, the majority of the students show little or no interest in physics and exhibit anxiety toward learning the subject. In order to address such a diverse and often unmotivated student population, and excite them about physics in a timely manner, we should deviate from conventional teaching techniques. Just-in-Time Teaching (JiTT) combined with wikis is an excellent way to accomplish this goal.

Modelling of microcracks image treated with fluorescent dye

NASA Astrophysics Data System (ADS)

Glebov, Victor; Lashmanov, Oleg U.

2015-06-01

The main reasons of catastrophes and accidents are high level of wear of equipment and violation of the production technology. The methods of nondestructive testing are designed to find out defects timely and to prevent break down of aggregates. These methods allow determining compliance of object parameters with technical requirements without destroying it. This work will discuss dye penetrant inspection or liquid penetrant inspection (DPI or LPI) methods and computer model of microcracks image treated with fluorescent dye. Usually cracks on image look like broken extended lines with small width (about 1 to 10 pixels) and ragged edges. The used method of inspection allows to detect microcracks with depth about 10 or more micrometers. During the work the mathematical model of image of randomly located microcracks treated with fluorescent dye was created in MATLAB environment. Background noises and distortions introduced by the optical systems are considered in the model. The factors that have influence on the image are listed below: 1. Background noise. Background noise is caused by the bright light from external sources and it reduces contrast on the objects edges. 2. Noises on the image sensor. Digital noise manifests itself in the form of randomly located points that are differing in their brightness and color. 3. Distortions caused by aberrations of optical system. After passing through the real optical system the homocentricity of the bundle of rays is violated or homocentricity remains but rays intersect at the point that doesn't coincide with the point of the ideal image. The stronger the influence of the above-listed factors, the worse the image quality and therefore the analysis of the image for control of the item finds difficulty. The mathematical model is created using the following algorithm: at the beginning the number of cracks that will be modeled is entered from keyboard. Then the point with random position is choosing on the matrix whose size is 1024x1024 pixels (result image size). This random pixel and two adjacent points are painted with random brightness, the points, located at the edges have lower brightness than the central pixel. The width of the paintbrush is 3 pixels. Further one of the eight possible directions is chosen and the painting continues in this direction. The number of `steps' is also entered at the beginning of the program. This method of cracks simulating is based on theory A.N. Galybin and A.V. Dyskin, which describe cracks propagation as random walk process. These operations are repeated as many times as many cracks it's necessary to simulate. After that background noises and Gaussian blur (for simulating bad focusing of optical system) are applied.

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…

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.

How to optimize tuberculosis case finding: explorations for Indonesia with a health system model

PubMed Central

2009-01-01

Background A mathematical model was designed to explore the impact of three strategies for better tuberculosis case finding. Strategies included: (1) reducing the number of tuberculosis patients who do not seek care; (2) reducing diagnostic delay; and (3) engaging non-DOTS providers in the referral of tuberculosis suspects to DOTS services in the Indonesian health system context. The impact of these strategies on tuberculosis mortality and treatment outcome was estimated using a mathematical model of the Indonesian health system. Methods The model consists of multiple compartments representing logical movement of a respiratory symptomatic (tuberculosis suspect) through the health system, including patient- and health system delays. Main outputs of the model are tuberculosis death rate and treatment outcome (i.e. full or partial cure). We quantified the model parameters for the Jogjakarta province context, using a two round Delphi survey with five Indonesian tuberculosis experts. Results The model validation shows that four critical model outputs (average duration of symptom onset to treatment, detection rate, cure rate, and death rate) were reasonably close to existing available data, erring towards more optimistic outcomes than are actually reported. The model predicted that an intervention to reduce the proportion of tuberculosis patients who never seek care would have the biggest impact on tuberculosis death prevention, while an intervention resulting in more referrals of tuberculosis suspects to DOTS facilities would yield higher cure rates. This finding is similar for situations where the alternative sector is a more important health resource, such as in most other parts of Indonesia. Conclusion We used mathematical modeling to explore the impact of Indonesian health system interventions on tuberculosis treatment outcome and deaths. Because detailed data were not available regarding the current Indonesian population, we relied on expert opinion to quantify the parameters. The fact that the model output showed similar results to epidemiological data suggests that the experts had an accurate understanding of this subject, thereby reassuring the quality of our predictions. The model highlighted the potential effectiveness of active case finding of tuberculosis patients with limited access to DOTS facilities in the developing country setting. PMID:19505296

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.

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.

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.

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 Investigation into Student Perceptions towards Mathematics and Their Performance in First Year Chemistry: Introduction of Online Maths Skills Support

ERIC Educational Resources Information Center

Johnston, Peter R.; Watters, Dianne J.; Brown, Christopher L.; Loughlin, Wendy A.

2016-01-01

An online Maths Skills Site was developed as an integrated support programme for first year Chemistry students, the content of which, was based on an analysis of their high-school mathematical backgrounds. This study examined the students' perceptions of Maths, their patterns of usage of the Maths Skills Site and whether there was a relationship…

Contribution of Mathematics In-Service Training Course to the Professional Development of Elementary School Teachers in Israel

ERIC Educational Resources Information Center

Mishal, Adina; Patkin, Dorit

2016-01-01

The present study aimed to explore the contribution of a mathematics in-service training course to elementary school teachers (1st-6th grades) in Israel. The study was conducted among 449 educators. They were required to respond to background questions. Moreover, they were asked to indicate their expectations from the in-service training course…

An Appraisal of an Online Tutorial System for the Teaching and Learning of Engineering Physics in Conjunction with Contextual Physics and Mathematics, and Relevant Mathematics

ERIC Educational Resources Information Center

Bhathal, Ragbir

2016-01-01

The number of students entering engineering schools in Australian universities has increased tremendously over the last few years because of the Australian Federal Government's policy of increasing the participation rates of Higher School Certificate students and students from low social economic status backgrounds in the tertiary sector. They now…

Student Task Persistence in the Third International Mathematics and Science Study: A Major Source of Acheievement Differences at the National, Classroom, and Student Levels.

ERIC Educational Resources Information Center

Boe, Erling E.; May, Henry,; Boruch, Robert F.

The Third International Mathematics and Science Study (TIMSS) contains no direct measures of student ability and motivation. Researchers created a new variable, Student Task Persistence (STP), that is an index of student engagement in providing answers to TIMSS questions on the background questionnaire. The purpose of this research was to…

Dealing with dissatisfaction in mathematical modelling to integrate QFD and Kano’s model

NASA Astrophysics Data System (ADS)

Retno Sari Dewi, Dian; Debora, Joana; Edy Sianto, Martinus

2017-12-01

The purpose of the study is to implement the integration of Quality Function Deployment (QFD) and Kano’s Model into mathematical model. Voice of customer data in QFD was collected using questionnaire and the questionnaire was developed based on Kano’s model. Then the operational research methodology was applied to build the objective function and constraints in the mathematical model. The relationship between voice of customer and engineering characteristics was modelled using linier regression model. Output of the mathematical model would be detail of engineering characteristics. The objective function of this model is to maximize satisfaction and minimize dissatisfaction as well. Result of this model is 62% .The major contribution of this research is to implement the existing mathematical model to integrate QFD and Kano’s Model in the case study of shoe cabinet.

Striking a Balance: Students' Tendencies to Oversimplify or Overcomplicate in Mathematical Modeling

ERIC Educational Resources Information Center

Gould, Heather; Wasserman, Nicholas H.

2014-01-01

With the adoption of the "Common Core State Standards for Mathematics" (CCSSM), the process of mathematical modeling has been given increased attention in mathematics education. This article reports on a study intended to inform the implementation of modeling in classroom contexts by examining students' interactions with the process of…

Attitudes of Pre-Service Mathematics Teachers towards Modelling: A South African Inquiry

ERIC Educational Resources Information Center

Jacobs, Gerrie J.; Durandt, Rina

2017-01-01

This study explores the attitudes of mathematics pre-service teachers, based on their initial exposure to a model-eliciting challenge. The new Curriculum and Assessment Policy Statement determines that mathematics students should be able to identify, investigate and solve problems via modelling. The unpreparedness of mathematics teachers in…

Achilles and the tortoise: Some caveats to mathematical modeling in biology.

PubMed

Gilbert, Scott F

2018-01-31

Mathematical modeling has recently become a much-lauded enterprise, and many funding agencies seek to prioritize this endeavor. However, there are certain dangers associated with mathematical modeling, and knowledge of these pitfalls should also be part of a biologist's training in this set of techniques. (1) Mathematical models are limited by known science; (2) Mathematical models can tell what can happen, but not what did happen; (3) A model does not have to conform to reality, even if it is logically consistent; (4) Models abstract from reality, and sometimes what they eliminate is critically important; (5) Mathematics can present a Platonic ideal to which biologically organized matter strives, rather than a trial-and-error bumbling through evolutionary processes. This "Unity of Science" approach, which sees biology as the lowest physical science and mathematics as the highest science, is part of a Western belief system, often called the Great Chain of Being (or Scala Natura), that sees knowledge emerge as one passes from biology to chemistry to physics to mathematics, in an ascending progression of reason being purification from matter. This is also an informal model for the emergence of new life. There are now other informal models for integrating development and evolution, but each has its limitations. Copyright © 2018 Elsevier Ltd. All rights reserved.

An effective automatic procedure for testing parameter identifiability of HIV/AIDS models.

PubMed

Saccomani, Maria Pia

2011-08-01

Realistic HIV models tend to be rather complex and many recent models proposed in the literature could not yet be analyzed by traditional identifiability testing techniques. In this paper, we check a priori global identifiability of some of these nonlinear HIV models taken from the recent literature, by using a differential algebra algorithm based on previous work of the author. The algorithm is implemented in a software tool, called DAISY (Differential Algebra for Identifiability of SYstems), which has been recently released (DAISY is freely available on the web site http://www.dei.unipd.it/~pia/ ). The software can be used to automatically check global identifiability of (linear and) nonlinear models described by polynomial or rational differential equations, thus providing a general and reliable tool to test global identifiability of several HIV models proposed in the literature. It can be used by researchers with a minimum of mathematical background.

Automatic mathematical modeling for real time simulation program (AI application)

NASA Technical Reports Server (NTRS)

Wang, Caroline; Purinton, Steve

1989-01-01

A methodology is described for automatic mathematical modeling and generating simulation models. The major objective was to create a user friendly environment for engineers to design, maintain, and verify their models; to automatically convert the mathematical models into conventional code for computation; and finally, to document the model automatically.

How to build a course in mathematical-biological modeling: content and processes for knowledge and skill.

PubMed

Hoskinson, Anne-Marie

2010-01-01

Biological problems in the twenty-first century are complex and require mathematical insight, often resulting in mathematical models of biological systems. Building mathematical-biological models requires cooperation among biologists and mathematicians, and mastery of building models. A new course in mathematical modeling presented the opportunity to build both content and process learning of mathematical models, the modeling process, and the cooperative process. There was little guidance from the literature on how to build such a course. Here, I describe the iterative process of developing such a course, beginning with objectives and choosing content and process competencies to fulfill the objectives. I include some inductive heuristics for instructors seeking guidance in planning and developing their own courses, and I illustrate with a description of one instructional model cycle. Students completing this class reported gains in learning of modeling content, the modeling process, and cooperative skills. Student content and process mastery increased, as assessed on several objective-driven metrics in many types of assessments.

A Computational Model of the Ionic Currents, Ca2+ Dynamics and Action Potentials Underlying Contraction of Isolated Uterine Smooth Muscle

PubMed Central

Tong, Wing-Chiu; Choi, Cecilia Y.; Karche, Sanjay; Holden, Arun V.; Zhang, Henggui; Taggart, Michael J.

2011-01-01

Uterine contractions during labor are discretely regulated by rhythmic action potentials (AP) of varying duration and form that serve to determine calcium-dependent force production. We have employed a computational biology approach to develop a fuller understanding of the complexity of excitation-contraction (E-C) coupling of uterine smooth muscle cells (USMC). Our overall aim is to establish a mathematical platform of sufficient biophysical detail to quantitatively describe known uterine E-C coupling parameters and thereby inform future empirical investigations of physiological and pathophysiological mechanisms governing normal and dysfunctional labors. From published and unpublished data we construct mathematical models for fourteen ionic currents of USMCs: currents (L- and T-type), current, an hyperpolarization-activated current, three voltage-gated currents, two -activated current, -activated current, non-specific cation current, - exchanger, - pump and background current. The magnitudes and kinetics of each current system in a spindle shaped single cell with a specified surface area∶volume ratio is described by differential equations, in terms of maximal conductances, electrochemical gradient, voltage-dependent activation/inactivation gating variables and temporal changes in intracellular computed from known fluxes. These quantifications are validated by the reconstruction of the individual experimental ionic currents obtained under voltage-clamp. Phasic contraction is modeled in relation to the time constant of changing . This integrated model is validated by its reconstruction of the different USMC AP configurations (spikes, plateau and bursts of spikes), the change from bursting to plateau type AP produced by estradiol and of simultaneous experimental recordings of spontaneous AP, and phasic force. In summary, our advanced mathematical model provides a powerful tool to investigate the physiological ionic mechanisms underlying the genesis of uterine electrical E-C coupling of labor and parturition. This will furnish the evolution of descriptive and predictive quantitative models of myometrial electrogenesis at the whole cell and tissue levels. PMID:21559514

Improving Embryonic Stem Cell Expansion through the Combination of Perfusion and Bioprocess Model Design

PubMed Central

Yeo, David; Kiparissides, Alexandros; Cha, Jae Min; Aguilar-Gallardo, Cristobal; Polak, Julia M.; Tsiridis, Elefterios; Pistikopoulos, Efstratios N.; Mantalaris, Athanasios

2013-01-01

Background High proliferative and differentiation capacity renders embryonic stem cells (ESCs) a promising cell source for tissue engineering and cell-based therapies. Harnessing their potential, however, requires well-designed, efficient and reproducible expansion and differentiation protocols as well as avoiding hazardous by-products, such as teratoma formation. Traditional, standard culture methodologies are fragmented and limited in their fed-batch feeding strategies that afford a sub-optimal environment for cellular metabolism. Herein, we investigate the impact of metabolic stress as a result of inefficient feeding utilizing a novel perfusion bioreactor and a mathematical model to achieve bioprocess improvement. Methodology/Principal Findings To characterize nutritional requirements, the expansion of undifferentiated murine ESCs (mESCs) encapsulated in hydrogels was performed in batch and perfusion cultures using bioreactors. Despite sufficient nutrient and growth factor provision, the accumulation of inhibitory metabolites resulted in the unscheduled differentiation of mESCs and a decline in their cell numbers in the batch cultures. In contrast, perfusion cultures maintained metabolite concentration below toxic levels, resulting in the robust expansion (>16-fold) of high quality ‘naïve’ mESCs within 4 days. A multi-scale mathematical model describing population segregated growth kinetics, metabolism and the expression of selected pluripotency (‘stemness’) genes was implemented to maximize information from available experimental data. A global sensitivity analysis (GSA) was employed that identified significant (6/29) model parameters and enabled model validation. Predicting the preferential propagation of undifferentiated ESCs in perfusion culture conditions demonstrates synchrony between theory and experiment. Conclusions/Significance The limitations of batch culture highlight the importance of cellular metabolism in maintaining pluripotency, which necessitates the design of suitable ESC bioprocesses. We propose a novel investigational framework that integrates a novel perfusion culture platform (controlled metabolic conditions) with mathematical modeling (information maximization) to enhance ESC bioprocess productivity and facilitate bioprocess optimization. PMID:24339957

Exposure time independent summary statistics for assessment of drug dependent cell line growth inhibition

PubMed Central

2014-01-01

Background In vitro generated dose-response curves of human cancer cell lines are widely used to develop new therapeutics. The curves are summarised by simplified statistics that ignore the conventionally used dose-response curves’ dependency on drug exposure time and growth kinetics. This may lead to suboptimal exploitation of data and biased conclusions on the potential of the drug in question. Therefore we set out to improve the dose-response assessments by eliminating the impact of time dependency. Results First, a mathematical model for drug induced cell growth inhibition was formulated and used to derive novel dose-response curves and improved summary statistics that are independent of time under the proposed model. Next, a statistical analysis workflow for estimating the improved statistics was suggested consisting of 1) nonlinear regression models for estimation of cell counts and doubling times, 2) isotonic regression for modelling the suggested dose-response curves, and 3) resampling based method for assessing variation of the novel summary statistics. We document that conventionally used summary statistics for dose-response experiments depend on time so that fast growing cell lines compared to slowly growing ones are considered overly sensitive. The adequacy of the mathematical model is tested for doxorubicin and found to fit real data to an acceptable degree. Dose-response data from the NCI60 drug screen were used to illustrate the time dependency and demonstrate an adjustment correcting for it. The applicability of the workflow was illustrated by simulation and application on a doxorubicin growth inhibition screen. The simulations show that under the proposed mathematical model the suggested statistical workflow results in unbiased estimates of the time independent summary statistics. Variance estimates of the novel summary statistics are used to conclude that the doxorubicin screen covers a significant diverse range of responses ensuring it is useful for biological interpretations. Conclusion Time independent summary statistics may aid the understanding of drugs’ action mechanism on tumour cells and potentially renew previous drug sensitivity evaluation studies. PMID:24902483

Think Pair Share Using Realistic Mathematics Education Approach in Geometry Learning

NASA Astrophysics Data System (ADS)

Afthina, H.; Mardiyana; Pramudya, I.

2017-09-01

This research aims to determine the impact of mathematics learning applying Think Pair Share (TPS) using Realistic Mathematics Education (RME) viewed from mathematical-logical intelligence in geometry learning. Method that used in this research is quasi experimental research The result of this research shows that (1) mathematics achievement applying TPS using RME approach gives a better result than those applying direct learning model; (2) students with high mathematical-logical intelligence can reach a better mathematics achievement than those with average and low one, whereas students with average mathematical-logical intelligence can reach a better achievement than those with low one; (3) there is no interaction between learning model and the level of students’ mathematical-logical intelligence in giving a mathematics achievement. The impact of this research is that TPS model using RME approach can be applied in mathematics learning so that students can learn more actively and understand the material more, and mathematics learning become more meaningful. On the other hand, internal factors of students must become a consideration toward the success of students’ mathematical achievement particularly in geometry material.

Preserving Pelicans with Models That Make Sense

ERIC Educational Resources Information Center

Moore, Tamara J.; Doerr, Helen M.; Glancy, Aran W.; Ntow, Forster D.

2015-01-01

Getting students to think deeply about mathematical concepts is not an easy job, which is why we often use problem-solving tasks to engage students in higher-level mathematical thinking. Mathematical modeling, one of the mathematical practices found in the Common Core State Standards for Mathematics (CCSSM), is a type of problem solving that can…

Two Project-Based Strategies in an Interdisciplinary Mathematical Modeling in Biology Course

ERIC Educational Resources Information Center

Ludwig, Patrice; Tongen, Anthony; Walton, Brian

2018-01-01

James Madison University faculty team-teach an interdisciplinary mathematical modeling course for mathematics and biology students. We have used two different project-based approaches to emphasize the mathematical concepts taught in class, while also exposing students to new areas of mathematics not formally covered in class. The first method…

Rockets: A Teacher's Guide with Activities in Science, Mathematics, and Technology. Grades K-12.

ERIC Educational Resources Information Center

Shearer, Deborah A.; Vogt, Gregory L.

This guide contains activities that emphasize hands-on involvement, prediction, data collection and interpretation, teamwork, and problem solving. It begins with background information on the history of rocketry, scientific principles, and practical rocketry. Following the background sections are a series of activities that demonstrate the basic…

Teaching Computer Languages and Elementary Theory for Mixed Audiences at University Level

ERIC Educational Resources Information Center

Christiansen, Henning

2004-01-01

Theoretical issues of computer science are traditionally taught in a way that presupposes a solid mathematical background and are usually considered more or less inaccessible for students without this. An effective methodology is described which has been developed for a target group of university students with different backgrounds such as natural…

Mathematical models of behavior of individual animals.

PubMed

Tsibulsky, Vladimir L; Norman, Andrew B

2007-01-01

This review is focused on mathematical modeling of behaviors of a whole organism with special emphasis on models with a clearly scientific approach to the problem that helps to understand the mechanisms underlying behavior. The aim is to provide an overview of old and contemporary mathematical models without complex mathematical details. Only deterministic and stochastic, but not statistical models are reviewed. All mathematical models of behavior can be divided into two main classes. First, models that are based on the principle of teleological determinism assume that subjects choose the behavior that will lead them to a better payoff in the future. Examples are game theories and operant behavior models both of which are based on the matching law. The second class of models are based on the principle of causal determinism, which assume that subjects do not choose from a set of possibilities but rather are compelled to perform a predetermined behavior in response to specific stimuli. Examples are perception and discrimination models, drug effects models and individual-based population models. A brief overview of the utility of each mathematical model is provided for each section.

Levels of line graph question interpretation with intermediate elementary students of varying scientific and mathematical knowledge and ability: A think aloud study

NASA Astrophysics Data System (ADS)

Keller, Stacy Kathryn

This study examined how intermediate elementary students' mathematics and science background knowledge affected their interpretation of line graphs and how their interpretations were affected by graph question levels. A purposive sample of 14 6th-grade students engaged in think aloud interviews (Ericsson & Simon, 1993) while completing an excerpted Test of Graphing in Science (TOGS) (McKenzie & Padilla, 1986). Hand gestures were video recorded. Student performance on the TOGS was assessed using an assessment rubric created from previously cited factors affecting students' graphing ability. Factors were categorized using Bertin's (1983) three graph question levels. The assessment rubric was validated by Padilla and a veteran mathematics and science teacher. Observational notes were also collected. Data were analyzed using Roth and Bowen's semiotic process of reading graphs (2001). Key findings from this analysis included differences in the use of heuristics, self-generated questions, science knowledge, and self-motivation. Students with higher prior achievement used a greater number and variety of heuristics and more often chose appropriate heuristics. They also monitored their understanding of the question and the adequacy of their strategy and answer by asking themselves questions. Most used their science knowledge spontaneously to check their understanding of the question and the adequacy of their answers. Students with lower and moderate prior achievement favored one heuristic even when it was not useful for answering the question and rarely asked their own questions. In some cases, if students with lower prior achievement had thought about their answers in the context of their science knowledge, they would have been able to recognize their errors. One student with lower prior achievement motivated herself when she thought the questions were too difficult. In addition, students answered the TOGS in one of three ways: as if they were mathematics word problems, science data to be analyzed, or they were confused and had to guess. A second set of findings corroborated how science background knowledge affected graph interpretation: correct science knowledge supported students' reasoning, but it was not necessary to answer any question correctly; correct science knowledge could not compensate for incomplete mathematics knowledge; and incorrect science knowledge often distracted students when they tried to use it while answering a question. Finally, using Roth and Bowen's (2001) two-stage semiotic model of reading graphs, representative vignettes showed emerging patterns from the study. This study added to our understanding of the role of science content knowledge during line graph interpretation, highlighted the importance of heuristics and mathematics procedural knowledge, and documented the importance of perception attentions, motivation, and students' self-generated questions. Recommendations were made for future research in line graph interpretation in mathematics and science education and for improving instruction in this area.

Problem Posing and Solving with Mathematical Modeling

ERIC Educational Resources Information Center

English, Lyn D.; Fox, Jillian L.; Watters, James J.

2005-01-01

Mathematical modeling is explored as both problem posing and problem solving from two perspectives, that of the child and the teacher. Mathematical modeling provides rich learning experiences for elementary school children and their teachers.

Building Mathematical Models of Simple Harmonic and Damped Motion.

ERIC Educational Resources Information Center

Edwards, Thomas

1995-01-01

By developing a sequence of mathematical models of harmonic motion, shows that mathematical models are not right or wrong, but instead are better or poorer representations of the problem situation. (MKR)

Taking the mystery out of mathematical model applications to karst aquifers—A primer

USGS Publications Warehouse

Kuniansky, Eve L.

2014-01-01

Advances in mathematical model applications toward the understanding of the complex flow, characterization, and water-supply management issues for karst aquifers have occurred in recent years. Different types of mathematical models can be applied successfully if appropriate information is available and the problems are adequately identified. The mathematical approaches discussed in this paper are divided into three major categories: 1) distributed parameter models, 2) lumped parameter models, and 3) fitting models. The modeling approaches are described conceptually with examples (but without equations) to help non-mathematicians understand the applications.

Secondary Teachers' Conceptions and Practices of Assessment Models: The Case for Mathematics Teachers in Jordan

ERIC Educational Resources Information Center

Al Duwairi, Ahmed

2013-01-01

This study aimed at investigating the extent to which secondary schools mathematics teachers practice to assessment models in their mathematics teaching and learning. Definitely, the study aimed at answering the following questions: (1) To what extent do secondary schools mathematics teachers practice each of the assessment models in their…

Reality-Theoretical Models-Mathematics: A Ternary Perspective on Physics Lessons in Upper-Secondary School

ERIC Educational Resources Information Center

Hansson, Lena; Hansson, Örjan; Juter, Kristina; Redfors, Andreas

2015-01-01

This article discusses the role of mathematics during physics lessons in upper-secondary school. Mathematics is an inherent part of theoretical models in physics and makes powerful predictions of natural phenomena possible. Ability to use both theoretical models and mathematics is central in physics. This paper takes as a starting point that the…

Mathematics Student Teachers' Modelling Approaches While Solving the Designed Esme Rug Problem

ERIC Educational Resources Information Center

Hidiroglu, Çaglar Naci; Dede, Ayse Tekin; Ünver, Semiha Kula; Güzel, Esra Bukova

2017-01-01

The purpose of the study is to analyze the mathematics student teachers' solutions on the Esme Rug Problem through 7-stage mathematical modelling process. This problem was designed by the researchers by considering the modelling problems' main properties. The study was conducted with twenty one secondary mathematics student teachers. The data were…

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.

"When Mathematical Activity Moves You": An Exploration of the Design and Use of Purposefully Embodied Mathematical Activities, Models, Contexts, and Environments

ERIC Educational Resources Information Center

Campbell, William James

2017-01-01

This dissertation describes a mathematics curriculum and instruction design experiment involving a series of embodied mathematical activities conducted in two Colorado elementary schools Activities designed for this experiment include multi-scalar number line models focused on supporting students' understanding of elementary mathematics. Realistic…

Mathematical Modeling Is Also Physics--Interdisciplinary Teaching between Mathematics and Physics in Danish Upper Secondary Education

ERIC Educational Resources Information Center

Michelsen, Claus

2015-01-01

Mathematics plays a crucial role in physics. This role is brought about predominantly through the building, employment, and assessment of mathematical models, and teachers and educators should capture this relationship in the classroom in an effort to improve students' achievement and attitude in both physics and mathematics. But although there…

Exploring Yellowstone National Park with Mathematical Modeling

ERIC Educational Resources Information Center

Wickstrom, Megan H.; Carr, Ruth; Lackey, Dacia

2017-01-01

Mathematical modeling, a practice standard in the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010), is a process by which students develop and use mathematics as a tool to make sense of the world around them. Students investigate a real-world situation by asking mathematical questions; along the way, they need to decide how to use…

"Model Your Genes the Mathematical Way"--A Mathematical Biology Workshop for Secondary School Teachers

ERIC Educational Resources Information Center

Martins, Ana Margarida; Vera-Licona, Paola; Laubenbacher, Reinhard

2008-01-01

This article describes a mathematical biology workshop given to secondary school teachers of the Danville area in Virginia, USA. The goal of the workshop was to enable teams of teachers with biology and mathematics expertise to incorporate lesson plans in mathematical modelling into the curriculum. The biological focus of the activities is the…

An Analysis of Pre-Service Mathematics Teachers' Performance in Modelling Tasks in Terms of Spatial Visualisation Ability

ERIC Educational Resources Information Center

Tasova, Halil Ibrahim; Delice, Ali

2012-01-01

Mathematical modelling involves mathematical constructions chosen to represent some real world situations and the relationships among them; it is the process of expressing a real world situation mathematically. Visualisation can play a significant role in the development of thinking or understanding mathematical concepts, and also makes abstract…

The Role of Introductory Geosciences in Students' Quantitative Literacy

NASA Astrophysics Data System (ADS)

Wenner, J. M.; Manduca, C.; Baer, E. M.

2006-12-01

Quantitative literacy is more than mathematics; it is about reasoning with data. Colleges and universities have begun to recognize the distinction between mathematics and quantitative literacy, modifying curricula to reflect the need for numerate citizens. Although students may view geology as 'rocks for jocks', the geosciences are truthfully rife with data, making introductory geoscience topics excellent context for developing the quantitative literacy of students with diverse backgrounds. In addition, many news items that deal with quantitative skills, such as the global warming phenomenon, have their basis in the Earth sciences and can serve as timely examples of the importance of quantitative literacy for all students in introductory geology classrooms. Participants at a workshop held in 2006, 'Infusing Quantitative Literacy into Introductory Geoscience Courses,' discussed and explored the challenges and opportunities associated with the inclusion of quantitative material and brainstormed about effective practices for imparting quantitative literacy to students with diverse backgrounds. The tangible results of this workshop add to the growing collection of quantitative materials available through the DLESE- and NSF-supported Teaching Quantitative Skills in the Geosciences website, housed at SERC. There, faculty can find a collection of pages devoted to the successful incorporation of quantitative literacy in introductory geoscience. The resources on the website are designed to help faculty to increase their comfort with presenting quantitative ideas to students with diverse mathematical abilities. A methods section on "Teaching Quantitative Literacy" (http://serc.carleton.edu/quantskills/methods/quantlit/index.html) focuses on connecting quantitative concepts with geoscience context and provides tips, trouble-shooting advice and examples of quantitative activities. The goal in this section is to provide faculty with material that can be readily incorporated into existing introductory geoscience courses. In addition, participants at the workshop (http://serc.carleton.edu/quantskills/workshop06/index.html) submitted and modified more than 20 activities and model courses (with syllabi) designed to use best practices for helping introductory geoscience students to become quantitatively literate. We present insights from the workshop and other sources for a framework that can aid in increasing quantitative literacy of students from a variety of backgrounds in the introductory geoscience classroom.

Components of Mathematics Anxiety: Factor Modeling of the MARS30-Brief

PubMed Central

Pletzer, Belinda; Wood, Guilherme; Scherndl, Thomas; Kerschbaum, Hubert H.; Nuerk, Hans-Christoph

2016-01-01

Mathematics anxiety involves feelings of tension, discomfort, high arousal, and physiological reactivity interfering with number manipulation and mathematical problem solving. Several factor analytic models indicate that mathematics anxiety is rather a multidimensional than unique construct. However, the factor structure of mathematics anxiety has not been fully clarified by now. This issue shall be addressed in the current study. The Mathematics Anxiety Rating Scale (MARS) is a reliable measure of mathematics anxiety (Richardson and Suinn, 1972), for which several reduced forms have been developed. Most recently, a shortened version of the MARS (MARS30-brief) with comparable reliability was published. Different studies suggest that mathematics anxiety involves up to seven different factors. Here we examined the factor structure of the MARS30-brief by means of confirmatory factor analysis. The best model fit was obtained by a six-factor model, dismembering the known two general factors “Mathematical Test Anxiety” (MTA) and “Numerical Anxiety” (NA) in three factors each. However, a more parsimonious 5-factor model with two sub-factors for MTA and three for NA fitted the data comparably well. Factors were differentially susceptible to sex differences and differences between majors. Measurement invariance for sex was established. PMID:26924996

Components of Mathematics Anxiety: Factor Modeling of the MARS30-Brief.

PubMed

Pletzer, Belinda; Wood, Guilherme; Scherndl, Thomas; Kerschbaum, Hubert H; Nuerk, Hans-Christoph

2016-01-01

Mathematics anxiety involves feelings of tension, discomfort, high arousal, and physiological reactivity interfering with number manipulation and mathematical problem solving. Several factor analytic models indicate that mathematics anxiety is rather a multidimensional than unique construct. However, the factor structure of mathematics anxiety has not been fully clarified by now. This issue shall be addressed in the current study. The Mathematics Anxiety Rating Scale (MARS) is a reliable measure of mathematics anxiety (Richardson and Suinn, 1972), for which several reduced forms have been developed. Most recently, a shortened version of the MARS (MARS30-brief) with comparable reliability was published. Different studies suggest that mathematics anxiety involves up to seven different factors. Here we examined the factor structure of the MARS30-brief by means of confirmatory factor analysis. The best model fit was obtained by a six-factor model, dismembering the known two general factors "Mathematical Test Anxiety" (MTA) and "Numerical Anxiety" (NA) in three factors each. However, a more parsimonious 5-factor model with two sub-factors for MTA and three for NA fitted the data comparably well. Factors were differentially susceptible to sex differences and differences between majors. Measurement invariance for sex was established.

Control of Crazyflie nano quadcopter using Simulink

NASA Astrophysics Data System (ADS)

Gopabhat Madhusudhan, Meghana

This thesis focuses on developing a mathematical model in Simulink to Crazyflie, an open source platform. Attitude, altitude and position controllers of a Crazyflie are designed in the mathematical model. The mathematical model is developed based on the quadcopter system dynamics using a non-linear approach. The parameters of translational and rotational dynamics of the quadcopter system are linearized and tuned individually. The tuned attitude and altitude controllers from the mathematical model are implemented on real time Crazyflie Simulink model to achieve autonomous and controlled flight.

Computational modeling of the cell-autonomous mammalian circadian oscillator.

PubMed

Podkolodnaya, Olga A; Tverdokhleb, Natalya N; Podkolodnyy, Nikolay L

2017-02-24

This review summarizes various mathematical models of cell-autonomous mammalian circadian clock. We present the basics necessary for understanding of the cell-autonomous mammalian circadian oscillator, modern experimental data essential for its reconstruction and some special problems related to the validation of mathematical circadian oscillator models. This work compares existing mathematical models of circadian oscillator and the results of the computational studies of the oscillating systems. Finally, we discuss applications of the mathematical models of mammalian circadian oscillator for solving specific problems in circadian rhythm biology.

The Effectiveness of the Mathematics, Engineering, Science Achievement (MESA) Program's Administrative and Policy-Making Processes. A Report to the Legislature in Response to Assembly Bill 610 (1985). Commission Report 89-4.

ERIC Educational Resources Information Center

California State Postsecondary Education Commission, Sacramento.

The Mathematics, Engineering, Science Achievement (MESA) Program was established in 1970 to increase the number of minority students in college programs. This paper reports the MESA administrative operations and policy-making processes. Part 1 summarizes the background of this study. Part 2 describes MESA's administrative operations and provides…

Board on Mathematical Sciences

DTIC Science & Technology

1990-02-20

20. DISTRIBUTION IAVAILAIIIY OF ABSTRACT 21. AISYRACr. SECURITY CLASSIFICATIO01 IDUNCLASSiFIEDAINumITE 0: SAME As RPT. C TIC USERS Unclassified 22a...RELEASE; DISTRIBUTION UNLIMITED t ’ C Availability Codes Avail and I or Specmial 90 04 09 118 BOARD ON MATHEMATICAL SCIENCES BACKGROUND The National...television film, "The Man Who Loved Numbers," based on the life of the Indian mathematician Srinivasa Ramanujan at the National Academy of Sciences (NAS

Investigating middle school students’ difficulties in mathematical literacy problems level 1 and 2

NASA Astrophysics Data System (ADS)

Setiawati, S.; Herman, T.; Jupri, A.

2017-11-01

The background of this study is the lack of mathematical literacy skills of students. The proficiency of students’ mathematical literacy skills based on the results of the PISA 2015 study shows that Indonesian students at the proficiency level 1. This fact gave rise to this study which aims to investigate middle school students’ difficulties in mathematical literacy problems level 1 and 2. Qualitative research was used in this study. An individual written test on mathematical literacy problems was administered, followed by interviews. The subjects of the study were 61 students grade VII in Bandung and 26 of them were interviewed afterward. Data analysis revealed that students’ error in performing arithmetic most frequently observed. Other observed difficulties concerned understanding about algebra concept, applying arithmetic operation in algebraic expressions, and interpreting symbols to represent the unknown. In solving mathematical literacy problems, students use their prior knowledge, although sometimes not relevant to the questions. Based on the results, we suggest that mathematics learning in contextual learning and which invites students to participate in the processes of understanding the concepts.

Students’ errors in solving combinatorics problems observed from the characteristics of RME modeling

NASA Astrophysics Data System (ADS)

Meika, I.; Suryadi, D.; Darhim

2018-01-01

This article was written based on the learning evaluation results of students’ errors in solving combinatorics problems observed from the characteristics of Realistic Mathematics Education (RME); that is modeling. Descriptive method was employed by involving 55 students from two international-based pilot state senior high schools in Banten. The findings of the study suggested that the students still committed errors in simplifying the problem as much 46%; errors in making mathematical model (horizontal mathematization) as much 60%; errors in finishing mathematical model (vertical mathematization) as much 65%; and errors in interpretation as well as validation as much 66%.

Eliciting candidate anatomical routes for protein interactions: a scenario from endocrine physiology

PubMed Central

2013-01-01

Background In this paper, we use: i) formalised anatomical knowledge of connectivity between body structures and ii) a formal theory of physiological transport between fluid compartments in order to define and make explicit the routes followed by proteins to a site of interaction. The underlying processes are the objects of mathematical models of physiology and, therefore, the motivation for the approach can be understood as using knowledge representation and reasoning methods to propose concrete candidate routes corresponding to correlations between variables in mathematical models of physiology. In so doing, the approach projects physiology models onto a representation of the anatomical and physiological reality which underpins them. Results The paper presents a method based on knowledge representation and reasoning for eliciting physiological communication routes. In doing so, the paper presents the core knowledge representation and algorithms using it in the application of the method. These are illustrated through the description of a prototype implementation and the treatment of a simple endocrine scenario whereby a candidate route of communication between ANP and its receptors on the external membrane of smooth muscle cells in renal arterioles is elicited. The potential of further development of the approach is illustrated through the informal discussion of a more complex scenario. Conclusions The work presented in this paper supports research in intercellular communication by enabling knowledge‐based inference on physiologically‐related biomedical data and models. PMID:23590598

An intermediate-level course on Biological Physics

NASA Astrophysics Data System (ADS)

Nelson, Phil

2004-03-01

I describe both undergraduate and graduate 1-semester courses designed to give a survey of Biological Physics. The courses cover classical as well as recent topics. The undergraduate version requires calculus-based first-year physics as its prerequisite. With this level of assumed background, we can arrive at topics such as molecular motors, manipulation of single molecules, and the propagation of nerve impulses. Students majoring in physics, chemistry, biochemistry, and every engineering major (as well as a few in biology), end up taking this course. The graduate course covers the same material but includes exercises with symbolic mathematics packages and data modeling.

The principle of superposition and its application in ground-water hydraulics

USGS Publications Warehouse

Reilly, Thomas E.; Franke, O. Lehn; Bennett, Gordon D.

1987-01-01

The principle of superposition, a powerful mathematical technique for analyzing certain types of complex problems in many areas of science and technology, has important applications in ground-water hydraulics and modeling of ground-water systems. The principle of superposition states that problem solutions can be added together to obtain composite solutions. This principle applies to linear systems governed by linear differential equations. This report introduces the principle of superposition as it applies to ground-water hydrology and provides background information, discussion, illustrative problems with solutions, and problems to be solved by the reader.

The Relationship between Big Data and Mathematical Modeling: A Discussion in a Mathematical Education Scenario

ERIC Educational Resources Information Center

Dalla Vecchia, Rodrigo

2015-01-01

This study discusses aspects of the association between Mathematical Modeling (MM) and Big Data in the scope of mathematical education. We present an example of an activity to discuss two ontological factors that involve MM. The first is linked to the modeling stages. The second involves the idea of pedagogical objectives. The main findings…

On a Mathematical Model with Noncompact Boundary Conditions Describing Bacterial Population

NASA Astrophysics Data System (ADS)

Boulanouar, Mohamed

2013-04-01

In this work, we are concerned with the well-posedness of a mathematical model describing a maturation-velocity structured bacterial population. Each bacterium is distinguished by its degree of maturity and its maturation velocity. The bacterial mitosis is mathematically described by noncompact boundary conditions. We show that the mathematical model is governed by a positive strongly continuous semigroup.

What’s about Peer Tutoring Learning Model?

NASA Astrophysics Data System (ADS)

Muthma'innah, M.

2017-09-01

Mathematics learning outcomes in Indonesia in general is still far from satisfactory. One effort that could be expected to solve the problem is to apply the model of peer tutoring learning in mathematics. This study aims to determine whether the results of students’ mathematics learning can be enhanced through peer tutoring learning models. This type of research is the study of literature, so that the method used is to summarize and analyze the results of relevant research that has been done. Peer tutoring learning model is a model of learning in which students learn in small groups that are grouped with different ability levels, all group members to work together and help each other to understand the material. By paying attention to the syntax of the learning, then learning will be invaluable peer tutoring for students who served as teachers and students are taught. In mathematics, the implementation of this learning model can make students understand each other mathematical concepts and help students in solving mathematical problems that are poorly understood, due to the interaction between students in learning. Then it will be able to improve learning outcomes in mathematics. The impact, it can be applied in mathematics learning.

Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models

PubMed Central

2011-01-01

Background Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Results Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity. Conclusions Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task. PMID:21867520

Current problems in applied mathematics and mathematical modeling

NASA Astrophysics Data System (ADS)

Alekseev, A. S.

Papers are presented on mathematical modeling noting applications to such fields as geophysics, chemistry, atmospheric optics, and immunology. Attention is also given to models of ocean current fluxes, atmospheric and marine interactions, and atmospheric pollution. The articles include studies of catalytic reactors, models of global climate phenomena, and computer-assisted atmospheric models.

In vivo quantitative analysis of Talin turnover in response to force

PubMed Central

Hákonardóttir, Guðlaug Katrín; López-Ceballos, Pablo; Herrera-Reyes, Alejandra Donají; Das, Raibatak; Coombs, Daniel; Tanentzapf, Guy

2015-01-01

Cell adhesion to the extracellular matrix (ECM) allows cells to form and maintain three-dimensional tissue architecture. Cell–ECM adhesions are stabilized upon exposure to mechanical force. In this study, we used quantitative imaging and mathematical modeling to gain mechanistic insight into how integrin-based adhesions respond to increased and decreased mechanical forces. A critical means of regulating integrin-based adhesion is provided by modulating the turnover of integrin and its adhesion complex (integrin adhesion complex [IAC]). The turnover of the IAC component Talin, a known mechanosensor, was analyzed using fluorescence recovery after photobleaching. Experiments were carried out in live, intact flies in genetic backgrounds that increased or decreased the force applied on sites of adhesion. This analysis showed that when force is elevated, the rate of assembly of new adhesions increases such that cell–ECM adhesion is stabilized. Moreover, under conditions of decreased force, the overall rate of turnover, but not the proportion of adhesion complex components undergoing turnover, increases. Using point mutations, we identify the key functional domains of Talin that mediate its response to force. Finally, by fitting a mathematical model to the data, we uncover the mechanisms that mediate the stabilization of ECM-based adhesion during development. PMID:26446844

Measuring Leaf Area in Soy Plants by HSI Color Model Filtering and Mathematical Morphology

NASA Astrophysics Data System (ADS)

Benalcázar, M.; Padín, J.; Brun, M.; Pastore, J.; Ballarin, V.; Peirone, L.; Pereyra, G.

2011-12-01

There has been lately a significant progress in automating tasks for the agricultural sector. One of the advances is the development of robots, based on computer vision, applied to care and management of soy crops. In this task, digital image processing plays an important role, but must solve some important problems, like the ones associated to the variations in lighting conditions during image acquisition. Such variations influence directly on the brightness level of the images to be processed. In this paper we propose an algorithm to segment and measure automatically the leaf area of soy plants. This information is used by the specialists to evaluate and compare the growth of different soy genotypes. This algorithm, based on color filtering using the HSI model, detects green objects from the image background. The segmentation of leaves (foliage) was made applying Mathematical Morphology. The foliage area was estimated counting the pixels that belong to the segmented leaves. From several experiments, consisting in applying the algorithm to measure the foliage of about fifty plants of various genotypes of soy, at different growth stages, we obtained successful results, despite the high brightness variations and shadows in the processed images.

Mathematical modeling of urea transport in the kidney.

PubMed

Layton, Anita T

2014-01-01

Mathematical modeling techniques have been useful in providing insights into biological systems, including the kidney. This article considers some of the mathematical models that concern urea transport in the kidney. Modeling simulations have been conducted to investigate, in the context of urea cycling and urine concentration, the effects of hypothetical active urea secretion into pars recta. Simulation results suggest that active urea secretion induces a "urea-selective" improvement in urine concentrating ability. Mathematical models have also been built to study the implications of the highly structured organization of tubules and vessels in the renal medulla on urea sequestration and cycling. The goal of this article is to show how physiological problems can be formulated and studied mathematically, and how such models may provide insights into renal functions.

The Effects of Mathematical Modeling on Creative Production Ability and Self-Directed Learning Attitude

ERIC Educational Resources Information Center

Kim, Sun Hee; Kim, Soojin

2010-01-01

What should we do to educate the mathematically gifted and how should we do it? In this research, to satisfy diverse mathematical and cognitive demands of the gifted who have excellent learning ability and task tenacity in mathematics, we sought to apply mathematical modeling. One of the objectives of the gifted education in Korea is cultivating…

A Mathematical Diet Model

ERIC Educational Resources Information Center

Toumasis, Charalampos

2004-01-01

Emphasis on problem solving and mathematical modeling has gained considerable attention in the last few years. Connecting mathematics to other subjects and to the real world outside the classroom has received increased attention in mathematics programs. This article describes an application of simple differential equations in the field of…

Social-Cognitive Predictors of STEM Career Interests and Goal Persistence in College Students with Disabilities from Racial and Ethnic Minority Backgrounds

ERIC Educational Resources Information Center

da Silva Cardoso, Elizabeth; Dutta, Alo; Chiu, Chung-Yi; Johnson, Ebonee T.; Kundu, Madan; Chan, Fong D.

2013-01-01

Objective: To examine the relations of science, technology, engineering, and mathematics's (STEM) self-efficacy, outcome expectations, interests, and contextual supports and barriers to STEM educational goals in college students with disabilities from racial and ethnic minority backgrounds. Design: Quantitative descriptive research design using…

Exploring the Extreme: High Performance Learning Activities in Mathematics, Science and Technology. An Educator's Guide. EG-2002-10-001-DFRC

ERIC Educational Resources Information Center

Dana, Judi; Kock, Meri; Lewis, Mike; Peterson, Bruce; Stowe, Steve

2010-01-01

The many activities contained in this teaching guide emphasize hands-on involvement, prediction, data collection and interpretation, teamwork, and problem solving. The guide also contains background information about aeronautical research that can help students learn how airplanes fly. Following the background sections are a series of activities…

The Teachers' Role in Developing, Opening, and Nurturing an Inclusive STEM-Focused School

ERIC Educational Resources Information Center

Slavit, David; Nelson, Tamara Holmlund; Lesseig, Kristin

2016-01-01

Background: This study is about teachers' collective activity during the development and initial year of a science, technology, engineering, and mathematics (STEM)-focused school in the USA. The target school of this study was inclusive, as it sought admission of students from varying backgrounds and levels of ability. Drawing from narrative…

An Introduction to Equilibrium Thermodynamics. A Rational Approach to Its Teaching. Part 2: Internal Energy, Entropy, and Temperature.

ERIC Educational Resources Information Center

Williams, Donald F.; Glasser, David

1991-01-01

An approach that may be used to introduce the fundamental ideas of thermodynamics using a mathematical background with the knowledge of the behavior of matter is described. The physical background, conservation of energy, predicting the behavior of a system, and solving problems are topics of discussion. (KR)

A Case Study Exploring Science Competence and Science Confidence of Middle School Girls from Marginalized Backgrounds

ERIC Educational Resources Information Center

Garcia, Yeni Violeta

2013-01-01

The inclusion of learners from underrepresented background in biology field research experiences has not been widely explored in the literature. Increased access and equity to experiences for groups historically underrepresented in science, technology, engineering, and mathematics (STEM) has been identified as a priority for many, yet little is…