The Applied Mathematics for Power Systems (AMPS)

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

Chertkov, Michael

2012-07-24

Increased deployment of new technologies, e.g., renewable generation and electric vehicles, is rapidly transforming electrical power networks by crossing previously distinct spatiotemporal scales and invalidating many traditional approaches for designing, analyzing, and operating power grids. This trend is expected to accelerate over the coming years, bringing the disruptive challenge of complexity, but also opportunities to deliver unprecedented efficiency and reliability. Our Applied Mathematics for Power Systems (AMPS) Center will discover, enable, and solve emerging mathematics challenges arising in power systems and, more generally, in complex engineered networks. We will develop foundational applied mathematics resulting in rigorous algorithms and simulation toolboxesmore » for modern and future engineered networks. The AMPS Center deconstruction/reconstruction approach 'deconstructs' complex networks into sub-problems within non-separable spatiotemporal scales, a missing step in 20th century modeling of engineered networks. These sub-problems are addressed within the appropriate AMPS foundational pillar - complex systems, control theory, and optimization theory - and merged or 'reconstructed' at their boundaries into more general mathematical descriptions of complex engineered networks where important new questions are formulated and attacked. These two steps, iterated multiple times, will bridge the growing chasm between the legacy power grid and its future as a complex engineered network.« less

What Mathematical Competencies Are Needed for Success in College.

ERIC Educational Resources Information Center

Garofalo, Joe

1990-01-01

Identifies requisite math skills for a microeconomics course, offering samples of supply curves, demand curves, equilibrium prices, elasticity, and complex graph problems. Recommends developmental mathematics competencies, including problem solving, reasoning, connections, communication, number and operation sense, algebra, relationships,…

Problem based learning - A brief review

NASA Astrophysics Data System (ADS)

Nunes, Sandra; Oliveira, Teresa A.; Oliveira, Amílcar

2017-07-01

Teaching is a complex mission that requires not only the theoretical knowledge transmission, but furthermore requires to provide the students the necessary skills for solving real problems in their respective professional activities where complex issues and problems must be frequently faced. Over more than twenty years we have been experiencing an increase in scholar failure in the scientific area of mathematics, which means that Teaching Mathematics and related areas can be even a more complex and hard task. Scholar failure is a complex phenomenon that depends on various factors as social factors, scholar factors or biophysical factors. After numerous attempts made in order to reduce scholar failure our goal in this paper is to understand the role of "Problem Based Learning" and how this methodology can contribute to the solution of both: increasing mathematical courses success and increasing skills in the near future professionals in Portugal. Before designing a proposal for applying this technique in our institutions, we decided to conduct a survey to provide us with the necessary information about and the respective advantages and disadvantages of this methodology, so this is the brief review aim.

Learner-Interface Interactions with Mobile-Assisted Learning in Mathematics: Effects on and Relationship with Mathematics Performance

ERIC Educational Resources Information Center

Bringula, Rex P.; Alvarez, John Nikko; Evangelista, Maron Angelo; So, Richard B.

2017-01-01

This study attempted to determine the effects on mathematics performance of learner-interface interaction with mobile-assisted learning in mathematics. It also determined the relationship between these interactions and students' mathematics performance. It revealed that students solved more complex problems as they went through the intervention…

Transfer of Algebraic and Graphical Thinking between Mathematics and Chemistry

ERIC Educational Resources Information Center

Potgieter, Marietjie; Harding, Ansie; Engelbrecht, Johann

2008-01-01

Students in undergraduate chemistry courses find, as a rule, topics with a strong mathematical basis difficult to master. In this study we investigate whether such mathematically related problems are due to deficiencies in their mathematics foundation or due to the complexity introduced by transfer of mathematics to a new scientific domain. In the…

Restart Operator Meta-heuristics for a Problem-Oriented Evolutionary Strategies Algorithm in Inverse Mathematical MISO Modelling Problem Solving

NASA Astrophysics Data System (ADS)

Ryzhikov, I. S.; Semenkin, E. S.

2017-02-01

This study is focused on solving an inverse mathematical modelling problem for dynamical systems based on observation data and control inputs. The mathematical model is being searched in the form of a linear differential equation, which determines the system with multiple inputs and a single output, and a vector of the initial point coordinates. The described problem is complex and multimodal and for this reason the proposed evolutionary-based optimization technique, which is oriented on a dynamical system identification problem, was applied. To improve its performance an algorithm restart operator was implemented.

Problem Solving in Technology Rich Contexts: Mathematics Sense Making in Out-of-School Environments

ERIC Educational Resources Information Center

Lowrie, Tom

2005-01-01

This investigation describes the way in which a case study participant (aged 7) represented, posed and solved problems in a technology game-based environment. The out-of-school problem-solving context placed numeracy demands on the participant that were more complex and sophisticated than the type of mathematics experiences he encountered in…

A Critical Approach to School Mathematical Knowledge: The Case of "Realistic" Problems in Greek Primary School Textbooks for Seven-Year-Old Pupils

ERIC Educational Resources Information Center

Zacharos, Konstantinos; Koustourakis, Gerassimos

2011-01-01

The reference contexts that accompany the "realistic" problems chosen for teaching mathematical concepts in the first school grades play a major educational role. However, choosing "realistic" problems in teaching is a complex process that must take into account various pedagogical, sociological and psychological parameters.…

Inducing mental set constrains procedural flexibility and conceptual understanding in mathematics.

PubMed

DeCaro, Marci S

2016-10-01

An important goal in mathematics is to flexibly use and apply multiple, efficient procedures to solve problems and to understand why these procedures work. One factor that may limit individuals' ability to notice and flexibly apply strategies is the mental set induced by the problem context. Undergraduate (N = 41, Experiment 1) and fifth- and sixth-grade students (N = 87, Experiment 2) solved mathematical equivalence problems in one of two set-inducing conditions. Participants in the complex-first condition solved problems without a repeated addend on both sides of the equal sign (e.g., 7 + 5 + 9 = 3 + _), which required multistep strategies. Then these students solved problems with a repeated addend (e.g., 7 + 5 + 9 = 7 + _), for which a shortcut strategy could be readily used (i.e., adding 5 + 9). Participants in the shortcut-first condition solved the same problem set but began with the shortcut problems. Consistent with laboratory studies of mental set, participants in the complex-first condition were less likely to use the more efficient shortcut strategy when possible. In addition, these participants were less likely to demonstrate procedural flexibility and conceptual understanding on a subsequent assessment of mathematical equivalence knowledge. These findings suggest that certain problem-solving contexts can help or hinder both flexibility in strategy use and deeper conceptual thinking about the problems.

Word Problem Solving in Contemporary Math Education: A Plea for Reading Comprehension Skills Training

PubMed Central

Boonen, Anton J. H.; de Koning, Björn B.; Jolles, Jelle; van der Schoot, Menno

2016-01-01

Successfully solving mathematical word problems requires both mental representation skills and reading comprehension skills. In Realistic Math Education (RME), however, students primarily learn to apply the first of these skills (i.e., representational skills) in the context of word problem solving. Given this, it seems legitimate to assume that students from a RME curriculum experience difficulties when asked to solve semantically complex word problems. We investigated this assumption under 80 sixth grade students who were classified as successful and less successful word problem solvers based on a standardized mathematics test. To this end, students completed word problems that ask for both mental representation skills and reading comprehension skills. The results showed that even successful word problem solvers had a low performance on semantically complex word problems, despite adequate performance on semantically less complex word problems. Based on this study, we concluded that reading comprehension skills should be given a (more) prominent role during word problem solving instruction in RME. PMID:26925012

Word Problem Solving in Contemporary Math Education: A Plea for Reading Comprehension Skills Training.

PubMed

Boonen, Anton J H; de Koning, Björn B; Jolles, Jelle; van der Schoot, Menno

2016-01-01

Successfully solving mathematical word problems requires both mental representation skills and reading comprehension skills. In Realistic Math Education (RME), however, students primarily learn to apply the first of these skills (i.e., representational skills) in the context of word problem solving. Given this, it seems legitimate to assume that students from a RME curriculum experience difficulties when asked to solve semantically complex word problems. We investigated this assumption under 80 sixth grade students who were classified as successful and less successful word problem solvers based on a standardized mathematics test. To this end, students completed word problems that ask for both mental representation skills and reading comprehension skills. The results showed that even successful word problem solvers had a low performance on semantically complex word problems, despite adequate performance on semantically less complex word problems. Based on this study, we concluded that reading comprehension skills should be given a (more) prominent role during word problem solving instruction in RME.

A Conceptual Approach to Absolute Value Equations and Inequalities

ERIC Educational Resources Information Center

Ellis, Mark W.; Bryson, Janet L.

2011-01-01

The absolute value learning objective in high school mathematics requires students to solve far more complex absolute value equations and inequalities. When absolute value problems become more complex, students often do not have sufficient conceptual understanding to make any sense of what is happening mathematically. The authors suggest that the…

Posing Complex Problems Requiring Multiplicative Thinking Prompts Students to Use Sophisticated Strategies and Build Mathematical Connections

ERIC Educational Resources Information Center

Downton, Ann; Sullivan, Peter

2017-01-01

While the general planning advice offered to mathematics teachers seems to be to start with simple examples and build complexity progressively, the research reported in this article is a contribution to the body of literature that argues the reverse. That is, posing of appropriately complex tasks may actually prompt the use of more sophisticated…

Predicting Development of Mathematical Word Problem Solving Across the Intermediate Grades

PubMed Central

Tolar, Tammy D.; Fuchs, Lynn; Cirino, Paul T.; Fuchs, Douglas; Hamlett, Carol L.; Fletcher, Jack M.

2012-01-01

This study addressed predictors of the development of word problem solving (WPS) across the intermediate grades. At beginning of 3rd grade, 4 cohorts of students (N = 261) were measured on computation, language, nonverbal reasoning skills, and attentive behavior and were assessed 4 times from beginning of 3rd through end of 5th grade on 2 measures of WPS at low and high levels of complexity. Language skills were related to initial performance at both levels of complexity and did not predict growth at either level. Computational skills had an effect on initial performance in low- but not high-complexity problems and did not predict growth at either level of complexity. Attentive behavior did not predict initial performance but did predict growth in low-complexity, whereas it predicted initial performance but not growth for high-complexity problems. Nonverbal reasoning predicted initial performance and growth for low-complexity WPS, but only growth for high-complexity WPS. This evidence suggests that although mathematical structure is fixed, different cognitive resources may act as limiting factors in WPS development when the WPS context is varied. PMID:23325985

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.

Shifting more than the goal posts: developing classroom norms of inquiry-based learning in mathematics

NASA Astrophysics Data System (ADS)

Makar, Katie; Fielding-Wells, Jill

2018-03-01

The 3-year study described in this paper aims to create new knowledge about inquiry norms in primary mathematics classrooms. Mathematical inquiry addresses complex problems that contain ambiguities, yet classroom environments often do not adopt norms that promote curiosity, risk-taking and negotiation needed to productively engage with complex problems. Little is known about how teachers and students initiate, develop and maintain norms of mathematical inquiry in primary classrooms. The research question guiding this study is, "How do classroom norms develop that facilitate student learning in primary classrooms which practice mathematical inquiry?" The project will (1) analyse a video archive of inquiry lessons to identify signature practices that enhance productive classroom norms of mathematical inquiry and facilitate learning, (2) engage expert inquiry teachers to collaborate to identify and design strategies for assisting teachers to develop and sustain norms over time that are conducive to mathematical inquiry and (3) support and study teachers new to mathematical inquiry adopting these practices in their classrooms. Anticipated outcomes include identification and illustration of classroom norms of mathematical inquiry, signature practices linked to these norms and case studies of primary teachers' progressive development of classroom norms of mathematical inquiry and how they facilitate learning.

6 Essential Questions for Problem Solving

ERIC Educational Resources Information Center

Kress, Nancy Emerson

2017-01-01

One of the primary expectations that the author has for her students is for them to develop greater independence when solving complex and unique mathematical problems. The story of how the author supports her students as they gain confidence and independence with complex and unique problem-solving tasks, while honoring their expectations with…

Exploring Gender Differences in Solving Open-Ended Mathematical Problems.

ERIC Educational Resources Information Center

Cai, Jinfa

Open-ended tasks were used to examine gender differences in complex mathematical problem solving. The results of this study suggest that, overall, males perform better than females, but the gender differences vary from task to task. A qualitative analysis of student responses to those tasks with gender differences showed that male and female…

The Power of Numbers. A Teacher's Guide to Mathematics in a Social Studies Context. An Interdisciplinary Curriculum.

ERIC Educational Resources Information Center

Gross, Fred E.; And Others

This document is the teacher's guide for a curriculum designed to teach mathematics in a social studies context. It provides mathematical experiences in real world contexts that help students interpret, experiment, communicate, and look for multiple solutions to complex problems. The curriculum uses mathematics in context to help students develop…

Mexican high school students' social representations of mathematics, its teaching and learning

NASA Astrophysics Data System (ADS)

Martínez-Sierra, Gustavo; Miranda-Tirado, Marisa

2015-07-01

This paper reports a qualitative research that identifies Mexican high school students' social representations of mathematics. For this purpose, the social representations of 'mathematics', 'learning mathematics' and 'teaching mathematics' were identified in a group of 50 students. Focus group interviews were carried out in order to obtain the data. The constant comparative style was the strategy used for the data analysis because it allowed the categories to emerge from the data. The students' social representations are: (A) Mathematics is…(1) important for daily life, (2) important for careers and for life, (3) important because it is in everything that surrounds us, (4) a way to solve problems of daily life, (5) calculations and operations with numbers, (6) complex and difficult, (7) exact and (6) a subject that develops thinking skills; (B) To learn mathematics is…(1) to possess knowledge to solve problems, (2) to be able to solve everyday problems, (3) to be able to make calculations and operations, and (4) to think logically to be able to solve problems; and (C) To teach mathematics is…(1) to transmit knowledge, (2) to know to share it, (3) to transmit the reasoning ability, and (4) to show how to solve problems.

Mathematics, anxiety, and the brain.

PubMed

Moustafa, Ahmed A; Tindle, Richard; Ansari, Zaheda; Doyle, Margery J; Hewedi, Doaa H; Eissa, Abeer

2017-05-24

Given that achievement in learning mathematics at school correlates with work and social achievements, it is important to understand the cognitive processes underlying abilities to learn mathematics efficiently as well as reasons underlying the occurrence of mathematics anxiety (i.e. feelings of tension and fear upon facing mathematical problems or numbers) among certain individuals. Over the last two decades, many studies have shown that learning mathematical and numerical concepts relies on many cognitive processes, including working memory, spatial skills, and linguistic abilities. In this review, we discuss the relationship between mathematical learning and cognitive processes as well as the neural substrates underlying successful mathematical learning and problem solving. More importantly, we also discuss the relationship between these cognitive processes, mathematics anxiety, and mathematics learning disabilities (dyscalculia). Our review shows that mathematical cognition relies on a complex brain network, and dysfunction to different segments of this network leads to varying manifestations of mathematical learning disabilities.

Dannie Heineman Prize for Mathematical Physics: Applying mathematical techniques to solve important problems in quantum theory

NASA Astrophysics Data System (ADS)

Bender, Carl

2017-01-01

The theory of complex variables is extremely useful because it helps to explain the mathematical behavior of functions of a real variable. Complex variable theory also provides insight into the nature of physical theories. For example, it provides a simple and beautiful picture of quantization and it explains the underlying reason for the divergence of perturbation theory. By using complex-variable methods one can generalize conventional Hermitian quantum theories into the complex domain. The result is a new class of parity-time-symmetric (PT-symmetric) theories whose remarkable physical properties have been studied and verified in many recent laboratory experiments.

Biological system interactions.

PubMed Central

Adomian, G; Adomian, G E; Bellman, R E

1984-01-01

Mathematical modeling of cellular population growth, interconnected subsystems of the body, blood flow, and numerous other complex biological systems problems involves nonlinearities and generally randomness as well. Such problems have been dealt with by mathematical methods often changing the actual model to make it tractable. The method presented in this paper (and referenced works) allows much more physically realistic solutions. PMID:6585837

Where Are the Quadratic's Complex Roots?

ERIC Educational Resources Information Center

Páll-Szabó, Ágnes Orsolya

2015-01-01

A picture is worth more than a thousand words--in mathematics too. Many students fail in learning mathematics because, in some cases, teachers do not offer the necessary visualization. Nowadays technology overcomes this problem: computer aided instruction is one of the most efficients methods in teaching mathematics. In this article we try to…

A New Approach to Teaching Business Oriented Students.

ERIC Educational Resources Information Center

Merchant, Ronald

1980-01-01

Describes a competency based business mathematics course offered at Spokane Falls Community College (Washington) in which students, through the use of calculators, master mathematical concepts without having to mentally add columns of figures or perform complex arithmetic problems on paper. Examines both the mathematical and 10-key skills…

Conceptual Complexity and Apparent Contradictions in Mathematics Language

ERIC Educational Resources Information Center

Gough, John

2007-01-01

Mathematics is like a language, although technically it is not a natural or informal human language, but a formal, that is, artificially constructed language. Importantly, educators use their natural everyday language to teach the formal language of mathematics. At times, however, instructors encounter problems when the technical words they use,…

Using Mental Computation Training to Improve Complex Mathematical Performance

ERIC Educational Resources Information Center

Liu, Allison S.; Kallai, Arava Y.; Schunn, Christian D.; Fiez, Julie A.

2015-01-01

Mathematical fluency is important for academic and mathematical success. Fluency training programs have typically focused on fostering retrieval, which leads to math performance that does not reliably transfer to non-trained problems. More recent studies have focused on training number understanding and representational precision, but few have…

A Guided Tour of Mathematical Methods - 2nd Edition

NASA Astrophysics Data System (ADS)

Snieder, Roel

2004-09-01

Mathematical methods are essential tools for all physical scientists. This second edition provides a comprehensive tour of the mathematical knowledge and techniques that are needed by students in this area. In contrast to more traditional textbooks, all the material is presented in the form of problems. Within these problems the basic mathematical theory and its physical applications are well integrated. The mathematical insights that the student acquires are therefore driven by their physical insight. Topics that are covered include vector calculus, linear algebra, Fourier analysis, scale analysis, complex integration, Green's functions, normal modes, tensor calculus, and perturbation theory. The second edition contains new chapters on dimensional analysis, variational calculus, and the asymptotic evaluation of integrals. This book can be used by undergraduates, and lower-level graduate students in the physical sciences. It can serve as a stand-alone text, or as a source of problems and examples to complement other textbooks. All the material is presented in the form of problems Mathematical insights are gained by getting the reader to develop answers themselves Many applications of the mathematics are given

The Social Essentials of Learning: An Experimental Investigation of Collaborative Problem Solving and Knowledge Construction in Mathematics Classrooms in Australia and China

ERIC Educational Resources Information Center

Chan, Man Ching Esther; Clarke, David; Cao, Yiming

2018-01-01

Interactive problem solving and learning are priorities in contemporary education, but these complex processes have proved difficult to research. This project addresses the question "How do we optimise social interaction for the promotion of learning in a mathematics classroom?" Employing the logic of multi-theoretic research design,…

Jabberwocky: The Complexities of Mathematical English

ERIC Educational Resources Information Center

Carter, Merilyn; Quinnell, Lorna

2012-01-01

Students find it hard to interpret mathematical problem texts. Mathematics is a unique language with its own symbols (grapho-phonics), vocabulary (lexicon), grammar (syntax), semantics and literature. As in any other language, to make meaning of the text, the student must learn: (1) signs and symbols (for example: [division], x, [not equal to]);…

Optimization of controlled processes in combined-cycle plant (new developments and researches)

NASA Astrophysics Data System (ADS)

Tverskoy, Yu S.; Muravev, I. K.

2017-11-01

All modern complex technical systems, including power units of TPP and nuclear power plants, work in the system-forming structure of multifunctional APCS. The development of the modern APCS mathematical support allows bringing the automation degree to the solution of complex optimization problems of equipment heat-mass-exchange processes in real time. The difficulty of efficient management of a binary power unit is related to the need to solve jointly at least three problems. The first problem is related to the physical issues of combined-cycle technologies. The second problem is determined by the criticality of the CCGT operation to changes in the regime and climatic factors. The third problem is related to a precise description of a vector of controlled coordinates of a complex technological object. To obtain a joint solution of this complex of interconnected problems, the methodology of generalized thermodynamic analysis, methods of the theory of automatic control and mathematical modeling are used. In the present report, results of new developments and studies are shown. These results allow improving the principles of process control and the automatic control systems structural synthesis of power units with combined-cycle plants that provide attainable technical and economic efficiency and operational reliability of equipment.

Teaching Pre-Service Teachers to Make Digital Stories That Explain Complex Mathematical Concepts in a Real-World Context: The "Math-eo" Project, Creating "Cool New Tools"

ERIC Educational Resources Information Center

Walters, Lynne Masel; Green, Martha R.; Goldsby, Dianne; Walters, Timothy N.; Wang, Liangyan

2016-01-01

This mixed methods study examines whether engaging in a problem-solving project to create Math-eos (digital videos) increases pre-service teachers' understanding of the relationship between visual, auditory, and verbal representation and critical thinking in mathematics. Additionally, the study looks at what aspects of a digital problem solving…

Shifting More than the Goal Posts: Developing Classroom Norms of Inquiry-Based Learning in Mathematics

ERIC Educational Resources Information Center

Makar, Katie; Fielding-Wells, Jill

2018-01-01

The 3-year study described in this paper aims to create new knowledge about inquiry norms in primary mathematics classrooms. Mathematical inquiry addresses complex problems that contain ambiguities, yet classroom environments often do not adopt norms that promote curiosity, risk-taking and negotiation needed to productively engage with complex…

Envisioning migration: Mathematics in both experimental analysis and modeling of cell behavior

PubMed Central

Zhang, Elizabeth R.; Wu, Lani F.; Altschuler, Steven J.

2013-01-01

The complex nature of cell migration highlights the power and challenges of applying mathematics to biological studies. Mathematics may be used to create model equations that recapitulate migration, which can predict phenomena not easily uncovered by experiments or intuition alone. Alternatively, mathematics may be applied to interpreting complex data sets with better resolution—potentially empowering scientists to discern subtle patterns amid the noise and heterogeneity typical of migrating cells. Iteration between these two methods is necessary in order to reveal connections within the cell migration signaling network, as well as to understand the behavior that arises from those connections. Here, we review recent quantitative analysis and mathematical modeling approaches to the cell migration problem. PMID:23660413

Envisioning migration: mathematics in both experimental analysis and modeling of cell behavior.

PubMed

Zhang, Elizabeth R; Wu, Lani F; Altschuler, Steven J

2013-10-01

The complex nature of cell migration highlights the power and challenges of applying mathematics to biological studies. Mathematics may be used to create model equations that recapitulate migration, which can predict phenomena not easily uncovered by experiments or intuition alone. Alternatively, mathematics may be applied to interpreting complex data sets with better resolution--potentially empowering scientists to discern subtle patterns amid the noise and heterogeneity typical of migrating cells. Iteration between these two methods is necessary in order to reveal connections within the cell migration signaling network, as well as to understand the behavior that arises from those connections. Here, we review recent quantitative analysis and mathematical modeling approaches to the cell migration problem. Copyright © 2013 Elsevier Ltd. All rights reserved.

Aspects of job scheduling

NASA Technical Reports Server (NTRS)

Phillips, K.

1976-01-01

A mathematical model for job scheduling in a specified context is presented. The model uses both linear programming and combinatorial methods. While designed with a view toward optimization of scheduling of facility and plant operations at the Deep Space Communications Complex, the context is sufficiently general to be widely applicable. The general scheduling problem including options for scheduling objectives is discussed and fundamental parameters identified. Mathematical algorithms for partitioning problems germane to scheduling are presented.

Translating concepts of complexity to the field of ergonomics.

PubMed

Walker, Guy H; Stanton, Neville A; Salmon, Paul M; Jenkins, Daniel P; Rafferty, Laura

2010-10-01

Since 1958 more than 80 journal papers from the mainstream ergonomics literature have used either the words 'complex' or 'complexity' in their titles. Of those, more than 90% have been published in only the past 20 years. This observation communicates something interesting about the way in which contemporary ergonomics problems are being understood. The study of complexity itself derives from non-linear mathematics but many of its core concepts have found analogies in numerous non-mathematical domains. Set against this cross-disciplinary background, the current paper aims to provide a similar initial mapping to the field of ergonomics. In it, the ergonomics problem space, complexity metrics and powerful concepts such as emergence raise complexity to the status of an important contingency factor in achieving a match between ergonomics problems and ergonomics methods. The concept of relative predictive efficiency is used to illustrate how this match could be achieved in practice. What is clear overall is that a major source of, and solution to, complexity are the humans in systems. Understanding complexity on its own terms offers the potential to leverage disproportionate effects from ergonomics interventions and to tighten up the often loose usage of the term in the titles of ergonomics papers. STATEMENT OF RELEVANCE: This paper reviews and discusses concepts from the study of complexity and maps them to ergonomics problems and methods. It concludes that humans are a major source of and solution to complexity in systems and that complexity is a powerful contingency factor, which should be considered to ensure that ergonomics approaches match the true nature of ergonomics problems.

Methodology and Results of Mathematical Modelling of Complex Technological Processes

NASA Astrophysics Data System (ADS)

Mokrova, Nataliya V.

2018-03-01

The methodology of system analysis allows us to draw a mathematical model of the complex technological process. The mathematical description of the plasma-chemical process was proposed. The importance the quenching rate and initial temperature decrease time was confirmed for producing the maximum amount of the target product. The results of numerical integration of the system of differential equations can be used to describe reagent concentrations, plasma jet rate and temperature in order to achieve optimal mode of hardening. Such models are applicable both for solving control problems and predicting future states of sophisticated technological systems.

A Skyscraping Feat

ERIC Educational Resources Information Center

Roberts, Sarah A.; Lee, Jean S.

2013-01-01

Research shows that the greatest gains in student learning in mathematics classrooms occur in classrooms in which there is sustained use of high cognitive demanding tasks throughout instruction (Boston and Smith 2009). High cognitive demanding tasks, which this article will refer to as rich tasks, are mathematics problems that are complex, less…

A brief history of the most remarkable numbers e, i and γ in mathematical sciences with applications

NASA Astrophysics Data System (ADS)

Debnath, Lokenath

2015-08-01

This paper deals with a brief history of the most remarkable Euler numbers e, i and γ in mathematical sciences. Included are many properties of the constants e, i and γ and their applications in algebra, geometry, physics, chemistry, ecology, business and industry. Special attention is given to the growth and decay phenomena in many real-world problems including stability and instability of their solutions. Some specific and modern applications of logarithms, complex numbers and complex exponential functions to electrical circuits and mechanical systems are presented with examples. Included are the use of complex numbers and complex functions in the description and analysis of chaos and fractals with the aid of modern computer technology. In addition, the phasor method is described with examples of applications in engineering science. The major focus of this paper is to provide basic information through historical approach to mathematics teaching and learning of the fundamental knowledge and skills required for students and teachers at all levels so that they can understand the concepts of mathematics, and mathematics education in science and technology.

Multi-Party, Whole-Body Interactions in Mathematical Activity

ERIC Educational Resources Information Center

Ma, Jasmine Y.

2017-01-01

This study interrogates the contributions of multi-party, whole-body interactions to students' collaboration and negotiation of mathematics ideas in a task setting called walking scale geometry, where bodies in interaction became complex resources for students' emerging goals in problem solving. Whole bodies took up overlapping roles representing…

Combining fuzzy mathematics with fuzzy logic to solve business management problems

NASA Astrophysics Data System (ADS)

Vrba, Joseph A.

1993-12-01

Fuzzy logic technology has been applied to control problems with great success. Because of this, many observers fell that fuzzy logic is applicable only in the control arena. However, business management problems almost never deal with crisp values. Fuzzy systems technology--a combination of fuzzy logic, fuzzy mathematics and a graphical user interface--is a natural fit for developing software to assist in typical business activities such as planning, modeling and estimating. This presentation discusses how fuzzy logic systems can be extended through the application of fuzzy mathematics and the use of a graphical user interface to make the information contained in fuzzy numbers accessible to business managers. As demonstrated through examples from actual deployed systems, this fuzzy systems technology has been employed successfully to provide solutions to the complex real-world problems found in the business environment.

A transformative model for undergraduate quantitative biology education.

PubMed

Usher, David C; Driscoll, Tobin A; Dhurjati, Prasad; Pelesko, John A; Rossi, Louis F; Schleiniger, Gilberto; Pusecker, Kathleen; White, Harold B

2010-01-01

The BIO2010 report recommended that students in the life sciences receive a more rigorous education in mathematics and physical sciences. The University of Delaware approached this problem by (1) developing a bio-calculus section of a standard calculus course, (2) embedding quantitative activities into existing biology courses, and (3) creating a new interdisciplinary major, quantitative biology, designed for students interested in solving complex biological problems using advanced mathematical approaches. To develop the bio-calculus sections, the Department of Mathematical Sciences revised its three-semester calculus sequence to include differential equations in the first semester and, rather than using examples traditionally drawn from application domains that are most relevant to engineers, drew models and examples heavily from the life sciences. The curriculum of the B.S. degree in Quantitative Biology was designed to provide students with a solid foundation in biology, chemistry, and mathematics, with an emphasis on preparation for research careers in life sciences. Students in the program take core courses from biology, chemistry, and physics, though mathematics, as the cornerstone of all quantitative sciences, is given particular prominence. Seminars and a capstone course stress how the interplay of mathematics and biology can be used to explain complex biological systems. To initiate these academic changes required the identification of barriers and the implementation of solutions.

A Transformative Model for Undergraduate Quantitative Biology Education

PubMed Central

Driscoll, Tobin A.; Dhurjati, Prasad; Pelesko, John A.; Rossi, Louis F.; Schleiniger, Gilberto; Pusecker, Kathleen; White, Harold B.

2010-01-01

The BIO2010 report recommended that students in the life sciences receive a more rigorous education in mathematics and physical sciences. The University of Delaware approached this problem by (1) developing a bio-calculus section of a standard calculus course, (2) embedding quantitative activities into existing biology courses, and (3) creating a new interdisciplinary major, quantitative biology, designed for students interested in solving complex biological problems using advanced mathematical approaches. To develop the bio-calculus sections, the Department of Mathematical Sciences revised its three-semester calculus sequence to include differential equations in the first semester and, rather than using examples traditionally drawn from application domains that are most relevant to engineers, drew models and examples heavily from the life sciences. The curriculum of the B.S. degree in Quantitative Biology was designed to provide students with a solid foundation in biology, chemistry, and mathematics, with an emphasis on preparation for research careers in life sciences. Students in the program take core courses from biology, chemistry, and physics, though mathematics, as the cornerstone of all quantitative sciences, is given particular prominence. Seminars and a capstone course stress how the interplay of mathematics and biology can be used to explain complex biological systems. To initiate these academic changes required the identification of barriers and the implementation of solutions. PMID:20810949

Analysis of students’ mathematical reasoning

NASA Astrophysics Data System (ADS)

Sukirwan; Darhim; Herman, T.

2018-01-01

The reasoning is one of the mathematical abilities that have very complex implications. This complexity causes reasoning including abilities that are not easily attainable by students. Similarly, studies dealing with reason are quite diverse, primarily concerned with the quality of mathematical reasoning. The objective of this study was to determine the quality of mathematical reasoning based perspective Lithner. Lithner looked at how the environment affects the mathematical reasoning. In this regard, Lithner made two perspectives, namely imitative reasoning and creative reasoning. Imitative reasoning can be memorized and algorithmic reasoning. The Result study shows that although the students generally still have problems in reasoning. Students tend to be on imitative reasoning which means that students tend to use a routine procedure when dealing with reasoning. It is also shown that the traditional approach still dominates on the situation of students’ daily learning.

Teaching Reductive Thinking

ERIC Educational Resources Information Center

Armoni, Michal; Gal-Ezer, Judith

2005-01-01

When dealing with a complex problem, solving it by reduction to simpler problems, or problems for which the solution is already known, is a common method in mathematics and other scientific disciplines, as in computer science and, specifically, in the field of computability. However, when teaching computational models (as part of computability)…

Proportional Reasoning in the Learning of Chemistry: Levels of Complexity

ERIC Educational Resources Information Center

Ramful, Ajay; Narod, Fawzia Bibi

2014-01-01

This interdisciplinary study sketches the ways in which proportional reasoning is involved in the solution of chemistry problems, more specifically, problems involving quantities in chemical reactions (commonly referred to as stoichiometry problems). By building on the expertise of both mathematics and chemistry education research, the present…

Algebraic Functions, Computer Programming, and the Challenge of Transfer

ERIC Educational Resources Information Center

Schanzer, Emmanuel Tanenbaum

2015-01-01

Students' struggles with algebra are well documented. Prior to the introduction of functions, mathematics is typically focused on applying a set of arithmetic operations to compute an answer. The introduction of functions, however, marks the point at which mathematics begins to focus on building up abstractions as a way to solve complex problems.…

From Poor Performance to Success under Stress: Working Memory, Strategy Selection, and Mathematical Problem Solving under Pressure

ERIC Educational Resources Information Center

Beilock, Sian L.; DeCaro, Marci S.

2007-01-01

Two experiments demonstrate how individual differences in working memory (WM) impact the strategies used to solve complex math problems and how consequential testing situations alter strategy use. In Experiment 1, individuals performed multistep math problems under low- or high-pressure conditions and reported their problem-solving strategies.…

Are Middle School Mathematics Teachers Able to Solve Word Problems without Using Variable?

ERIC Educational Resources Information Center

Gökkurt Özdemir, Burçin; Erdem, Emrullah; Örnek, Tugba; Soylu, Yasin

2018-01-01

Many people consider problem solving as a complex process in which variables such as "x," "y" are used. Problems may not be solved by only using "variable." Problem solving can be rationalized and made easier using practical strategies. When especially the development of children at younger ages is considered, it is…

Mathematical concepts for modeling human behavior in complex man-machine systems

NASA Technical Reports Server (NTRS)

Johannsen, G.; Rouse, W. B.

1979-01-01

Many human behavior (e.g., manual control) models have been found to be inadequate for describing processes in certain real complex man-machine systems. An attempt is made to find a way to overcome this problem by examining the range of applicability of existing mathematical models with respect to the hierarchy of human activities in real complex tasks. Automobile driving is chosen as a baseline scenario, and a hierarchy of human activities is derived by analyzing this task in general terms. A structural description leads to a block diagram and a time-sharing computer analogy.

Cognitive Complexity of Mathematics Instructional Tasks in a Taiwanese Classroom: An Examination of Task Sources

ERIC Educational Resources Information Center

Hsu, Hui-Yu; Silver, Edward A.

2014-01-01

We examined geometric calculation with number tasks used within a unit of geometry instruction in a Taiwanese classroom, identifying the source of each task used in classroom instruction and analyzing the cognitive complexity of each task with respect to 2 distinct features: diagram complexity and problem-solving complexity. We found that…

Are middle school mathematics teachers able to solve word problems without using variable?

NASA Astrophysics Data System (ADS)

Gökkurt Özdemir, Burçin; Erdem, Emrullah; Örnek, Tuğba; Soylu, Yasin

2018-01-01

Many people consider problem solving as a complex process in which variables such as x, y are used. Problems may not be solved by only using 'variable.' Problem solving can be rationalized and made easier using practical strategies. When especially the development of children at younger ages is considered, it is obvious that mathematics teachers should solve problems through concrete processes. In this context, middle school mathematics teachers' skills to solve word problems without using variables were examined in the current study. Through the case study method, this study was conducted with 60 middle school mathematics teachers who have different professional experiences in five provinces in Turkey. A test consisting of five open-ended word problems was used as the data collection tool. The content analysis technique was used to analyze the data. As a result of the analysis, it was seen that the most of the teachers used trial-and-error strategy or area model as the solution strategy. On the other hand, the teachers who solved the problems using variables such as x, a, n or symbols such as Δ, □, ○, * and who also felt into error by considering these solutions as without variable were also seen in the study.

The complexity of proving chaoticity and the Church-Turing thesis

NASA Astrophysics Data System (ADS)

Calude, Cristian S.; Calude, Elena; Svozil, Karl

2010-09-01

Proving the chaoticity of some dynamical systems is equivalent to solving the hardest problems in mathematics. Conversely, classical physical systems may "compute the hard or even the incomputable" by measuring observables which correspond to computationally hard or even incomputable problems.

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.

Word problems: a review of linguistic and numerical factors contributing to their difficulty

PubMed Central

Daroczy, Gabriella; Wolska, Magdalena; Meurers, Walt Detmar; Nuerk, Hans-Christoph

2015-01-01

Word problems (WPs) belong to the most difficult and complex problem types that pupils encounter during their elementary-level mathematical development. In the classroom setting, they are often viewed as merely arithmetic tasks; however, recent research shows that a number of linguistic verbal components not directly related to arithmetic contribute greatly to their difficulty. In this review, we will distinguish three components of WP difficulty: (i) the linguistic complexity of the problem text itself, (ii) the numerical complexity of the arithmetic problem, and (iii) the relation between the linguistic and numerical complexity of a problem. We will discuss the impact of each of these factors on WP difficulty and motivate the need for a high degree of control in stimuli design for experiments that manipulate WP difficulty for a given age group. PMID:25883575

Translating across Macroscopic, Submicroscopic, and Symbolic Levels: The Role of Instructor Facilitation in an Inquiry-Oriented Physical Chemistry Class

ERIC Educational Resources Information Center

Becker, Nicole; Stanford, Courtney; Towns, Marcy; Cole, Renee

2015-01-01

In physical chemistry classrooms, mathematical and graphical representations are critical tools for reasoning about chemical phenomena. However, there is abundant evidence that to be successful in understanding complex thermodynamics topics, students must go beyond rote mathematical problem solving in order to connect their understanding of…

Integration of Digital Technology and Innovative Strategies for Learning and Teaching Large Classes: A Calculus Case Study

ERIC Educational Resources Information Center

Vajravelu, Kuppalapalle; Muhs, Tammy

2016-01-01

Successful science and engineering programs require proficiency and dynamics in mathematics classes to enhance the learning of complex subject matter with a sufficient amount of practical problem solving. Improving student performance and retention in mathematics classes requires inventive approaches. At the University of Central Florida (UCF) the…

When Districts Encounter Teacher Shortages: The Challenges of Recruiting and Retaining Mathematics Teachers in Urban Districts

ERIC Educational Resources Information Center

Liu, Edward; Rosenstein, Joseph G.; Swan, Aubrie E.; Khalil, Deena

2008-01-01

Administrators in six urban districts were interviewed to understand the nature and extent of their problems with recruiting and retaining high quality mathematics teachers. Findings suggest that the math staffing challenge is quite complex, and administrators have had to make difficult compromises because of deficiencies in the quantity and…

Learning biology through connecting mathematics to scientific mechanisms: Student outcomes and teacher supports

NASA Astrophysics Data System (ADS)

Schuchardt, Anita

Integrating mathematics into science classrooms has been part of the conversation in science education for a long time. However, studies on student learning after incorporating mathematics in to the science classroom have shown mixed results. Understanding the mixed effects of including mathematics in science has been hindered by a historical focus on characteristics of integration tangential to student learning (e.g., shared elements, extent of integration). A new framework is presented emphasizing the epistemic role of mathematics in science. An epistemic role of mathematics missing from the current literature is identified: use of mathematics to represent scientific mechanisms, Mechanism Connected Mathematics (MCM). Building on prior theoretical work, it is proposed that having students develop mathematical equations that represent scientific mechanisms could elevate their conceptual understanding and quantitative problem solving. Following design and implementation of an MCM unit in inheritance, a large-scale quantitative analysis of pre and post implementation test results showed MCM students, compared to traditionally instructed students) had significantly greater gains in conceptual understanding of mathematically modeled scientific mechanisms, and their ability to solve complex quantitative problems. To gain insight into the mechanism behind the gain in quantitative problem solving, a small-scale qualitative study was conducted of two contrasting groups: 1) within-MCM instruction: competent versus struggling problem solvers, and 2) within-competent problem solvers: MCM instructed versus traditionally instructed. Competent MCM students tended to connect their mathematical inscriptions to the scientific phenomenon and to switch between mathematical and scientifically productive approaches during problem solving in potentially productive ways. The other two groups did not. To address concerns about teacher capacity presenting barriers to scalability of MCM approaches, the types and amount of teacher support needed to achieve these types of student learning gains were investigated. In the context of providing teachers with access to educative materials, students achieved learning gains in both areas in the absence of face-to-face teacher professional development. However, maximal student learning gains required the investment of face-to-face professional development. This finding can govern distribution of scarce resources, but does not preclude implementation of MCM instruction even where resource availability does not allow for face-to-face professional development.

Geometric Series: A New Solution to the Dog Problem

ERIC Educational Resources Information Center

Dion, Peter; Ho, Anthony

2013-01-01

This article describes what is often referred to as the dog, beetle, mice, ant, or turtle problem. Solutions to this problem exist, some being variations of each other, which involve mathematics of a wide range of complexity. Herein, the authors describe the intuitive solution and the calculus solution and then offer a completely new solution…

The Teaching of Creativity in Information Systems Programmes at South African Higher Education Institutions

ERIC Educational Resources Information Center

Turpin, Marita; Matthee, Machdel; Kruger, Anine

2015-01-01

The development of problem solving skills is a shared goal in science, engineering, mathematics and technology education. In the applied sciences, problems are often open-ended and complex, requiring a multidisciplinary approach as well as new designs. In such cases, problem solving requires not only analytical capabilities, but also creativity…

Perceptual learning modules in mathematics: enhancing students' pattern recognition, structure extraction, and fluency.

PubMed

Kellman, Philip J; Massey, Christine M; Son, Ji Y

2010-04-01

Learning in educational settings emphasizes declarative and procedural knowledge. Studies of expertise, however, point to other crucial components of learning, especially improvements produced by experience in the extraction of information: perceptual learning (PL). We suggest that such improvements characterize both simple sensory and complex cognitive, even symbolic, tasks through common processes of discovery and selection. We apply these ideas in the form of perceptual learning modules (PLMs) to mathematics learning. We tested three PLMs, each emphasizing different aspects of complex task performance, in middle and high school mathematics. In the MultiRep PLM, practice in matching function information across multiple representations improved students' abilities to generate correct graphs and equations from word problems. In the Algebraic Transformations PLM, practice in seeing equation structure across transformations (but not solving equations) led to dramatic improvements in the speed of equation solving. In the Linear Measurement PLM, interactive trials involving extraction of information about units and lengths produced successful transfer to novel measurement problems and fraction problem solving. Taken together, these results suggest (a) that PL techniques have the potential to address crucial, neglected dimensions of learning, including discovery and fluent processing of relations; (b) PL effects apply even to complex tasks that involve symbolic processing; and (c) appropriately designed PL technology can produce rapid and enduring advances in learning. Copyright © 2009 Cognitive Science Society, Inc.

Computer Systems for Teaching Complex Concepts.

ERIC Educational Resources Information Center

Feurzeig, Wallace

Four Programing systems--Mentor, Stringcomp, Simon, and Logo--were designed and implemented as integral parts of research into the various ways computers may be used for teaching problem-solving concepts and skills. Various instructional contexts, among them medicine, mathematics, physics, and basic problem-solving for elementary school children,…

Applied mathematical problems in modern electromagnetics

NASA Astrophysics Data System (ADS)

Kriegsman, Gregory

1994-05-01

We have primarily investigated two classes of electromagnetic problems. The first contains the quantitative description of microwave heating of dispersive and conductive materials. Such problems arise, for example, when biological tissue are exposed, accidentally or purposefully, to microwave radiation. Other instances occur in ceramic processing, such as sintering and microwave assisted chemical vapor infiltration and other industrial drying processes, such as the curing of paints and concrete. The second class characterizes the scattering of microwaves by complex targets which possess two or more disparate length and/or time scales. Spatially complex scatterers arise in a variety of applications, such as large gratings and slowly changing guiding structures. The former are useful in developing microstrip energy couplers while the later can be used to model anatomical subsystems (e.g., the open guiding structure composed of two legs and the adjoining lower torso). Temporally complex targets occur in applications involving dispersive media whose relaxation times differ by orders of magnitude from thermal and/or electromagnetic time scales. For both cases the mathematical description of the problems gives rise to complicated ill-conditioned boundary value problems, whose accurate solutions require a blend of both asymptotic techniques, such as multiscale methods and matched asymptotic expansions, and numerical methods incorporating radiation boundary conditions, such as finite differences and finite elements.

Overview of Aro Program on Network Science for Human Decision Making

NASA Astrophysics Data System (ADS)

West, Bruce J.

This program brings together researchers from disparate disciplines to work on a complex research problem that defies confinement within any single discipline. Consequently, not only are new and rewarding solutions sought and obtained for a problem of importance to society and the Army, that is, the human dimension of complex networks, but, in addition, collaborations are established that would not otherwise have formed given the traditional disciplinary compartmentalization of research. This program develops the basic research foundation of a science of networks supporting the linkage between the physical and human (cognitive and social) domains as they relate to human decision making. The strategy is to extend the recent methods of non-equilibrium statistical physics to non-stationary, renewal stochastic processes that appear to be characteristic of the interactions among nodes in complex networks. We also pursue understanding of the phenomenon of synchronization, whose mathematical formulation has recently provided insight into how complex networks reach accommodation and cooperation. The theoretical analyses of complex networks, although mathematically rigorous, often elude analytic solutions and require computer simulation and computation to analyze the underlying dynamic process.

A Cognition Analysis of QUASAR's Mathematics Performance Assessment Tasks and Their Sensitivity to Measuring Changes in Middle School Students' Thinking and Reasoning.

ERIC Educational Resources Information Center

Cai, Jinfa, And Others

1996-01-01

Presents a conceptual framework for analyzing students' mathematical understanding, reasoning, problem solving, and communication. Analyses of student responses indicated that the tasks appear to measure the complex thinking and reasoning processes that they were designed to assess. Concludes that the QUASAR assessment tasks can capture changes in…

Novel Image Quality Control Systems(Add-On). Innovative Computational Methods for Inverse Problems in Optical and SAR Imaging

DTIC Science & Technology

2007-02-28

Iterative Ultrasonic Signal and Image Deconvolution for Estimation of the Complex Medium Response, International Journal of Imaging Systems and...1767-1782, 2006. 31. Z. Mu, R. Plemmons, and P. Santago. Iterative Ultrasonic Signal and Image Deconvolution for Estimation of the Complex...rigorous mathematical and computational research on inverse problems in optical imaging of direct interest to the Army and also the intelligence agencies

The Smarties-Box Challenge: Supporting Systematic Approaches to Problem Solving

ERIC Educational Resources Information Center

Russo, James

2016-01-01

The Smarties-Box Challenge encourages students to apply several different mathematical capabilities and concepts--such as, estimation, multiplication, and the notion of being systematic--to solve a complex, multistep problem. To effectively engage in the Smarties-Box Challenge, students are required to demonstrate aspects of all four proficiency…

Bayesian linkage and segregation analysis: factoring the problem.

PubMed

Matthysse, S

2000-01-01

Complex segregation analysis and linkage methods are mathematical techniques for the genetic dissection of complex diseases. They are used to delineate complex modes of familial transmission and to localize putative disease susceptibility loci to specific chromosomal locations. The computational problem of Bayesian linkage and segregation analysis is one of integration in high-dimensional spaces. In this paper, three available techniques for Bayesian linkage and segregation analysis are discussed: Markov Chain Monte Carlo (MCMC), importance sampling, and exact calculation. The contribution of each to the overall integration will be explicitly discussed.

Expanding the Space of Plausible Solutions in a Medical Tutoring System for Problem-Based Learning

ERIC Educational Resources Information Center

Kazi, Hameedullah; Haddawy, Peter; Suebnukarn, Siriwan

2009-01-01

In well-defined domains such as Physics, Mathematics, and Chemistry, solutions to a posed problem can objectively be classified as correct or incorrect. In ill-defined domains such as medicine, the classification of solutions to a patient problem as correct or incorrect is much more complex. Typical tutoring systems accept only a small set of…

Identity: a complex structure for researching students' academic behavior in science and mathematics

NASA Astrophysics Data System (ADS)

Aydeniz, Mehmet; Hodge, Lynn Liao

2011-06-01

This article is a response to Pike and Dunne's research. The focus of their analysis is on reflections of studying science post-16. Pike and Dunne draw attention to under enrollments in science, technology, engineering, and mathematics (STEM) fields, in particular, in the field of physics, chemistry and biology in the United Kingdom. We provide an analysis of how the authors conceptualize the problem of scientific career choices, the theoretical framework through which they study the problem, and the methodology they use to collect and analyze data. In addition, we examine the perspective they provide in light of new developments in the field of students' attitudes towards science and mathematics. More precisely, we draw attention to and explicate the authors' use of identity from the perspective of emerging theories that explore the relationships between the learner and culture in the context of science and mathematics.

Nuclear Deterrence. Applications of Elementary Probability to International Relations. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Unit 327.

ERIC Educational Resources Information Center

Smith, Harvey A.

This module is designed to apply mathematical models to nuclear deterrent problems, and to aid users in developing enlightened skepticism about the use of linear models in stability analyses and long-term predictions. An attempt is made at avoiding overwhelming complexities through concentration on land-based missile forces. It is noted that after…

Combinatorial and Algorithmic Rigidity: Beyond Two Dimensions

DTIC Science & Technology

2012-12-01

problem. Manuscript, 2010. [35] G. Panina and I. Streinu. Flattening single-vertex origami : the non- expansive case. Computational Geometry : Theory and...in 2008, under the DARPA solicitation “Mathemat- ical Challenges, BAA 07-68”. It addressed Mathematical Challenge Ten: Al- gorithmic Origami and...a number of optimal algorithms and provided critical complexity analysis. The topic of algorithmic origami was successfully engaged from the same

Brain organization underlying superior mathematical abilities in children with autism.

PubMed

Iuculano, Teresa; Rosenberg-Lee, Miriam; Supekar, Kaustubh; Lynch, Charles J; Khouzam, Amirah; Phillips, Jennifer; Uddin, Lucina Q; Menon, Vinod

2014-02-01

Autism spectrum disorder (ASD) is a neurodevelopmental disorder characterized by social and communication deficits. While such deficits have been the focus of most research, recent evidence suggests that individuals with ASD may exhibit cognitive strengths in domains such as mathematics. Cognitive assessments and functional brain imaging were used to investigate mathematical abilities in 18 children with ASD and 18 age-, gender-, and IQ-matched typically developing (TD) children. Multivariate classification and regression analyses were used to investigate whether brain activity patterns during numerical problem solving were significantly different between the groups and predictive of individual mathematical abilities. Children with ASD showed better numerical problem solving abilities and relied on sophisticated decomposition strategies for single-digit addition problems more frequently than TD peers. Although children with ASD engaged similar brain areas as TD children, they showed different multivariate activation patterns related to arithmetic problem complexity in ventral temporal-occipital cortex, posterior parietal cortex, and medial temporal lobe. Furthermore, multivariate activation patterns in ventral temporal-occipital cortical areas typically associated with face processing predicted individual numerical problem solving abilities in children with ASD but not in TD children. Our study suggests that superior mathematical information processing in children with ASD is characterized by a unique pattern of brain organization and that cortical regions typically involved in perceptual expertise may be utilized in novel ways in ASD. Our findings of enhanced cognitive and neural resources for mathematics have critical implications for educational, professional, and social outcomes for individuals with this lifelong disorder. Copyright © 2014 Society of Biological Psychiatry. Published by Elsevier Inc. All rights reserved.

Disentangling the effects of working memory, language, parental education, and non-verbal intelligence on children’s mathematical abilities

PubMed Central

Pina, Violeta; Fuentes, Luis J.; Castillo, Alejandro; Diamantopoulou, Sofia

2014-01-01

It is assumed that children’s performance in mathematical abilities is influenced by several factors such as working memory (WM), verbal ability, intelligence, and socioeconomic status. The present study explored the contribution of those factors to mathematical performance taking a componential view of both WM and mathematics. We explored the existing relationship between different WM components (verbal and spatial) with tasks that make differential recruitment of the central executive, and simple and complex mathematical skills in a sample of 102 children in grades 4–6. The main findings point to a relationship between the verbal WM component and complex word arithmetic problems, whereas language and non-verbal intelligence were associated with knowledge of quantitative concepts and arithmetic ability. The spatial WM component was associated with the subtest Series, whereas the verbal component was with the subtest Concepts. The results also suggest a positive relationship between parental educational level and children’s performance on Quantitative Concepts. These findings suggest that specific cognitive skills might be trained in order to improve different aspects of mathematical ability. PMID:24847306

Simulation of a manual electric-arc welding in a working gas pipeline. 1. Formulation of the problem

NASA Astrophysics Data System (ADS)

Baikov, V. I.; Gishkelyuk, I. A.; Rus', A. M.; Sidorovich, T. V.; Tonkonogov, B. A.

2010-11-01

Problems of mathematical simulation of the temperature stresses arising in the wall of a pipe of a cross-country gas pipeline in the process of electric-arc welding of defects in it have been considered. Mathematical models of formation of temperatures, deformations, and stresses in a gas pipe subjected to phase transformations have been developed. These models were numerically realized in the form of algorithms representing a part of an application-program package. Results of verification of the computational complex and calculation results obtained with it are presented.

Topics in geophysical fluid dynamics: Atmospheric dynamics, dynamo theory, and climate dynamics

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

Ghil, M.; Childress, S.

1987-01-01

This text is the first study to apply systematically the successive bifurcations approach to complex time-dependent processes in large scale atmospheric dynamics, geomagnetism, and theoretical climate dynamics. The presentation of recent results on planetary-scale phenomena in the earth's atmosphere, ocean, cryosphere, mantle and core provides an integral account of mathematical theory and methods together with physical phenomena and processes. The authors address a number of problems in rapidly developing areas of geophysics, bringing into closer contact the modern tools of nonlinear mathematics and the novel problems of global change in the environment.

A Complementary Measure of Heterogeneity on Mathematical Skills

ERIC Educational Resources Information Center

Fedriani, Eugenio M.; Moyano, Rafael

2012-01-01

Finding educational truths is an inherently multivariate problem. There are many factors affecting each student and their performances. Because of this, both measuring of skills and assessing students are always complex processes. This is a well-known problem, and a number of solutions have been proposed by specialists. One of its ramifications is…

What's My Math Course Got to Do with Biology?

ERIC Educational Resources Information Center

Burks, Robert; Lindquist, Joseph; McMurran, Shawnee

2008-01-01

At United States Military Academy, a unit on biological modeling applications forms the culminating component of the first semester core mathematics course for freshmen. The course emphasizes the use of problem-solving strategies and modeling to solve complex and ill-defined problems. Topic areas include functions and their shapes, data fitting,…

Transport of reacting solutes in porous media: Relation between mathematical nature of problem formulation and chemical nature of reactions

USGS Publications Warehouse

Rubin, Jacob

1983-01-01

Examples involving six broad reaction classes show that the nature of transport-affecting chemistry may have a profound effect on the mathematical character of solute transport problem formulation. Substantive mathematical diversity among such formulations is brought about principally by reaction properties that determine whether (1) the reaction can be regarded as being controlled by local chemical equilibria or whether it must be considered as being controlled by kinetics, (2) the reaction is homogeneous or heterogeneous, (3) the reaction is a surface reaction (adsorption, ion exchange) or one of the reactions of classical chemistry (e.g., precipitation, dissolution, oxidation, reduction, complex formation). These properties, as well as the choice of means to describe them, stipulate, for instance, (1) the type of chemical entities for which a formulation's basic, mass-balance equations should be written; (2) the nature of mathematical transformations needed to change the problem's basic equations into operational ones. These and other influences determine such mathematical features of problem formulations as the nature of the operational transport-equation system (e.g., whether it involves algebraic, partial-differential, or integro-partial-differential simultaneous equations), the type of nonlinearities of such a system, and the character of the boundaries (e.g., whether they are stationary or moving). Exploration of the reasons for the dependence of transport mathematics on transport chemistry suggests that many results of this dependence stem from the basic properties of the reactions' chemical-relation (i.e., equilibrium or rate) equations.

Matched field localization based on CS-MUSIC algorithm

NASA Astrophysics Data System (ADS)

Guo, Shuangle; Tang, Ruichun; Peng, Linhui; Ji, Xiaopeng

2016-04-01

The problem caused by shortness or excessiveness of snapshots and by coherent sources in underwater acoustic positioning is considered. A matched field localization algorithm based on CS-MUSIC (Compressive Sensing Multiple Signal Classification) is proposed based on the sparse mathematical model of the underwater positioning. The signal matrix is calculated through the SVD (Singular Value Decomposition) of the observation matrix. The observation matrix in the sparse mathematical model is replaced by the signal matrix, and a new concise sparse mathematical model is obtained, which means not only the scale of the localization problem but also the noise level is reduced; then the new sparse mathematical model is solved by the CS-MUSIC algorithm which is a combination of CS (Compressive Sensing) method and MUSIC (Multiple Signal Classification) method. The algorithm proposed in this paper can overcome effectively the difficulties caused by correlated sources and shortness of snapshots, and it can also reduce the time complexity and noise level of the localization problem by using the SVD of the observation matrix when the number of snapshots is large, which will be proved in this paper.

Applying Cognitive Science to Education: Thinking and Learning in Scientific and Other Complex Domains

ERIC Educational Resources Information Center

Reif, Frederick

2008-01-01

Many students find it difficult to learn the kinds of knowledge and thinking required by college or high school courses in mathematics, science, or other complex domains. Thus they often emerge with significant misconceptions, fragmented knowledge, and inadequate problem-solving skills. Most instructors or textbook authors approach their teaching…

Dynamic pathway modeling of signal transduction networks: a domain-oriented approach.

PubMed

Conzelmann, Holger; Gilles, Ernst-Dieter

2008-01-01

Mathematical models of biological processes become more and more important in biology. The aim is a holistic understanding of how processes such as cellular communication, cell division, regulation, homeostasis, or adaptation work, how they are regulated, and how they react to perturbations. The great complexity of most of these processes necessitates the generation of mathematical models in order to address these questions. In this chapter we provide an introduction to basic principles of dynamic modeling and highlight both problems and chances of dynamic modeling in biology. The main focus will be on modeling of s transduction pathways, which requires the application of a special modeling approach. A common pattern, especially in eukaryotic signaling systems, is the formation of multi protein signaling complexes. Even for a small number of interacting proteins the number of distinguishable molecular species can be extremely high. This combinatorial complexity is due to the great number of distinct binding domains of many receptors and scaffold proteins involved in signal transduction. However, these problems can be overcome using a new domain-oriented modeling approach, which makes it possible to handle complex and branched signaling pathways.

Novel Approach on the Optimisation of Mid-Course Corrections Along Interplanetary Trajectories

NASA Astrophysics Data System (ADS)

Iorfida, Elisabetta; Palmer, Phil; Roberts, Mark

The primer vector theory, firstly proposed by Lawden, defines a set of necessary conditions to characterise whether an impulsive thrust trajectory is optimal with respect to propellant usage, within a two-body problem context. If the conditions are not satisfied, one or more potential intermediate impulses are performed along the transfer arc, in order to lower the overall cost. The method is based on the propagation of the state transition matrix and on the solution of a boundary value problem, which leads to a mathematical and computational complexity.In this paper, a different approach is introduced. It is based on a polar coordinates transformation of the primer vector which allows the decoupling between its in-plane and out-of-plane components. The out-of-plane component is solved analytically while for the in-plane ones a Hamiltonian approximation is made.The novel procedure reduces the mathematical complexity and the computational cost of Lawden's problem and gives also a different perspective about the optimisation of a transfer trajectory.

Interpretations of Quantum Theory in the Light of Modern Cosmology

NASA Astrophysics Data System (ADS)

Castagnino, Mario; Fortin, Sebastian; Laura, Roberto; Sudarsky, Daniel

2017-11-01

The difficult issues related to the interpretation of quantum mechanics and, in particular, the "measurement problem" are revisited using as motivation the process of generation of structure from quantum fluctuations in inflationary cosmology. The unessential mathematical complexity of the particular problem is bypassed, facilitating the discussion of the conceptual issues, by considering, within the paradigm set up by the cosmological problem, another problem where symmetry serves as a focal point: a simplified version of Mott's problem.

On deformation of complex continuum immersed in a plane space

NASA Astrophysics Data System (ADS)

Kovalev, V. A.; Murashkin, E. V.; Radayev, Y. N.

2018-05-01

The present paper is devoted to mathematical modelling of complex continua deformations considered as immersed in an external plane space. The complex continuum is defined as a differential manifold supplied with metrics induced by the external space. A systematic derivation of strain tensors by notion of isometric immersion of the complex continuum into a plane space of a higher dimension is proposed. Problem of establishing complete systems of irreducible objective strain and extrastrain tensors for complex continuum immersed in an external plane space is resolved. The solution to the problem is obtained by methods of the field theory and the theory of rational algebraic invariants. Strain tensors of the complex continuum are derived as irreducible algebraic invariants of contravariant vectors of the external space emerging as functional arguments in the complex continuum action density. Present analysis is restricted to rational algebraic invariants. Completeness of the considered systems of rational algebraic invariants is established for micropolar elastic continua. Rational syzygies for non-quadratic invariants are discussed. Objective strain tensors (indifferent to frame rotations in the external plane space) for micropolar continuum are alternatively obtained by properly combining multipliers of polar decompositions of deformation and extra-deformation gradients. The latter is realized only for continua immersed in a plane space of the equal mathematical dimension.

Molecular Mechanics and Dynamics Characterization of an "in silico" Mutated Protein: A Stand-Alone Lab Module or Support Activity for "in vivo" and "in vitro" Analyses of Targeted Proteins

ERIC Educational Resources Information Center

Chiang, Harry; Robinson, Lucy C.; Brame, Cynthia J.; Messina, Troy C.

2013-01-01

Over the past 20 years, the biological sciences have increasingly incorporated chemistry, physics, computer science, and mathematics to aid in the development and use of mathematical models. Such combined approaches have been used to address problems from protein structure-function relationships to the workings of complex biological systems.…

Integrating Cost Engineering and Project Management in a Junior Engineering Economics Course and a Senior Capstone Project Design Course

ERIC Educational Resources Information Center

Tickles, Virginia C.; Li, Yadong; Walters, Wilbur L.

2013-01-01

Much criticism exists concerning a lack of focus on real-world problem-solving in the science, technology, engineering and mathematics (STEM) infrastructures. Many of these critics say that current educational infrastructures are incapable in preparing future scientists and engineers to solve the complex and multidisciplinary problems this society…

Nonlinear functional approximation with networks using adaptive neurons

NASA Technical Reports Server (NTRS)

Tawel, Raoul

1992-01-01

A novel mathematical framework for the rapid learning of nonlinear mappings and topological transformations is presented. It is based on allowing the neuron's parameters to adapt as a function of learning. This fully recurrent adaptive neuron model (ANM) has been successfully applied to complex nonlinear function approximation problems such as the highly degenerate inverse kinematics problem in robotics.

Complex Langevin method: When can it be trusted?

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

Aarts, Gert; Seiler, Erhard; Stamatescu, Ion-Olimpiu

2010-03-01

We analyze to what extent the complex Langevin method, which is in principle capable of solving the so-called sign problems, can be considered as reliable. We give a formal derivation of the correctness and then point out various mathematical loopholes. The detailed study of some simple examples leads to practical suggestions about the application of the method.

Mathematical Models to Determine Stable Behavior of Complex Systems

NASA Astrophysics Data System (ADS)

Sumin, V. I.; Dushkin, A. V.; Smolentseva, T. E.

2018-05-01

The paper analyzes a possibility to predict functioning of a complex dynamic system with a significant amount of circulating information and a large number of random factors impacting its functioning. Functioning of the complex dynamic system is described as a chaotic state, self-organized criticality and bifurcation. This problem may be resolved by modeling such systems as dynamic ones, without applying stochastic models and taking into account strange attractors.

Software For Least-Squares And Robust Estimation

NASA Technical Reports Server (NTRS)

Jeffreys, William H.; Fitzpatrick, Michael J.; Mcarthur, Barbara E.; Mccartney, James

1990-01-01

GAUSSFIT computer program includes full-featured programming language facilitating creation of mathematical models solving least-squares and robust-estimation problems. Programming language designed to make it easy to specify complex reduction models. Written in 100 percent C language.

Expert system development for commonality analysis in space programs

NASA Technical Reports Server (NTRS)

Yeager, Dorian P.

1987-01-01

This report is a combination of foundational mathematics and software design. A mathematical model of the Commonality Analysis problem was developed and some important properties discovered. The complexity of the problem is described herein and techniques, both deterministic and heuristic, for reducing that complexity are presented. Weaknesses are pointed out in the existing software (System Commonality Analysis Tool) and several improvements are recommended. It is recommended that: (1) an expert system for guiding the design of new databases be developed; (2) a distributed knowledge base be created and maintained for the purpose of encoding the commonality relationships between design items in commonality databases; (3) a software module be produced which automatically generates commonality alternative sets from commonality databases using the knowledge associated with those databases; and (4) a more complete commonality analysis module be written which is capable of generating any type of feasible solution.

Using Technology to Facilitate and Enhance Project-based Learning in Mathematical Physics

NASA Astrophysics Data System (ADS)

Duda, Gintaras

2011-04-01

Problem-based and project-based learning are two pedagogical techniques that have several clear advantages over traditional instructional methods: 1) both techniques are active and student centered, 2) students confront real-world and/or highly complex problems, and 3) such exercises model the way science and engineering are done professionally. This talk will present an experiment in project/problem-based learning in a mathematical physics course. The group project in the course involved modeling a zombie outbreak of the type seen in AMC's ``The Walking Dead.'' Students researched, devised, and solved their mathematical models for the spread of zombie-like infection. Students used technology in all stages; in fact, since analytical solutions to the models were often impossible, technology was a necessary and critical component of the challenge. This talk will explore the use of technology in general in problem and project-based learning and will detail some specific examples of how technology was used to enhance student learning in this course. A larger issue of how students use the Internet to learn will also be explored.

Achieving meaningful mathematics literacy for students with learning disabilities. Cognition and Technology Group at Vanderbilt.

PubMed

Goldman, S R; Hasselbring, T S

1997-01-01

In this article we consider issues relevant to the future of mathematics instruction and achievement for students with learning disabilities. The starting point for envisioning the future is the changing standards for mathematics learning and basic mathematical literacy. We argue that the shift from behaviorist learning theories to constructivist and social constructivist theories (see Rivera, this series) provides an opportunity to develop and implement a hybrid model of mathematics instruction. The hybrid model we propose embeds, or situates, important skill learning in meaningful contexts. We discuss some examples of instructional approaches to complex mathematical problem solving that make use of meaningful contexts. Evaluation data on these approaches have yielded positive and encouraging results for students with learning disabilities as well as general education students. Finally, we discuss various ways in which technology is important for realizing hybrid instructional models in mathematics.

A Cognitive Analysis of Students’ Mathematical Problem Solving Ability on Geometry

NASA Astrophysics Data System (ADS)

Rusyda, N. A.; Kusnandi, K.; Suhendra, S.

2017-09-01

The purpose of this research is to analyze of mathematical problem solving ability of students in one of secondary school on geometry. This research was conducted by using quantitative approach with descriptive method. Population in this research was all students of that school and the sample was twenty five students that was chosen by purposive sampling technique. Data of mathematical problem solving were collected through essay test. The results showed the percentage of achievement of mathematical problem solving indicators of students were: 1) solve closed mathematical problems with context in math was 50%; 2) solve the closed mathematical problems with the context beyond mathematics was 24%; 3) solving open mathematical problems with contexts in mathematics was 35%; And 4) solving open mathematical problems with contexts outside mathematics was 44%. Based on the percentage, it can be concluded that the level of achievement of mathematical problem solving ability in geometry still low. This is because students are not used to solving problems that measure mathematical problem solving ability, weaknesses remember previous knowledge, and lack of problem solving framework. So the students’ ability of mathematical problems solving need to be improved with implement appropriate learning strategy.

On the tumbling toast problem

NASA Astrophysics Data System (ADS)

Borghi, Riccardo

2012-09-01

A didactical revisitation of the so-called tumbling toast problem is presented here. The numerical solution of the related Newton's equations has been found in the space domain, without resorting to the complete time-based law of motion, with a considerable reduction of the mathematical complexity of the problem. This could allow the effect of the different physical mechanisms ruling the overall dynamics to be appreciated in a more transparent way, even by undergraduates. Moreover, the availability from the literature of experimental investigations carried out on tumbling toast allows us to propose different theoretical models of growing complexity in order to show the corresponding improvement of the agreement between theory and observation.

Using Forensic Investigations and CAS to Motivate Student Interest in Mathematics

ERIC Educational Resources Information Center

Leinbach, Patricia; Leinbach, Carl

2010-01-01

In this paper, we are proposing the use of forensic case studies as a means to provide students with interesting problem solving opportunities that capitalise on the popularity of several TV series and shows. It also satisfies their natural curiosity about how answers are found to seemingly complex real life problems. We begin with a very brief…

An analysis of running skyline load path.

Treesearch

Ward W. Carson; Charles N. Mann

1971-01-01

This paper is intended for those who wish to prepare an algorithm to determine the load path of a running skyline. The mathematics of a simplified approach to this running skyline design problem are presented. The approach employs assumptions which reduce the complexity of the problem to the point where it can be solved on desk-top computers of limited capacities. The...

Optimal multi-floor plant layout based on the mathematical programming and particle swarm optimization.

PubMed

Lee, Chang Jun

2015-01-01

In the fields of researches associated with plant layout optimization, the main goal is to minimize the costs of pipelines and pumping between connecting equipment under various constraints. However, what is the lacking of considerations in previous researches is to transform various heuristics or safety regulations into mathematical equations. For example, proper safety distances between equipments have to be complied for preventing dangerous accidents on a complex plant. Moreover, most researches have handled single-floor plant. However, many multi-floor plants have been constructed for the last decade. Therefore, the proper algorithm handling various regulations and multi-floor plant should be developed. In this study, the Mixed Integer Non-Linear Programming (MINLP) problem including safety distances, maintenance spaces, etc. is suggested based on mathematical equations. The objective function is a summation of pipeline and pumping costs. Also, various safety and maintenance issues are transformed into inequality or equality constraints. However, it is really hard to solve this problem due to complex nonlinear constraints. Thus, it is impossible to use conventional MINLP solvers using derivatives of equations. In this study, the Particle Swarm Optimization (PSO) technique is employed. The ethylene oxide plant is illustrated to verify the efficacy of this study.

Mathematical and Numerical Techniques in Energy and Environmental Modeling

NASA Astrophysics Data System (ADS)

Chen, Z.; Ewing, R. E.

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

What Would Pascal Think About Space Safety?

NASA Astrophysics Data System (ADS)

Pfitzer, Tom

2013-09-01

Blaise Pascal was a true Renaissance man being well versed in science, physics, religion, philosophy, and especially mathematics. He had a knack for simplifying complex problems into mathematical formulae. He had well-formed opinions about the scientific issues of his day, in particular about risk. There is little doubt that were he alive today, he would have opinions useful to this society. This paper addresses what he thought then as a foundation for what he would have thought now.

Intelligent classifier for dynamic fault patterns based on hidden Markov model

NASA Astrophysics Data System (ADS)

Xu, Bo; Feng, Yuguang; Yu, Jinsong

2006-11-01

It's difficult to build precise mathematical models for complex engineering systems because of the complexity of the structure and dynamics characteristics. Intelligent fault diagnosis introduces artificial intelligence and works in a different way without building the analytical mathematical model of a diagnostic object, so it's a practical approach to solve diagnostic problems of complex systems. This paper presents an intelligent fault diagnosis method, an integrated fault-pattern classifier based on Hidden Markov Model (HMM). This classifier consists of dynamic time warping (DTW) algorithm, self-organizing feature mapping (SOFM) network and Hidden Markov Model. First, after dynamic observation vector in measuring space is processed by DTW, the error vector including the fault feature of being tested system is obtained. Then a SOFM network is used as a feature extractor and vector quantization processor. Finally, fault diagnosis is realized by fault patterns classifying with the Hidden Markov Model classifier. The importing of dynamic time warping solves the problem of feature extracting from dynamic process vectors of complex system such as aeroengine, and makes it come true to diagnose complex system by utilizing dynamic process information. Simulating experiments show that the diagnosis model is easy to extend, and the fault pattern classifier is efficient and is convenient to the detecting and diagnosing of new faults.

The Construction of Mathematical Literacy Problems for Geometry

NASA Astrophysics Data System (ADS)

Malasari, P. N.; Herman, T.; Jupri, A.

2017-09-01

The students of junior high school should have mathematical literacy ability to formulate, apply, and interpret mathematics in problem solving of daily life. Teaching these students are not enough by giving them ordinary mathematics problems. Teaching activities for these students brings consequence for teacher to construct mathematical literacy problems. Therefore, the aim of this study is to construct mathematical literacy problems to assess mathematical literacy ability. The steps of this study that consists of analysing, designing, theoretical validation, revising, limited testing to students, and evaluating. The data was collected with written test to 38 students of grade IX at one of state junior high school. Mathematical literacy problems consist of three essays with three indicators and three levels at polyhedron subject. The Indicators are formulating and employing mathematics. The results show that: (1) mathematical literacy problems which are constructed have been valid and practical, (2) mathematical literacy problems have good distinguishing characteristics and adequate distinguishing characteristics, (3) difficulty levels of problems are easy and moderate. The final conclusion is mathematical literacy problems which are constructed can be used to assess mathematical literacy ability.

The Mathematics of High School Physics

NASA Astrophysics Data System (ADS)

Kanderakis, Nikos

2016-10-01

In the seventeenth and eighteenth centuries, mathematicians and physical philosophers managed to study, via mathematics, various physical systems of the sublunar world through idealized and simplified models of these systems, constructed with the help of geometry. By analyzing these models, they were able to formulate new concepts, laws and theories of physics and then through models again, to apply these concepts and theories to new physical phenomena and check the results by means of experiment. Students' difficulties with the mathematics of high school physics are well known. Science education research attributes them to inadequately deep understanding of mathematics and mainly to inadequate understanding of the meaning of symbolic mathematical expressions. There seem to be, however, more causes of these difficulties. One of them, not independent from the previous ones, is the complex meaning of the algebraic concepts used in school physics (e.g. variables, parameters, functions), as well as the complexities added by physics itself (e.g. that equations' symbols represent magnitudes with empirical meaning and units instead of pure numbers). Another source of difficulties is that the theories and laws of physics are often applied, via mathematics, to simplified, and idealized physical models of the world and not to the world itself. This concerns not only the applications of basic theories but also all authentic end-of-the-chapter problems. Hence, students have to understand and participate in a complex interplay between physics concepts and theories, physical and mathematical models, and the real world, often without being aware that they are working with models and not directly with the real world.

[Reflex epilepsy evoked by decision making: report of a case (author's transl)].

PubMed

Mutani, R; Ganga, A; Agnetti, V

1980-01-01

A 17-year-old girl with a story of Gran Mal attacks occurring during lessons of mathematics or solving mathematical problems, was investigated with prolonged EEG recordings. During the sessions, relax periods were alternated with arithmetical or mathematical testing, with card or checkers games and solution of puzzles and crossword problems, and with different neuropsychological tests. EGG recordings were characterized by the appearance, on a normal background, of bilaterally synchronous and symmetrical spike-and-wave and polispike-and-wave discharges, associated with loss of consciousness. During relax their mean frequency was one/54 min., it doubled during execution of tests involved with nonsequential decision making, and was eight times as high (one/7 min.) during tests involving sequential decision making. Some tension, challenge and complexity of the performance were also important as precipitating factors. Their lack deprived sequential tests of their efficacy, while on the contrary their presence sometimes gave nonsequential tests full efficacy.

Status of Complex Langevin

NASA Astrophysics Data System (ADS)

Seiler, Erhard

2018-03-01

I review the status of the Complex Langevin method, which was invented to make simulations of models with complex action feasible. I discuss the mathematical justification of the procedure, as well as its limitations and open questions. Various pragmatic measures for dealing with the existing problems are described. Finally I report on the progress in the application of the method to QCD, with the goal of determining the phase diagram of QCD as a function of temperature and baryonic chemical potential.

Engineering Problem-Solving Knowledge: The Impact of Context

ERIC Educational Resources Information Center

Wolff, Karin

2017-01-01

Employer complaints of engineering graduate inability to "apply knowledge" suggests a need to interrogate the complex theory-practice relationship in twenty-first century real world contexts. Focussing specifically on the application of mathematics, physics and logic-based disciplinary knowledge, the research examines engineering…

The social essentials of learning: an experimental investigation of collaborative problem solving and knowledge construction in mathematics classrooms in Australia and China

NASA Astrophysics Data System (ADS)

Chan, Man Ching Esther; Clarke, David; Cao, Yiming

2018-03-01

Interactive problem solving and learning are priorities in contemporary education, but these complex processes have proved difficult to research. This project addresses the question "How do we optimise social interaction for the promotion of learning in a mathematics classroom?" Employing the logic of multi-theoretic research design, this project uses the newly built Science of Learning Research Classroom (ARC-SR120300015) at The University of Melbourne and equivalent facilities in China to investigate classroom learning and social interactions, focusing on collaborative small group problem solving as a way to make the social aspects of learning visible. In Australia and China, intact classes of local year 7 students with their usual teacher will be brought into the research classroom facilities with built-in video cameras and audio recording equipment to participate in purposefully designed activities in mathematics. The students will undertake a sequence of tasks in the social units of individual, pair, small group (typically four students) and whole class. The conditions for student collaborative problem solving and learning will be manipulated so that student and teacher contributions to that learning process can be distinguished. Parallel and comparative analyses will identify culture-specific interactive patterns and provide the basis for hypotheses about the learning characteristics underlying collaborative problem solving performance documented in the research classrooms in each country. The ultimate goals of the project are to generate, develop and test more sophisticated hypotheses for the optimisation of social interaction in the mathematics classroom in the interest of improving learning and, particularly, student collaborative problem solving.

Numerical Modeling in Geodynamics: Success, Failure and Perspective

NASA Astrophysics Data System (ADS)

Ismail-Zadeh, A.

2005-12-01

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

From boring to scoring - a collaborative serious game for learning and practicing mathematical logic for computer science education

NASA Astrophysics Data System (ADS)

Schäfer, Andreas; Holz, Jan; Leonhardt, Thiemo; Schroeder, Ulrik; Brauner, Philipp; Ziefle, Martina

2013-06-01

In this study, we address the problem of low retention and high dropout rates of computer science university students in early semesters of the studies. Complex and high abstract mathematical learning materials have been identified as one reason for the dropout rate. In order to support the understanding and practicing of core mathematical concepts, we developed a game-based multitouch learning environment in which the need for a suitable learning environment for mathematical logic was combined with the ability to train cooperation and collaboration in a learning scenario. As application domain, the field of mathematical logic had been chosen. The development process was accomplished along three steps: First, ethnographic interviews were run with 12 students of computer science revealing typical problems with mathematical logic. Second, a multitouch learning environment was developed. The game consists of multiple learning and playing modes in which teams of students can collaborate or compete against each other. Finally, a twofold evaluation of the environment was carried out (user study and cognitive walk-through). Overall, the evaluation showed that the game environment was easy to use and rated as helpful: The chosen approach of a multiplayer game supporting competition, collaboration, and cooperation is perceived as motivating and "fun."

Persistence of Undergraduate Women in STEM Fields

ERIC Educational Resources Information Center

Pedone, Maggie Helene

2016-01-01

The underrepresentation of women in science, technology, engineering, and mathematics (STEM) is a complex problem that continues to persist at the postsecondary level, particularly in computer science and engineering fields. This dissertation explored the pre-college and college level factors that influenced undergraduate women's persistence in…

Learning by Heart.

ERIC Educational Resources Information Center

Rist, Marilee C.

1992-01-01

Although rote learning is a heretical notion to many educators, memorizing, reciting, and drilling may be what is needed to improve test scores and provide students with the necessary skills for solving problems and developing complex thinking skills. Sidebars summarize direct-teaching methods for mathematics and a Core Knowledge curriculum…

Find the Dimensions: Students Solving a Tiling Problem

ERIC Educational Resources Information Center

Obara, Samuel

2018-01-01

Students learn mathematics by solving problems. Mathematics textbooks are full of problems, and mathematics teachers use these problems to test students' understanding of mathematical concepts. This paper discusses how problem-solving skills can be fostered with a geometric tiling problem.

Understanding immunology via engineering design: the role of mathematical prototyping.

PubMed

Klinke, David J; Wang, Qing

2012-01-01

A major challenge in immunology is how to translate data into knowledge given the inherent complexity and dynamics of human physiology. Both the physiology and engineering communities have rich histories in applying computational approaches to translate data obtained from complex systems into knowledge of system behavior. However, there are some differences in how disciplines approach problems. By referring to mathematical models as mathematical prototypes, we aim to highlight aspects related to the process (i.e., prototyping) rather than the product (i.e., the model). The objective of this paper is to review how two related engineering concepts, specifically prototyping and "fitness for use," can be applied to overcome the pressing challenge in translating data into improved knowledge of basic immunology that can be used to improve therapies for disease. These concepts are illustrated using two immunology-related examples. The prototypes presented focus on the beta cell mass at the onset of type 1 diabetes and the dynamics of dendritic cells in the lung. This paper is intended to illustrate some of the nuances associated with applying mathematical modeling to improve understanding of the dynamics of disease progression in humans.

What Makes a Problem Mathematically Interesting? Inviting Prospective Teachers to Pose Better Problems

ERIC Educational Resources Information Center

Crespo, Sandra; Sinclair, Nathalie

2008-01-01

School students of all ages, including those who subsequently become teachers, have limited experience posing their own mathematical problems. Yet problem posing, both as an act of mathematical inquiry and of mathematics teaching, is part of the mathematics education reform vision that seeks to promote mathematics as an worthy intellectual…

Computational ecology as an emerging science

PubMed Central

Petrovskii, Sergei; Petrovskaya, Natalia

2012-01-01

It has long been recognized that numerical modelling and computer simulations can be used as a powerful research tool to understand, and sometimes to predict, the tendencies and peculiarities in the dynamics of populations and ecosystems. It has been, however, much less appreciated that the context of modelling and simulations in ecology is essentially different from those that normally exist in other natural sciences. In our paper, we review the computational challenges arising in modern ecology in the spirit of computational mathematics, i.e. with our main focus on the choice and use of adequate numerical methods. Somewhat paradoxically, the complexity of ecological problems does not always require the use of complex computational methods. This paradox, however, can be easily resolved if we recall that application of sophisticated computational methods usually requires clear and unambiguous mathematical problem statement as well as clearly defined benchmark information for model validation. At the same time, many ecological problems still do not have mathematically accurate and unambiguous description, and available field data are often very noisy, and hence it can be hard to understand how the results of computations should be interpreted from the ecological viewpoint. In this scientific context, computational ecology has to deal with a new paradigm: conventional issues of numerical modelling such as convergence and stability become less important than the qualitative analysis that can be provided with the help of computational techniques. We discuss this paradigm by considering computational challenges arising in several specific ecological applications. PMID:23565336

Dynamic programming methods for concurrent design and dynamic allocation of vehicles embedded in a system-of-systems

NASA Astrophysics Data System (ADS)

Nusawardhana

2007-12-01

Recent developments indicate a changing perspective on how systems or vehicles should be designed. Such transition comes from the way decision makers in defense related agencies address complex problems. Complex problems are now often posed in terms of the capabilities desired, rather than in terms of requirements for a single systems. As a result, the way to provide a set of capabilities is through a collection of several individual, independent systems. This collection of individual independent systems is often referred to as a "System of Systems'' (SoS). Because of the independent nature of the constituent systems in an SoS, approaches to design an SoS, and more specifically, approaches to design a new system as a member of an SoS, will likely be different than the traditional design approaches for complex, monolithic (meaning the constituent parts have no ability for independent operation) systems. Because a system of system evolves over time, this simultaneous system design and resource allocation problem should be investigated in a dynamic context. Such dynamic optimization problems are similar to conventional control problems. However, this research considers problems which not only seek optimizing policies but also seek the proper system or vehicle to operate under these policies. This thesis presents a framework and a set of analytical tools to solve a class of SoS problems that involves the simultaneous design of a new system and allocation of the new system along with existing systems. Such a class of problems belongs to the problems of concurrent design and control of a new systems with solutions consisting of both optimal system design and optimal control strategy. Rigorous mathematical arguments show that the proposed framework solves the concurrent design and control problems. Many results exist for dynamic optimization problems of linear systems. In contrary, results on optimal nonlinear dynamic optimization problems are rare. The proposed framework is equipped with the set of analytical tools to solve several cases of nonlinear optimal control problems: continuous- and discrete-time nonlinear problems with applications on both optimal regulation and tracking. These tools are useful when mathematical descriptions of dynamic systems are available. In the absence of such a mathematical model, it is often necessary to derive a solution based on computer simulation. For this case, a set of parameterized decision may constitute a solution. This thesis presents a method to adjust these parameters based on the principle of stochastic approximation simultaneous perturbation using continuous measurements. The set of tools developed here mostly employs the methods of exact dynamic programming. However, due to the complexity of SoS problems, this research also develops suboptimal solution approaches, collectively recognized as approximate dynamic programming solutions, for large scale problems. The thesis presents, explores, and solves problems from an airline industry, in which a new aircraft is to be designed and allocated along with an existing fleet of aircraft. Because the life cycle of an aircraft is on the order of 10 to 20 years, this problem is to be addressed dynamically so that the new aircraft design is the best design for the fleet over a given time horizon.

Statistical physics of hard combinatorial optimization: Vertex cover problem

NASA Astrophysics Data System (ADS)

Zhao, Jin-Hua; Zhou, Hai-Jun

2014-07-01

Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years, the replica-symmetry-breaking mean field theory of spin glasses and the associated message-passing algorithms have greatly deepened our understanding of typical-case computation complexity. In this paper, we use the vertex cover problem, a basic nondeterministic-polynomial (NP)-complete combinatorial optimization problem of wide application, as an example to introduce the statistical physical methods and algorithms. We do not go into the technical details but emphasize mainly the intuitive physical meanings of the message-passing equations. A nonfamiliar reader shall be able to understand to a large extent the physics behind the mean field approaches and to adjust the mean field methods in solving other optimization problems.

Math 3011--College Algebra and Trigonometry. Course Outline.

ERIC Educational Resources Information Center

New York Inst. of Tech., Old Westbury.

This document contains the course syllabus and 12 independent practice modules for a college level mathematics course designed to provide the necessary foundation for success in calculus, develop logical thinking skills, and enhance analytic skills through problem solving. Topics include relations and functions; inequalities; complex numbers;…

Boom. Bust. Build.

ERIC Educational Resources Information Center

Kite, Vance; Park, Soonhye

2018-01-01

In 2006 Jeanette Wing, a professor of computer science at Carnegie Mellon University, proposed computational thinking (CT) as a literacy just as important as reading, writing, and mathematics. Wing defined CT as a set of skills and strategies computer scientists use to solve complex, computational problems (Wing 2006). The computer science and…

Finite element meshing approached as a global minimization process

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

WITKOWSKI,WALTER R.; JUNG,JOSEPH; DOHRMANN,CLARK R.

2000-03-01

The ability to generate a suitable finite element mesh in an automatic fashion is becoming the key to being able to automate the entire engineering analysis process. However, placing an all-hexahedron mesh in a general three-dimensional body continues to be an elusive goal. The approach investigated in this research is fundamentally different from any other that is known of by the authors. A physical analogy viewpoint is used to formulate the actual meshing problem which constructs a global mathematical description of the problem. The analogy used was that of minimizing the electrical potential of a system charged particles within amore » charged domain. The particles in the presented analogy represent duals to mesh elements (i.e., quads or hexes). Particle movement is governed by a mathematical functional which accounts for inter-particles repulsive, attractive and alignment forces. This functional is minimized to find the optimal location and orientation of each particle. After the particles are connected a mesh can be easily resolved. The mathematical description for this problem is as easy to formulate in three-dimensions as it is in two- or one-dimensions. The meshing algorithm was developed within CoMeT. It can solve the two-dimensional meshing problem for convex and concave geometries in a purely automated fashion. Investigation of the robustness of the technique has shown a success rate of approximately 99% for the two-dimensional geometries tested. Run times to mesh a 100 element complex geometry were typically in the 10 minute range. Efficiency of the technique is still an issue that needs to be addressed. Performance is an issue that is critical for most engineers generating meshes. It was not for this project. The primary focus of this work was to investigate and evaluate a meshing algorithm/philosophy with efficiency issues being secondary. The algorithm was also extended to mesh three-dimensional geometries. Unfortunately, only simple geometries were tested before this project ended. The primary complexity in the extension was in the connectivity problem formulation. Defining all of the interparticle interactions that occur in three-dimensions and expressing them in mathematical relationships is very difficult.« less

An Algorithm for Integrated Subsystem Embodiment and System Synthesis

NASA Technical Reports Server (NTRS)

Lewis, Kemper

1997-01-01

Consider the statement,'A system has two coupled subsystems, one of which dominates the design process. Each subsystem consists of discrete and continuous variables, and is solved using sequential analysis and solution.' To address this type of statement in the design of complex systems, three steps are required, namely, the embodiment of the statement in terms of entities on a computer, the mathematical formulation of subsystem models, and the resulting solution and system synthesis. In complex system decomposition, the subsystems are not isolated, self-supporting entities. Information such as constraints, goals, and design variables may be shared between entities. But many times in engineering problems, full communication and cooperation does not exist, information is incomplete, or one subsystem may dominate the design. Additionally, these engineering problems give rise to mathematical models involving nonlinear functions of both discrete and continuous design variables. In this dissertation an algorithm is developed to handle these types of scenarios for the domain-independent integration of subsystem embodiment, coordination, and system synthesis using constructs from Decision-Based Design, Game Theory, and Multidisciplinary Design Optimization. Implementation of the concept in this dissertation involves testing of the hypotheses using example problems and a motivating case study involving the design of a subsonic passenger aircraft.

The problem-solving approach in the teaching of number theory

NASA Astrophysics Data System (ADS)

Toh, Pee Choon; Hoong Leong, Yew; Toh, Tin Lam; Dindyal, Jaguthsing; Quek, Khiok Seng; Guan Tay, Eng; Him Ho, Foo

2014-02-01

Mathematical problem solving is the mainstay of the mathematics curriculum for Singapore schools. In the preparation of prospective mathematics teachers, the authors, who are mathematics teacher educators, deem it important that pre-service mathematics teachers experience non-routine problem solving and acquire an attitude that predisposes them to adopt a Pólya-style approach in learning mathematics. The Practical Worksheet is an instructional scaffold we adopted to help our pre-service mathematics teachers develop problem-solving dispositions alongside the learning of the subject matter. The Worksheet was initially used in a design experiment aimed at teaching problem solving in a secondary school. In this paper, we describe an application and adaptation of the MProSE (Mathematical Problem Solving for Everyone) design experiment to a university level number theory course for pre-service mathematics teachers. The goal of the enterprise was to help the pre-service mathematics teachers develop problem-solving dispositions alongside the learning of the subject matter. Our analysis of the pre-service mathematics teachers' work shows that the MProSE design holds promise for mathematics courses at the tertiary level.

Data based identification and prediction of nonlinear and complex dynamical systems

NASA Astrophysics Data System (ADS)

Wang, Wen-Xu; Lai, Ying-Cheng; Grebogi, Celso

2016-07-01

The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and economics. The classic approach to phase-space reconstruction through the methodology of delay-coordinate embedding has been practiced for more than three decades, but the paradigm is effective mostly for low-dimensional dynamical systems. Often, the methodology yields only a topological correspondence of the original system. There are situations in various fields of science and engineering where the systems of interest are complex and high dimensional with many interacting components. A complex system typically exhibits a rich variety of collective dynamics, and it is of great interest to be able to detect, classify, understand, predict, and control the dynamics using data that are becoming increasingly accessible due to the advances of modern information technology. To accomplish these goals, especially prediction and control, an accurate reconstruction of the original system is required. Nonlinear and complex systems identification aims at inferring, from data, the mathematical equations that govern the dynamical evolution and the complex interaction patterns, or topology, among the various components of the system. With successful reconstruction of the system equations and the connecting topology, it may be possible to address challenging and significant problems such as identification of causal relations among the interacting components and detection of hidden nodes. The "inverse" problem thus presents a grand challenge, requiring new paradigms beyond the traditional delay-coordinate embedding methodology. The past fifteen years have witnessed rapid development of contemporary complex graph theory with broad applications in interdisciplinary science and engineering. The combination of graph, information, and nonlinear dynamical systems theories with tools from statistical physics, optimization, engineering control, applied mathematics, and scientific computing enables the development of a number of paradigms to address the problem of nonlinear and complex systems reconstruction. In this Review, we describe the recent advances in this forefront and rapidly evolving field, with a focus on compressive sensing based methods. In particular, compressive sensing is a paradigm developed in recent years in applied mathematics, electrical engineering, and nonlinear physics to reconstruct sparse signals using only limited data. It has broad applications ranging from image compression/reconstruction to the analysis of large-scale sensor networks, and it has become a powerful technique to obtain high-fidelity signals for applications where sufficient observations are not available. We will describe in detail how compressive sensing can be exploited to address a diverse array of problems in data based reconstruction of nonlinear and complex networked systems. The problems include identification of chaotic systems and prediction of catastrophic bifurcations, forecasting future attractors of time-varying nonlinear systems, reconstruction of complex networks with oscillatory and evolutionary game dynamics, detection of hidden nodes, identification of chaotic elements in neuronal networks, reconstruction of complex geospatial networks and nodal positioning, and reconstruction of complex spreading networks with binary data.. A number of alternative methods, such as those based on system response to external driving, synchronization, and noise-induced dynamical correlation, will also be discussed. Due to the high relevance of network reconstruction to biological sciences, a special section is devoted to a brief survey of the current methods to infer biological networks. Finally, a number of open problems including control and controllability of complex nonlinear dynamical networks are discussed. The methods outlined in this Review are principled on various concepts in complexity science and engineering such as phase transitions, bifurcations, stabilities, and robustness. The methodologies have the potential to significantly improve our ability to understand a variety of complex dynamical systems ranging from gene regulatory systems to social networks toward the ultimate goal of controlling such systems.

Domain decomposition method for the Baltic Sea based on theory of adjoint equation and inverse problem.

NASA Astrophysics Data System (ADS)

Lezina, Natalya; Agoshkov, Valery

2017-04-01

Domain decomposition method (DDM) allows one to present a domain with complex geometry as a set of essentially simpler subdomains. This method is particularly applied for the hydrodynamics of oceans and seas. In each subdomain the system of thermo-hydrodynamic equations in the Boussinesq and hydrostatic approximations is solved. The problem of obtaining solution in the whole domain is that it is necessary to combine solutions in subdomains. For this purposes iterative algorithm is created and numerical experiments are conducted to investigate an effectiveness of developed algorithm using DDM. For symmetric operators in DDM, Poincare-Steklov's operators [1] are used, but for the problems of the hydrodynamics, it is not suitable. In this case for the problem, adjoint equation method [2] and inverse problem theory are used. In addition, it is possible to create algorithms for the parallel calculations using DDM on multiprocessor computer system. DDM for the model of the Baltic Sea dynamics is numerically studied. The results of numerical experiments using DDM are compared with the solution of the system of hydrodynamic equations in the whole domain. The work was supported by the Russian Science Foundation (project 14-11-00609, the formulation of the iterative process and numerical experiments). [1] V.I. Agoshkov, Domain Decompositions Methods in the Mathematical Physics Problem // Numerical processes and systems, No 8, Moscow, 1991 (in Russian). [2] V.I. Agoshkov, Optimal Control Approaches and Adjoint Equations in the Mathematical Physics Problem, Institute of Numerical Mathematics, RAS, Moscow, 2003 (in Russian).

Problem Solving: How Do In-Service Secondary School Teachers of Mathematics Make Sense of a Non-Routine Problem Context?

ERIC Educational Resources Information Center

Mwei, Philip K.

2017-01-01

The concept of mathematical problem solving is an important mathematical process in mathematics curricula of education systems worldwide. These math curricula demand that learners are exposed to authentic problems that foster successful problem solving. To attain this very important goal, there must be mathematics teachers well versed in content…

Evaluating the Suitability of Mathematical Thinking Problems for Senior High-School Students by Including Mathematical Sense Making and Global Planning

ERIC Educational Resources Information Center

van Velzen, Joke H.

2016-01-01

The mathematics curriculum often provides for relatively few mathematical thinking problems or non-routine problems that focus on a deepening of understanding mathematical concepts and the problem-solving process. To develop such problems, methods are required to evaluate their suitability. The purpose of this preliminary study was to find such an…

Students’ Mathematical Problem-Solving Abilities Through The Application of Learning Models Problem Based Learning

NASA Astrophysics Data System (ADS)

Nasution, M. L.; Yerizon, Y.; Gusmiyanti, R.

2018-04-01

One of the purpose mathematic learning is to develop problem solving abilities. Problem solving is obtained through experience in questioning non-routine. Improving students’ mathematical problem-solving abilities required an appropriate strategy in learning activities one of them is models problem based learning (PBL). Thus, the purpose of this research is to determine whether the problem solving abilities of mathematical students’ who learn to use PBL better than on the ability of students’ mathematical problem solving by applying conventional learning. This research included quasi experiment with static group design and population is students class XI MIA SMAN 1 Lubuk Alung. Class experiment in the class XI MIA 5 and class control in the class XI MIA 6. The instrument of final test students’ mathematical problem solving used essay form. The result of data final test in analyzed with t-test. The result is students’ mathematical problem solving abilities with PBL better then on the ability of students’ mathematical problem solving by applying conventional learning. It’s seen from the high percentage achieved by the group of students who learn to use PBL for each indicator of students’ mathematical problem solving.

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

PubMed

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

2008-01-01

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

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.

Performance evaluation of functioning of natural-industrial system of mining-processing complex with help of analytical and mathematical models

NASA Astrophysics Data System (ADS)

Bosikov, I. I.; Klyuev, R. V.; Revazov, V. Ch; Pilieva, D. E.

2018-03-01

The article describes research and analysis of hazardous processes occurring in the natural-industrial system and effectiveness assessment of its functioning using mathematical models. Studies of the functioning regularities of the natural and industrial system are becoming increasingly relevant in connection with the formulation of the task of modernizing production and the economy of Russia as a whole. In connection with a significant amount of poorly structured data, it is complicated by regulations for the effective functioning of production processes, social and natural complexes, under which a sustainable development of the natural-industrial system of the mining and processing complex would be ensured. Therefore, the scientific and applied problems, the solution of which allows one to formalize the hidden structural functioning patterns of the natural-industrial system and to make managerial decisions of organizational and technological nature to improve the efficiency of the system, are very relevant.

Accuracy and Calibration of High Explosive Thermodynamic Equations of State

NASA Astrophysics Data System (ADS)

Baker, Ernest L.; Capellos, Christos; Stiel, Leonard I.; Pincay, Jack

2010-10-01

The Jones-Wilkins-Lee-Baker (JWLB) equation of state (EOS) was developed to more accurately describe overdriven detonation while maintaining an accurate description of high explosive products expansion work output. The increased mathematical complexity of the JWLB high explosive equations of state provides increased accuracy for practical problems of interest. Increased numbers of parameters are often justified based on improved physics descriptions but can also mean increased calibration complexity. A generalized extent of aluminum reaction Jones-Wilkins-Lee (JWL)-based EOS was developed in order to more accurately describe the observed behavior of aluminized explosives detonation products expansion. A calibration method was developed to describe the unreacted, partially reacted, and completely reacted explosive using nonlinear optimization. A reasonable calibration of a generalized extent of aluminum reaction JWLB EOS as a function of aluminum reaction fraction has not yet been achieved due to the increased mathematical complexity of the JWLB form.

We Can't Change What We Don't Recognize: Understanding the Special Needs of Gifted Females.

ERIC Educational Resources Information Center

Reis, Sally M.

1987-01-01

The article considers major issues, questions, and problems related to gifted females including underachievement, creative productivity, male dominance in mathematics and science, cultural stereotyping, sex roles and mixed messages, lack of planning, the perfection complex, the impostor syndrome, and counseling. (Author/CB)

Decision Making and Systems Thinking: Educational Issues

ERIC Educational Resources Information Center

Yurtseven, M. Kudret; Buchanan, Walter W.

2016-01-01

Decision making in most universities is taught within the conventional OR/MS (Operations Research/Management Science) paradigm. This paradigm is known to be "hard" since it is consisted of mathematical tools, and normally suitable for solving structured problems. In complex situations the conventional OR/MS paradigm proves to be…

Using Microcomputers for Assessment and Error Analysis. Monograph #23.

ERIC Educational Resources Information Center

Hasselbring, Ted S.; And Others

This monograph provides an overview of computer-based assessment and error analysis in the instruction of elementary students with complex medical, learning, and/or behavioral problems. Information on generating and scoring tests using the microcomputer is offered, as are ideas for using computers in the analysis of mathematical strategies and…

Computer program determines chemical composition of physical system at equilibrium

NASA Technical Reports Server (NTRS)

Kwong, S. S.

1966-01-01

FORTRAN 4 digital computer program calculates equilibrium composition of complex, multiphase chemical systems. This is a free energy minimization method with solution of the problem reduced to mathematical operations, without concern for the chemistry involved. Also certain thermodynamic properties are determined as byproducts of the main calculations.

Enhancing Students' Scientific and Quantitative Literacies through an Inquiry-Based Learning Project on Climate Change

ERIC Educational Resources Information Center

McCright, Aaron M.

2012-01-01

Promoting sustainability and dealing with complex environmental problems like climate change demand a citizenry with considerable scientific and quantitative literacy. In particular, students in the STEM disciplines of (biophysical) science, technology, engineering, and mathematics need to develop interdisciplinary skills that help them understand…

Examination of the Computational Thinking Skills of Students

ERIC Educational Resources Information Center

Korucu, Agah Tugrul; Gencturk, Abdullah Tarik; Gundogdu, Mustafa Mucahit

2017-01-01

Computational thinking is generally considered as a kind of analytical way of thinking. According to Wings (2008) it shares with mathematical thinking, engineering thinking and scientific thinking in the general ways in which we may use for solving a problem, designing and evaluating complex systems or understanding computability and intelligence…

Exploring New Physics Frontiers Through Numerical Relativity.

PubMed

Cardoso, Vitor; Gualtieri, Leonardo; Herdeiro, Carlos; Sperhake, Ulrich

2015-01-01

The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We review techniques for solving Einstein's equations in generic spacetimes, focusing on fully nonlinear evolutions but also on how to benchmark those results with perturbative approaches. The results address problems in high-energy physics, holography, mathematical physics, fundamental physics, astrophysics and cosmology.

The Music of Mathematics: Toward a New Problem Typology

NASA Astrophysics Data System (ADS)

Quarfoot, David

Halmos (1980) once described problems and their solutions as "the heart of mathematics". Following this line of thinking, one might naturally ask: "What, then, is the heart of problems?". In this work, I attempt to answer this question using techniques from statistics, information visualization, and machine learning. I begin the journey by cataloging the features of problems delineated by the mathematics and mathematics education communities. These dimensions are explored in a large data set of students working thousands of problems at the Art of Problem Solving, an online company that provides adaptive mathematical training for students around the world. This analysis is able to concretely show how the fabric of mathematical problems changes across different subjects, difficulty levels, and students. Furthermore, it locates problems that stand out in the crowd -- those that synergize cognitive engagement, learning, and difficulty. This quantitatively-heavy side of the dissertation is partnered with a qualitatively-inspired portion that involves human scoring of 105 problems and their solutions. In this setting, I am able to capture elusive features of mathematical problems and derive a fuller picture of the space of mathematical problems. Using correlation matrices, principal components analysis, and clustering techniques, I explore the relationships among those features frequently discussed in mathematics problems (e.g., difficulty, creativity, novelty, affective engagement, authenticity). Along the way, I define a new set of uncorrelated features in problems and use these as the basis for a New Mathematical Problem Typology (NMPT). Grounded in the terminology of classical music, the NMPT works to quickly convey the essence and value of a problem, just as terms like "etude" and "mazurka" do for musicians. Taken together, these quantitative and qualitative analyses seek to terraform the landscape of mathematical problems and, concomitantly, the current thinking about that world. Most importantly, this work highlights and names the panoply of problems that exist, expanding the myopic vision of contemporary mathematical problem solving.

A complementary measure of heterogeneity on mathematical skills

NASA Astrophysics Data System (ADS)

Fedriani, Eugenio M.; Moyano, Rafael

2012-06-01

Finding educational truths is an inherently multivariate problem. There are many factors affecting each student and their performances. Because of this, both measuring of skills and assessing students are always complex processes. This is a well-known problem, and a number of solutions have been proposed by specialists. One of its ramifications is that the variety of progress levels of students in the Mathematics classroom makes teaching more difficult. We think that a measure of the heterogeneity of the different student groups could be interesting in order to prepare some strategies to deal with these kinds of difficulties. The major aim of this study is to develop new tools, complementary to the statistical ones that are commonly used for these purposes, to study situations related to education (mainly to the detection of levels of mathematical education) in which several variables are involved. These tools are thought to simplify these educational analyses and, through a better comprehension of the topic, to improve our teaching. Several authors in our research group have developed some mathematical, theoretical tools, to deal with multidimensional phenomena, and have applied them to measure poverty and also to other business models. These tools are based on multidigraphs. In this article, we implement these tools using symbolic computational software and apply them to study a specific situation related to mathematical education.

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…

Unraveling the Mystery of the Origin of Mathematical Problems: Using a Problem-Posing Framework with Prospective Mathematics Teachers

ERIC Educational Resources Information Center

Contreras, Jose

2007-01-01

In this article, I model how a problem-posing framework can be used to enhance our abilities to systematically generate mathematical problems by modifying the attributes of a given problem. The problem-posing model calls for the application of the following fundamental mathematical processes: proving, reversing, specializing, generalizing, and…

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.

Problem solving in the borderland between mathematics and physics

NASA Astrophysics Data System (ADS)

Jensen, Jens Højgaard; Niss, Martin; Jankvist, Uffe Thomas

2017-01-01

The article addresses the problématique of where mathematization is taught in the educational system, and who teaches it. Mathematization is usually not a part of mathematics programs at the upper secondary level, but we argue that physics teaching has something to offer in this respect, if it focuses on solving so-called unformalized problems, where a major challenge is to formalize the problems in mathematics and physics terms. We analyse four concrete examples of unformalized problems for which the formalization involves different order of mathematization and applying physics to the problem, but all require mathematization. The analysis leads to the formulation of a model by which we attempt to capture the important steps of the process of solving unformalized problems by means of mathematization and physicalization.

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

Solutions for Dynamic Variants of Eshelby's Inclusion Problem

NASA Astrophysics Data System (ADS)

Michelitsch, Thomas M.; Askes, Harm; Wang, Jizeng; Levin, Valery M.

The dynamic variant of Eshelby's inclusion problem plays a crucial role in many areas of mechanics and theoretical physics. Because of its mathematical complexity, dynamic variants of the inclusion problems so far are only little touched. In this paper we derive solutions for dynamic variants of the Eshelby inclusion problem for arbitrary scalar source densities of the eigenstrain. We study a series of examples of Eshelby problems which are of interest for applications in materials sciences, such as for instance cubic and prismatic inclusions. The method which covers both the time and frequency domain is especially useful for dynamically transforming inclusions of any shape.

Mathematics applied to the climate system: outstanding challenges and recent progress

PubMed Central

Williams, Paul D.; Cullen, Michael J. P.; Davey, Michael K.; Huthnance, John M.

2013-01-01

The societal need for reliable climate predictions and a proper assessment of their uncertainties is pressing. Uncertainties arise not only from initial conditions and forcing scenarios, but also from model formulation. Here, we identify and document three broad classes of problems, each representing what we regard to be an outstanding challenge in the area of mathematics applied to the climate system. First, there is the problem of the development and evaluation of simple physically based models of the global climate. Second, there is the problem of the development and evaluation of the components of complex models such as general circulation models. Third, there is the problem of the development and evaluation of appropriate statistical frameworks. We discuss these problems in turn, emphasizing the recent progress made by the papers presented in this Theme Issue. Many pressing challenges in climate science require closer collaboration between climate scientists, mathematicians and statisticians. We hope the papers contained in this Theme Issue will act as inspiration for such collaborations and for setting future research directions. PMID:23588054

Solving ordinary differential equations by electrical analogy: a multidisciplinary teaching tool

NASA Astrophysics Data System (ADS)

Sanchez Perez, J. F.; Conesa, M.; Alhama, I.

2016-11-01

Ordinary differential equations are the mathematical formulation for a great variety of problems in science and engineering, and frequently, two different problems are equivalent from a mathematical point of view when they are formulated by the same equations. Students acquire the knowledge of how to solve these equations (at least some types of them) using protocols and strict algorithms of mathematical calculation without thinking about the meaning of the equation. The aim of this work is that students learn to design network models or circuits in this way; with simple knowledge of them, students can establish the association of electric circuits and differential equations and their equivalences, from a formal point of view, that allows them to associate knowledge of two disciplines and promote the use of this interdisciplinary approach to address complex problems. Therefore, they learn to use a multidisciplinary tool that allows them to solve these kinds of equations, even students of first course of engineering, whatever the order, grade or type of non-linearity. This methodology has been implemented in numerous final degree projects in engineering and science, e.g., chemical engineering, building engineering, industrial engineering, mechanical engineering, architecture, etc. Applications are presented to illustrate the subject of this manuscript.

Writing in Groups as a Tool for Non-Routine Problem Solving in First Year University Mathematics

ERIC Educational Resources Information Center

Taylor, J. A.; McDonald, C.

2007-01-01

Development of mathematical problem solving skills is an age old problem in mathematics. This paper details the design of a component of a first year university mathematics course in which group work and mathematical communication skills, especially writing skills, are used as a tool to develop non-routine problem solving skills. In this design…

Human behaviours in evacuation crowd dynamics: From modelling to "big data" toward crisis management

NASA Astrophysics Data System (ADS)

Bellomo, N.; Clarke, D.; Gibelli, L.; Townsend, P.; Vreugdenhil, B. J.

2016-09-01

This paper proposes an essay concerning the understanding of human behaviours and crisis management of crowds in extreme situations, such as evacuation through complex venues. The first part focuses on the understanding of the main features of the crowd viewed as a living, hence complex system. The main concepts are subsequently addressed, in the second part, to a critical analysis of mathematical models suitable to capture them, as far as it is possible. Then, the third part focuses on the use, toward safety problems, of a model derived by the methods of the mathematical kinetic theory and theoretical tools of evolutionary game theory. It is shown how this model can depict critical situations and how these can be managed with the aim of minimizing the risk of catastrophic events.

Weak task-related modulation and stimulus representations during arithmetic problem solving in children with developmental dyscalculia

PubMed Central

Ashkenazi, Sarit; Rosenberg-Lee, Miriam; Tenison, Caitlin; Menon, Vinod

2015-01-01

Developmental dyscalculia (DD) is a disability that impacts math learning and skill acquisition in school-age children. Here we investigate arithmetic problem solving deficits in young children with DD using univariate and multivariate analysis of fMRI data. During fMRI scanning, 17 children with DD (ages 7–9, grades 2 and 3) and 17 IQ- and reading ability-matched typically developing (TD) children performed complex and simple addition problems which differed only in arithmetic complexity. While the TD group showed strong modulation of brain responses with increasing arithmetic complexity, children with DD failed to show such modulation. Children with DD showed significantly reduced activation compared to TD children in the intraparietal sulcus, superior parietal lobule, supramarginal gyrus and bilateral dorsolateral prefrontal cortex in relation to arithmetic complexity. Critically, multivariate representational similarity revealed that brain response patterns to complex and simple problems were less differentiated in the DD group in bilateral anterior IPS, independent of overall differences in signal level. Taken together, these results show that children with DD not only under-activate key brain regions implicated in mathematical cognition, but they also fail to generate distinct neural responses and representations for different arithmetic problems. Our findings provide novel insights into the neural basis of DD. PMID:22682904

Weak task-related modulation and stimulus representations during arithmetic problem solving in children with developmental dyscalculia.

PubMed

Ashkenazi, Sarit; Rosenberg-Lee, Miriam; Tenison, Caitlin; Menon, Vinod

2012-02-15

Developmental dyscalculia (DD) is a disability that impacts math learning and skill acquisition in school-age children. Here we investigate arithmetic problem solving deficits in young children with DD using univariate and multivariate analysis of fMRI data. During fMRI scanning, 17 children with DD (ages 7-9, grades 2 and 3) and 17 IQ- and reading ability-matched typically developing (TD) children performed complex and simple addition problems which differed only in arithmetic complexity. While the TD group showed strong modulation of brain responses with increasing arithmetic complexity, children with DD failed to show such modulation. Children with DD showed significantly reduced activation compared to TD children in the intraparietal sulcus, superior parietal lobule, supramarginal gyrus and bilateral dorsolateral prefrontal cortex in relation to arithmetic complexity. Critically, multivariate representational similarity revealed that brain response patterns to complex and simple problems were less differentiated in the DD group in bilateral anterior IPS, independent of overall differences in signal level. Taken together, these results show that children with DD not only under-activate key brain regions implicated in mathematical cognition, but they also fail to generate distinct neural responses and representations for different arithmetic problems. Our findings provide novel insights into the neural basis of DD. Copyright © 2011 Elsevier Ltd. All rights reserved.

The knowledge instinct, cognitive algorithms, modeling of language and cultural evolution

NASA Astrophysics Data System (ADS)

Perlovsky, Leonid I.

2008-04-01

The talk discusses mechanisms of the mind and their engineering applications. The past attempts at designing "intelligent systems" encountered mathematical difficulties related to algorithmic complexity. The culprit turned out to be logic, which in one way or another was used not only in logic rule systems, but also in statistical, neural, and fuzzy systems. Algorithmic complexity is related to Godel's theory, a most fundamental mathematical result. These difficulties were overcome by replacing logic with a dynamic process "from vague to crisp," dynamic logic. It leads to algorithms overcoming combinatorial complexity, and resulting in orders of magnitude improvement in classical problems of detection, tracking, fusion, and prediction in noise. I present engineering applications to pattern recognition, detection, tracking, fusion, financial predictions, and Internet search engines. Mathematical and engineering efficiency of dynamic logic can also be understood as cognitive algorithm, which describes fundamental property of the mind, the knowledge instinct responsible for all our higher cognitive functions: concepts, perception, cognition, instincts, imaginations, intuitions, emotions, including emotions of the beautiful. I present our latest results in modeling evolution of languages and cultures, their interactions in these processes, and role of music in cultural evolution. Experimental data is presented that support the theory. Future directions are outlined.

Secondary Teachers’ Mathematics-related Beliefs and Knowledge about Mathematical Problem-solving

NASA Astrophysics Data System (ADS)

E Siswono, T. Y.; Kohar, A. W.; Hartono, S.

2017-02-01

This study investigates secondary teachers’ belief about the three mathematics-related beliefs, i.e. nature of mathematics, teaching mathematics, learning mathematics, and knowledge about mathematical problem solving. Data were gathered through a set of task-based semi-structured interviews of three selected teachers with different philosophical views of teaching mathematics, i.e. instrumental, platonist, and problem solving. Those teachers were selected from an interview using a belief-related task from purposively selected teachers in Surabaya and Sidoarjo. While the interviews about knowledge examine teachers’ problem solving content and pedagogical knowledge, the interviews about beliefs examine their views on several cases extracted from each of such mathematics-related beliefs. Analysis included the categorization and comparison on each of beliefs and knowledge as well as their interaction. Results indicate that all the teachers did not show a high consistency in responding views of their mathematics-related beliefs, while they showed weaknesses primarily on problem solving content knowledge. Findings also point out that teachers’ beliefs have a strong relationship with teachers’ knowledge about problem solving. In particular, the instrumental teacher’s beliefs were consistent with his insufficient knowledge about problem-solving, while both platonist and problem-solving teacher’s beliefs were consistent with their sufficient knowledge of either content or pedagogical problem solving.

Understanding Immunology via Engineering Design: The Role of Mathematical Prototyping

PubMed Central

Klinke, David J.; Wang, Qing

2012-01-01

A major challenge in immunology is how to translate data into knowledge given the inherent complexity and dynamics of human physiology. Both the physiology and engineering communities have rich histories in applying computational approaches to translate data obtained from complex systems into knowledge of system behavior. However, there are some differences in how disciplines approach problems. By referring to mathematical models as mathematical prototypes, we aim to highlight aspects related to the process (i.e., prototyping) rather than the product (i.e., the model). The objective of this paper is to review how two related engineering concepts, specifically prototyping and “fitness for use,” can be applied to overcome the pressing challenge in translating data into improved knowledge of basic immunology that can be used to improve therapies for disease. These concepts are illustrated using two immunology-related examples. The prototypes presented focus on the beta cell mass at the onset of type 1 diabetes and the dynamics of dendritic cells in the lung. This paper is intended to illustrate some of the nuances associated with applying mathematical modeling to improve understanding of the dynamics of disease progression in humans. PMID:22973412

Pre-service mathematics teachers’ ability in solving well-structured problem

NASA Astrophysics Data System (ADS)

Paradesa, R.

2018-01-01

This study aimed to describe the mathematical problem-solving ability of undergraduate students of mathematics education in solving the well-structured problem. The type of this study was qualitative descriptive. The subjects in this study were 100 undergraduate students of Mathematics Education at one of the private universities in Palembang city. The data in this study was collected through two test items with essay form. The results of this study showed that, from the first problem, only 8% students can solve it, but do not check back again to validate the process. Based on a scoring rubric that follows Polya strategy, their answer satisfied 2 4 2 0 patterns. But, from the second problem, 45% students satisfied it. This is because the second problem imitated from the example that was given in learning process. The average score of undergraduate students mathematical problem-solving ability in solving well-structured problems showed 56.00 with standard deviation was 13.22. It means that, from 0 - 100 scale, undergraduate students mathematical problem-solving ability can be categorized low. From this result, the conclusion was undergraduate students of mathematics education in Palembang still have a problem in solving mathematics well-structured problem.

Research Mathematicians' Practices in Selecting Mathematical Problems

ERIC Educational Resources Information Center

Misfeldt, Morten; Johansen, Mikkel Willum

2015-01-01

Developing abilities to create, inquire into, qualify, and choose among mathematical problems is an important educational goal. In this paper, we elucidate how mathematicians work with mathematical problems in order to understand this mathematical process. More specifically, we investigate how mathematicians select and pose problems and discuss to…

On the complexity of a combined homotopy interior method for convex programming

NASA Astrophysics Data System (ADS)

Yu, Bo; Xu, Qing; Feng, Guochen

2007-03-01

In [G.C. Feng, Z.H. Lin, B. Yu, Existence of an interior pathway to a Karush-Kuhn-Tucker point of a nonconvex programming problem, Nonlinear Anal. 32 (1998) 761-768; G.C. Feng, B. Yu, Combined homotopy interior point method for nonlinear programming problems, in: H. Fujita, M. Yamaguti (Eds.), Advances in Numerical Mathematics, Proceedings of the Second Japan-China Seminar on Numerical Mathematics, Lecture Notes in Numerical and Applied Analysis, vol. 14, Kinokuniya, Tokyo, 1995, pp. 9-16; Z.H. Lin, B. Yu, G.C. Feng, A combined homotopy interior point method for convex programming problem, Appl. Math. Comput. 84 (1997) 193-211.], a combined homotopy was constructed for solving non-convex programming and convex programming with weaker conditions, without assuming the logarithmic barrier function to be strictly convex and the solution set to be bounded. It was proven that a smooth interior path from an interior point of the feasible set to a K-K-T point of the problem exists. This shows that combined homotopy interior point methods can solve the problem that commonly used interior point methods cannot solveE However, so far, there is no result on its complexity, even for linear programming. The main difficulty is that the objective function is not monotonically decreasing on the combined homotopy path. In this paper, by taking a piecewise technique, under commonly used conditions, polynomiality of a combined homotopy interior point method is given for convex nonlinear programming.

Designing a Better Experience: A Qualitative Investigation of Student Engineering Internships

ERIC Educational Resources Information Center

Paknejad, Mohammad R.

2016-01-01

Science, Technology, Engineering and Mathematics (STEM) education play a very important role in preparing students with skills necessary to obtain better jobs, solve real-world challenges, and compete in the global economy. STEM education develops critical thinking and the ability to solve complex problems. Research showed that 8 out of 10 most…

Identifying Common Mathematical Misconceptions from Actions in Educational Video Games. CRESST Report 838

ERIC Educational Resources Information Center

Kerr, Deirdre

2014-01-01

Educational video games provide an opportunity for students to interact with and explore complex representations of academic content and allow for the examination of problem-solving strategies and mistakes that can be difficult to capture in more traditional environments. However, data from such games are notoriously difficult to analyze. This…

Understanding Introductory Students' Application of Integrals in Physics from Multiple Perspectives

ERIC Educational Resources Information Center

Hu, Dehui

2013-01-01

Calculus is used across many physics topics from introductory to upper-division level college courses. The concepts of differentiation and integration are important tools for solving real world problems. Using calculus or any mathematical tool in physics is much more complex than the straightforward application of the equations and algorithms that…

Light-Emitting Diodes: Solving Complex Problems

ERIC Educational Resources Information Center

Planinšic, Gorazd; Etkina, Eugenia

2015-01-01

This is the fourth paper in our Light-Emitting Diodes series. The series aims to create a systematic library of LED-based materials and to provide readers with the description of experiments and the pedagogical treatment that would help their students construct, test, and apply physics concepts and mathematical relations. The first paper provided…

Reference Framework for Describing and Assessing Students' Understanding in First Year Calculus

ERIC Educational Resources Information Center

Kannemeyer, Larry

2005-01-01

This paper presents aspects of a study that investigates the development of an instrument, a reference framework, to analyse students' written responses to non-routine problems in a first year calculus course in order to describe the complexities of their understanding and to assess their understanding of particular mathematical concepts.…

Integrated STEM: Focus on Informal Education and Community Collaboration through Engineering

ERIC Educational Resources Information Center

Burrows, Andrea; Lockwood, Meghan; Borowczak, Mike; Janak, Edward; Barber, Brian

2018-01-01

This article showcases STEM as an interdisciplinary field in which the disciplines strengthen and support each other (not as separate science, technology, engineering, and mathematics disciplines). The authors focus on an open-ended, complex problem--water quality--as the primary teaching and learning task. The participants, middle school female…

A mixed integer program to model spatial wildfire behavior and suppression placement decisions

Treesearch

Erin J. Belval; Yu Wei; Michael Bevers

2015-01-01

Wildfire suppression combines multiple objectives and dynamic fire behavior to form a complex problem for decision makers. This paper presents a mixed integer program designed to explore integrating spatial fire behavior and suppression placement decisions into a mathematical programming framework. Fire behavior and suppression placement decisions are modeled using...

"Accepting Emotional Complexity": A Socio-Constructivist Perspective on the Role of Emotions in the Mathematics Classroom

ERIC Educational Resources Information Center

Eynde, Peter Op't; De Corte, Erik; Verschaffel, Lieven

2006-01-01

A socio-constructivist account of learning and emotions stresses the situatedness of every learning activity and points to the close interactions between cognitive, conative and affective factors in students' learning and problem solving. Emotions are perceived as being constituted by the dynamic interplay of cognitive, physiological, and…

Changes in Science Teachers' Conceptions and Connections of STEM Concepts and Earthquake Engineering

ERIC Educational Resources Information Center

Cavlazoglu, Baki; Stuessy, Carol

2017-01-01

The authors find justification for integrating science, technology, engineering, and mathematics (STEM) in the complex problems that today's students will face as tomorrow's STEM professionals. Teachers with individual subject-area specialties in the STEM content areas have limited experience in integrating STEM. In this study, the authors…

Synthesizing Results from Empirical Research on Computer-Based Scaffolding in STEM Education: A Meta-Analysis

ERIC Educational Resources Information Center

Belland, Brian R.; Walker, Andrew E.; Kim, Nam Ju; Lefler, Mason

2017-01-01

Computer-based scaffolding assists students as they generate solutions to complex problems, goals, or tasks, helping increase and integrate their higher order skills in the process. However, despite decades of research on scaffolding in STEM (science, technology, engineering, and mathematics) education, no existing comprehensive meta-analysis has…

The Search Is on: Engendering Faculty Diversity through More Effective Search and Recruitment

ERIC Educational Resources Information Center

Bilimoria, Diana; Buch, Kimberly K.

2010-01-01

The underrepresentation of women and minority faculty in the science, technology, engineering, and mathematics (STEM) disciplines continues to be a major concern to university leaders, policy makers, and scientists. While a number of complex factors across the entire academic pipeline play significant roles in this problem, important contributing…

The Role of Expository Writing in Mathematical Problem Solving

ERIC Educational Resources Information Center

Craig, Tracy S.

2016-01-01

Mathematical problem-solving is notoriously difficult to teach in a standard university mathematics classroom. The project on which this article reports aimed to investigate the effect of the writing of explanatory strategies in the context of mathematical problem solving on problem-solving behaviour. This article serves to describe the…

Using Diagrams as Tools for the Solution of Non-Routine Mathematical Problems

ERIC Educational Resources Information Center

Pantziara, Marilena; Gagatsis, Athanasios; Elia, Iliada

2009-01-01

The Mathematics education community has long recognized the importance of diagrams in the solution of mathematical problems. Particularly, it is stated that diagrams facilitate the solution of mathematical problems because they represent problems' structure and information (Novick & Hurley, 2001; Diezmann, 2005). Novick and Hurley were the first…

The Problem-Solving Approach in the Teaching of Number Theory

ERIC Educational Resources Information Center

Toh, Pee Choon; Leong, Yew Hoong; Toh, Tin Lam; Dindyal, Jaguthsing; Quek, Khiok Seng; Tay, Eng Guan; Ho, Foo Him

2014-01-01

Mathematical problem solving is the mainstay of the mathematics curriculum for Singapore schools. In the preparation of prospective mathematics teachers, the authors, who are mathematics teacher educators, deem it important that pre-service mathematics teachers experience non-routine problem solving and acquire an attitude that predisposes them to…

Early stage response problem for post-disaster incidents

NASA Astrophysics Data System (ADS)

Kim, Sungwoo; Shin, Youngchul; Lee, Gyu M.; Moon, Ilkyeong

2018-07-01

Research on evacuation plans for reducing damages and casualties has been conducted to advise defenders against threats. However, despite the attention given to the research in the past, emergency response management, designed to neutralize hazards, has been undermined since planners frequently fail to apprehend the complexities and contexts of the emergency situation. Therefore, this study considers a response problem with unique characteristics for the duration of the emergency. An early stage response problem is identified to find the optimal routing and scheduling plan for responders to prevent further hazards. Due to the complexity of the proposed mathematical model, two algorithms are developed. Data from a high-rise building, called Central City in Seoul, Korea, are used to evaluate the algorithms. Results show that the proposed algorithms can procure near-optimal solutions within a reasonable time.

Science of the science, drug discovery and artificial neural networks.

PubMed

Patel, Jigneshkumar

2013-03-01

Drug discovery process many times encounters complex problems, which may be difficult to solve by human intelligence. Artificial Neural Networks (ANNs) are one of the Artificial Intelligence (AI) technologies used for solving such complex problems. ANNs are widely used for primary virtual screening of compounds, quantitative structure activity relationship studies, receptor modeling, formulation development, pharmacokinetics and in all other processes involving complex mathematical modeling. Despite having such advanced technologies and enough understanding of biological systems, drug discovery is still a lengthy, expensive, difficult and inefficient process with low rate of new successful therapeutic discovery. In this paper, author has discussed the drug discovery science and ANN from very basic angle, which may be helpful to understand the application of ANN for drug discovery to improve efficiency.

How do open-ended problems promote mathematical creativity? A reflection of bare mathematics problem and contextual problem

NASA Astrophysics Data System (ADS)

Wijaya, A.

2018-03-01

Creativity is often seen as one of the fundamental aspects of character education. As one of the 21st century skills, creativity has also been considered as an important goal of education across the world. This paper reports a study on promoting mathematical creativity through the use of open-ended mathematics problems. A total of 53 undergraduate students participated in the study. These students worked on open-ended problems in two types, i.e. bare mathematics problem and contextual problem. The contextual problem was presented in the form of paper-based and Geogebra-based. The students’ works were analysed qualitatively in order to describe how students’ mathematical creativity developed. It was found that the open-ended problems successfully promote students’ creativity as indicated by various solutions or strategies that were used by students to solve the problems. The analysis of students’ works show that students’ creativity developed through three kinds of exploration, i. e. (1) exploration of contexts, (2) exploration of software features, and (3) exploration of mathematics concepts. The use of metacognitive questioning was found to be helpful to develop the first two explorations into mathematical exploration.

The semantic system is involved in mathematical problem solving.

PubMed

Zhou, Xinlin; Li, Mengyi; Li, Leinian; Zhang, Yiyun; Cui, Jiaxin; Liu, Jie; Chen, Chuansheng

2018-02-01

Numerous studies have shown that the brain regions around bilateral intraparietal cortex are critical for number processing and arithmetical computation. However, the neural circuits for more advanced mathematics such as mathematical problem solving (with little routine arithmetical computation) remain unclear. Using functional magnetic resonance imaging (fMRI), this study (N = 24 undergraduate students) compared neural bases of mathematical problem solving (i.e., number series completion, mathematical word problem solving, and geometric problem solving) and arithmetical computation. Direct subject- and item-wise comparisons revealed that mathematical problem solving typically had greater activation than arithmetical computation in all 7 regions of the semantic system (which was based on a meta-analysis of 120 functional neuroimaging studies on semantic processing). Arithmetical computation typically had greater activation in the supplementary motor area and left precentral gyrus. The results suggest that the semantic system in the brain supports mathematical problem solving. Copyright © 2017 Elsevier Inc. All rights reserved.

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.

What Is the Problem in Problem-Based Learning in Higher Education Mathematics

ERIC Educational Resources Information Center

Dahl, Bettina

2018-01-01

Problem and Project-Based Learning (PBL) emphasise collaborate work on problems relevant to society and emphases the relation between theory and practice. PBL fits engineering students as preparation for their future professions but what about mathematics? Mathematics is not just applied mathematics, but it is also a body of abstract knowledge…

Learning to Solve Story Problems--Supporting Transitions between Reality and Mathematics

ERIC Educational Resources Information Center

Große, Cornelia S.

2014-01-01

Applying mathematics to real problems is increasingly emphasized in school education; however, it is often complained that many students are not able to solve mathematical problems embedded in contexts. In order to solve story problems, a transition from a textual description to a mathematical notation has to be found, intra-mathematical…

Making mathematics and science integration happen: key aspects of practice

NASA Astrophysics Data System (ADS)

Ríordáin, Máire Ní; Johnston, Jennifer; Walshe, Gráinne

2016-02-01

The integration of mathematics and science teaching and learning facilitates student learning, engagement, motivation, problem-solving, criticality and real-life application. However, the actual implementation of an integrative approach to the teaching and learning of both subjects at classroom level, with in-service teachers working collaboratively, at second-level education, is under-researched due to the complexities of school-based research. This study reports on a year-long case study on the implementation of an integrated unit of learning on distance, speed and time, within three second-level schools in Ireland. This study employed a qualitative approach and examined the key aspects of practice that impact on the integration of mathematics and science teaching and learning. We argue that teacher perspective, teacher knowledge of the 'other subject' and of technological pedagogical content knowledge (TPACK), and teacher collaboration and support all impact on the implementation of an integrative approach to mathematics and science education.

Individualized Math Problems in Percent. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. This volume includes problems concerned with computing percents.…

Individualized Math Problems in Algebra. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic, and contains problems related to diverse vocations. Solutions are provided for all problems. Problems presented in this package concern ratios used in food…

Individualized Math Problems in Fractions. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. This package contains problems involving computation with common…

Individualized Math Problems in Geometry. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. The volume contains problems in applied geometry. Measurement of…

Individualized Math Problems in Measurement and Conversion. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. This volume includes problems involving measurement, computation of…

Individualized Math Problems in Integers. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. This volume presents problems involving operations with positive and…

Complex optimization for big computational and experimental neutron datasets

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

Bao, Feng; Oak Ridge National Lab.; Archibald, Richard

Here, we present a framework to use high performance computing to determine accurate solutions to the inverse optimization problem of big experimental data against computational models. We demonstrate how image processing, mathematical regularization, and hierarchical modeling can be used to solve complex optimization problems on big data. We also demonstrate how both model and data information can be used to further increase solution accuracy of optimization by providing confidence regions for the processing and regularization algorithms. Finally, we use the framework in conjunction with the software package SIMPHONIES to analyze results from neutron scattering experiments on silicon single crystals, andmore » refine first principles calculations to better describe the experimental data.« less

Complex optimization for big computational and experimental neutron datasets

DOE PAGES

Bao, Feng; Oak Ridge National Lab.; Archibald, Richard; ...

2016-11-07

Here, we present a framework to use high performance computing to determine accurate solutions to the inverse optimization problem of big experimental data against computational models. We demonstrate how image processing, mathematical regularization, and hierarchical modeling can be used to solve complex optimization problems on big data. We also demonstrate how both model and data information can be used to further increase solution accuracy of optimization by providing confidence regions for the processing and regularization algorithms. Finally, we use the framework in conjunction with the software package SIMPHONIES to analyze results from neutron scattering experiments on silicon single crystals, andmore » refine first principles calculations to better describe the experimental data.« less

Aerodynamics of an airfoil with a jet issuing from its surface

NASA Technical Reports Server (NTRS)

Tavella, D. A.; Karamcheti, K.

1982-01-01

A simple, two dimensional, incompressible and inviscid model for the problem posed by a two dimensional wing with a jet issuing from its lower surface is considered and a parametric analysis is carried out to observe how the aerodynamic characteristics depend on the different parameters. The mathematical problem constitutes a boundary value problem where the position of part of the boundary is not known a priori. A nonlinear optimization approach was used to solve the problem, and the analysis reveals interesting characteristics that may help to better understand the physics involved in more complex situations in connection with high lift systems.

On Riemann boundary value problems for null solutions of the two dimensional Helmholtz equation

NASA Astrophysics Data System (ADS)

Bory Reyes, Juan; Abreu Blaya, Ricardo; Rodríguez Dagnino, Ramón Martin; Kats, Boris Aleksandrovich

2018-01-01

The Riemann boundary value problem (RBVP to shorten notation) in the complex plane, for different classes of functions and curves, is still widely used in mathematical physics and engineering. For instance, in elasticity theory, hydro and aerodynamics, shell theory, quantum mechanics, theory of orthogonal polynomials, and so on. In this paper, we present an appropriate hyperholomorphic approach to the RBVP associated to the two dimensional Helmholtz equation in R^2 . Our analysis is based on a suitable operator calculus.

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.

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.

What is the problem in problem-based learning in higher education mathematics

NASA Astrophysics Data System (ADS)

Dahl, Bettina

2018-01-01

Problem and Project-Based Learning (PBL) emphasise collaborate work on problems relevant to society and emphases the relation between theory and practice. PBL fits engineering students as preparation for their future professions but what about mathematics? Mathematics is not just applied mathematics, but it is also a body of abstract knowledge where the application in society is not always obvious. Does mathematics, including pure mathematics, fit into a PBL curriculum? This paper argues that it does for two reasons: (1) PBL resembles the working methods of research mathematicians. (2) The concept of society includes the society of researchers to whom theoretical mathematics is relevant. The paper describes two cases of university PBL projects in mathematics; one in pure mathematics and the other in applied mathematics. The paper also discusses that future engineers need to understand the world of mathematics as well as how engineers fit into a process of fundamental-research-turned-into-applied-science.

Protocol Analysis of Group Problem Solving in Mathematics: A Cognitive-Metacognitive Framework for Assessment.

ERIC Educational Resources Information Center

Artzt, Alice F.; Armour-Thomas, Eleanor

The roles of cognition and metacognition were examined in the mathematical problem-solving behaviors of students as they worked in small groups. As an outcome, a framework that links the literature of cognitive science and mathematical problem solving was developed for protocol analysis of mathematical problem solving. Within this framework, each…

Mathematical Profiles and Problem Solving Abilities of Mathematically Promising Students

ERIC Educational Resources Information Center

Budak, Ibrahim

2012-01-01

Mathematically promising students are defined as those who have the potential to become the leaders and problem solvers of the future. The purpose of this research is to reveal what problem solving abilities mathematically promising students show in solving non-routine problems and type of profiles they present in the classroom and during problem…

Engaging Future Teachers in Problem-Based Learning with the Park City Mathematics Institute Problems

ERIC Educational Resources Information Center

Pilgrim, Mary E.

2014-01-01

Problem-based learning (PBL) is a pedagogical technique recommended for K-12 mathematics classrooms. However, the mathematics courses in future teachers' degree programs are often lecture based. Students typically learn about problem-based learning in theory, but rarely get to experience it first-hand in their mathematics courses. The premise…

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…

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…

Developing Instruction Materials Based on Joyful PBL to Improve Students Mathematical Representation Ability

ERIC Educational Resources Information Center

Minarni, Ani; Napitupulu, E. Elvis

2017-01-01

Solving problem either within mathematics or beyond is one of the ultimate goal students learn mathematics. It is since mathematics takes role tool as well as vehicle to develop problem solving ability. One of the supporting components to problem solving is mathematical representation ability (MRA). Nowadays, many teachers and researchers find out…

Using the Wonder of Inequalities between Averages for Mathematics Problems Solving

ERIC Educational Resources Information Center

Shaanan, Rachel Mogilevsky; Gordon, Moshe Stupel

2016-01-01

The study presents an introductory idea of using mathematical averages as a tool for enriching mathematical problem solving. Throughout students' activities, a research was conducted on their ability to solve mathematical problems, and how to cope with a variety of mathematical tasks, in a variety of ways, using the skills, tools and experiences…

A Critical Discourse Analysis of Practical Problems in a Foundation Mathematics Course at a South African University

ERIC Educational Resources Information Center

le Roux, Kate; Adler, Jill

2016-01-01

Mathematical problems that make links to the everyday and to disciplines other than mathematics--variously referred to as practical, realistic, real-world or applied problems in the literature--feature in school and undergraduate mathematics reforms aimed at increasing mathematics participation in contexts of inequity and diversity. In this…

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…

Atomistic full-quantum transport model for zigzag graphene nanoribbon-based structures: Complex energy-band method

NASA Astrophysics Data System (ADS)

Chen, Chun-Nan; Luo, Win-Jet; Shyu, Feng-Lin; Chung, Hsien-Ching; Lin, Chiun-Yan; Wu, Jhao-Ying

2018-01-01

Using a non-equilibrium Green’s function framework in combination with the complex energy-band method, an atomistic full-quantum model for solving quantum transport problems for a zigzag-edge graphene nanoribbon (zGNR) structure is proposed. For transport calculations, the mathematical expressions from the theory for zGNR-based device structures are derived in detail. The transport properties of zGNR-based devices are calculated and studied in detail using the proposed method.

Using student feedback to improve student attitudes and mathematical confidence in a first year interdisciplinary quantitative course: from the ashes of disaster!

NASA Astrophysics Data System (ADS)

Everingham, Yvette; Gyuris, Emma; Sexton, Justin

2013-09-01

Today's scientist is faced with complex problems that require interdisciplinary solutions. Consequently, tertiary science educators have had to develop and deliver interdisciplinary science courses to equip students with the skills required to solve the evolving real-world challenges of today and tomorrow. There are few reported studies of the lessons learned from designing and delivering first year compulsory interdisciplinary science subjects at regional universities. Even fewer studies assess the impact that teaching interventions within interdisciplinary courses have on students' attitudes towards mathematics and technology, and mathematics anxiety. This paper discusses the feedback received from the first student cohort of a new compulsory, first year interdisciplinary science subject at a regional Australian university which resulted in curricular revisions. These revisions included a greater emphasis on the subject relevance and increased student support in tutorials. Assessment practices were also dramatically modified. The change in student attitudes and anxiety levels a priori and a posteriori to the interventions was measured quantitatively and qualitatively. Post-intervention, female and non-mathematics major students had grown in mathematical confidence and were less anxious. It is important that positive and negative research findings are reported, so science educators can learn from one another, and can better prepare their students for the challenges they will face in bringing interdisciplinary solutions to contemporary real-world problems.

A Strategy for Improving US Middle School Student Mathematics Word Problem Solving Performance

NASA Technical Reports Server (NTRS)

Thomas, Valerie L.

2004-01-01

U.S. middle school students have difficulty understanding and solving mathematics word problems. Their mathematics performance on the Third International Mathematics and Science Study (TIMMS) is far below their international peers, and minority students are less likely than high socioeconomic status (SES) White/Asian students to be exposed to higher-level mathematics concepts. Research literature also indicates that when students use both In-School and Out-of-School knowledge and experiences to create authentic mathematics word problems, student achievement improves. This researcher developed a Strategy for improving mathematics problem solving performance and a Professional Development Model (PDM) to effectively implement the Strategy.

An Investigation of Secondary Teachers’ Understanding and Belief on Mathematical Problem Solving

NASA Astrophysics Data System (ADS)

Yuli Eko Siswono, Tatag; Wachidul Kohar, Ahmad; Kurniasari, Ika; Puji Astuti, Yuliani

2016-02-01

Weaknesses on problem solving of Indonesian students as reported by recent international surveys give rise to questions on how Indonesian teachers bring out idea of problem solving in mathematics lesson. An explorative study was undertaken to investigate how secondary teachers who teach mathematics at junior high school level understand and show belief toward mathematical problem solving. Participants were teachers from four cities in East Java province comprising 45 state teachers and 25 private teachers. Data was obtained through questionnaires and written test. The results of this study point out that the teachers understand pedagogical problem solving knowledge well as indicated by high score of observed teachers‘ responses showing understanding on problem solving as instruction as well as implementation of problem solving in teaching practice. However, they less understand on problem solving content knowledge such as problem solving strategies and meaning of problem itself. Regarding teacher's difficulties, teachers admitted to most frequently fail in (1) determining a precise mathematical model or strategies when carrying out problem solving steps which is supported by data of test result that revealed transformation error as the most frequently observed errors in teachers’ work and (2) choosing suitable real situation when designing context-based problem solving task. Meanwhile, analysis of teacher's beliefs on problem solving shows that teachers tend to view both mathematics and how students should learn mathematics as body static perspective, while they tend to believe to apply idea of problem solving as dynamic approach when teaching mathematics.

Tractable Experiment Design via Mathematical Surrogates

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

Williams, Brian J.

This presentation summarizes the development and implementation of quantitative design criteria motivated by targeted inference objectives for identifying new, potentially expensive computational or physical experiments. The first application is concerned with estimating features of quantities of interest arising from complex computational models, such as quantiles or failure probabilities. A sequential strategy is proposed for iterative refinement of the importance distributions used to efficiently sample the uncertain inputs to the computational model. In the second application, effective use of mathematical surrogates is investigated to help alleviate the analytical and numerical intractability often associated with Bayesian experiment design. This approach allows formore » the incorporation of prior information into the design process without the need for gross simplification of the design criterion. Illustrative examples of both design problems will be presented as an argument for the relevance of these research problems.« less

An Introduction to Kristof's Theorem for Solving Least-Square Optimization Problems Without Calculus.

PubMed

Waller, Niels

2018-01-01

Kristof's Theorem (Kristof, 1970 ) describes a matrix trace inequality that can be used to solve a wide-class of least-square optimization problems without calculus. Considering its generality, it is surprising that Kristof's Theorem is rarely used in statistics and psychometric applications. The underutilization of this method likely stems, in part, from the mathematical complexity of Kristof's ( 1964 , 1970 ) writings. In this article, I describe the underlying logic of Kristof's Theorem in simple terms by reviewing four key mathematical ideas that are used in the theorem's proof. I then show how Kristof's Theorem can be used to provide novel derivations to two cognate models from statistics and psychometrics. This tutorial includes a glossary of technical terms and an online supplement with R (R Core Team, 2017 ) code to perform the calculations described in the text.

Individualized Math Problems in Ratio and Proportion. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. This volume contains problems involving ratio and proportion. Some…

Individualized Math Problems in Whole Numbers. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems in this set require computations involving whole numbers.…

Individualized Math Problems in Graphs and Tables. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems involving the construction and interpretation of graphs and…

Individualized Math Problems in Simple Equations. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems in this volume require solution of linear equations, systems…

Individualized Math Problems in Trigonometry. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems in this volume require the use of trigonometric and inverse…

Individualized Math Problems in Decimals. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

THis is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems in this volume concern use of decimals and are related to the…

Individualized Math Problems in Volume. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems in this booklet require the computation of volumes of solids,…

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.

Program Helps To Determine Chemical-Reaction Mechanisms

NASA Technical Reports Server (NTRS)

Bittker, D. A.; Radhakrishnan, K.

1995-01-01

General Chemical Kinetics and Sensitivity Analysis (LSENS) computer code developed for use in solving complex, homogeneous, gas-phase, chemical-kinetics problems. Provides for efficient and accurate chemical-kinetics computations and provides for sensitivity analysis for variety of problems, including problems involving honisothermal conditions. Incorporates mathematical models for static system, steady one-dimensional inviscid flow, reaction behind incident shock wave (with boundary-layer correction), and perfectly stirred reactor. Computations of equilibrium properties performed for following assigned states: enthalpy and pressure, temperature and pressure, internal energy and volume, and temperature and volume. Written in FORTRAN 77 with exception of NAMELIST extensions used for input.

Reconciliation of Gene and Species Trees

PubMed Central

Rusin, L. Y.; Lyubetskaya, E. V.; Gorbunov, K. Y.; Lyubetsky, V. A.

2014-01-01

The first part of the paper briefly overviews the problem of gene and species trees reconciliation with the focus on defining and algorithmic construction of the evolutionary scenario. Basic ideas are discussed for the aspects of mapping definitions, costs of the mapping and evolutionary scenario, imposing time scales on a scenario, incorporating horizontal gene transfers, binarization and reconciliation of polytomous trees, and construction of species trees and scenarios. The review does not intend to cover the vast diversity of literature published on these subjects. Instead, the authors strived to overview the problem of the evolutionary scenario as a central concept in many areas of evolutionary research. The second part provides detailed mathematical proofs for the solutions of two problems: (i) inferring a gene evolution along a species tree accounting for various types of evolutionary events and (ii) trees reconciliation into a single species tree when only gene duplications and losses are allowed. All proposed algorithms have a cubic time complexity and are mathematically proved to find exact solutions. Solving algorithms for problem (ii) can be naturally extended to incorporate horizontal transfers, other evolutionary events, and time scales on the species tree. PMID:24800245

Redesigning the Quantum Mechanics Curriculum to Incorporate Problem Solving Using a Computer Algebra System

NASA Astrophysics Data System (ADS)

Roussel, Marc R.

1999-10-01

One of the traditional obstacles to learning quantum mechanics is the relatively high level of mathematical proficiency required to solve even routine problems. Modern computer algebra systems are now sufficiently reliable that they can be used as mathematical assistants to alleviate this difficulty. In the quantum mechanics course at the University of Lethbridge, the traditional three lecture hours per week have been replaced by two lecture hours and a one-hour computer-aided problem solving session using a computer algebra system (Maple). While this somewhat reduces the number of topics that can be tackled during the term, students have a better opportunity to familiarize themselves with the underlying theory with this course design. Maple is also available to students during examinations. The use of a computer algebra system expands the class of feasible problems during a time-limited exercise such as a midterm or final examination. A modern computer algebra system is a complex piece of software, so some time needs to be devoted to teaching the students its proper use. However, the advantages to the teaching of quantum mechanics appear to outweigh the disadvantages.

The Ability of Conceptual Monitoring and the Quality of Working Memory at Children With Calculation Difficulties

ERIC Educational Resources Information Center

Arsic, Sladjana; Eminovic, Fadilj; Stankovic, Ivona

2011-01-01

Calculia is considered to be the ability of performing arithmetic operations, the preconditions for the development of mathematical skills in the complex functioning of psychological functions represented in neuro-anatomical systems, as well in the interaction with the environment. Problems in acquiring arithmetic skills can be described as…

Conceptualizing Vectors in College Geometry: A New Framework for Analysis of Student Approaches and Difficulties

ERIC Educational Resources Information Center

Kwon, Oh Hoon

2012-01-01

This dissertation documents a new way of conceptualizing vectors in college mathematics, especially in geometry. First, I will introduce three problems to show the complexity and subtlety of the construct of vectors with the classical vector representations. These highlight the need for a new framework that: (1) differentiates abstraction from a…

Using Expectancy-Value Theory to Explore Aspects of Motivation and Engagement in Inquiry-Based Learning in Primary Mathematics

ERIC Educational Resources Information Center

Fielding-Wells, Jill; O'Brien, Mia; Makar, Katie

2017-01-01

Inquiry-based learning (IBL) is a pedagogical approach in which students address complex, ill-structured problems set in authentic contexts. While IBL is gaining ground in Australia as an instructional practice, there has been little research that considers implications for student motivation and engagement. Expectancy-value theory (Eccles and…

Experiencing a Mathematical Problem-Solving Teaching Approach: Opportunities to Identify Ambitious Teaching Practices

ERIC Educational Resources Information Center

Bailey, Judy; Taylor, Merilyn

2015-01-01

Learning to teach is a complex matter, and many different models of pre-service teacher education have been used to support novice teachers' preparation for the classroom. More recently there have been calls for a focus on core high-leverage teaching practices and for novice teachers to engage in representations, decompositions, and approximations…

Multiple Alternatives for Educational Evaluation and Decision-Making. Interim Draft. Paper and Report Series No. 72.

ERIC Educational Resources Information Center

Wholeben, Brent E.

This volume is an exposition of a mathematical modeling technique for use in the evaluation and solution of complex educational problems at all levels. It explores in detail the application of simple algebraic techniques to such issues as program reduction, fiscal rollbacks, and computer curriculum planning. Part I ("Introduction to the…

Good-Enough Understanding: Theorising about the Learning of Complex Ideas (Part 1)

ERIC Educational Resources Information Center

Zack, Vicki; Reid, David A.

2003-01-01

Vicki Zack, a classroom teacher and researcher, returned to the fifth grade classroom in 1989 after more than a decade of teaching in a university faculty of education in order to teach in the changing ecologies of classrooms (with problem-solving approaches in mathematics and literature-based approaches in reading) and to research from the…

Using Teacher Evaluation Reform and Professional Development to Support Common Core Assessments

ERIC Educational Resources Information Center

Youngs, Peter

2013-01-01

The Common Core State Standards Initiative, in its aim to align diverse state curricula and improve educational outcomes, calls for K-12 teachers in the United States to engage all students in mathematical problem solving along with reading and writing complex text through the use of rigorous academic content. Until recently, most teacher…

The contribution of general cognitive abilities and number abilities to different aspects of mathematics in children.

PubMed

Träff, Ulf

2013-10-01

This study examined the relative contributions of general cognitive abilities and number abilities to word problem solving, calculation, and arithmetic fact retrieval in a sample of 134 children aged 10 to 13 years. The following tasks were administered: listening span, visual matrix span, verbal fluency, color naming, Raven's Progressive Matrices, enumeration, number line estimation, and digit comparison. Hierarchical multiple regressions demonstrated that number abilities provided an independent contribution to fact retrieval and word problem solving. General cognitive abilities contributed to problem solving and calculation. All three number tasks accounted for a similar amount of variance in fact retrieval, whereas only the number line estimation task contributed unique variance in word problem solving. Verbal fluency and Raven's matrices accounted for an equal amount of variance in problem solving and calculation. The current findings demonstrate, in accordance with Fuchs and colleagues' developmental model of mathematical learning (Developmental Psychology, 2010, Vol. 46, pp. 1731-1746), that both number abilities and general cognitive abilities underlie 10- to 13-year-olds' proficiency in problem solving, whereas only number abilities underlie arithmetic fact retrieval. Thus, the amount and type of cognitive contribution to arithmetic proficiency varies between the different aspects of arithmetic. Furthermore, how closely linked a specific aspect of arithmetic is to the whole number representation systems is not the only factor determining the amount and type of cognitive contribution in 10- to 13-year-olds. In addition, the mathematical complexity of the task appears to influence the amount and type of cognitive support. Copyright © 2013 Elsevier Inc. All rights reserved.

A new simulation system of traffic flow based on cellular automata principle

NASA Astrophysics Data System (ADS)

Shan, Junru

2017-05-01

Traffic flow is a complex system of multi-behavior so it is difficult to give a specific mathematical equation to express it. With the rapid development of computer technology, it is an important method to study the complex traffic behavior by simulating the interaction mechanism between vehicles and reproduce complex traffic behavior. Using the preset of multiple operating rules, cellular automata is a kind of power system which has discrete time and space. It can be a good simulation of the real traffic process and a good way to solve the traffic problems.

Building a Career Mathematics File: Challenging Students to Find the Importance of Mathematics in a Variety of Occupations

ERIC Educational Resources Information Center

Keleher, Lori A.

2006-01-01

The Career Mathematics file is an occupational problem-solving system, which includes a wide range of mathematical problems and solutions, collected from various resources and helps students establish connections between mathematics and their environment. The study shows that the problems given can be used as realistic examples to study and…

An Investigation of Relationships between Students' Mathematical Problem-Posing Abilities and Their Mathematical Content Knowledge

ERIC Educational Resources Information Center

Van Harpen, Xianwei Y.; Presmeg, Norma C.

2013-01-01

The importance of students' problem-posing abilities in mathematics has been emphasized in the K-12 curricula in the USA and China. There are claims that problem-posing activities are helpful in developing creative approaches to mathematics. At the same time, there are also claims that students' mathematical content knowledge could be highly…

Creativity and Mathematical Problem Posing: An Analysis of High School Students' Mathematical Problem Posing in China and the USA

ERIC Educational Resources Information Center

Van Harpen, Xianwei Y.; Sriraman, Bharath

2013-01-01

In the literature, problem-posing abilities are reported to be an important aspect/indicator of creativity in mathematics. The importance of problem-posing activities in mathematics is emphasized in educational documents in many countries, including the USA and China. This study was aimed at exploring high school students' creativity in…

Recent Trends in Japanese Mathematics Textbooks for Elementary Grades: Supporting Teachers to Teach Mathematics through Problem Solving

ERIC Educational Resources Information Center

Takahashi, Akihiko

2016-01-01

Problem solving has been a major theme in Japanese mathematics curricula for nearly 50 years. Numerous teacher reference books and lesson plans using problem solving have been published since the 1960s. Government-authorized mathematics textbooks for elementary grades, published by six private companies, have had more and more problem solving over…

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.

Mathematical models of functioning and allocation indicators of road-transport complex resources in the fuel and raw materials region

NASA Astrophysics Data System (ADS)

Buyvis, V. A.; Novichikhin, A. V.; Temlyantsev, M. V.

2017-09-01

A number of features of coal industry functioning was determined for the conditions of Kemerovo region, and the specifics of planning and organization of coal transportation were revealed. The analysis of indicators of motor and railway types of transport in the process of coal transportation was executed. The necessity of improving the tools of coal products transportation in the modern conditions is substantiated. Specific features of functioning of a road-transport complex in the fuel and raw material region (on the example of Kemerovo region) are determined. The modern scientific and applied problems of functioning and allocation of the road-transport complex resources are identified. To justify the management decisions on the development and improvement of road-transport complex a set of indicators are proposed: infrastructural, transportation performance, operating, social and economic. Mathematical models of indicators are recommended for formulation and justification of decisions made during operational and strategic planning of development, evaluation and development of algorithms of functioning and allocation of road-transport sector in Kemerovo region in the future.

Mathematical model of compact type evaporator

NASA Astrophysics Data System (ADS)

Borovička, Martin; Hyhlík, Tomáš

2018-06-01

In this paper, development of the mathematical model for evaporator used in heat pump circuits is covered, with focus on air dehumidification application. Main target of this ad-hoc numerical model is to simulate heat and mass transfer in evaporator for prescribed inlet conditions and different geometrical parameters. Simplified 2D mathematical model is developed in MATLAB SW. Solvers for multiple heat and mass transfer problems - plate surface temperature, condensate film temperature, local heat and mass transfer coefficients, refrigerant temperature distribution, humid air enthalpy change are included as subprocedures of this model. An automatic procedure of data transfer is developed in order to use results of MATLAB model in more complex simulation within commercial CFD code. In the end, Proper Orthogonal Decomposition (POD) method is introduced and implemented into MATLAB model.

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

NASA Astrophysics Data System (ADS)

Shadid, J. N.; Smith, T. M.; Cyr, E. C.; Wildey, T. M.; Pawlowski, R. P.

2016-09-01

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. In this respect the understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In this study we report on initial efforts to apply integrated adjoint-based computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier-Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. Initial results are presented that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

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

Shadid, J.N., E-mail: jnshadi@sandia.gov; Department of Mathematics and Statistics, University of New Mexico; Smith, T.M.

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. In this respect the understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In this study we report on initial efforts tomore » apply integrated adjoint-based computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. Initial results are presented that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.« less

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

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

Shadid, J. N.; Smith, T. M.; Cyr, E. C.

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. The understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In our study we report on initial efforts to apply integrated adjoint-basedmore » computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. We present the initial results that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.« less

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

DOE PAGES

Shadid, J. N.; Smith, T. M.; Cyr, E. C.; ...

2016-05-20

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. The understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In our study we report on initial efforts to apply integrated adjoint-basedmore » computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. We present the initial results that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.« less

Equation-free modeling unravels the behavior of complex ecological systems

USGS Publications Warehouse

DeAngelis, Donald L.; Yurek, Simeon

2015-01-01

Ye et al. (1) address a critical problem confronting the management of natural ecosystems: How can we make forecasts of possible future changes in populations to help guide management actions? This problem is especially acute for marine and anadromous fisheries, where the large interannual fluctuations of populations, arising from complex nonlinear interactions among species and with varying environmental factors, have defied prediction over even short time scales. The empirical dynamic modeling (EDM) described in Ye et al.’s report, the latest in a series of papers by Sugihara and his colleagues, offers a promising quantitative approach to building models using time series to successfully project dynamics into the future. With the term “equation-free” in the article title, Ye et al. (1) are suggesting broader implications of their approach, considering the centrality of equations in modern science. From the 1700s on, nature has been increasingly described by mathematical equations, with differential or difference equations forming the basic framework for describing dynamics. The use of mathematical equations for ecological systems came much later, pioneered by Lotka and Volterra, who showed that population cycles might be described in terms of simple coupled nonlinear differential equations. It took decades for Lotka–Volterra-type models to become established, but the development of appropriate differential equations is now routine in modeling ecological dynamics. There is no question that the injection of mathematical equations, by forcing “clarity and precision into conjecture” (2), has led to increased understanding of population and community dynamics. As in science in general, in ecology equations are a key method of communication and of framing hypotheses. These equations serve as compact representations of an enormous amount of empirical data and can be analyzed by the powerful methods of mathematics.

Representations in Problem Solving: A Case Study with Optimization Problems

ERIC Educational Resources Information Center

Villegas, Jose L.; Castro, Enrique; Gutierrez, Jose

2009-01-01

Introduction: Representations play an essential role in mathematical thinking. They favor the understanding of mathematical concepts and stimulate the development of flexible and versatile thinking in problem solving. Here our focus is on their use in optimization problems, a type of problem considered important in mathematics teaching and…

Mathematical Modelling in the Early School Years

ERIC Educational Resources Information Center

English, Lyn D.; Watters, James J.

2005-01-01

In this article we explore young children's development of mathematical knowledge and reasoning processes as they worked two modelling problems (the "Butter Beans Problem" and the "Airplane Problem"). The problems involve authentic situations that need to be interpreted and described in mathematical ways. Both problems include tables of data,…

FOURTH SEMINAR TO THE MEMORY OF D.N. KLYSHKO: Algebraic solution of the synthesis problem for coded sequences

NASA Astrophysics Data System (ADS)

Leukhin, Anatolii N.

2005-08-01

The algebraic solution of a 'complex' problem of synthesis of phase-coded (PC) sequences with the zero level of side lobes of the cyclic autocorrelation function (ACF) is proposed. It is shown that the solution of the synthesis problem is connected with the existence of difference sets for a given code dimension. The problem of estimating the number of possible code combinations for a given code dimension is solved. It is pointed out that the problem of synthesis of PC sequences is related to the fundamental problems of discrete mathematics and, first of all, to a number of combinatorial problems, which can be solved, as the number factorisation problem, by algebraic methods by using the theory of Galois fields and groups.

Model verification of mixed dynamic systems. [POGO problem in liquid propellant rockets

NASA Technical Reports Server (NTRS)

Chrostowski, J. D.; Evensen, D. A.; Hasselman, T. K.

1978-01-01

A parameter-estimation method is described for verifying the mathematical model of mixed (combined interactive components from various engineering fields) dynamic systems against pertinent experimental data. The model verification problem is divided into two separate parts: defining a proper model and evaluating the parameters of that model. The main idea is to use differences between measured and predicted behavior (response) to adjust automatically the key parameters of a model so as to minimize response differences. To achieve the goal of modeling flexibility, the method combines the convenience of automated matrix generation with the generality of direct matrix input. The equations of motion are treated in first-order form, allowing for nonsymmetric matrices, modeling of general networks, and complex-mode analysis. The effectiveness of the method is demonstrated for an example problem involving a complex hydraulic-mechanical system.

Developing a new stochastic competitive model regarding inventory and price

NASA Astrophysics Data System (ADS)

Rashid, Reza; Bozorgi-Amiri, Ali; Seyedhoseini, S. M.

2015-09-01

Within the competition in today's business environment, the design of supply chains becomes more complex than before. This paper deals with the retailer's location problem when customers choose their vendors, and inventory costs have been considered for retailers. In a competitive location problem, price and location of facilities affect demands of customers; consequently, simultaneous optimization of the location and inventory system is needed. To prepare a realistic model, demand and lead time have been assumed as stochastic parameters, and queuing theory has been used to develop a comprehensive mathematical model. Due to complexity of the problem, a branch and bound algorithm has been developed, and its performance has been validated in several numerical examples, which indicated effectiveness of the algorithm. Also, a real case has been prepared to demonstrate performance of the model for real world.

LinguisticBelief: a java application for linguistic evaluation using belief, fuzzy sets, and approximate reasoning.

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

Darby, John L.

LinguisticBelief is a Java computer code that evaluates combinations of linguistic variables using an approximate reasoning rule base. Each variable is comprised of fuzzy sets, and a rule base describes the reasoning on combinations of variables fuzzy sets. Uncertainty is considered and propagated through the rule base using the belief/plausibility measure. The mathematics of fuzzy sets, approximate reasoning, and belief/ plausibility are complex. Without an automated tool, this complexity precludes their application to all but the simplest of problems. LinguisticBelief automates the use of these techniques, allowing complex problems to be evaluated easily. LinguisticBelief can be used free of chargemore » on any Windows XP machine. This report documents the use and structure of the LinguisticBelief code, and the deployment package for installation client machines.« less

Game theory and extremal optimization for community detection in complex dynamic networks.

PubMed

Lung, Rodica Ioana; Chira, Camelia; Andreica, Anca

2014-01-01

The detection of evolving communities in dynamic complex networks is a challenging problem that recently received attention from the research community. Dynamics clearly add another complexity dimension to the difficult task of community detection. Methods should be able to detect changes in the network structure and produce a set of community structures corresponding to different timestamps and reflecting the evolution in time of network data. We propose a novel approach based on game theory elements and extremal optimization to address dynamic communities detection. Thus, the problem is formulated as a mathematical game in which nodes take the role of players that seek to choose a community that maximizes their profit viewed as a fitness function. Numerical results obtained for both synthetic and real-world networks illustrate the competitive performance of this game theoretical approach.

Exploring Primary Student's Problem-Solving Ability by Doing Tasks Like PISA's Question

ERIC Educational Resources Information Center

Novita, Rita; Zulkardi; Hartono, Yusuf

2012-01-01

Problem solving plays an important role in mathematics and should have a prominent role in the mathematics education. The term "problem solving" refers to mathematics tasks that have the potential to provide intellectual challenges for enhancing students' mathematical understanding and development. In addition, the contextual problem…

On the Relationships between (Relatively) Advanced Mathematical Knowledge and (Relatively) Advanced Problem-Solving Behaviours

ERIC Educational Resources Information Center

Koichu, Boris

2010-01-01

This article discusses an issue of inserting mathematical knowledge within the problem-solving processes. Relatively advanced mathematical knowledge is defined in terms of "three mathematical worlds"; relatively advanced problem-solving behaviours are defined in terms of taxonomies of "proof schemes" and "heuristic behaviours". The relationships…

Minimalism as a Guiding Principle: Linking Mathematical Learning to Everyday Knowledge

ERIC Educational Resources Information Center

Inoue, Noriyuki

2008-01-01

Studies report that students often fail to consider familiar aspects of reality in solving mathematical word problems. This study explored how different features of mathematical problems influence the way that undergraduate students employ realistic considerations in mathematical problem solving. Incorporating familiar contents in the word…

Pose and Solve Varignon Converse Problems

ERIC Educational Resources Information Center

Contreras, José N.

2014-01-01

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

Applications: Students, the Mathematics Curriculum and Mathematics Textbooks

ERIC Educational Resources Information Center

Kilic, Cigdem

2013-01-01

Problem posing is one of the most important topics in a mathematics education. Through problem posing, students gain mathematical abilities and concepts and teachers can evaluate their students and arrange adequate learning environments. The aim of the present study is to investigate Turkish primary school teachers' opinions about problem posing…

ABC Problem in Elementary Mathematics Education: Arithmetic "before" Comprehension

ERIC Educational Resources Information Center

Boote, Stacy K.; Boote, David N.

2018-01-01

Mathematical habits of prospective teachers affect problem comprehension and success and expose their beliefs about mathematics. Prospective elementary teachers (PSTs) (n = 121) engaged in a problem solving activity each week in class. Data were collected from PSTs enrolled in an undergraduate elementary mathematics methods course at a…

Pre-Service Class Teacher' Ability in Solving Mathematical Problems and Skills in Solving Daily Problems

ERIC Educational Resources Information Center

Aljaberi, Nahil M.; Gheith, Eman

2016-01-01

This study aims to investigate the ability of pre-service class teacher at University of Petrain solving mathematical problems using Polya's Techniques, their level of problem solving skills in daily-life issues. The study also investigates the correlation between their ability to solve mathematical problems and their level of problem solving…

Faded-example as a Tool to Acquire and Automate Mathematics Knowledge

NASA Astrophysics Data System (ADS)

Retnowati, E.

2017-04-01

Students themselves accomplish Knowledge acquisition and automation. The teacher plays a role as the facilitator by creating mathematics tasks that assist students in building knowledge efficiently and effectively. Cognitive load caused by learning material presented by teachers should be considered as a critical factor. While the intrinsic cognitive load is related to the degree of complexity of the material learning ones can handle, the extraneous cognitive load is directly caused by how the material is presented. Strategies to present a learning material in computational learning domains like mathematics are a namely worked example (fully-guided task) or problem-solving (discovery task with no guidance). According to the empirical evidence, learning based on problem-solving may cause high-extraneous cognitive load for students who have limited prior knowledge, conversely learn based on worked example may cause high-extraneous cognitive load for students who have mastered the knowledge base. An alternative is a faded example consisting of the partly-completed task. Learning from faded-example can facilitate students who already acquire some knowledge about the to-be-learned material but still need more practice to automate the knowledge further. This instructional strategy provides a smooth transition from a fully-guided into an independent problem solver. Designs of faded examples for learning trigonometry are discussed.

On designing for quality

NASA Technical Reports Server (NTRS)

Vajingortin, L. D.; Roisman, W. P.

1991-01-01

The problem of ensuring the required quality of products and/or technological processes often becomes more difficult due to the fact that there is not general theory of determining the optimal sets of value of the primary factors, i.e., of the output parameters of the parts and units comprising an object and ensuring the correspondence of the object's parameters to the quality requirements. This is the main reason for the amount of time taken to finish complex vital article. To create this theory, one has to overcome a number of difficulties and to solve the following tasks: the creation of reliable and stable mathematical models showing the influence of the primary factors on the output parameters; finding a new technique of assigning tolerances for primary factors with regard to economical, technological, and other criteria, the technique being based on the solution of the main problem; well reasoned assignment of nominal values for primary factors which serve as the basis for creating tolerances. Each of the above listed tasks is of independent importance. An attempt is made to give solutions for this problem. The above problem dealing with quality ensuring an mathematically formalized aspect is called the multiple inverse problem.

Investigating Mathematics Teachers Candidates' Knowledge about Problem Solving Strategies through Problem Posing

ERIC Educational Resources Information Center

Ünlü, Melihan

2017-01-01

The aim of the study was to determine mathematics teacher candidates' knowledge about problem solving strategies through problem posing. This qualitative research was conducted with 95 mathematics teacher candidates studying at education faculty of a public university during the first term of the 2015-2016 academic year in Turkey. Problem Posing…

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.

The Impact of Problem Posing on Elementary Teachers' Beliefs about Mathematics and Mathematics Teaching

ERIC Educational Resources Information Center

Barlow, Angela T.; Cates, Janie M.

2006-01-01

This study investigated the impact of incorporating problem posing in elementary classrooms on the beliefs held by elementary teachers about mathematics and mathematics teaching. Teachers participated in a year-long staff development project aimed at facilitating the incorporation of problem posing into their classrooms. Beliefs were examined via…

Leveling of Critical Thinking Abilities of Students of Mathematics Education in Mathematical Problem Solving

ERIC Educational Resources Information Center

Rasiman

2015-01-01

This research aims to determine the leveling of critical thinking abilities of students of mathematics education in mathematical problem solving. It includes qualitative-explorative study that was conducted at University of PGRI Semarang. The generated data in the form of information obtained problem solving question and interview guides. The…

Problem Solving in Swedish Mathematics Textbooks for Upper Secondary School

ERIC Educational Resources Information Center

Brehmer, Daniel; Ryve, Andreas; Van Steenbrugge, Hendrik

2016-01-01

The aim of this study is to analyse how mathematical problem solving is represented in mathematical textbooks for Swedish upper secondary school. The analysis comprises dominating Swedish textbook series, and relates to uncovering (a) the quantity of tasks that are actually mathematical problems, (b) their location in the chapter, (c) their…

Adolescent Mathematical Problem Solving: The Role of Metacognition, Strategies and Beliefs.

ERIC Educational Resources Information Center

Fitzpatrick, Corine

Mathematical problem solving has been the focus of much concern. This study investigated the relationship of various cognitive factors, attributions, and gender to the solution of mathematics problems by 100 high school seniors. The independent variables examined in this study included: (1) mathematics knowledge as measured by a score on the…

An Astronomical Problem in a Japanese Traditional Mathematical Text: The 49th Problem of the Kenki-sanpo of Takebe Katahiro

NASA Astrophysics Data System (ADS)

Ôhashi, Yukio

During the Edo period (Tokugawa-shogunate period) (1603-1867), there was a mathematical tradition now called "Wasan" which was primarily based on Chinese mathematics, but Japanese mathematicians also created new devices. It was quite popular, and common people could enjoy solving mathematical problems through Wasan regardless of their social status. Some astronomical problems were also treated there.

The application of brain-based learning principles aided by GeoGebra to improve mathematical representation ability

NASA Astrophysics Data System (ADS)

Priatna, Nanang

2017-08-01

The use of Information and Communication Technology (ICT) in mathematics instruction will help students in building conceptual understanding. One of the software products used in mathematics instruction is GeoGebra. The program enables simple visualization of complex geometric concepts and helps improve students' understanding of geometric concepts. Instruction applying brain-based learning principles is one oriented at the efforts of naturally empowering the brain potentials which enable students to build their own knowledge. One of the goals of mathematics instruction in school is to develop mathematical communication ability. Mathematical representation is regarded as a part of mathematical communication. It is a description, expression, symbolization, or modeling of mathematical ideas/concepts as an attempt of clarifying meanings or seeking for solutions to the problems encountered by students. The research aims to develop a learning model and teaching materials by applying the principles of brain-based learning aided by GeoGebra to improve junior high school students' mathematical representation ability. It adopted a quasi-experimental method with the non-randomized control group pretest-posttest design and the 2x3 factorial model. Based on analysis of the data, it is found that the increase in the mathematical representation ability of students who were treated with mathematics instruction applying the brain-based learning principles aided by GeoGebra was greater than the increase of the students given conventional instruction, both as a whole and based on the categories of students' initial mathematical ability.

Problem Solvers: Problem--Jesse's Train

ERIC Educational Resources Information Center

James, Julie; Steimle, Alice

2014-01-01

Persevering in problem solving and constructing and critiquing mathematical arguments are some of the mathematical practices included in the Common Core State Standards for Mathematics (CCSSI 2010). To solve unfamiliar problems, students must make sense of the situation and apply current knowledge. Teachers can present such opportunities by…

Categorization and analysis of explanatory writing in mathematics

NASA Astrophysics Data System (ADS)

Craig, Tracy S.

2011-10-01

The aim of this article is to present a scheme for coding and categorizing students' written explanations of mathematical problem-solving activities. The scheme was used successfully within a study project carried out to determine whether student problem-solving behaviour could be positively affected by writing explanatory strategies to mathematical problem-solving processes. The rationale for the study was the recognized importance of mathematical problem-solving, the widely acknowledged challenge of teaching problem-solving skills directly and the evidence in the literature that writing in mathematics provides a tool for learning. The study was carried out in a first-year mathematics course at the University of Cape Town, South Africa. Students' written submissions were categorized and analysed through use of an adaptation of a journal entry classification scheme. The scheme successfully observed positive changes over the experimental period in students' level of engagement with the mathematical material and with their stance towards knowledge.

Simulation of physiological systems in order to evaluate and predict the human condition in a space flight

NASA Technical Reports Server (NTRS)

Verigo, V. V.

1979-01-01

Simulation models were used to study theoretical problems of space biology and medicine. The reaction and adaptation of the main physiological systems to the complex effects of space flight were investigated. Mathematical models were discussed in terms of their significance in the selection of the structure and design of biological life support systems.

Modeling of Economy Considering Crisis

NASA Astrophysics Data System (ADS)

Petrov, Lev F.

2009-09-01

We discuss main modeling's problems of economy dynamic processes and the reason forecast's absence of economic crisis. We present a structure of complexity level of system and models and discuss expected results concerning crisis phenomena. We formulate the basic perspective directions of the mathematical modeling of economy, including possibility of the analysis of the pre crisis, crisis and post crisis phenomena in economic systems.

Modeling of polymer networks for application to solid propellant formulating

NASA Technical Reports Server (NTRS)

Marsh, H. E.

1979-01-01

Methods for predicting the network structural characteristics formed by the curing of pourable elastomers were presented; as well as the logic which was applied in the development of mathematical models. A universal approach for modeling was developed and verified by comparison with other methods in application to a complex system. Several applications of network models to practical problems are described.

A Calculating Web Site Could Ignite a New Campus "Math War"

ERIC Educational Resources Information Center

Young, Jeffrey R.

2009-01-01

The long-running debate over whether students should be allowed to wield calculators during mathematics exams may soon seem quaint. The latest dilemma facing professors is whether to let students turn to a Web site called WolframAlpha, which not only solves complex math problems, but also can spell out the steps leading to those solutions. In…

A Preliminary Analysis of the Linguistic Complexity of Numeracy Skills Test Items for Pre Service Teachers

ERIC Educational Resources Information Center

O'Keeffe, Lisa

2016-01-01

Language is frequently discussed as barrier to mathematics word problems. Hence this paper presents the initial findings of a linguistic analysis of numeracy skills test sample items. The theoretical perspective of multi-modal text analysis underpinned this study, in which data was extracted from the ten sample numeracy test items released by the…

Risk Analysis for Resource Planning Optimization

NASA Technical Reports Server (NTRS)

Chueng, Kar-Ming

2008-01-01

The main purpose of this paper is to introduce a risk management approach that allows planners to quantify the risk and efficiency tradeoff in the presence of uncertainties, and to make forward-looking choices in the development and execution of the plan. Demonstrate a planning and risk analysis framework that tightly integrates mathematical optimization, empirical simulation, and theoretical analysis techniques to solve complex problems.

Coding in Senior School Mathematics with Live Editing

ERIC Educational Resources Information Center

Thompson, Ian

2017-01-01

In this paper, an example is offered of a problem-solving task for senior secondary school students which was given in the context of a story. As the story unfolds, the task requires progressively more complex forms of linear programming to be applied. Coding in MATLAB is used throughout the task in such a way that it supports the increasing…

Hidden physics models: Machine learning of nonlinear partial differential equations

NASA Astrophysics Data System (ADS)

Raissi, Maziar; Karniadakis, George Em

2018-03-01

While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from small data. In particular, we introduce hidden physics models, which are essentially data-efficient learning machines capable of leveraging the underlying laws of physics, expressed by time dependent and nonlinear partial differential equations, to extract patterns from high-dimensional data generated from experiments. The proposed methodology may be applied to the problem of learning, system identification, or data-driven discovery of partial differential equations. Our framework relies on Gaussian processes, a powerful tool for probabilistic inference over functions, that enables us to strike a balance between model complexity and data fitting. The effectiveness of the proposed approach is demonstrated through a variety of canonical problems, spanning a number of scientific domains, including the Navier-Stokes, Schrödinger, Kuramoto-Sivashinsky, and time dependent linear fractional equations. The methodology provides a promising new direction for harnessing the long-standing developments of classical methods in applied mathematics and mathematical physics to design learning machines with the ability to operate in complex domains without requiring large quantities of data.

Improving of Junior High School Visual Thinking Representation Ability in Mathematical Problem Solving by CTL

ERIC Educational Resources Information Center

Surya, Edy; Sabandar, Jozua; Kusumah, Yaya S.; Darhim

2013-01-01

The students' difficulty which was found is in the problem of understanding, drawing diagrams, reading the charts correctly, conceptual formal mathematical understanding, and mathematical problem solving. The appropriate problem representation is the basic way in order to understand the problem itself and make a plan to solve it. This research was…

Optimisation by hierarchical search

NASA Astrophysics Data System (ADS)

Zintchenko, Ilia; Hastings, Matthew; Troyer, Matthias

2015-03-01

Finding optimal values for a set of variables relative to a cost function gives rise to some of the hardest problems in physics, computer science and applied mathematics. Although often very simple in their formulation, these problems have a complex cost function landscape which prevents currently known algorithms from efficiently finding the global optimum. Countless techniques have been proposed to partially circumvent this problem, but an efficient method is yet to be found. We present a heuristic, general purpose approach to potentially improve the performance of conventional algorithms or special purpose hardware devices by optimising groups of variables in a hierarchical way. We apply this approach to problems in combinatorial optimisation, machine learning and other fields.

Improved multi-objective ant colony optimization algorithm and its application in complex reasoning

NASA Astrophysics Data System (ADS)

Wang, Xinqing; Zhao, Yang; Wang, Dong; Zhu, Huijie; Zhang, Qing

2013-09-01

The problem of fault reasoning has aroused great concern in scientific and engineering fields. However, fault investigation and reasoning of complex system is not a simple reasoning decision-making problem. It has become a typical multi-constraint and multi-objective reticulate optimization decision-making problem under many influencing factors and constraints. So far, little research has been carried out in this field. This paper transforms the fault reasoning problem of complex system into a paths-searching problem starting from known symptoms to fault causes. Three optimization objectives are considered simultaneously: maximum probability of average fault, maximum average importance, and minimum average complexity of test. Under the constraints of both known symptoms and the causal relationship among different components, a multi-objective optimization mathematical model is set up, taking minimizing cost of fault reasoning as the target function. Since the problem is non-deterministic polynomial-hard(NP-hard), a modified multi-objective ant colony algorithm is proposed, in which a reachability matrix is set up to constrain the feasible search nodes of the ants and a new pseudo-random-proportional rule and a pheromone adjustment mechinism are constructed to balance conflicts between the optimization objectives. At last, a Pareto optimal set is acquired. Evaluation functions based on validity and tendency of reasoning paths are defined to optimize noninferior set, through which the final fault causes can be identified according to decision-making demands, thus realize fault reasoning of the multi-constraint and multi-objective complex system. Reasoning results demonstrate that the improved multi-objective ant colony optimization(IMACO) can realize reasoning and locating fault positions precisely by solving the multi-objective fault diagnosis model, which provides a new method to solve the problem of multi-constraint and multi-objective fault diagnosis and reasoning of complex system.

An Intuitionistic Fuzzy Logic Models for Multicriteria Decision Making Under Uncertainty

NASA Astrophysics Data System (ADS)

Jana, Biswajit; Mohanty, Sachi Nandan

2017-04-01

The purpose of this paper is to enhance the applicability of the fuzzy sets for developing mathematical models for decision making under uncertainty, In general a decision making process consist of four stages, namely collection of information from various sources, compile the information, execute the information and finally take the decision/action. Only fuzzy sets theory is capable to quantifying the linguistic expression to mathematical form in complex situation. Intuitionistic fuzzy set (IFSs) which reflects the fact that the degree of non membership is not always equal to one minus degree of membership. There may be some degree of hesitation. Thus, there are some situations where IFS theory provides a more meaningful and applicable to cope with imprecise information present for solving multiple criteria decision making problem. This paper emphasis on IFSs, which is help for solving real world problem in uncertainty situation.

Model correlation and damage location for large space truss structures: Secant method development and evaluation

NASA Technical Reports Server (NTRS)

Smith, Suzanne Weaver; Beattie, Christopher A.

1991-01-01

On-orbit testing of a large space structure will be required to complete the certification of any mathematical model for the structure dynamic response. The process of establishing a mathematical model that matches measured structure response is referred to as model correlation. Most model correlation approaches have an identification technique to determine structural characteristics from the measurements of the structure response. This problem is approached with one particular class of identification techniques - matrix adjustment methods - which use measured data to produce an optimal update of the structure property matrix, often the stiffness matrix. New methods were developed for identification to handle problems of the size and complexity expected for large space structures. Further development and refinement of these secant-method identification algorithms were undertaken. Also, evaluation of these techniques is an approach for model correlation and damage location was initiated.

Processes involved in solving mathematical problems

NASA Astrophysics Data System (ADS)

Shahrill, Masitah; Putri, Ratu Ilma Indra; Zulkardi, Prahmana, Rully Charitas Indra

2018-04-01

This study examines one of the instructional practices features utilized within the Year 8 mathematics lessons in Brunei Darussalam. The codes from the TIMSS 1999 Video Study were applied and strictly followed, and from the 183 mathematics problems recorded, there were 95 problems with a solution presented during the public segments of the video-recorded lesson sequences of the four sampled teachers. The analyses involved firstly, identifying the processes related to mathematical problem statements, and secondly, examining the different processes used in solving the mathematical problems for each problem publicly completed during the lessons. The findings revealed that for three of the teachers, their problem statements coded as `using procedures' ranged from 64% to 83%, while the remaining teacher had 40% of his problem statements coded as `making connections.' The processes used when solving the problems were mainly `using procedures', and none of the problems were coded as `giving results only'. Furthermore, all four teachers made use of making the relevant connections in solving the problems given to their respective students.

A Parallel Biological Optimization Algorithm to Solve the Unbalanced Assignment Problem Based on DNA Molecular Computing.

PubMed

Wang, Zhaocai; Pu, Jun; Cao, Liling; Tan, Jian

2015-10-23

The unbalanced assignment problem (UAP) is to optimally resolve the problem of assigning n jobs to m individuals (m < n), such that minimum cost or maximum profit obtained. It is a vitally important Non-deterministic Polynomial (NP) complete problem in operation management and applied mathematics, having numerous real life applications. In this paper, we present a new parallel DNA algorithm for solving the unbalanced assignment problem using DNA molecular operations. We reasonably design flexible-length DNA strands representing different jobs and individuals, take appropriate steps, and get the solutions of the UAP in the proper length range and O(mn) time. We extend the application of DNA molecular operations and simultaneity to simplify the complexity of the computation.

Using Technology to Meet the Developmental Needs of Deaf Students To Improve Their Mathematical Word Problem Solving Skills.

ERIC Educational Resources Information Center

Kelly, Ronald R.

2003-01-01

Presents "Project Solve," a web-based problem-solving instruction and guided practice for mathematical word problems. Discusses implications for college students for whom reading and comprehension of mathematical word problem solving are difficult, especially learning disabled students. (Author/KHR)

Obstacles Related to Structuring for Mathematization Encountered by Students When Solving Physics Problems

ERIC Educational Resources Information Center

Niss, Martin

2017-01-01

This paper studies the cognitive obstacles related to one aspect of mathematization in physics problem-solving, namely, what might be called "structuring for mathematization," where the problem situation is structured in such a way that a translation to a mathematical universe can be done. We report the results of an analysis of four…

Incorporating the Common Core's Problem Solving Standard for Mathematical Practice into an Early Elementary Inclusive Classroom

ERIC Educational Resources Information Center

Fletcher, Nicole

2014-01-01

Mathematics curriculum designers and policy decision makers are beginning to recognize the importance of problem solving, even at the earliest stages of mathematics learning. The Common Core includes sense making and perseverance in solving problems in its standards for mathematical practice for students at all grade levels. Incorporating problem…

Promoting Access to Common Core Mathematics for Students with Severe Disabilities through Mathematical Problem Solving

ERIC Educational Resources Information Center

Spooner, Fred; Saunders, Alicia; Root, Jenny; Brosh, Chelsi

2017-01-01

There is a need to teach the pivotal skill of mathematical problem solving to students with severe disabilities, moving beyond basic skills like computation to higher level thinking skills. Problem solving is emphasized as a Standard for Mathematical Practice in the Common Core State Standards across grade levels. This article describes a…

Students’ Representation in Mathematical Word Problem-Solving: Exploring Students’ Self-efficacy

NASA Astrophysics Data System (ADS)

Sahendra, A.; Budiarto, M. T.; Fuad, Y.

2018-01-01

This descriptive qualitative research aims at investigating student represented in mathematical word problem solving based on self-efficacy. The research subjects are two eighth graders at a school in Surabaya with equal mathematical ability consisting of two female students with high and low self-efficacy. The subjects were chosen based on the results of test of mathematical ability, documentation of the result of middle test in even semester of 2016/2017 academic year, and results of questionnaire of mathematics word problem in terms of self-efficacy scale. The selected students were asked to do mathematical word problem solving and be interviewed. The result of this study shows that students with high self-efficacy tend to use multiple representations of sketches and mathematical models, whereas students with low self-efficacy tend to use single representation of sketches or mathematical models only in mathematical word problem-solving. This study emphasizes that teachers should pay attention of student’s representation as a consideration of designing innovative learning in order to increase the self-efficacy of each student to achieve maximum mathematical achievement although it still requires adjustment to the school situation and condition.

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…

The stability issues in problems of mathematical modeling

NASA Astrophysics Data System (ADS)

Mokin, A. Yu.; Savenkova, N. P.; Udovichenko, N. S.

2018-03-01

In the paper it is briefly considered various aspects of stability concepts, which are used in physics, mathematics and numerical methods of solution. The interrelation between these concepts is described, the questions of preliminary stability research before the numerical solution of the problem and the correctness of the mathematical statement of the physical problem are discussed. Examples of concrete mathematical statements of individual physical problems are given: a nonlocal problem for the heat equation, the Korteweg-de Fries equation with boundary conditions at infinity, the sine-Gordon equation, the problem of propagation of femtosecond light pulses in an area with a cubic nonlinearity.

Profile of male-field dependent (FD) prospective teacher's reflective thinking in solving contextual mathematical problem

NASA Astrophysics Data System (ADS)

Agustan, S.; Juniati, Dwi; Siswono, Tatag Yuli Eko

2017-08-01

Reflective thinking is an important component in the world of education, especially in professional education of teachers. In learning mathematics, reflective thinking is one way to solve mathematical problem because it can improve student's curiosity when student faces a mathematical problem. Reflective thinking is also a future competence that should be taught to students to face the challenges and to respond of demands of the 21st century. There are many factors which give impact toward the student's reflective thinking when student solves mathematical problem. One of them is cognitive style. For this reason, reflective thinking and cognitive style are important things in solving contextual mathematical problem. This research paper describes aspect of reflective thinking in solving contextual mathematical problem involved solution by using some mathematical concept, namely linear program, algebra arithmetic operation, and linear equations of two variables. The participant, in this research paper, is a male-prospective teacher who has Field Dependent. The purpose of this paper is to describe aspect of prospective teachers' reflective thinking in solving contextual mathematical problem. This research paper is a descriptive by using qualitative approach. To analyze the data, the researchers focus in four main categories which describe prospective teacher's activities using reflective thinking, namely; (a) formulation and synthesis of experience, (b) orderliness of experience, (c) evaluating the experience and (d) testing the selected solution based on the experience.

Application of satellite data in variational analysis for global cyclonic systems

NASA Technical Reports Server (NTRS)

Achtemeier, G. L.

1987-01-01

The research goal was a variational data assimilation method that incorporates as dynamical constraints, the primitive equations for a moist, convectively unstable atmosphere and the radiative transfer equation. Variables to be adjusted include the three-dimensional vector wind, height, temperature, and moisture from rawinsonde data, and cloud-wind vectors, moisture, and radiance from satellite data. This presents a formidable mathematical problem. In order to facilitate thorough analysis of each of the model components, four variational models that divide the problem naturally according to increasing complexity are defined. Each model is summarized.

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.

The algorithmic details of polynomials application in the problems of heat and mass transfer control on the hypersonic aircraft permeable surfaces

NASA Astrophysics Data System (ADS)

Bilchenko, G. G.; Bilchenko, N. G.

2018-03-01

The hypersonic aircraft permeable surfaces heat and mass transfer effective control mathematical modeling problems are considered. The analysis of the control (the blowing) constructive and gasdynamical restrictions is carried out for the porous and perforated surfaces. The functions classes allowing realize the controls taking into account the arising types of restrictions are suggested. Estimates of the computational complexity of the W. G. Horner scheme application in the case of using the C. Hermite interpolation polynomial are given.

Risky business

NASA Astrophysics Data System (ADS)

James, Jessica

2008-04-01

Riccardo Rebonato is a man with a clear and deep understanding of the most complex elements of the financial markets. His first book, Interest Rate Option Models, was one of the earliest proper mathematical texts on the complexities of "interest rate options" - investment tools in which the pay-offs depend on the future level of interest rates - and it is still relevant today. But is he the right person to write a book, without equations, about the fundamental problems underlying risk management in the markets? Before I opened Plight of the Fortune Tellers I have to confess to being dubious.

Allied Health Applications Integrated into Developmental Mathematics Using Problem Based Learning

ERIC Educational Resources Information Center

Shore, Mark; Shore, JoAnna; Boggs, Stacey

2004-01-01

For this FIPSE funded project, mathematics faculty attended allied health classes and allied health faculty attended developmental mathematics courses to incorporate health examples into the developmental mathematics curriculum. Through the course of this grant a 450-page developmental mathematics book was written with many problems from a variety…

Latinas and Problem Solving: What They Say and What They Do

ERIC Educational Resources Information Center

Guerra, Paula; Lim, Woong

2014-01-01

In this article, the authors present three adolescent Latinas' perceptions of ideal mathematical competencies, their perception of their individual "abilities" in mathematics, and their work on a mathematics problem-solving task. Results indicate that these Latinas recognize flexible mathematics as the ideal mathematical competency in…

A coherent Ising machine for 2000-node optimization problems

NASA Astrophysics Data System (ADS)

Inagaki, Takahiro; Haribara, Yoshitaka; Igarashi, Koji; Sonobe, Tomohiro; Tamate, Shuhei; Honjo, Toshimori; Marandi, Alireza; McMahon, Peter L.; Umeki, Takeshi; Enbutsu, Koji; Tadanaga, Osamu; Takenouchi, Hirokazu; Aihara, Kazuyuki; Kawarabayashi, Ken-ichi; Inoue, Kyo; Utsunomiya, Shoko; Takesue, Hiroki

2016-11-01

The analysis and optimization of complex systems can be reduced to mathematical problems collectively known as combinatorial optimization. Many such problems can be mapped onto ground-state search problems of the Ising model, and various artificial spin systems are now emerging as promising approaches. However, physical Ising machines have suffered from limited numbers of spin-spin couplings because of implementations based on localized spins, resulting in severe scalability problems. We report a 2000-spin network with all-to-all spin-spin couplings. Using a measurement and feedback scheme, we coupled time-multiplexed degenerate optical parametric oscillators to implement maximum cut problems on arbitrary graph topologies with up to 2000 nodes. Our coherent Ising machine outperformed simulated annealing in terms of accuracy and computation time for a 2000-node complete graph.

An Investigation of the Effects on Students' Attitudes, Beliefs, and Abilities in Problem Solving and Mathematics after One Year of a Systematic Approach to the Learning of Problem Solving.

ERIC Educational Resources Information Center

Higgins, Karen M.

This study investigated the effects of Oregon's Lane County "Problem Solving in Mathematics" (PSM) materials on middle-school students' attitudes, beliefs, and abilities in problem solving and mathematics. The instructional approach advocated in PSM includes: the direct teaching of five problem-solving skills, weekly challenge problems,…

Problem Posing as a Pedagogical Strategy: A Teacher's Perspective

ERIC Educational Resources Information Center

Staebler-Wiseman, Heidi A.

2011-01-01

Student problem posing has been advocated for mathematics instruction, and it has been suggested that problem posing can be used to develop students' mathematical content knowledge. But, problem posing has rarely been utilized in university-level mathematics courses. The goal of this teacher-as-researcher study was to develop and investigate…

Teaching Global Issues Through Mathematics. Development Education Paper No. 20.

ERIC Educational Resources Information Center

Schwartz, Richard H.

The document shows how teachers can use mathematics problems to teach fourth, fifth, and sixth grade students about critical global issues. The problems are arranged according to development topics. For each problem, the solution, reference source, and mathematical skills to be strengthened are given; global issues related to each problem are also…

A Comparison of Geometry Problems in Middle-Grade Mathematics Textbooks from Taiwan, Singapore, Finland, and the United States

ERIC Educational Resources Information Center

Yang, Der-Ching; Tseng, Yi-Kuan; Wang, Tzu-Ling

2017-01-01

This study analyzed geometry problems in four middle-grade mathematics textbook series from Taiwan, Singapore, Finland, and the United States, while exploring the expectations for students' learning experiences with these problems. An analytical framework developed for mathematics textbook problem analysis had three dimensions: representation…

Different Procedures for Solving Mathematical Word Problems in High School

ERIC Educational Resources Information Center

Gasco, Javier; Villarroel, Jose Domingo; Zuazagoitia, Dani

2014-01-01

The teaching and learning of mathematics cannot be understood without considering the resolution of word problems. These kinds of problems not only connect mathematical concepts with language (and therefore with reality) but also promote the learning related to other scientific areas. In primary school, problems are solved by using basic…

An Analysis of Problem-Posing Tasks in Chinese and US Elementary Mathematics Textbooks

ERIC Educational Resources Information Center

Cai, Jinfa; Jiang, Chunlian

2017-01-01

This paper reports on 2 studies that examine how mathematical problem posing is integrated in Chinese and US elementary mathematics textbooks. Study 1 involved a historical analysis of the problem-posing (PP) tasks in 3 editions of the most widely used elementary mathematics textbook series published by People's Education Press in China over 3…

"I Think I Can, but I'm Afraid to Try": The Role of Self-Efficacy Beliefs and Mathematics Anxiety in Mathematics Problem-Solving Efficiency

ERIC Educational Resources Information Center

Hoffman, Bobby

2010-01-01

This study investigated the role of self-efficacy beliefs, mathematics anxiety, and working memory capacity in problem-solving accuracy, response time, and efficiency (the ratio of problem-solving accuracy to response time). Pre-service teachers completed a mathematics anxiety inventory measuring cognitive and affective dispositions for…

Mathematical Problem-Solving Styles in the Education of Deaf and Hard-of-Hearing Individuals

ERIC Educational Resources Information Center

Erickson, Elizabeth E. A.

2012-01-01

This study explored the mathematical problem-solving styles of middle school and high school deaf and hard-of-hearing students and the mathematical problem-solving styles of the mathematics teachers of middle school and high school deaf and hard-of-hearing students. The research involved 45 deaf and hard-of-hearing students and 19 teachers from a…

Investigating adaptive reasoning and strategic competence: Difference male and female

NASA Astrophysics Data System (ADS)

Syukriani, Andi; Juniati, Dwi; Siswono, Tatag Yuli Eko

2017-08-01

The series of adaptive reasoning and strategic competencies represent the five components of mathematical proficiency to describe the students' mathematics learning success. Gender contribute to the problem-solving process. This qualitative research approach investigated the adaptive reasoning and strategic competence aspects of a male student and a female student when they solved mathematical problem. They were in the eleventh grade of high school in Makassar. Both also had similar mathematics ability and were in the highest category. The researcher as the main instrument used secondary instrument to obtain the appropriate subject and to investigate the aspects of adaptive reasoning and strategic competence. Test of mathematical ability was used to locate the subjects with similar mathematical ability. The unstructured guideline interview was used to investigate aspects of adaptive reasoning and strategic competence when the subject completed the task of mathematical problem. The task of mathematical problem involves several concepts as the right solution, such as the circle concept, triangle concept, trigonometry concept, and Pythagoras concept. The results showed that male and female subjects differed in applying a strategy to understand, formulate and represent the problem situation. Furthermore, both also differed in explaining the strategy used and the relationship between concepts and problem situations.

How to Build a Course in Mathematical–Biological Modeling: Content and Processes for Knowledge and Skill

PubMed Central

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. PMID:20810966

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

NASA Astrophysics Data System (ADS)

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

2009-12-01

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

Low-Complexity User Selection for Rate Maximization in MIMO Broadcast Channels with Downlink Beamforming

PubMed Central

Silva, Adão; Gameiro, Atílio

2014-01-01

We present in this work a low-complexity algorithm to solve the sum rate maximization problem in multiuser MIMO broadcast channels with downlink beamforming. Our approach decouples the user selection problem from the resource allocation problem and its main goal is to create a set of quasiorthogonal users. The proposed algorithm exploits physical metrics of the wireless channels that can be easily computed in such a way that a null space projection power can be approximated efficiently. Based on the derived metrics we present a mathematical model that describes the dynamics of the user selection process which renders the user selection problem into an integer linear program. Numerical results show that our approach is highly efficient to form groups of quasiorthogonal users when compared to previously proposed algorithms in the literature. Our user selection algorithm achieves a large portion of the optimum user selection sum rate (90%) for a moderate number of active users. PMID:24574928

Property-Based Software Engineering Measurement

NASA Technical Reports Server (NTRS)

Briand, Lionel; Morasca, Sandro; Basili, Victor R.

1995-01-01

Little theory exists in the field of software system measurement. Concepts such as complexity, coupling, cohesion or even size are very often subject to interpretation and appear to have inconsistent definitions in the literature. As a consequence, there is little guidance provided to the analyst attempting to define proper measures for specific problems. Many controversies in the literature are simply misunderstandings and stem from the fact that some people talk about different measurement concepts under the same label (complexity is the most common case). There is a need to define unambiguously the most important measurement concepts used in the measurement of software products. One way of doing so is to define precisely what mathematical properties characterize these concepts regardless of the specific software artifacts to which these concepts are applied. Such a mathematical framework could generate a consensus in the software engineering community and provide a means for better communication among researchers, better guidelines for analysis, and better evaluation methods for commercial static analyzers for practitioners. In this paper, we propose a mathematical framework which is generic, because it is not specific to any particular software artifact, and rigorous, because it is based on precise mathematical concepts. This framework defines several important measurement concepts (size, length, complexity, cohesion, coupling). It is not intended to be complete or fully objective; other frameworks could have been proposed and different choices could have been made. However, we believe that the formalism and properties we introduce are convenient and intuitive. In addition, we have reviewed the literature on this subject and compared it with our work. This framework contributes constructively to a firmer theoretical ground of software measurement.

Property-Based Software Engineering Measurement

NASA Technical Reports Server (NTRS)

Briand, Lionel C.; Morasca, Sandro; Basili, Victor R.

1997-01-01

Little theory exists in the field of software system measurement. Concepts such as complexity, coupling, cohesion or even size are very often subject to interpretation and appear to have inconsistent definitions in the literature. As a consequence, there is little guidance provided to the analyst attempting to define proper measures for specific problems. Many controversies in the literature are simply misunderstandings and stem from the fact that some people talk about different measurement concepts under the same label (complexity is the most common case). There is a need to define unambiguously the most important measurement concepts used in the measurement of software products. One way of doing so is to define precisely what mathematical properties characterize these concepts, regardless of the specific software artifacts to which these concepts are applied. Such a mathematical framework could generate a consensus in the software engineering community and provide a means for better communication among researchers, better guidelines for analysts, and better evaluation methods for commercial static analyzers for practitioners. In this paper, we propose a mathematical framework which is generic, because it is not specific to any particular software artifact and rigorous, because it is based on precise mathematical concepts. We use this framework to propose definitions of several important measurement concepts (size, length, complexity, cohesion, coupling). It does not intend to be complete or fully objective; other frameworks could have been proposed and different choices could have been made. However, we believe that the formalisms and properties we introduce are convenient and intuitive. This framework contributes constructively to a firmer theoretical ground of software measurement.

Scattering and Diffraction of Elastodynamic Waves in a Concentric Cylindrical Phantom for MR Elastography

PubMed Central

Schwartz, Benjamin L.; Yin, Ziying; Yaşar, Temel K.; Liu, Yifei; Khan, Altaf A.; Ye, Allen Q.; Royston, Thomas J.; Magin, Richard L.

2016-01-01

Aim The focus of this paper is to report on the design and construction of a multiply connected phantom for use in magnetic resonance elasography (MRE)–an imaging technique that allows for the non-invasive visualization of the displacement field throughout an object from externally driven harmonic motion–as well as its inverse modeling with a closed-form analytic solution which is derived herein from first principles. Methods Mathematically, the phantom is described as two infinite concentric circular cylinders with unequal complex shear moduli, harmonically vibrated at the exterior surface in a direction along their common axis. Each concentric cylinder is made of a hydrocolloid with its own specific solute concentration. They are assembled in a multi-step process for which custom scaffolding was designed and built. A customized spin-echo based MR elastography sequence with a sinusoidal motion-sensitizing gradient was used for data acquisition on a 9.4 T Agilent small-animal MR scanner. Complex moduli obtained from the inverse model are used to solve the forward problem with a finite element method. Results Both complex shear moduli show a significant frequency dependence (p < 0.001) in keeping with previous work. Conclusion The novel multiply connected phantom and mathematical model are validated as a viable tool for MRE studies. Significance On a small enough scale much of physiology can be mathematically modeled with basic geometric shapes, e.g. a cylinder representing a blood vessel. This work demonstrates the possibility of elegant mathematical analysis of phantoms specifically designed and carefully constructed for biomedical MRE studies. PMID:26886963

Teacher Mathematical Literacy: Case Study of Junior High School Teachers in Pasaman

NASA Astrophysics Data System (ADS)

Ahmad, D.; Suherman, S.; Maulana, H.

2018-04-01

The aim of this paper was to examine the ability of junior high school mathematics teachers to solve mathematical literacy base Problems (PISA and PISA-like problems) for the case Pasaman regency. The data was collected by interviews and test. As the results of this study, teacher ability in solving mathematical literacy base problems for level 1 until 3 has been good, but for level 4 or above is still low. It is caused by teacher knowledge about mathematical literacy still few.

Problems in Mathematics--Moving towards a Holistic Approach.

ERIC Educational Resources Information Center

Maree, J. G.

1992-01-01

Explanations for problems in mathematics are offered, and examples that may lead to a better understanding of problems in mathematics are discussed. Examples include the developmental, dyscalculia, dyspedagogia, behaviorist, medical, psychoanalytic, cultural, curricular, social, transactional, moral, and eclectic models. A case study exemplifies…

Current problems in applied mathematics and mathematical physics

NASA Astrophysics Data System (ADS)

Samarskii, A. A.

Papers are presented on such topics as mathematical models in immunology, mathematical problems of medical computer tomography, classical orthogonal polynomials depending on a discrete variable, and boundary layer methods for singular perturbation problems in partial derivatives. Consideration is also given to the computer simulation of supernova explosion, nonstationary internal waves in a stratified fluid, the description of turbulent flows by unsteady solutions of the Navier-Stokes equations, and the reduced Galerkin method for external diffraction problems using the spline approximation of fields.

Computational complexity of ecological and evolutionary spatial dynamics

PubMed Central

Ibsen-Jensen, Rasmus; Chatterjee, Krishnendu; Nowak, Martin A.

2015-01-01

There are deep, yet largely unexplored, connections between computer science and biology. Both disciplines examine how information proliferates in time and space. Central results in computer science describe the complexity of algorithms that solve certain classes of problems. An algorithm is deemed efficient if it can solve a problem in polynomial time, which means the running time of the algorithm is a polynomial function of the length of the input. There are classes of harder problems for which the fastest possible algorithm requires exponential time. Another criterion is the space requirement of the algorithm. There is a crucial distinction between algorithms that can find a solution, verify a solution, or list several distinct solutions in given time and space. The complexity hierarchy that is generated in this way is the foundation of theoretical computer science. Precise complexity results can be notoriously difficult. The famous question whether polynomial time equals nondeterministic polynomial time (i.e., P = NP) is one of the hardest open problems in computer science and all of mathematics. Here, we consider simple processes of ecological and evolutionary spatial dynamics. The basic question is: What is the probability that a new invader (or a new mutant) will take over a resident population? We derive precise complexity results for a variety of scenarios. We therefore show that some fundamental questions in this area cannot be answered by simple equations (assuming that P is not equal to NP). PMID:26644569

Biologically-inspired approaches for self-organization, adaptation, and collaboration of heterogeneous autonomous systems

NASA Astrophysics Data System (ADS)

Steinberg, Marc

2011-06-01

This paper presents a selective survey of theoretical and experimental progress in the development of biologicallyinspired approaches for complex surveillance and reconnaissance problems with multiple, heterogeneous autonomous systems. The focus is on approaches that may address ISR problems that can quickly become mathematically intractable or otherwise impractical to implement using traditional optimization techniques as the size and complexity of the problem is increased. These problems require dealing with complex spatiotemporal objectives and constraints at a variety of levels from motion planning to task allocation. There is also a need to ensure solutions are reliable and robust to uncertainty and communications limitations. First, the paper will provide a short introduction to the current state of relevant biological research as relates to collective animal behavior. Second, the paper will describe research on largely decentralized, reactive, or swarm approaches that have been inspired by biological phenomena such as schools of fish, flocks of birds, ant colonies, and insect swarms. Next, the paper will discuss approaches towards more complex organizational and cooperative mechanisms in team and coalition behaviors in order to provide mission coverage of large, complex areas. Relevant team behavior may be derived from recent advances in understanding of the social and cooperative behaviors used for collaboration by tens of animals with higher-level cognitive abilities such as mammals and birds. Finally, the paper will briefly discuss challenges involved in user interaction with these types of systems.

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…

Investigating and developing engineering students' mathematical modelling and problem-solving skills

NASA Astrophysics Data System (ADS)

Wedelin, Dag; Adawi, Tom; Jahan, Tabassum; Andersson, Sven

2015-09-01

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 problem solvers, unaware of the importance of understanding the problem and exploring alternatives, and impeded by inappropriate beliefs, attitudes and expectations. Important impacts of the course belong to the metacognitive domain. The nature of the problems, the supervision and the follow-up lectures were emphasised as contributing to the impacts of the course, where students show major development. We discuss these empirical results in relation to a framework for mathematical thinking and the notion of cognitive apprenticeship. Based on the results, we argue that this kind of teaching should be considered in the education of all engineers.

Mathematical marriages: intercourse between mathematics and Semiotic choice.

PubMed

Wagner, Roy

2009-04-01

This paper examines the interaction between Semiotic choices and the presentation and solution of a family of contemporary mathematical problems centred around the so-called 'stable marriage problem'. I investigate how a socially restrictive choice of signs impacts mathematical production both in terms of problem formation and of solutions. I further note how the choice of gendered language ends up constructing a reality, which duplicates the very structural framework that it imported into mathematical analysis in the first place. I go on to point out some semiotic lines of flight from this interlocking grip of mathematics and gendered language.

Towards the Construction of a Framework to Deal with Routine Problems to Foster Mathematical Inquiry

ERIC Educational Resources Information Center

Santos-Trigo, Manuel; Camacho-Machin, Matias

2009-01-01

To what extent does the process of solving textbook problems help students develop a way of thinking that is consistent with mathematical practice? Can routine problems be transformed into problem solving activities that promote students' mathematical reflection? These questions are used to outline and discuss features of an inquiry framework…

WWC Review of the Report "Benefits of Practicing 4 = 2 + 2: Nontraditional Problem Formats Facilitate Children's Understanding of Mathematical Equivalence." What Works Clearinghouse Single Study Review

ERIC Educational Resources Information Center

What Works Clearinghouse, 2014

2014-01-01

The 2011 study, "Benefits of Practicing 4 = 2 + 2: Nontraditional Problem Formats Facilitate Children's Understanding of Mathematical Equivalence," examined the effects of addition practice using nontraditional problem formats on students' understanding of mathematical equivalence. In nontraditional problem formats, operations appear on…

Using Predictor-Corrector Methods in Numerical Solutions to Mathematical Problems of Motion

ERIC Educational Resources Information Center

Lewis, Jerome

2005-01-01

In this paper, the author looks at some classic problems in mathematics that involve motion in the plane. Many case problems like these are difficult and beyond the mathematical skills of most undergraduates, but computational approaches often require less insight into the subtleties of the problems and can be used to obtain reliable solutions.…

Using Video Prompting to Teach Mathematical Problem Solving of Real-World Video-Simulation Problems

ERIC Educational Resources Information Center

Saunders, Alicia F.; Spooner, Fred; Ley Davis, Luann

2018-01-01

Mathematical problem solving is necessary in many facets of everyday life, yet little research exists on how to teach students with more severe disabilities higher order mathematics like problem solving. Using a multiple probe across participants design, three middle school students with moderate intellectual disability (ID) were taught to solve…

Teaching Elementary Mathematics through Problem Solving and Its Relationship to Mathematics Achievement

ERIC Educational Resources Information Center

Bullock, Audrey N.

2017-01-01

Problem solving in mathematics has been a goal for students for decades. In the reviewed literature, problem solving was most often treated as the dependent variable and was defined very broadly; however, few studies were found that included problem solving as a treatment or independent variable. The purpose of this study was to investigate the…

Sex and Training Differences in Mental Rotation: A Behavioral and Neurophysiological Comparison of Gifted Achievers, Gifted Underachievers and Average Intelligent Achievers

ERIC Educational Resources Information Center

Bergner, Sabine; Neubauer, Aljoscha C.

2011-01-01

A male advantage in spatial abilities is assumed to underlie their superior performance in complex mathematical problems. In this study we investigated whether sex differences in mental rotation (MR) tasks are related to female underachievement and whether training effects of a MR training can be generalized across achievers and underachievers.…

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…

The relation between children’s constructive play activities, spatial ability, and mathematical word problem-solving performance: a mediation analysis in sixth-grade students

PubMed Central

Oostermeijer, Meike; Boonen, Anton J. H.; Jolles, Jelle

2014-01-01

The scientific literature shows that constructive play activities are positively related to children’s spatial ability. Likewise, a close positive relation is found between spatial ability and mathematical word problem-solving performances. The relation between children’s constructive play and their performance on mathematical word problems is, however, not reported yet. The aim of the present study was to investigate whether spatial ability acted as a mediator in the relation between constructive play and mathematical word problem-solving performance in 128 sixth-grade elementary school children. This mediating role of spatial ability was tested by utilizing the current mediation approaches suggested by Preacher and Hayes (2008). Results showed that 38.16% of the variance in mathematical word problem-solving performance is explained by children’s constructive play activities and spatial ability. More specifically, spatial ability acted as a partial mediator, explaining 31.58% of the relation between constructive play and mathematical word problem-solving performance. PMID:25101038

Modeling the chemistry of complex petroleum mixtures.

PubMed Central

Quann, R J

1998-01-01

Determining the complete molecular composition of petroleum and its refined products is not feasible with current analytical techniques because of the astronomical number of molecular components. Modeling the composition and behavior of such complex mixtures in refinery processes has accordingly evolved along a simplifying concept called lumping. Lumping reduces the complexity of the problem to a manageable form by grouping the entire set of molecular components into a handful of lumps. This traditional approach does not have a molecular basis and therefore excludes important aspects of process chemistry and molecular property fundamentals from the model's formulation. A new approach called structure-oriented lumping has been developed to model the composition and chemistry of complex mixtures at a molecular level. The central concept is to represent an individual molecular or a set of closely related isomers as a mathematical construct of certain specific and repeating structural groups. A complex mixture such as petroleum can then be represented as thousands of distinct molecular components, each having a mathematical identity. This enables the automated construction of large complex reaction networks with tens of thousands of specific reactions for simulating the chemistry of complex mixtures. Further, the method provides a convenient framework for incorporating molecular physical property correlations, existing group contribution methods, molecular thermodynamic properties, and the structure--activity relationships of chemical kinetics in the development of models. PMID:9860903

Behavioral Executive Functions Among Adolescents With Mathematics Difficulties.

PubMed

Holm, Marja E; Aunio, Pirjo; Björn, Piia M; Klenberg, Liisa; Korhonen, Johan; Hannula, Markku S

2017-07-01

This study investigates behavioral executive functions (EFs) in the mathematics classroom context among adolescents with different mathematics performance levels. The EF problems were assessed by teachers using a behavioral rating inventory. Using cutoff scores on a standardized mathematics assessment, groups with mathematics difficulties (MD; n = 124), low mathematics performance (LA; n = 140), and average or higher scores (AC; n = 355) were identified. Results showed that the MD group had more problems with distractibility, directing attention, shifting attention, initiative, execution of action, planning, and evaluation than the LA group, whereas the differences in hyperactivity, impulsivity, and sustaining attention were not significant. Compared to the AC group, the MD group showed more problems with all behavioral EFs except hyperactivity and impulsivity, while the LA group showed more problems only with shifting attention. Male adolescents showed more behavioral EF problems than female adolescents, but this gender difference was negligible within the MD group. The practical implications of the results are discussed.

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

NASA Astrophysics Data System (ADS)

Loucks, Daniel

2016-04-01

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

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

Ferrada, J.J.; Osborne-Lee, I.W.; Grizzaffi, P.A.

Expert systems are known to be useful in capturing expertise and applying knowledge to chemical engineering problems such as diagnosis, process control, process simulation, and process advisory. However, expert system applications are traditionally limited to knowledge domains that are heuristic and involve only simple mathematics. Neural networks, on the other hand, represent an emerging technology capable of rapid recognition of patterned behavior without regard to mathematical complexity. Although useful in problem identification, neural networks are not very efficient in providing in-depth solutions and typically do not promote full understanding of the problem or the reasoning behind its solutions. Hence, applicationsmore » of neural networks have certain limitations. This paper explores the potential for expanding the scope of chemical engineering areas where neural networks might be utilized by incorporating expert systems and neural networks into the same application, a process called hybridization. In addition, hybrid applications are compared with those using more traditional approaches, the results of the different applications are analyzed, and the feasibility of converting the preliminary prototypes described herein into useful final products is evaluated. 12 refs., 8 figs.« less

AQMAN; linear and quadratic programming matrix generator using two-dimensional ground-water flow simulation for aquifer management modeling

USGS Publications Warehouse

Lefkoff, L.J.; Gorelick, S.M.

1987-01-01

A FORTRAN-77 computer program code that helps solve a variety of aquifer management problems involving the control of groundwater hydraulics. It is intended for use with any standard mathematical programming package that uses Mathematical Programming System input format. The computer program creates the input files to be used by the optimization program. These files contain all the hydrologic information and management objectives needed to solve the management problem. Used in conjunction with a mathematical programming code, the computer program identifies the pumping or recharge strategy that achieves a user 's management objective while maintaining groundwater hydraulic conditions within desired limits. The objective may be linear or quadratic, and may involve the minimization of pumping and recharge rates or of variable pumping costs. The problem may contain constraints on groundwater heads, gradients, and velocities for a complex, transient hydrologic system. Linear superposition of solutions to the transient, two-dimensional groundwater flow equation is used by the computer program in conjunction with the response matrix optimization method. A unit stress is applied at each decision well and transient responses at all control locations are computed using a modified version of the U.S. Geological Survey two dimensional aquifer simulation model. The program also computes discounted cost coefficients for the objective function and accounts for transient aquifer conditions. (Author 's abstract)

Quantitative modelling in cognitive ergonomics: predicting signals passed at danger.

PubMed

Moray, Neville; Groeger, John; Stanton, Neville

2017-02-01

This paper shows how to combine field observations, experimental data and mathematical modelling to produce quantitative explanations and predictions of complex events in human-machine interaction. As an example, we consider a major railway accident. In 1999, a commuter train passed a red signal near Ladbroke Grove, UK, into the path of an express. We use the Public Inquiry Report, 'black box' data, and accident and engineering reports to construct a case history of the accident. We show how to combine field data with mathematical modelling to estimate the probability that the driver observed and identified the state of the signals, and checked their status. Our methodology can explain the SPAD ('Signal Passed At Danger'), generate recommendations about signal design and placement and provide quantitative guidance for the design of safer railway systems' speed limits and the location of signals. Practitioner Summary: Detailed ergonomic analysis of railway signals and rail infrastructure reveals problems of signal identification at this location. A record of driver eye movements measures attention, from which a quantitative model for out signal placement and permitted speeds can be derived. The paper is an example of how to combine field data, basic research and mathematical modelling to solve ergonomic design problems.

Problem Posing with Realistic Mathematics Education Approach in Geometry Learning

NASA Astrophysics Data System (ADS)

Mahendra, R.; Slamet, I.; Budiyono

2017-09-01

One of the difficulties of students in the learning of geometry is on the subject of plane that requires students to understand the abstract matter. The aim of this research is to determine the effect of Problem Posing learning model with Realistic Mathematics Education Approach in geometry learning. This quasi experimental research was conducted in one of the junior high schools in Karanganyar, Indonesia. The sample was taken using stratified cluster random sampling technique. The results of this research indicate that the model of Problem Posing learning with Realistic Mathematics Education Approach can improve students’ conceptual understanding significantly in geometry learning especially on plane topics. It is because students on the application of Problem Posing with Realistic Mathematics Education Approach are become to be active in constructing their knowledge, proposing, and problem solving in realistic, so it easier for students to understand concepts and solve the problems. Therefore, the model of Problem Posing learning with Realistic Mathematics Education Approach is appropriately applied in mathematics learning especially on geometry material. Furthermore, the impact can improve student achievement.

Protecting Information

NASA Astrophysics Data System (ADS)

Loepp, Susan; Wootters, William K.

2006-09-01

For many everyday transmissions, it is essential to protect digital information from noise or eavesdropping. This undergraduate introduction to error correction and cryptography is unique in devoting several chapters to quantum cryptography and quantum computing, thus providing a context in which ideas from mathematics and physics meet. By covering such topics as Shor's quantum factoring algorithm, this text informs the reader about current thinking in quantum information theory and encourages an appreciation of the connections between mathematics and science.Of particular interest are the potential impacts of quantum physics:(i) a quantum computer, if built, could crack our currently used public-key cryptosystems; and (ii) quantum cryptography promises to provide an alternative to these cryptosystems, basing its security on the laws of nature rather than on computational complexity. No prior knowledge of quantum mechanics is assumed, but students should have a basic knowledge of complex numbers, vectors, and matrices. Accessible to readers familiar with matrix algebra, vector spaces and complex numbers First undergraduate text to cover cryptography, error-correction, and quantum computation together Features exercises designed to enhance understanding, including a number of computational problems, available from www.cambridge.org/9780521534765

Initial Ada components evaluation

NASA Technical Reports Server (NTRS)

Moebes, Travis

1989-01-01

The SAIC has the responsibility for independent test and validation of the SSE. They have been using a mathematical functions library package implemented in Ada to test the SSE IV and V process. The library package consists of elementary mathematical functions and is both machine and accuracy independent. The SSE Ada components evaluation includes code complexity metrics based on Halstead's software science metrics and McCabe's measure of cyclomatic complexity. Halstead's metrics are based on the number of operators and operands on a logical unit of code and are compiled from the number of distinct operators, distinct operands, and total number of occurrences of operators and operands. These metrics give an indication of the physical size of a program in terms of operators and operands and are used diagnostically to point to potential problems. McCabe's Cyclomatic Complexity Metrics (CCM) are compiled from flow charts transformed to equivalent directed graphs. The CCM is a measure of the total number of linearly independent paths through the code's control structure. These metrics were computed for the Ada mathematical functions library using Software Automated Verification and Validation (SAVVAS), the SSE IV and V tool. A table with selected results was shown, indicating that most of these routines are of good quality. Thresholds for the Halstead measures indicate poor quality if the length metric exceeds 260 or difficulty is greater than 190. The McCabe CCM indicated a high quality of software products.

The Effect of Cognitive- and Metacognitive-Based Instruction on Problem Solving by Elementary Students with Mathematical Learning Difficulties

ERIC Educational Resources Information Center

Grizzle-Martin, Tamieka

2014-01-01

Children who struggle in mathematics may also lack cognitive awareness in mathematical problem solving. The cognitively-driven program IMPROVE, a multidimensional method for teaching mathematics, has been shown to be helpful for students with mathematical learning difficulties (MLD). Guided by cognitive theory, the purpose of this…

Problem-Posing as a Didactic Resource in Formal Mathematics Courses to Train Future Secondary School Mathematics Teachers

ERIC Educational Resources Information Center

Solórzano, Lorena Salazar

2015-01-01

Beginning university training programs must focus on different competencies for mathematics teachers, i.e., not only on solving problems, but also on posing them and analyzing the mathematical activity. This paper reports the results of an exploratory study conducted with future secondary school mathematics teachers on the introduction of…

Analytical derivation: An epistemic game for solving mathematically based physics problems

NASA Astrophysics Data System (ADS)

Bajracharya, Rabindra R.; Thompson, John R.

2016-06-01

Problem solving, which often involves multiple steps, is an integral part of physics learning and teaching. Using the perspective of the epistemic game, we documented a specific game that is commonly pursued by students while solving mathematically based physics problems: the analytical derivation game. This game involves deriving an equation through symbolic manipulations and routine mathematical operations, usually without any physical interpretation of the processes. This game often creates cognitive obstacles in students, preventing them from using alternative resources or better approaches during problem solving. We conducted hour-long, semi-structured, individual interviews with fourteen introductory physics students. Students were asked to solve four "pseudophysics" problems containing algebraic and graphical representations. The problems required the application of the fundamental theorem of calculus (FTC), which is one of the most frequently used mathematical concepts in physics problem solving. We show that the analytical derivation game is necessary, but not sufficient, to solve mathematically based physics problems, specifically those involving graphical representations.

Using Problem Solving to Assess Young Children's Mathematics Knowledge

ERIC Educational Resources Information Center

Charlesworth, Rosalind; Leali, Shirley A.

2012-01-01

Mathematics problem solving provides a means for obtaining a view of young children's understanding of mathematics as they move through the early childhood concept development sequence. Assessment information can be obtained through observations and interviews as children develop problem solutions. Examples of preschool, kindergarten, and primary…

Prospective Elementary Teachers' Beliefs about Collaborative Problem Solving and Dialogue in Mathematics

ERIC Educational Resources Information Center

Xenofontos, Constantinos; Kyriakou, Artemis

2017-01-01

This study is concerned with prospective elementary teachers' beliefs about collaborative problem solving and dialogue in mathematics classrooms. Participants (n = 16) attended an undergraduate module titled "Problem Solving in Primary Mathematics", which was specifically designed to provide them with opportunities in collaborative…

Mathematical Problem Solving through Sequential Process Analysis

ERIC Educational Resources Information Center

Codina, A.; Cañadas, M. C.; Castro, E.

2015-01-01

Introduction: The macroscopic perspective is one of the frameworks for research on problem solving in mathematics education. Coming from this perspective, our study addresses the stages of thought in mathematical problem solving, offering an innovative approach because we apply sequential relations and global interrelations between the different…

Information modeling system for blast furnace control

NASA Astrophysics Data System (ADS)

Spirin, N. A.; Gileva, L. Y.; Lavrov, V. V.

2016-09-01

Modern Iron & Steel Works as a rule are equipped with powerful distributed control systems (DCS) and databases. Implementation of DSC system solves the problem of storage, control, protection, entry, editing and retrieving of information as well as generation of required reporting data. The most advanced and promising approach is to use decision support information technologies based on a complex of mathematical models. The model decision support system for control of blast furnace smelting is designed and operated. The basis of the model system is a complex of mathematical models created using the principle of natural mathematical modeling. This principle provides for construction of mathematical models of two levels. The first level model is a basic state model which makes it possible to assess the vector of system parameters using field data and blast furnace operation results. It is also used to calculate the adjustment (adaptation) coefficients of the predictive block of the system. The second-level model is a predictive model designed to assess the design parameters of the blast furnace process when there are changes in melting conditions relative to its current state. Tasks for which software is developed are described. Characteristics of the main subsystems of the blast furnace process as an object of modeling and control - thermal state of the furnace, blast, gas dynamic and slag conditions of blast furnace smelting - are presented.

Analyzing the Effects of a Mathematics Problem-Solving Program, Exemplars, on Mathematics Problem-Solving Scores with Deaf and Hard-of-Hearing Students

ERIC Educational Resources Information Center

Chilvers, Amanda Leigh

2013-01-01

Researchers have noted that mathematics achievement for deaf and hard-of-hearing (d/hh) students has been a concern for many years, including the ability to problem solve. This quasi-experimental study investigates the use of the Exemplars mathematics program with students in grades 2-8 in a school for the deaf that utilizes American Sign Language…

A Parallel Biological Optimization Algorithm to Solve the Unbalanced Assignment Problem Based on DNA Molecular Computing

PubMed Central

Wang, Zhaocai; Pu, Jun; Cao, Liling; Tan, Jian

2015-01-01

The unbalanced assignment problem (UAP) is to optimally resolve the problem of assigning n jobs to m individuals (m < n), such that minimum cost or maximum profit obtained. It is a vitally important Non-deterministic Polynomial (NP) complete problem in operation management and applied mathematics, having numerous real life applications. In this paper, we present a new parallel DNA algorithm for solving the unbalanced assignment problem using DNA molecular operations. We reasonably design flexible-length DNA strands representing different jobs and individuals, take appropriate steps, and get the solutions of the UAP in the proper length range and O(mn) time. We extend the application of DNA molecular operations and simultaneity to simplify the complexity of the computation. PMID:26512650

Learning to Write about Mathematics

ERIC Educational Resources Information Center

Parker, Renee; Breyfogle, M. Lynn

2011-01-01

Beginning in third grade, Pennsylvania students are required to take the Pennsylvania State Standardized Assessment (PSSA), which presents multiple-choice mathematics questions and open-ended mathematics problems. Consistent with the Communication Standard of the National Council of Teachers of Mathematics, while solving the open-ended problems,…

The Acquisition of Problem-Solving Skills in Mathematics: How Animations Can Aid Understanding of Structural Problem Features and Solution Procedures

ERIC Educational Resources Information Center

Scheiter, Katharina; Gerjets, Peter; Schuh, Julia

2010-01-01

In this paper the augmentation of worked examples with animations for teaching problem-solving skills in mathematics is advocated as an effective instructional method. First, in a cognitive task analysis different knowledge prerequisites are identified for solving mathematical word problems. Second, it is argued that so called hybrid animations…

The Use of a Bar Model Drawing to Teach Word Problem Solving to Students with Mathematics Difficulties

ERIC Educational Resources Information Center

Morin, Lisa L.; Watson, Silvana M. R.; Hester, Peggy; Raver, Sharon

2017-01-01

For students with mathematics difficulties (MD), math word problem solving is especially challenging. The purpose of this study was to examine the effects of a problem-solving strategy, bar model drawing, on the mathematical problem-solving skills of students with MD. The study extended previous research that suggested that schematic-based…

Engaging Pre-Service Middle-School Teacher-Education Students in Mathematical Problem Posing: Development of an Active Learning Framework

ERIC Educational Resources Information Center

Ellerton, Nerida F.

2013-01-01

Although official curriculum documents make cursory mention of the need for problem posing in school mathematics, problem posing rarely becomes part of the implemented or assessed curriculum. This paper provides examples of how problem posing can be made an integral part of mathematics teacher education programs. It is argued that such programs…

Teaching Problem Solving to Students Receiving Tiered Interventions Using the Concrete-Representational-Abstract Sequence and Schema-Based Instruction

ERIC Educational Resources Information Center

Flores, Margaret M.; Hinton, Vanessa M.; Burton, Megan E.

2016-01-01

Mathematical word problems are the most common form of mathematics problem solving implemented in K-12 schools. Identifying key words is a frequent strategy taught in classrooms in which students struggle with problem solving and show low success rates in mathematics. Researchers show that using the concrete-representational-abstract (CRA)…

Investigating a Proposed Problem Solving Theory in the Context of Mathematical Problem Solving: A Multi-Case Study

ERIC Educational Resources Information Center

Mills, Nadia Monrose

2015-01-01

The ability to succeed in Science, Technology, Engineering, and Mathematics (STEM) careers is contingent on a student's ability to engage in mathematical problem solving. As a result, there has been increased focus on students' ability to think critically by providing them more with problem solving experiences in the classroom. Much research has…

Limitations to Teaching Children 2 + 2 = 4: Typical Arithmetic Problems Can Hinder Learning of Mathematical Equivalence

ERIC Educational Resources Information Center

McNeil, Nicole M.

2008-01-01

Do typical arithmetic problems hinder learning of mathematical equivalence? Second and third graders (7-9 years old; N= 80) received lessons on mathematical equivalence either with or without typical arithmetic problems (e.g., 15 + 13 = 28 vs. 28 = 28, respectively). Children then solved math equivalence problems (e.g., 3 + 9 + 5 = 6 + __),…

Applying Lakatos' Theory to the Theory of Mathematical Problem Solving.

ERIC Educational Resources Information Center

Nunokawa, Kazuhiko

1996-01-01

The relation between Lakatos' theory and issues in mathematics education, especially mathematical problem solving, is investigated by examining Lakatos' methodology of a scientific research program. (AIM)

Mathematics and complex systems.

PubMed

Foote, Richard

2007-10-19

Contemporary researchers strive to understand complex physical phenomena that involve many constituents, may be influenced by numerous forces, and may exhibit unexpected or emergent behavior. Often such "complex systems" are macroscopic manifestations of other systems that exhibit their own complex behavior and obey more elemental laws. This article proposes that areas of mathematics, even ones based on simple axiomatic foundations, have discernible layers, entirely unexpected "macroscopic" outcomes, and both mathematical and physical ramifications profoundly beyond their historical beginnings. In a larger sense, the study of mathematics itself, which is increasingly surpassing the capacity of researchers to verify "by hand," may be the ultimate complex system.

Dynamic deformation of soft soil media: Experimental studies and mathematical modeling

NASA Astrophysics Data System (ADS)

Balandin, V. V.; Bragov, A. M.; Igumnov, L. A.; Konstantinov, A. Yu.; Kotov, V. L.; Lomunov, A. K.

2015-05-01

A complex experimental-theoretical approach to studying the problem of high-rate strain of soft soil media is presented. This approach combines the following contemporary methods of dynamical tests: the modified Hopkinson-Kolsky method applied tomedium specimens contained in holders and the method of plane wave shock experiments. The following dynamic characteristics of sand soils are obtained: shock adiabatic curves, bulk compressibility curves, and shear resistance curves. The obtained experimental data are used to study the high-rate strain process in the system of a split pressure bar, and the constitutive relations of Grigoryan's mathematical model of soft soil medium are verified by comparing the results of computational and natural test experiments of impact and penetration.

Extreme-Scale Bayesian Inference for Uncertainty Quantification of Complex Simulations

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

Biros, George

Uncertainty quantification (UQ)—that is, quantifying uncertainties in complex mathematical models and their large-scale computational implementations—is widely viewed as one of the outstanding challenges facing the field of CS&E over the coming decade. The EUREKA project set to address the most difficult class of UQ problems: those for which both the underlying PDE model as well as the uncertain parameters are of extreme scale. In the project we worked on these extreme-scale challenges in the following four areas: 1. Scalable parallel algorithms for sampling and characterizing the posterior distribution that exploit the structure of the underlying PDEs and parameter-to-observable map. Thesemore » include structure-exploiting versions of the randomized maximum likelihood method, which aims to overcome the intractability of employing conventional MCMC methods for solving extreme-scale Bayesian inversion problems by appealing to and adapting ideas from large-scale PDE-constrained optimization, which have been very successful at exploring high-dimensional spaces. 2. Scalable parallel algorithms for construction of prior and likelihood functions based on learning methods and non-parametric density estimation. Constructing problem-specific priors remains a critical challenge in Bayesian inference, and more so in high dimensions. Another challenge is construction of likelihood functions that capture unmodeled couplings between observations and parameters. We will create parallel algorithms for non-parametric density estimation using high dimensional N-body methods and combine them with supervised learning techniques for the construction of priors and likelihood functions. 3. Bayesian inadequacy models, which augment physics models with stochastic models that represent their imperfections. The success of the Bayesian inference framework depends on the ability to represent the uncertainty due to imperfections of the mathematical model of the phenomena of interest. This is a central challenge in UQ, especially for large-scale models. We propose to develop the mathematical tools to address these challenges in the context of extreme-scale problems. 4. Parallel scalable algorithms for Bayesian optimal experimental design (OED). Bayesian inversion yields quantified uncertainties in the model parameters, which can be propagated forward through the model to yield uncertainty in outputs of interest. This opens the way for designing new experiments to reduce the uncertainties in the model parameters and model predictions. Such experimental design problems have been intractable for large-scale problems using conventional methods; we will create OED algorithms that exploit the structure of the PDE model and the parameter-to-output map to overcome these challenges. Parallel algorithms for these four problems were created, analyzed, prototyped, implemented, tuned, and scaled up for leading-edge supercomputers, including UT-Austin’s own 10 petaflops Stampede system, ANL’s Mira system, and ORNL’s Titan system. While our focus is on fundamental mathematical/computational methods and algorithms, we will assess our methods on model problems derived from several DOE mission applications, including multiscale mechanics and ice sheet dynamics.« less

Instructional Qualities of a Successful Mathematical Problem-Solving Class.

ERIC Educational Resources Information Center

Santos-Trigo, Manuel

1998-01-01

Describes activities that have been successfully implemented by an expert during a mathematical problem-solving course. Focuses on the identification of the qualities of these problems used to promote the development of student strategies and values that reflect mathematical practice in the classroom. Contains 17 references. (ASK)

Problem-Posing Research in Mathematics Education: Looking Back, Looking Around, and Looking Ahead

ERIC Educational Resources Information Center

Silver, Edward A.

2013-01-01

In this paper, I comment on the set of papers in this special issue on mathematical problem posing. I offer some observations about the papers in relation to several key issues, and I suggest some productive directions for continued research inquiry on mathematical problem posing.

Mathematical Problem Solving. Issues in Research.

ERIC Educational Resources Information Center

Lester, Frank K., Jr., Ed.; Garofalo, Joe, Ed.

This set of papers was originally developed for a conference on Issues and Directions in Mathematics Problem Solving Research held at Indiana University in May 1981. The purpose is to contribute to the clear formulation of the key issues in mathematical problem-solving research by presenting the ideas of actively involved researchers. An…

The Association between Mathematical Word Problems and Reading Comprehension

ERIC Educational Resources Information Center

Vilenius-Tuohimaa, Piia Maria; Aunola, Kaisa; Nurmi, Jari-Erik

2008-01-01

This study aimed to investigate the interplay between mathematical word problem skills and reading comprehension. The participants were 225 children aged 9-10 (Grade 4). The children's text comprehension and mathematical word problem-solving performance was tested. Technical reading skills were investigated in order to categorise participants as…

A Problem on Optimal Transportation

ERIC Educational Resources Information Center

Cechlarova, Katarina

2005-01-01

Mathematical optimization problems are not typical in the classical curriculum of mathematics. In this paper we show how several generalizations of an easy problem on optimal transportation were solved by gifted secondary school pupils in a correspondence mathematical seminar, how they can be used in university courses of linear programming and…

CASMI: Virtual Learning Collaborative Environment for Mathematical Enrichment

ERIC Educational Resources Information Center

Freiman, Viktor; Manuel, Dominic; Lirette-Pitre, Nicole

2007-01-01

Challenging problems can make mathematics more attractive to all learners, including the gifted. Application problems that one still finds in regular textbooks often can be resolved by applying a single mathematical concept, operation, or formula. These problems do not require a higher order of thinking. They are, therefore, less cognitively and…

Investigating the Impact of Field Trips on Teachers' Mathematical Problem Posing

ERIC Educational Resources Information Center

Courtney, Scott A.; Caniglia, Joanne; Singh, Rashmi

2014-01-01

This study examines the impact of field trip experiences on teachers' mathematical problem posing. Teachers from a large urban public school system in the Midwest participated in a professional development program that incorporated experiential learning with mathematical problem formulation experiences. During 2 weeks of summer 2011, 68 teachers…

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…

Students' Activity in Computer-Supported Collaborative Problem Solving in Mathematics

ERIC Educational Resources Information Center

Hurme, Tarja-riitta; Jarvela, Sanna

2005-01-01

The purpose of this study was to analyse secondary school students' (N = 16) computer-supported collaborative mathematical problem solving. The problem addressed in the study was: What kinds of metacognitive processes appear during computer-supported collaborative learning in mathematics? Another aim of the study was to consider the applicability…

The Mathematical Preparation of Prospective Elementary Teachers: Reflections from Solving an "Interesting Problem"

ERIC Educational Resources Information Center

Ellis, Mark W.; Contreras, Jose; Martinez-Cruz, Armando M.

2009-01-01

Problem solving tasks offer valuable opportunities to strengthen prospective elementary teachers' knowledge of and disposition toward mathematics, providing them with new experiences doing mathematics. Mathematics educators can influence future instruction by modeling effective pedagogical strategies that engage students in making sense of…

Student Teachers' Mathematics Attitudes, Authentic Investigations and Use of Metacognitive Tools

ERIC Educational Resources Information Center

Afamasaga-Fuata'i, Karoline; Sooaemalelagi, Lumaava

2014-01-01

Based on findings from a semester-long study, this article examines the development of Samoan prospective teachers' mathematical understandings and mathematics attitudes when investigating authentic contexts and applying working mathematically processes, mental computations and problem-solving strategies to find solutions of problems. The…

Equity and Access: All Students Are Mathematical Problem Solvers

ERIC Educational Resources Information Center

Franz, Dana Pompkyl; Ivy, Jessica; McKissick, Bethany R.

2016-01-01

Often mathematical instruction for students with disabilities, especially those with learning disabilities, includes an overabundance of instruction on mathematical computation and does not include high-quality instruction on mathematical reasoning and problem solving. In fact, it is a common misconception that students with learning disabilities…

Pattern of mathematic representation ability in magnetic electricity problem

NASA Astrophysics Data System (ADS)

Hau, R. R. H.; Marwoto, P.; Putra, N. M. D.

2018-03-01

The mathematic representation ability in solving magnetic electricity problem gives information about the way students understand magnetic electricity. Students have varied mathematic representation pattern ability in solving magnetic electricity problem. This study aims to determine the pattern of students' mathematic representation ability in solving magnet electrical problems.The research method used is qualitative. The subject of this study is the fourth semester students of UNNES Physics Education Study Program. The data collection is done by giving a description test that refers to the test of mathematical representation ability and interview about field line topic and Gauss law. The result of data analysis of student's mathematical representation ability in solving magnet electric problem is categorized into high, medium and low category. The ability of mathematical representations in the high category tends to use a pattern of making known and asked symbols, writing equations, using quantities of physics, substituting quantities into equations, performing calculations and final answers. The ability of mathematical representation in the medium category tends to use several patterns of writing the known symbols, writing equations, using quantities of physics, substituting quantities into equations, performing calculations and final answers. The ability of mathematical representations in the low category tends to use several patterns of making known symbols, writing equations, substituting quantities into equations, performing calculations and final answer.

Child-Level Predictors of Responsiveness to Evidence-Based Mathematics Intervention.

PubMed

Powell, Sarah R; Cirino, Paul T; Malone, Amelia S

2017-07-01

We identified child-level predictors of responsiveness to 2 types of mathematics (calculation and word-problem) intervention among 2nd-grade children with mathematics difficulty. Participants were 250 children in 107 classrooms in 23 schools pretested on mathematics and general cognitive measures and posttested on mathematics measures. We assigned classrooms randomly assigned to calculation intervention, word-problem intervention, or business-as-usual control. Intervention lasted 17 weeks. Path analyses indicated that scores on working memory and language comprehension assessments moderated responsiveness to calculation intervention. No moderators were identified for responsiveness to word-problem intervention. Across both intervention groups and the control group, attentive behavior predicted both outcomes. Initial calculation skill predicted the calculation outcome, and initial language comprehension predicted word-problem outcomes. These results indicate that screening for calculation intervention should include a focus on working memory, language comprehension, attentive behavior, and calculations. Screening for word-problem intervention should focus on attentive behavior and word problems.

The airport gate assignment problem: a survey.

PubMed

Bouras, Abdelghani; Ghaleb, Mageed A; Suryahatmaja, Umar S; Salem, Ahmed M

2014-01-01

The airport gate assignment problem (AGAP) is one of the most important problems operations managers face daily. Many researches have been done to solve this problem and tackle its complexity. The objective of the task is assigning each flight (aircraft) to an available gate while maximizing both conveniences to passengers and the operational efficiency of airport. This objective requires a solution that provides the ability to change and update the gate assignment data on a real time basis. In this paper, we survey the state of the art of these problems and the various methods to obtain the solution. Our survey covers both theoretical and real AGAP with the description of mathematical formulations and resolution methods such as exact algorithms, heuristic algorithms, and metaheuristic algorithms. We also provide a research trend that can inspire researchers about new problems in this area.

A new parallel DNA algorithm to solve the task scheduling problem based on inspired computational model.

PubMed

Wang, Zhaocai; Ji, Zuwen; Wang, Xiaoming; Wu, Tunhua; Huang, Wei

2017-12-01

As a promising approach to solve the computationally intractable problem, the method based on DNA computing is an emerging research area including mathematics, computer science and molecular biology. The task scheduling problem, as a well-known NP-complete problem, arranges n jobs to m individuals and finds the minimum execution time of last finished individual. In this paper, we use a biologically inspired computational model and describe a new parallel algorithm to solve the task scheduling problem by basic DNA molecular operations. In turn, we skillfully design flexible length DNA strands to represent elements of the allocation matrix, take appropriate biological experiment operations and get solutions of the task scheduling problem in proper length range with less than O(n 2 ) time complexity. Copyright © 2017. Published by Elsevier B.V.

The Airport Gate Assignment Problem: A Survey

PubMed Central

Ghaleb, Mageed A.; Salem, Ahmed M.

2014-01-01

The airport gate assignment problem (AGAP) is one of the most important problems operations managers face daily. Many researches have been done to solve this problem and tackle its complexity. The objective of the task is assigning each flight (aircraft) to an available gate while maximizing both conveniences to passengers and the operational efficiency of airport. This objective requires a solution that provides the ability to change and update the gate assignment data on a real time basis. In this paper, we survey the state of the art of these problems and the various methods to obtain the solution. Our survey covers both theoretical and real AGAP with the description of mathematical formulations and resolution methods such as exact algorithms, heuristic algorithms, and metaheuristic algorithms. We also provide a research trend that can inspire researchers about new problems in this area. PMID:25506074

Challenges in Math.

ERIC Educational Resources Information Center

Feng, Chengde

1992-01-01

Fourteen mathematics problems from the 1987 Chinese Primary School Mathematics Examination for fifth and sixth grade students are presented. The word problems, accompanied by answers, involve algebra, division, ratios, areas, and other mathematical processes. (JDD)

Analysis of creative mathematical thinking ability by using model eliciting activities (MEAs)

NASA Astrophysics Data System (ADS)

Winda, A.; Sufyani, P.; Elah, N.

2018-05-01

Lack of creative mathematical thinking ability can lead to not accustomed with open ended problem. Students’ creative mathematical thinking ability in the first grade at one of junior high school in Tangerang City is not fully developed. The reason of students’ creative mathematical thinking ability is not optimally developed is so related with learning process which has done by the mathematics teacher, maybe the learning design that teacher use is unsuitable for increasing students’ activity in the learning process. This research objective is to see the differences in students’ ways of answering the problems in terms of students’ creative mathematical thinking ability during the implementation of Model Eliciting Activities (MEAs). This research use post-test experimental class design. The indicators for creative mathematical thinking ability in this research arranged in three parts, as follow: (1) Fluency to answer the problems; (2) Flexibility to solve the problems; (3) Originality of answers. The result of this research found that by using the same learning model and same instrument from Model Eliciting Activities (MEAs) there are some differences in the way students answer the problems and Model Eliciting Activities (MEAs) can be one of approach used to increase students’ creative mathematical thinking ability.

Developing Teaching Material Software Assisted for Numerical Methods

NASA Astrophysics Data System (ADS)

Handayani, A. D.; Herman, T.; Fatimah, S.

2017-09-01

The NCTM vision shows the importance of two things in school mathematics, which is knowing the mathematics of the 21st century and the need to continue to improve mathematics education to answer the challenges of a changing world. One of the competencies associated with the great challenges of the 21st century is the use of help and tools (including IT), such as: knowing the existence of various tools for mathematical activity. One of the significant challenges in mathematical learning is how to teach students about abstract concepts. In this case, technology in the form of mathematics learning software can be used more widely to embed the abstract concept in mathematics. In mathematics learning, the use of mathematical software can make high level math activity become easier accepted by student. Technology can strengthen student learning by delivering numerical, graphic, and symbolic content without spending the time to calculate complex computing problems manually. The purpose of this research is to design and develop teaching materials software assisted for numerical method. The process of developing the teaching material starts from the defining step, the process of designing the learning material developed based on information obtained from the step of early analysis, learners, materials, tasks that support then done the design step or design, then the last step is the development step. The development of teaching materials software assisted for numerical methods is valid in content. While validator assessment for teaching material in numerical methods is good and can be used with little revision.

Stability Analysis of Finite Difference Schemes for Hyperbolic Systems, and Problems in Applied and Computational Linear Algebra.

DTIC Science & Technology

FINITE DIFFERENCE THEORY, * LINEAR ALGEBRA , APPLIED MATHEMATICS, APPROXIMATION(MATHEMATICS), BOUNDARY VALUE PROBLEMS, COMPUTATIONS, HYPERBOLAS, MATHEMATICAL MODELS, NUMERICAL ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS, STABILITY.

Turkish Primary School Students' Strategies in Solving a Non-Routine Mathematical Problem and Some Implications for the Curriculum Design and Implementation

ERIC Educational Resources Information Center

Erdogan, Abdulkadir

2015-01-01

Turkish primary mathematics curriculum emphasizes the role of problem solving for teaching mathematics and pays particular attention to problem solving strategies. Patterns as a subject and the use of patterns as a non-routine problem solving strategy are also emphasized in the curriculum. The primary purpose of this study was to determine how…

Tutoring Mathematical Word Problems Using Solution Trees: Text Comprehension, Situation Comprehension, and Mathematization in Solving Story Problems. Research Report No. 8.

ERIC Educational Resources Information Center

Reusser, Kurt; And Others

The main concern of this paper is on the psychological processes of how students understand and solve mathematical word problems, and on how this knowledge can be applied to computer-based tutoring. It is argued that only a better understanding of the psychological requirements for understanding and solving those problems will lead to…

The enhancement of students' mathematical problem solving ability through teaching with metacognitive scaffolding approach

NASA Astrophysics Data System (ADS)

Prabawanto, Sufyani

2017-05-01

This research aims to investigate the enhancement of students' mathematical problem solving through teaching with metacognitive scaffolding approach. This research used a quasi-experimental design with pretest-posttest control. The subjects were pre-service elementary school teachers in a state university in Bandung. In this study, there were two groups: experimental and control groups. The experimental group consists of 60 studentswho acquire teaching mathematicsunder metacognitive scaffolding approach, while the control group consists of 58 studentswho acquire teaching mathematicsunder direct approach. Students were classified into three categories based on the mathematical prior ability, namely high, middle, and low. Data collection instruments consist of mathematical problem solving test instruments. By usingmean difference test, two conclusions of the research:(1) there is a significant difference in the enhancement of mathematical problem solving between the students who attended the course under metacognitive scaffolding approach and students who attended the course under direct approach, and(2) thereis no significant interaction effect of teaching approaches and ability level based on the mathematical prior ability toward enhancement of students' mathematical problem solving.

Enhancing Mathematical Problem Solving for Secondary Students with or at Risk of Learning Disabilities: A Literature Review

ERIC Educational Resources Information Center

Hwang, Jiwon; Riccomini, Paul J.

2016-01-01

Requirements for reasoning, explaining, and generalizing mathematical concepts increase as students advance through the educational system; hence, improving overall mathematical proficiency is critical. Mathematical proficiency requires students to interpret quantities and their corresponding relationships during problem-solving tasks as well as…

The Microevolution of Mathematical Representations in Children's Activity.

ERIC Educational Resources Information Center

Meira, Luciano

1995-01-01

Discusses children's design of mathematical representations on paper. Suggests that the design of displays during problem solving shapes one's mathematical activity and sense making in crucial ways, and that knowledge of mathematical representations is not simply recalled and applied to problem solving, but also emerges out of one's interactions…

Using Analogies to Facilitate Conceptual Change in Mathematics Learning

ERIC Educational Resources Information Center

Vamvakoussi, Xenia

2017-01-01

The problem of adverse effects of prior knowledge in mathematics learning has been amply documented and theorized by mathematics educators as well as cognitive/developmental psychologists. This problem emerges when students' prior knowledge about a mathematical notion comes in contrast with new information coming from instruction, giving rise to…

Mathematical Problem Solving Ability of Eleventh Standard Students

ERIC Educational Resources Information Center

Priya, J. Johnsi

2017-01-01

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

Examining the Impact of Writing and Literacy Connections on Mathematics Learning

ERIC Educational Resources Information Center

Martin, Christie; Polly, Drew

2016-01-01

In this study, we examine how literacy connections with multiple step mathematics problems affected mathematics learning for 4th grade students. Three fourth grade teachers incorporated writing activities in their mathematics classroom for two weeks. The level of teacher scaffolding decreased as students progressed through the problems. The…

Kernelization

NASA Astrophysics Data System (ADS)

Fomin, Fedor V.

Preprocessing (data reduction or kernelization) as a strategy of coping with hard problems is universally used in almost every implementation. The history of preprocessing, like applying reduction rules simplifying truth functions, can be traced back to the 1950's [6]. A natural question in this regard is how to measure the quality of preprocessing rules proposed for a specific problem. For a long time the mathematical analysis of polynomial time preprocessing algorithms was neglected. The basic reason for this anomaly was that if we start with an instance I of an NP-hard problem and can show that in polynomial time we can replace this with an equivalent instance I' with |I'| < |I| then that would imply P=NP in classical complexity.

Enhancing students’ mathematical problem posing skill through writing in performance tasks strategy

NASA Astrophysics Data System (ADS)

Kadir; Adelina, R.; Fatma, M.

2018-01-01

Many researchers have studied the Writing in Performance Task (WiPT) strategy in learning, but only a few paid attention on its relation to the problem-posing skill in mathematics. The problem-posing skill in mathematics covers problem reformulation, reconstruction, and imitation. The purpose of the present study was to examine the effect of WiPT strategy on students’ mathematical problem-posing skill. The research was conducted at a Public Junior Secondary School in Tangerang Selatan. It used a quasi-experimental method with randomized control group post-test. The samples were 64 students consists of 32 students of the experiment group and 32 students of the control. A cluster random sampling technique was used for sampling. The research data were obtained by testing. The research shows that the problem-posing skill of students taught by WiPT strategy is higher than students taught by a conventional strategy. The research concludes that the WiPT strategy is more effective in enhancing the students’ mathematical problem-posing skill compared to the conventional strategy.

A cognitive framework for analyzing and describing introductory students' use and understanding of mathematics in physics

NASA Astrophysics Data System (ADS)

Tuminaro, Jonathan

Many introductory, algebra-based physics students perform poorly on mathematical problem solving tasks in physics. There are at least two possible, distinct reasons for this poor performance: (1) students simply lack the mathematical skills needed to solve problems in physics, or (2) students do not know how to apply the mathematical skills they have to particular problem situations in physics. While many students do lack the requisite mathematical skills, a major finding from this work is that the majority of students possess the requisite mathematical skills, yet fail to use or interpret them in the context of physics. In this thesis I propose a theoretical framework to analyze and describe students' mathematical thinking in physics. In particular, I attempt to answer two questions. What are the cognitive tools involved in formal mathematical thinking in physics? And, why do students make the kinds of mistakes they do when using mathematics in physics? According to the proposed theoretical framework there are three major theoretical constructs: mathematical resources, which are the knowledge elements that are activated in mathematical thinking and problem solving; epistemic games, which are patterns of activities that use particular kinds of knowledge to create new knowledge or solve a problem; and frames, which are structures of expectations that determine how individuals interpret situations or events. The empirical basis for this study comes from videotaped sessions of college students solving homework problems. The students are enrolled in an algebra-based introductory physics course. The videotapes were transcribed and analyzed using the aforementioned theoretical framework. Two important results from this work are: (1) the construction of a theoretical framework that offers researchers a vocabulary (ontological classification of cognitive structures) and grammar (relationship between the cognitive structures) for understanding the nature and origin of mathematical use in the context physics, and (2) a detailed understanding, in terms of the proposed theoretical framework, of the errors that students make when using mathematics in the context of physics.

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

NASA Astrophysics Data System (ADS)

Kuzle, A.

2018-06-01

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

Improving mathematical problem solving skills through visual media

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Modeling human target acquisition in ground-to-air weapon systems

NASA Technical Reports Server (NTRS)

Phatak, A. V.; Mohr, R. L.; Vikmanis, M.; Wei, K. C.

1982-01-01

The problems associated with formulating and validating mathematical models for describing and predicting human target acquisition response are considered. In particular, the extension of the human observer model to include the acquisition phase as well as the tracking segment is presented. Relationship of the Observer model structure to the more complex Standard Optimal Control model formulation and to the simpler Transfer Function/Noise representation is discussed. Problems pertinent to structural identifiability and the form of the parameterization are elucidated. A systematic approach toward the identification of the observer acquisition model parameters from ensemble tracking error data is presented.

Evanescent waves and deaf bands in sonic crystals

NASA Astrophysics Data System (ADS)

Romero-García, V.; Garcia-Raffi, L. M.; Sánchez-Pérez, J. V.

2011-12-01

The properties of sonic crystals (SC) are theoretically investigated in this work by solving the inverse problem k(ω) using the extended plane wave expansion (EPWE). The solution of the resulting eigenvalue problem gives the complex band structure which takes into account both the propagating and the evanescent modes. In this work we show the complete mathematical formulation of the EPWE for SC and the supercell approximation for its use in both a complete SC and a SC with defects. As an example we show a novel interpretation of the deaf bands in a complete SC in good agreement with multiple scattering simulations.

Constructive Metacognitive Activity Shift in Mathematical Problem Solving

ERIC Educational Resources Information Center

Hastuti, Intan Dwi; Nusantara, Toto; Subanji; Susanto, Hery

2016-01-01

This study aims to describe the constructive metacognitive activity shift of eleventh graders in solving a mathematical problem. Subjects in this study were 10 students in grade 11 of SMAN 1 Malang. They were divided into 4 groups. Three types of metacognitive activity undertaken by students when completing mathematical problem are awareness,…

Shifting College Students' Epistemological Framing Using Hypothetical Debate Problems

ERIC Educational Resources Information Center

Hu, Dehui; Rebello, N. Sanjay

2014-01-01

Developing expertise in physics problem solving requires the ability to use mathematics effectively in physical scenarios. Novices and experts often perceive the use of mathematics in physics differently. Students' perceptions and how they frame the use of mathematics in physics play an important role in their physics problem solving. In this…

Empowering Educationally Disadvantaged Mathematics Students through a Strategies-Based Problem Solving Approach

ERIC Educational Resources Information Center

Ramnarain, Umesh

2014-01-01

A major impediment to problem solving in mathematics in the great majority of South African schools is that disadvantaged students from seriously impoverished learning environments are lacking in the necessary informal mathematical knowledge to develop their own strategies for solving non-routine problems. A randomized pretest-posttest control…

Examining How Students with Diverse Abilities Use Diagrams to Solve Mathematics Word Problems

ERIC Educational Resources Information Center

van Garderen, Delinda; Scheuermann, Amy; Jackson, Christa

2013-01-01

This study examined students' understanding of diagrams and their use of diagrams as tools to solve mathematical word problems. Students with learning disabilities (LD), typically achieving students, and gifted students in Grades 4 through 7 ("N" = 95) participated. Students were presented with novel mathematical word problem-solving…

The Investigation of Elementary Mathematics Teacher Candidates' Problem Solving Skills According to Various Variables

ERIC Educational Resources Information Center

Kaya, Deniz; Izgiol, Dilek; Kesan, Cenk

2014-01-01

The aim was to determine elementary mathematics teacher candidates' problem solving skills and analyze problem solving skills according to various variables. The data were obtained from total 306 different grade teacher candidates receiving education in Department of Elementary Mathematics Education, Buca Faculty of Education, Dokuz Eylul…

Improving Primary Students' Mathematical Literacy through Problem Based Learning and Direct Instruction

ERIC Educational Resources Information Center

Firdaus, Fery Muhamad; Wahyudin; Herman, Tatang

2017-01-01

This research was done on primary school students who are able to understand mathematical concepts, but unable to apply them in solving real life problems. Therefore, this study aims to improve primary school students' mathematical literacy through problem-based learning and direct instruction. In addition, the research was conducted to determine…

Best Known Problem Solving Strategies in "High-Stakes" Assessments

ERIC Educational Resources Information Center

Hong, Dae S.

2011-01-01

In its mathematics standards, National Council of Teachers of Mathematics (NCTM) states that problem solving is an integral part of all mathematics learning and exposure to problem solving strategies should be embedded across the curriculum. Furthermore, by high school, students should be able to use, decide and invent a wide range of strategies.…

Models of resource allocation optimization when solving the control problems in organizational systems

NASA Astrophysics Data System (ADS)

Menshikh, V.; Samorokovskiy, A.; Avsentev, O.

2018-03-01

The mathematical model of optimizing the allocation of resources to reduce the time for management decisions and algorithms to solve the general problem of resource allocation. The optimization problem of choice of resources in organizational systems in order to reduce the total execution time of a job is solved. This problem is a complex three-level combinatorial problem, for the solving of which it is necessary to implement the solution to several specific problems: to estimate the duration of performing each action, depending on the number of performers within the group that performs this action; to estimate the total execution time of all actions depending on the quantitative composition of groups of performers; to find such a distribution of the existing resource of performers in groups to minimize the total execution time of all actions. In addition, algorithms to solve the general problem of resource allocation are proposed.

From geometry to algebra and vice versa: Realistic mathematics education principles for analyzing geometry tasks

NASA Astrophysics Data System (ADS)

Jupri, Al

2017-04-01

In this article we address how Realistic Mathematics Education (RME) principles, including the intertwinement and the reality principles, are used to analyze geometry tasks. To do so, we carried out three phases of a small-scale study. First we analyzed four geometry problems - considered as tasks inviting the use of problem solving and reasoning skills - theoretically in the light of the RME principles. Second, we tested two problems to 31 undergraduate students of mathematics education program and other two problems to 16 master students of primary mathematics education program. Finally, we analyzed student written work and compared these empirical to the theoretical results. We found that there are discrepancies between what we expected theoretically and what occurred empirically in terms of mathematization and of intertwinement of mathematical concepts from geometry to algebra and vice versa. We conclude that the RME principles provide a fruitful framework for analyzing geometry tasks that, for instance, are intended for assessing student problem solving and reasoning skills.

The Effect of Problem Posing Oriented Analyses-II Course on the Attitudes toward Mathematics and Mathematics Self-Efficacy of Elementary Prospective Mathematics Teachers

ERIC Educational Resources Information Center

Akay, Hayri; Boz, Nihat

2010-01-01

Research on mathematics teaching and learning has recently focused on affective variables, which were found to play an essential role that influences behaviour and learning. Despite its importance, problem posing has not yet received the attention it warrants from the mathematics education community. Perceived self-efficacy beliefs have been found…

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

PubMed

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

2017-01-01

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

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%.

Assessing Mathematics 4. Problem Solving: The APU Approach.

ERIC Educational Resources Information Center

Foxman, Derek; And Others

1984-01-01

Presented are examples of problem-solving items from practical and written mathematics tests. These tests are part of an English survey designed to assess the mathematics achievement of students aged 11 and 15. (JN)

The Effect of Dynamic and Interactive Mathematics Learning Environments (DIMLE), Supporting Multiple Representations, on Perceptions of Elementary Mathematics Pre-Service Teachers in Problem Solving Process

ERIC Educational Resources Information Center

Ozdemir, S.; Reis, Z. Ayvaz

2013-01-01

Mathematics is an important discipline, providing crucial tools, such as problem solving, to improve our cognitive abilities. In order to solve a problem, it is better to envision and represent through multiple means. Multiple representations can help a person to redefine a problem with his/her own words in that envisioning process. Dynamic and…

Solving the three-body Coulomb breakup problem using exterior complex scaling

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

McCurdy, C.W.; Baertschy, M.; Rescigno, T.N.

2004-05-17

Electron-impact ionization of the hydrogen atom is the prototypical three-body Coulomb breakup problem in quantum mechanics. The combination of subtle correlation effects and the difficult boundary conditions required to describe two electrons in the continuum have made this one of the outstanding challenges of atomic physics. A complete solution of this problem in the form of a ''reduction to computation'' of all aspects of the physics is given by the application of exterior complex scaling, a modern variant of the mathematical tool of analytic continuation of the electronic coordinates into the complex plane that was used historically to establish themore » formal analytic properties of the scattering matrix. This review first discusses the essential difficulties of the three-body Coulomb breakup problem in quantum mechanics. It then describes the formal basis of exterior complex scaling of electronic coordinates as well as the details of its numerical implementation using a variety of methods including finite difference, finite elements, discrete variable representations, and B-splines. Given these numerical implementations of exterior complex scaling, the scattering wave function can be generated with arbitrary accuracy on any finite volume in the space of electronic coordinates, but there remains the fundamental problem of extracting the breakup amplitudes from it. Methods are described for evaluating these amplitudes. The question of the volume-dependent overall phase that appears in the formal theory of ionization is resolved. A summary is presented of accurate results that have been obtained for the case of electron-impact ionization of hydrogen as well as a discussion of applications to the double photoionization of helium.« less

[Three dimensional mathematical model of tooth for finite element analysis].

PubMed

Puskar, Tatjana; Vasiljević, Darko; Marković, Dubravka; Jevremović, Danimir; Pantelić, Dejan; Savić-Sević, Svetlana; Murić, Branka

2010-01-01

The mathematical model of the abutment tooth is the starting point of the finite element analysis of stress and deformation of dental structures. The simplest and easiest way is to form a model according to the literature data of dimensions and morphological characteristics of teeth. Our method is based on forming 3D models using standard geometrical forms (objects) in programmes for solid modeling. Forming the mathematical model of abutment of the second upper premolar for finite element analysis of stress and deformation of dental structures. The abutment tooth has a form of a complex geometric object. It is suitable for modeling in programs for solid modeling SolidWorks. After analysing the literature data about the morphological characteristics of teeth, we started the modeling dividing the tooth (complex geometric body) into simple geometric bodies (cylinder, cone, pyramid,...). Connecting simple geometric bodies together or substricting bodies from the basic body, we formed complex geometric body, tooth. The model is then transferred into Abaqus, a computational programme for finite element analysis. Transferring the data was done by standard file format for transferring 3D models ACIS SAT. Using the programme for solid modeling SolidWorks, we developed three models of abutment of the second maxillary premolar: the model of the intact abutment, the model of the endodontically treated tooth with two remaining cavity walls and the model of the endodontically treated tooth with two remaining walls and inserted post. Mathematical models of the abutment made according to the literature data are very similar with the real abutment and the simplifications are minimal. These models enable calculations of stress and deformation of the dental structures. The finite element analysis provides useful information in understanding biomechanical problems and gives guidance for clinical research.

Effects of Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties.

PubMed

Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun

2015-01-01

Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil's Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children's LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions.

Effects of Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties

PubMed Central

Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun

2015-01-01

Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil’s Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children’s LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions. PMID:26090806

Visual Representations in Mathematics Teaching: An Experiment with Students

ERIC Educational Resources Information Center

Debrenti, Edith

2015-01-01

General problem-solving skills are of central importance in school mathematics achievement. Word problems play an important role not just in mathematical education, but in general education as well. Meaningful learning and understanding are basic aspects of all kinds of learning and it is even more important in the case of learning mathematics. In…

Mission Mathematics: Linking Aerospace and the NCTM Standards, K-6.

ERIC Educational Resources Information Center

Hynes, Mary Ellen, Ed.

This book is designed to present mathematical problems and tasks that focus on the National Council of Teachers of Mathematics (NCTM) curriculum and evaluation standards in the context of aerospace activities. It aims at actively engaging students in NCTM's four process standards: (1) problem solving; (2) mathematical reasoning; (3) communicating…

Improving Primary School Prospective Teachers' Understanding of the Mathematics Modeling Process

ERIC Educational Resources Information Center

Bal, Aytgen Pinar; Doganay, Ahmet

2014-01-01

The development of mathematical thinking plays an important role on the solution of problems faced in daily life. Determining the relevant variables and necessary procedural steps in order to solve problems constitutes the essence of mathematical thinking. Mathematical modeling provides an opportunity for explaining thoughts in real life by making…

Improvement of Word Problem Solving and Basic Mathematics Competencies in Students with Attention Deficit/Hyperactivity Disorder and Mathematical Learning Difficulties

ERIC Educational Resources Information Center

González-Castro, Paloma; Cueli, Marisol; Areces, Débora; Rodríguez, Celestino; Sideridis, Georgios

2016-01-01

Problem solving represents a salient deficit in students with mathematical learning difficulties (MLD) primarily caused by difficulties with informal and formal mathematical competencies. This study proposes a computerized intervention tool, the integrated dynamic representation (IDR), for enhancing the early learning of basic mathematical…

Projects, Puzzles and Other Pedagogies: Working with Kids to Solve Local Problems

ERIC Educational Resources Information Center

Marshman, Margaret

2012-01-01

Engaging and extending middle years students in mathematics is a continual challenge. One of the aims of the "Australian Curriculum: Mathematics" is to ensure that students are "confident, creative users and communicators of mathematics" (ACARA, 2011). Use of mathematical models and/or problems has been suggested as methods of…

Using Mathematics and Engineering to Solve Problems in Secondary Level Biology

ERIC Educational Resources Information Center

Cox, Charles; Reynolds, Birdy; Schunn, Christian; Schuchardt, Anita

2016-01-01

There are strong classroom ties between mathematics and the sciences of physics and chemistry, but those ties seem weaker between mathematics and biology. Practicing biologists realize both that there are interesting mathematics problems in biology, and that viewing classroom biology in the context of another discipline could support students'…

Science Modelling in Pre-Calculus: How to Make Mathematics Problems Contextually Meaningful

ERIC Educational Resources Information Center

Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

2011-01-01

"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…

Elementary Students' Spontaneous Metacognitive Functions in Different Types of Mathematical Problems

ERIC Educational Resources Information Center

Mokos, Evagelos; Kafoussi, Sonia

2013-01-01

Metacognition is the mind's ability to monitor and control itself or, in other words, the ability to know about our knowing (Dunlosky & Bjork, 2008). In mathematics education, the importance of the investigation of students' metacognition during their mathematical activity has been focused on the area of mathematics problem solving. This study…

Assessing the Relation between Seventh-Grade Students' Engagement and Mathematical Problem Solving Performance

ERIC Educational Resources Information Center

Lein, Amy E.; Jitendra, Asha K.; Starosta, Kristin M.; Dupuis, Danielle N.; Hughes-Reid, Cheyenne L.; Star, Jon R.

2016-01-01

In this study, the authors assessed the contribution of engagement (on-task behavior) to the mathematics problem-solving performance of seventh-grade students after accounting for prior mathematics achievement. A subsample of seventh-grade students in four mathematics classrooms (one high-, two average-, and one low-achieving) from a larger…

Measuring the Effectiveness of a Mathematics Support Service: An Email Survey

ERIC Educational Resources Information Center

Gillard, Jonathan; Robathan, Kirsty; Wilson, Robert

2011-01-01

Over the last decade the "mathematics problem" (students lacking basic mathematical skills on entry into higher education), and proposed solutions of this problem have been widely debated. One method to help combat this issue has been the introduction of mathematics support centres across higher education institutions. This article describes the…

An Examination of the Relationship between Computation, Problem Solving, and Reading

ERIC Educational Resources Information Center

Cormier, Damien C.; Yeo, Seungsoo; Christ, Theodore J.; Offrey, Laura D.; Pratt, Katherine

2016-01-01

The purpose of this study is to evaluate the relationship of mathematics calculation rate (curriculum-based measurement of mathematics; CBM-M), reading rate (curriculum-based measurement of reading; CBM-R), and mathematics application and problem solving skills (mathematics screener) among students at four levels of proficiency on a statewide…

First-Year Students' Beliefs about Context Problems in Mathematics in University Science Programmes

ERIC Educational Resources Information Center

Drobnic Vidic, Andreja

2015-01-01

Mathematics-related beliefs play an important role in the willingness to engage in academic activities in mathematics education. Such beliefs might not be consistent with the beliefs students hold about context problems that require sufficient mathematical knowledge and the application of such knowledge to various real-life situations. This study…

Students Use Graphic Organizers to Improve Mathematical Problem-Solving Communications

ERIC Educational Resources Information Center

Zollman, Alan

2009-01-01

Improving students' problem-solving abilities is a major, if not the major, goal of middle grades mathematics. To address this goal, the author, who is a university mathematics educator, and nine inner-city middle school teachers developed a math/science action research project. This article describes their unique approach to mathematical problem…

Event- and Time-Driven Techniques Using Parallel CPU-GPU Co-processing for Spiking Neural Networks

PubMed Central

Naveros, Francisco; Garrido, Jesus A.; Carrillo, Richard R.; Ros, Eduardo; Luque, Niceto R.

2017-01-01

Modeling and simulating the neural structures which make up our central neural system is instrumental for deciphering the computational neural cues beneath. Higher levels of biological plausibility usually impose higher levels of complexity in mathematical modeling, from neural to behavioral levels. This paper focuses on overcoming the simulation problems (accuracy and performance) derived from using higher levels of mathematical complexity at a neural level. This study proposes different techniques for simulating neural models that hold incremental levels of mathematical complexity: leaky integrate-and-fire (LIF), adaptive exponential integrate-and-fire (AdEx), and Hodgkin-Huxley (HH) neural models (ranged from low to high neural complexity). The studied techniques are classified into two main families depending on how the neural-model dynamic evaluation is computed: the event-driven or the time-driven families. Whilst event-driven techniques pre-compile and store the neural dynamics within look-up tables, time-driven techniques compute the neural dynamics iteratively during the simulation time. We propose two modifications for the event-driven family: a look-up table recombination to better cope with the incremental neural complexity together with a better handling of the synchronous input activity. Regarding the time-driven family, we propose a modification in computing the neural dynamics: the bi-fixed-step integration method. This method automatically adjusts the simulation step size to better cope with the stiffness of the neural model dynamics running in CPU platforms. One version of this method is also implemented for hybrid CPU-GPU platforms. Finally, we analyze how the performance and accuracy of these modifications evolve with increasing levels of neural complexity. We also demonstrate how the proposed modifications which constitute the main contribution of this study systematically outperform the traditional event- and time-driven techniques under increasing levels of neural complexity. PMID:28223930

Strategic competence of senior secondary school students in solving mathematics problem based on cognitive style

NASA Astrophysics Data System (ADS)

Syukriani, Andi; Juniati, Dwi; Siswono, Tatag Yuli Eko

2017-08-01

The purpose of this study was to explore the strategic competence of senior secondary school students in solving mathematics problems. Terdapat dua subjek, satu bergaya kognitif field-independent dan satu bergaya kognitif field-dependent tetapi keduanya memiliki tingkat prestasi belajar matematika yang setara. There were two subjects, one field-independent cognitive style and one field-dependent cognitive style. They had an equivalent high level of mathematics achievement. Keduanya dipilih berdasarkan hasil tes kompetensi matematika dan GEFT (Group Embedded Figures Test). Subjects were selected based on the test results of mathematics competence and GEFT (Group Embedded Figures Test). Kompetensi strategis dapat merangsang perkembangan otonomi dan fleksibilitas dalam diri siswa karena merupakan keterampilan yang sangat dibutuhkan di sepanjang abad 21. Gaya kognitif merupakan kecenderungan siswa dalam mengolah informasi sangat mempengaruhi performance dalam menyelesaikan masalah matematika. Strategic competence can stimulate the development of autonomy and flexibility of students and they are skills which are needed in the 21st century. Cognitive style is the tendency of students in processing informations and it greatly affects the performance in solving mathematics problems. Hasil penelitian menunjukkan bahwa subjek FI cenderung analitis baik pada pembentukan bayangannya maupun pada gambar yang dibuatnya untuk memproses informasi berdasarkan dengan struktur pengetahuannya sendiri (Internally directed). The research result showed that subject FI tended to be analytical both in forming the mental imagination and the picture to process information in accordance with his own knowledge structure (internally directed). Subjek FD kurang analitis dan tidak dapat mengenal bentuk sederhana (konsep matematika) dari bentuk yang kompleks (Exeternally directed) sehingga menerima ide sebagaimana yang disajikan. Subject FD was less analytical and unable to recognize simple form (mathematical concept) of a complex form (Externally directed), so he received the idea as presented. Hasil penelitian ini penting sebagai bahan masukan untuk guru dan pengembang ilmu pendidikan matematika untuk meningkatkan fleksibilitas (Flexibility) siswa dalam keberagaman karakteristiknya melalui penelitian terkait dengan pengembangan bahan instruksi, perangkat dan model pembelajaran matematika. The results of this research are important as input for teachers and mathematics education developers to increase the flexibility of students in the characteristics diversity through the research related to the development of instruction materials and mathematics learning model. Penelitian selanjutnya, sebaiknya melihat bagaimana FI dan FD dapat memberikan penjelasan dan pembenaran atas strategi yang telah diusahakan supaya terlihat lebih jelas bagaimana perbedaan FI dan FD dalam mengkontruksi konsep matematika pada pengalaman belajarnya Further research should study about how the explanation and justification for the strategy that has been attempted in order to look more clearly how constructing mathematical concepts in their learning experience.

South African Grade 9 Mathematics Teachers' Views on the Teaching of Problem Solving

ERIC Educational Resources Information Center

Chirinda, Brantina; Barmby, Patrick

2018-01-01

The South African curriculum emphasizes the teaching of problem solving in mathematics. However, little is known about South African teachers' views on the teaching of mathematical problem solving (MPS). The purpose of this study was to establish Grade 9 South African teachers' views, teaching strategies and the support required in their teaching…

Teaching Mathematical Word Problem Solving: The Quality of Evidence for Strategy Instruction Priming the Problem Structure

ERIC Educational Resources Information Center

Jitendra, Asha K.; Petersen-Brown, Shawna; Lein, Amy E.; Zaslofsky, Anne F.; Kunkel, Amy K.; Jung, Pyung-Gang; Egan, Andrea M.

2015-01-01

This study examined the quality of the research base related to strategy instruction priming the underlying mathematical problem structure for students with learning disabilities and those at risk for mathematics difficulties. We evaluated the quality of methodological rigor of 18 group research studies using the criteria proposed by Gersten et…

Mathematical Enculturation from the Students' Perspective: Shifts in Problem-Solving Beliefs and Behaviour during the Bachelor Programme

ERIC Educational Resources Information Center

Perrenet, Jacob; Taconis, Ruurd

2009-01-01

This study investigates the changes in mathematical problem-solving beliefs and behaviour of mathematics students during the years after entering university. Novice bachelor students fill in a questionnaire about their problem-solving beliefs and behaviour. At the end of their bachelor programme, as experienced bachelor students, they again fill…

Teachers Implementing Mathematical Problem Posing in the Classroom: Challenges and Strategies

ERIC Educational Resources Information Center

Leung, Shuk-kwan S.

2013-01-01

This paper reports a study about how a teacher educator shared knowledge with teachers when they worked together to implement mathematical problem posing (MPP) in the classroom. It includes feasible methods for getting practitioners to use research-based tasks aligned to the curriculum in order to encourage children to pose mathematical problems.…

Fostering Modeling Competencies: Benefits of Worked Examples, Problems to Be Solved, and Fading Procedures

ERIC Educational Resources Information Center

Große, Cornelia S.

2015-01-01

The application of mathematics to real-world problems is moving more and more in the focus of attention of mathematics education; however, many learners experience huge difficulties in relating "pure" mathematics to everyday contents. In order to solve "modeling problems", it is first necessary to find a transition from a…

Model-Eliciting Activities (MEAs) as a Bridge between Engineering Education Research and Mathematics Education Research

ERIC Educational Resources Information Center

Hamilton, Eric; Lesh, Richard; Lester, Frank; Brilleslyper, Michael

2008-01-01

This article introduces Model-Eliciting Activities (MEAs) as a form of case study team problem-solving. MEA design focuses on eliciting from students conceptual models that they iteratively revise in problem-solving. Though developed by mathematics education researchers to study the evolution of mathematical problem-solving expertise in middle…

The Motivation of Secondary School Students in Mathematical Word Problem Solving

ERIC Educational Resources Information Center

Gasco, Javier; Villarroel, Jose-Domingo

2014-01-01

Introduction: Motivation is an important factor in the learning of mathematics. Within this area of education, word problem solving is central in most mathematics curricula of Secondary School. The objective of this research is to detect the differences in motivation in terms of the strategies used to solve word problems. Method: It analyzed the…

Cognitive Benefits and Costs of Bilingualism in Elementary School Students: The Case of Mathematical Word Problems

ERIC Educational Resources Information Center

Kempert, Sebastian; Saalbach, Henrik; Hardy, Ilonca

2011-01-01

Previous research has emphasized the importance of language for learning mathematics. This is especially true when mathematical problems have to be extracted from a meaningful context, as in arithmetic word problems. Bilingual learners with a low command of the instructional language thus may face challenges when dealing with mathematical…

Space Mathematics, A Resource for Teachers Outlining Supplementary Space-Related Problems in Mathematics.

ERIC Educational Resources Information Center

Reynolds, Thomas D.; And Others

This compilation of 138 problems illustrating applications of high school mathematics to various aspects of space science is intended as a resource from which the teacher may select questions to supplement his regular course. None of the problems require a knowledge of calculus or physics, and solutions are presented along with the problem…

A new fast algorithm for solving the minimum spanning tree problem based on DNA molecules computation.

PubMed

Wang, Zhaocai; Huang, Dongmei; Meng, Huajun; Tang, Chengpei

2013-10-01

The minimum spanning tree (MST) problem is to find minimum edge connected subsets containing all the vertex of a given undirected graph. It is a vitally important NP-complete problem in graph theory and applied mathematics, having numerous real life applications. Moreover in previous studies, DNA molecular operations usually were used to solve NP-complete head-to-tail path search problems, rarely for NP-hard problems with multi-lateral path solutions result, such as the minimum spanning tree problem. In this paper, we present a new fast DNA algorithm for solving the MST problem using DNA molecular operations. For an undirected graph with n vertex and m edges, we reasonably design flexible length DNA strands representing the vertex and edges, take appropriate steps and get the solutions of the MST problem in proper length range and O(3m+n) time complexity. We extend the application of DNA molecular operations and simultaneity simplify the complexity of the computation. Results of computer simulative experiments show that the proposed method updates some of the best known values with very short time and that the proposed method provides a better performance with solution accuracy over existing algorithms. Copyright © 2013 The Authors. Published by Elsevier Ireland Ltd.. All rights reserved.

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

Thompson, S.

This report describes the use of several subroutines from the CORLIB core mathematical subroutine library for the solution of a model fluid flow problem. The model consists of the Euler partial differential equations. The equations are spatially discretized using the method of pseudo-characteristics. The resulting system of ordinary differential equations is then integrated using the method of lines. The stiff ordinary differential equation solver LSODE (2) from CORLIB is used to perform the time integration. The non-stiff solver ODE (4) is used to perform a related integration. The linear equation solver subroutines DECOMP and SOLVE are used to solve linearmore » systems whose solutions are required in the calculation of the time derivatives. The monotone cubic spline interpolation subroutines PCHIM and PCHFE are used to approximate water properties. The report describes the use of each of these subroutines in detail. It illustrates the manner in which modules from a standard mathematical software library such as CORLIB can be used as building blocks in the solution of complex problems of practical interest. 9 refs., 2 figs., 4 tabs.« less

The Role of Motion Concepts in Understanding Non-Motion Concepts

PubMed Central

Khatin-Zadeh, Omid; Banaruee, Hassan; Khoshsima, Hooshang; Marmolejo-Ramos, Fernando

2017-01-01

This article discusses a specific type of metaphor in which an abstract non-motion domain is described in terms of a motion event. Abstract non-motion domains are inherently different from concrete motion domains. However, motion domains are used to describe abstract non-motion domains in many metaphors. Three main reasons are suggested for the suitability of motion events in such metaphorical descriptions. Firstly, motion events usually have high degrees of concreteness. Secondly, motion events are highly imageable. Thirdly, components of any motion event can be imagined almost simultaneously within a three-dimensional space. These three characteristics make motion events suitable domains for describing abstract non-motion domains, and facilitate the process of online comprehension throughout language processing. Extending the main point into the field of mathematics, this article discusses the process of transforming abstract mathematical problems into imageable geometric representations within the three-dimensional space. This strategy is widely used by mathematicians to solve highly abstract and complex problems. PMID:29240715

Dynamic behaviour of thin composite plates for different boundary conditions

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

Sprintu, Iuliana, E-mail: sprintui@yahoo.com, E-mail: rotaruconstantin@yahoo.com; Rotaru, Constantin, E-mail: sprintui@yahoo.com, E-mail: rotaruconstantin@yahoo.com

2014-12-10

In the context of composite materials technology, which is increasingly present in industry, this article covers a topic of great interest and theoretical and practical importance. Given the complex design of fiber-reinforced materials and their heterogeneous nature, mathematical modeling of the mechanical response under different external stresses is very difficult to address in the absence of simplifying assumptions. In most structural applications, composite structures can be idealized as beams, plates, or shells. The analysis is reduced from a three-dimensional elasticity problem to a oneor two-dimensional problem, based on certain simplifying assumptions that can be made because the structure is thin.more » This paper aims to validate a mathematical model illustrating how thin rectangular orthotropic plates respond to the actual load. Thus, from the theory of thin plates, new analytical solutions are proposed corresponding to orthotropic rectangular plates having different boundary conditions. The proposed analytical solutions are considered both for solving equation orthotropic rectangular plates and for modal analysis.« less

Technical Mathematics.

ERIC Educational Resources Information Center

Flannery, Carol A.

This manuscript provides information and problems for teaching mathematics to vocational education students. Problems reflect applications of mathematical concepts to specific technical areas. The materials are organized into six chapters. Chapter 1 covers basic arithmetic, including fractions, decimals, ratio and proportions, percentages, and…

Nash equilibrium and multi criterion aerodynamic optimization

NASA Astrophysics Data System (ADS)

Tang, Zhili; Zhang, Lianhe

2016-06-01

Game theory and its particular Nash Equilibrium (NE) are gaining importance in solving Multi Criterion Optimization (MCO) in engineering problems over the past decade. The solution of a MCO problem can be viewed as a NE under the concept of competitive games. This paper surveyed/proposed four efficient algorithms for calculating a NE of a MCO problem. Existence and equivalence of the solution are analyzed and proved in the paper based on fixed point theorem. Specific virtual symmetric Nash game is also presented to set up an optimization strategy for single objective optimization problems. Two numerical examples are presented to verify proposed algorithms. One is mathematical functions' optimization to illustrate detailed numerical procedures of algorithms, the other is aerodynamic drag reduction of civil transport wing fuselage configuration by using virtual game. The successful application validates efficiency of algorithms in solving complex aerodynamic optimization problem.

The mathematical statement for the solving of the problem of N-version software system design

NASA Astrophysics Data System (ADS)

Kovalev, I. V.; Kovalev, D. I.; Zelenkov, P. V.; Voroshilova, A. A.

2015-10-01

The N-version programming, as a methodology of the fault-tolerant software systems design, allows successful solving of the mentioned tasks. The use of N-version programming approach turns out to be effective, since the system is constructed out of several parallel executed versions of some software module. Those versions are written to meet the same specification but by different programmers. The problem of developing an optimal structure of N-version software system presents a kind of very complex optimization problem. This causes the use of deterministic optimization methods inappropriate for solving the stated problem. In this view, exploiting heuristic strategies looks more rational. In the field of pseudo-Boolean optimization theory, the so called method of varied probabilities (MVP) has been developed to solve problems with a large dimensionality.

Can goal-free problems facilitating students' flexible thinking?

NASA Astrophysics Data System (ADS)

Maulidya, Sity Rahmy; Hasanah, Rusi Ulfa; Retnowati, Endah

2017-08-01

Problem solving is the key of doing and also learning mathematics. It takes also the fundamental role of developing mathematical knowledge. Responding to the current reform movement in mathematics, students are expected to learn to be a flexible thinker. The ability to think flexible is challenged by the globalisation, hence influence mathematics education. A flexible thinking includes ability to apply knowledge in different contexts rather than simply use it in similar context when it is studied. Arguably problem solving activities can contribute to the development of the ability to apply skills to unfamiliar situations. Accordingly, an appropriate classroom instructional strategy must be developed. A cognitive load theory suggests that by reducing extraneous cognitive load during learning could enhance transfer learning. A goal-free problem strategy that is developed based in cognitive load theory have been showed to be effective for transfer learning. This strategy enables students to learn a large numbers of problem solving moves from a mathematics problem. The instruction in a goal-free problem directs students to `calculate as many solution as you can' rather than to calculate a single given goal. Many experiment research evident goal-free problem enhance learning. This literature review will discuss evidence goal-free problem facilitate students to solve problems flexibly and thus enhance their problem solving skills, including how its implication in the classroom.

Reflective thinking in solving an algebra problem: a case study of field independent-prospective teacher

NASA Astrophysics Data System (ADS)

Agustan, S.; Juniati, Dwi; Yuli Eko Siswono, Tatag

2017-10-01

Nowadays, reflective thinking is one of the important things which become a concern in learning mathematics, especially in solving a mathematical problem. The purpose of this paper is to describe how the student used reflective thinking when solved an algebra problem. The subject of this research is one female student who has field independent cognitive style. This research is a descriptive exploratory study with data analysis using qualitative approach to describe in depth reflective thinking of prospective teacher in solving an algebra problem. Four main categories are used to analyse the reflective thinking in solving an algebra problem: (1) formulation and synthesis of experience, (2) orderliness of experience, (3) evaluating the experience and (4) testing the selected solution based on the experience. The results showed that the subject described the problem by using another word and the subject also found the difficulties in making mathematical modelling. The subject analysed two concepts used in solving problem. For instance, geometry related to point and line while algebra is related to algebra arithmetic operation. The subject stated that solution must have four aspect to get effective solution, specifically the ability to (a) understand the meaning of every words; (b) make mathematical modelling; (c) calculate mathematically; (d) interpret solution obtained logically. To test the internal consistency or error in solution, the subject checked and looked back related procedures and operations used. Moreover, the subject tried to resolve the problem in a different way to compare the answers which had been obtained before. The findings supported the assertion that reflective thinking provides an opportunity for the students in improving their weakness in mathematical problem solving. It can make a grow accuracy and concentration in solving a mathematical problem. Consequently, the students will get the right and logic answer by reflective thinking.

Students’ Mathematical Creative Thinking through Problem Posing Learning

NASA Astrophysics Data System (ADS)

Ulfah, U.; Prabawanto, S.; Jupri, A.

2017-09-01

The research aims to investigate the differences in enhancement of students’ mathematical creative thinking ability of those who received problem posing approach assisted by manipulative media and students who received problem posing approach without manipulative media. This study was a quasi experimental research with non-equivalent control group design. Population of this research was third-grade students of a primary school in Bandung city in 2016/2017 academic year. Sample of this research was two classes as experiment class and control class. The instrument used is a test of mathematical creative thinking ability. Based on the results of the research, it is known that the enhancement of the students’ mathematical creative thinking ability of those who received problem posing approach with manipulative media aid is higher than the ability of those who received problem posing approach without manipulative media aid. Students who get learning problem posing learning accustomed in arranging mathematical sentence become matter of story so it can facilitate students to comprehend about story

Error analysis of mathematical problems on TIMSS: A case of Indonesian secondary students

NASA Astrophysics Data System (ADS)

Priyani, H. A.; Ekawati, R.

2018-01-01

Indonesian students’ competence in solving mathematical problems is still considered as weak. It was pointed out by the results of international assessment such as TIMSS. This might be caused by various types of errors made. Hence, this study aimed at identifying students’ errors in solving mathematical problems in TIMSS in the topic of numbers that considered as the fundamental concept in Mathematics. This study applied descriptive qualitative analysis. The subject was three students with most errors in the test indicators who were taken from 34 students of 8th graders. Data was obtained through paper and pencil test and student’s’ interview. The error analysis indicated that in solving Applying level problem, the type of error that students made was operational errors. In addition, for reasoning level problem, there are three types of errors made such as conceptual errors, operational errors and principal errors. Meanwhile, analysis of the causes of students’ errors showed that students did not comprehend the mathematical problems given.

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…

The Art of Problem Solving: A Resource for the Mathematics Teacher.

ERIC Educational Resources Information Center

Posamentier, Alfred S.; Schulz, Wolfgang

This book is designed to give mathematics teachers a host of interesting and useful ideas thereby raising their consciousness level and enabling an enrichment of the mathematics instruction program. The chapters in this book capture a broad spectrum of ideas in the area of mathematics problem solving. Chapters are: (1) "Strategies for Problem…

Teaching Problem-Posing and Inquiry to Teachers Using a Non-Traditional Operation

ERIC Educational Resources Information Center

White, D.; Sullivan, E.

2018-01-01

Teaching teachers to participate in mathematical inquiry has the potential to both transform belief systems about mathematics and to transform teachers from consumers of mathematics to producers of mathematics. The focus of this paper is to describe the use of a problem, based on a non-traditional binary operation, to encourage and teach…

Is There a Causal Relation between Mathematical Creativity and Mathematical Problem-Solving Performance?

ERIC Educational Resources Information Center

Tyagi, Tarun Kumar

2016-01-01

The relationship between mathematical creativity (MC) and mathematical problem-solving performance (MP) has often been studied but the causal relation between these two constructs has yet to be clearly reported. The main purpose of this study was to define the causal relationship between MC and MP. Data from a representative sample of 480…

An Examination of Preservice Teachers' Capacity to Create Mathematical Modeling Problems for Children

ERIC Educational Resources Information Center

Paolucci, Catherine; Wessels, Helena

2017-01-01

This study examined preservice teachers' (PSTs) capacity to create mathematical modeling problems (MMPs) for grades 1 to 3. PSTs created MMPs for their choice of grade level and aligned the mathematical content of their MMPs with the relevant mathematics curriculum. PSTs were given criteria adapted from Galbraith's MMP design principles to guide…

Is Mathematical Representation of Problems an Evidence-Based Strategy for Students with Mathematics Difficulties?

ERIC Educational Resources Information Center

Jitendra, Asha K.; Nelson, Gena; Pulles, Sandra M.; Kiss, Allyson J.; Houseworth, James

2016-01-01

The purpose of the present review was to evaluate the quality of the research and evidence base for representation of problems as a strategy to enhance the mathematical performance of students with learning disabilities and those at risk for mathematics difficulties. The authors evaluated 25 experimental and quasiexperimental studies according to…

Impulsive-Analytic Disposition in Mathematical Problem Solving: A Survey and a Mathematics Test

ERIC Educational Resources Information Center

Lim, Kien H.; Wagler, Amy

2012-01-01

The Likelihood-to-Act (LtA) survey and a mathematics test were used in this study to assess students' impulsive-analytic disposition in the context of mathematical problem solving. The results obtained from these two instruments were compared to those obtained using two widely-used scales: Need for Cognition (NFC) and Barratt Impulsivity Scale…

Problem Solving in the Borderland between Mathematics and Physics

ERIC Educational Resources Information Center

Jensen, Jens Højgaard; Niss, Martin; Jankvist, Uffe Thomas

2017-01-01

The article addresses the problématique of where mathematization is taught in the educational system, and who teaches it. Mathematization is usually not a part of mathematics programs at the upper secondary level, but we argue that physics teaching has something to offer in this respect, if it focuses on solving so-called unformalized problems,…

Investigating Grade Nine Textbook Problems for Characteristics Related to Mathematical Literacy

ERIC Educational Resources Information Center

Gatabi, Abolfazl Rafiepour; Stacey, Kaye; Gooya, Zahra

2012-01-01

This study presents a content analysis of the new Iranian Grade 9 mathematics textbook and two Australian Year 9 mathematics textbooks, examining the extent to which the problems show characteristics associated in the literature with promoting mathematical literacy. The new Iranian book was produced to meet a range of needs including several well…

Lectures on Selected Topics in Mathematical Physics: Elliptic Functions and Elliptic Integrals

NASA Astrophysics Data System (ADS)

Schwalm, William A.

2015-12-01

This volume is a basic introduction to certain aspects of elliptic functions and elliptic integrals. Primarily, the elliptic functions stand out as closed solutions to a class of physical and geometrical problems giving rise to nonlinear differential equations. While these nonlinear equations may not be the types of greatest interest currently, the fact that they are solvable exactly in terms of functions about which much is known makes up for this. The elliptic functions of Jacobi, or equivalently the Weierstrass elliptic functions, inhabit the literature on current problems in condensed matter and statistical physics, on solitons and conformal representations, and all sorts of famous problems in classical mechanics. The lectures on elliptic functions have evolved as part of the first semester of a course on theoretical and mathematical methods given to first- and second-year graduate students in physics and chemistry at the University of North Dakota. They are for graduate students or for researchers who want an elementary introduction to the subject that nevertheless leaves them with enough of the details to address real problems. The style is supposed to be informal. The intention is to introduce the subject as a moderate extension of ordinary trigonometry in which the reference circle is replaced by an ellipse. This entre depends upon fewer tools and has seemed less intimidating that other typical introductions to the subject that depend on some knowledge of complex variables. The first three lectures assume only calculus, including the chain rule and elementary knowledge of differential equations. In the later lectures, the complex analytic properties are introduced naturally so that a more complete study becomes possible.

A new mathematical modeling for pure parsimony haplotyping problem.

PubMed

Feizabadi, R; Bagherian, M; Vaziri, H R; Salahi, M

2016-11-01

Pure parsimony haplotyping (PPH) problem is important in bioinformatics because rational haplotyping inference plays important roles in analysis of genetic data, mapping complex genetic diseases such as Alzheimer's disease, heart disorders and etc. Haplotypes and genotypes are m-length sequences. Although several integer programing models have already been presented for PPH problem, its NP-hardness characteristic resulted in ineffectiveness of those models facing the real instances especially instances with many heterozygous sites. In this paper, we assign a corresponding number to each haplotype and genotype and based on those numbers, we set a mixed integer programing model. Using numbers, instead of sequences, would lead to less complexity of the new model in comparison with previous models in a way that there are neither constraints nor variables corresponding to heterozygous nucleotide sites in it. Experimental results approve the efficiency of the new model in producing better solution in comparison to two state-of-the art haplotyping approaches. Copyright © 2016 Elsevier Inc. All rights reserved.

Computation of the Genetic Code

NASA Astrophysics Data System (ADS)

Kozlov, Nicolay N.; Kozlova, Olga N.

2018-03-01

One of the problems in the development of mathematical theory of the genetic code (summary is presented in [1], the detailed -to [2]) is the problem of the calculation of the genetic code. Similar problems in the world is unknown and could be delivered only in the 21st century. One approach to solving this problem is devoted to this work. For the first time provides a detailed description of the method of calculation of the genetic code, the idea of which was first published earlier [3]), and the choice of one of the most important sets for the calculation was based on an article [4]. Such a set of amino acid corresponds to a complete set of representations of the plurality of overlapping triple gene belonging to the same DNA strand. A separate issue was the initial point, triggering an iterative search process all codes submitted by the initial data. Mathematical analysis has shown that the said set contains some ambiguities, which have been founded because of our proposed compressed representation of the set. As a result, the developed method of calculation was limited to the two main stages of research, where the first stage only the of the area were used in the calculations. The proposed approach will significantly reduce the amount of computations at each step in this complex discrete structure.

The fractal heart — embracing mathematics in the cardiology clinic

PubMed Central

Captur, Gabriella; Karperien, Audrey L.; Hughes, Alun D.; Francis, Darrel P.; Moon, James C.

2017-01-01

For clinicians grappling with quantifying the complex spatial and temporal patterns of cardiac structure and function (such as myocardial trabeculae, coronary microvascular anatomy, tissue perfusion, myocyte histology, electrical conduction, heart rate, and blood-pressure variability), fractal analysis is a powerful, but still underused, mathematical tool. In this Perspectives article, we explain some fundamental principles of fractal geometry and place it in a familiar medical setting. We summarize studies in the cardiovascular sciences in which fractal methods have successfully been used to investigate disease mechanisms, and suggest potential future clinical roles in cardiac imaging and time series measurements. We believe that clinical researchers can deploy innovative fractal solutions to common cardiac problems that might ultimately translate into advancements for patient care. PMID:27708281

Quantum Gauss-Jordan Elimination and Simulation of Accounting Principles on Quantum Computers

NASA Astrophysics Data System (ADS)

Diep, Do Ngoc; Giang, Do Hoang; Van Minh, Nguyen

2017-06-01

The paper is devoted to a version of Quantum Gauss-Jordan Elimination and its applications. In the first part, we construct the Quantum Gauss-Jordan Elimination (QGJE) Algorithm and estimate the complexity of computation of Reduced Row Echelon Form (RREF) of N × N matrices. The main result asserts that QGJE has computation time is of order 2 N/2. The second part is devoted to a new idea of simulation of accounting by quantum computing. We first expose the actual accounting principles in a pure mathematics language. Then, we simulate the accounting principles on quantum computers. We show that, all accounting actions are exhousted by the described basic actions. The main problems of accounting are reduced to some system of linear equations in the economic model of Leontief. In this simulation, we use our constructed Quantum Gauss-Jordan Elimination to solve the problems and the complexity of quantum computing is a square root order faster than the complexity in classical computing.

Effective algorithm for solving complex problems of production control and of material flows control of industrial enterprise

NASA Astrophysics Data System (ADS)

Mezentsev, Yu A.; Baranova, N. V.

2018-05-01

A universal economical and mathematical model designed for determination of optimal strategies for managing subsystems (components of subsystems) of production and logistics of enterprises is considered. Declared universality allows taking into account on the system level both production components, including limitations on the ways of converting raw materials and components into sold goods, as well as resource and logical restrictions on input and output material flows. The presented model and generated control problems are developed within the framework of the unified approach that allows one to implement logical conditions of any complexity and to define corresponding formal optimization tasks. Conceptual meaning of used criteria and limitations are explained. The belonging of the generated tasks of the mixed programming with the class of NP is shown. An approximate polynomial algorithm for solving the posed optimization tasks for mixed programming of real dimension with high computational complexity is proposed. Results of testing the algorithm on the tasks in a wide range of dimensions are presented.

An Investigation of Preservice Teachers' Use of Guess and Check in Solving a Semi Open-Ended Mathematics Problem

ERIC Educational Resources Information Center

Capraro, Mary Margaret; An, Song A.; Ma, Tingting; Rangel-Chavez, A. Fabiola; Harbaugh, Adam

2012-01-01

Open-ended problems have been regarded as powerful tools for teaching mathematics. This study examined the problem solving of eight mathematics/science middle-school teachers. A semi-structured interview was conducted with (PTs) after completing an open-ended triangle task with four unique solutions. Of particular emphasis was how the PTs used a…

Effects of the SOLVE Strategy on the Mathematical Problem Solving Skills of Secondary Students with Learning Disabilities

ERIC Educational Resources Information Center

Freeman-Green, Shaqwana M.; O'Brien, Chris; Wood, Charles L.; Hitt, Sara Beth

2015-01-01

This study examined the effects of explicit instruction in the SOLVE Strategy on the mathematical problem solving skills of six Grade 8 students with specific learning disabilities. The SOLVE Strategy is an explicit instruction, mnemonic-based learning strategy designed to help students in solving mathematical word problems. Using a multiple probe…

Mathematical Problem Solving with Technology: The Techno-Mathematical Fluency of a Student-with-GeoGebra

ERIC Educational Resources Information Center

Jacinto, Hélia; Carreira, Susana

2017-01-01

This study offers a view on students' technology-based problem solving activity through the lens of a theoretical model which accounts for the relationship between mathematical and technological knowledge in successful problem solving. This study takes a qualitative approach building on the work of a 13-year-old girl as an exemplary case of the…

Mathematics as a Course of Study in Problem Solving: Then and Now.

ERIC Educational Resources Information Center

Ellis, Wade, Jr.

The mathematics curriculum in the first 2 years of college is a tool created to assist in solving problems. The current mathematics curriculum has changed little; the same topics, tied to the engineering and science curriculum, are taught as they were being taught in 1945. The problems that students need to solve have changed however. Both the…

The Interrelationship of Sex, Visual Spatial Abilities, and Mathematical Problem Solving Ability in Grade Seven. Parts 1, 2, and 3.

ERIC Educational Resources Information Center

Schonberger, Ann Koch

This three-volume report deals with the hypothesis that males are more successful at solving mathematical and spatial problems than females. The general relationship between visual spatial abilities and mathematical problem-solving ability is also investigated. The research sample consisted of seventh graders. Each pupil took five spatial tests…

Use of a Mathematics Word Problem Strategy to Improve Achievement for Students with Mild Disabilities

ERIC Educational Resources Information Center

Taber, Mary R.

2013-01-01

Mathematics can be a difficult topic both to teach and to learn. Word problems specifically can be difficult for students with disabilities because they have to conceptualize what the problem is asking for, and they must perform the correct operation accurately. Current trends in mathematics instruction stem from the National Council of Teachers…

Student performance and attitudes in a collaborative and flipped linear algebra course

NASA Astrophysics Data System (ADS)

Murphy, Julia; Chang, Jen-Mei; Suaray, Kagba

2016-07-01

Flipped learning is gaining traction in K-12 for enhancing students' problem-solving skills at an early age; however, there is relatively little large-scale research showing its effectiveness in promoting better learning outcomes in higher education, especially in mathematics classes. In this study, we examined the data compiled from both quantitative and qualitative measures such as item scores on a common final and attitude survey results between a flipped and a traditional Introductory Linear Algebra class taught by two individual instructors at a state university in California in Fall 2013. Students in the flipped class were asked to watch short video lectures made by the instructor and complete a short online quiz prior to each class attendance. The class time was completely devoted to problem solving in group settings where students were prompted to communicate their reasoning with proper mathematical terms and structured sentences verbally and in writing. Examination of the quality and depth of student responses from the common final exam showed that students in the flipped class produced more comprehensive and well-explained responses to the questions that required reasoning, creating examples, and more complex use of mathematical objects. Furthermore, students in the flipped class performed superiorly in the overall comprehension of the content with a 21% increase in the median final exam score. Overall, students felt more confident about their ability to learn mathematics independently, showed better retention of materials over time, and enjoyed the flipped experience.

Embedding Game-Based Problem-Solving Phase into Problem-Posing System for Mathematics Learning

ERIC Educational Resources Information Center

Chang, Kuo-En; Wu, Lin-Jung; Weng, Sheng-En; Sung, Yao-Ting

2012-01-01

A problem-posing system is developed with four phases including posing problem, planning, solving problem, and looking back, in which the "solving problem" phase is implemented by game-scenarios. The system supports elementary students in the process of problem-posing, allowing them to fully engage in mathematical activities. In total, 92 fifth…

The Complexity of Primary Care Psychology: Theoretical Foundations.

PubMed

Smit, E H; Derksen, J J L

2015-07-01

How does primary care psychology deal with organized complexity? Has it escaped Newtonian science? Has it, as Weaver (1991) suggests, found a way to 'manage problems with many interrelated factors that cannot be dealt by statistical techniques'? Computer simulations and mathematical models in psychology are ongoing positive developments in the study of complex systems. However, the theoretical development of complex systems in psychology lags behind these advances. In this article we use complexity science to develop a theory on experienced complexity in the daily practice of primary care psychologists. We briefly answer the ontological question of what we see (from the perspective of primary care psychology) as reality, the epistemological question of what we can know, the methodological question of how to act, and the ethical question of what is good care. Following our empirical study, we conclude that complexity science can describe the experienced complexity of the psychologist and offer room for personalized client-centered care. Complexity science is slowly filling the gap between the dominant reductionist theory and complex daily practice.

Thinking Process of Naive Problem Solvers to Solve Mathematical Problems

ERIC Educational Resources Information Center

Mairing, Jackson Pasini

2017-01-01

Solving problems is not only a goal of mathematical learning. Students acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations by learning to solve problems. In fact, there were students who had difficulty in solving problems. The students were naive problem solvers. This research aimed to describe…

Dynamics of local grid manipulations for internal flow problems

NASA Technical Reports Server (NTRS)

Eiseman, Peter R.; Snyder, Aaron; Choo, Yung K.

1991-01-01

The control point method of algebraic grid generation is briefly reviewed. The review proceeds from the general statement of the method in 2-D unencumbered by detailed mathematical formulation. The method is supported by an introspective discussion which provides the basis for confidence in the approach. The more complex 3-D formulation is then presented as a natural generalization. Application of the method is carried out through 2-D examples which demonstrate the technique.

Occlusions in Camera Networks and Vision: The Bridge between Topological Recovery and Metric Reconstruction

DTIC Science & Technology

2009-05-18

serves as a didactic tool to understand the information required for the approach to coordinate free tracking and navigation problems. Observe that the...layout (left), and in the CN -Complex (right). These paths can be compared by using the algebraic topological tools covered in chapter 2. . . . 34 3.9...right). mathematical tools necessary to make our discussion formal; chapter 3 will present the construction of a simplicial representation called

University Students' Problem Posing Abilities and Attitudes towards Mathematics.

ERIC Educational Resources Information Center

Grundmeier, Todd A.

2002-01-01

Explores the problem posing abilities and attitudes towards mathematics of students in a university pre-calculus class and a university mathematical proof class. Reports a significant difference in numeric posing versus non-numeric posing ability in both classes. (Author/MM)

The relationship between mathematical problem-solving skills and self-regulated learning through homework behaviours, motivation, and metacognition

NASA Astrophysics Data System (ADS)

Çiğdem Özcan, Zeynep

2016-04-01

Studies highlight that using appropriate strategies during problem solving is important to improve problem-solving skills and draw attention to the fact that using these skills is an important part of students' self-regulated learning ability. Studies on this matter view the self-regulated learning ability as key to improving problem-solving skills. The aim of this study is to investigate the relationship between mathematical problem-solving skills and the three dimensions of self-regulated learning (motivation, metacognition, and behaviour), and whether this relationship is of a predictive nature. The sample of this study consists of 323 students from two public secondary schools in Istanbul. In this study, the mathematics homework behaviour scale was administered to measure students' homework behaviours. For metacognition measurements, the mathematics metacognition skills test for students was administered to measure offline mathematical metacognitive skills, and the metacognitive experience scale was used to measure the online mathematical metacognitive experience. The internal and external motivational scales used in the Programme for International Student Assessment (PISA) test were administered to measure motivation. A hierarchic regression analysis was conducted to determine the relationship between the dependent and independent variables in the study. Based on the findings, a model was formed in which 24% of the total variance in students' mathematical problem-solving skills is explained by the three sub-dimensions of the self-regulated learning model: internal motivation (13%), willingness to do homework (7%), and post-problem retrospective metacognitive experience (4%).

Scilab software as an alternative low-cost computing in solving the linear equations problem

NASA Astrophysics Data System (ADS)

Agus, Fahrul; Haviluddin

2017-02-01

Numerical computation packages are widely used both in teaching and research. These packages consist of license (proprietary) and open source software (non-proprietary). One of the reasons to use the package is a complexity of mathematics function (i.e., linear problems). Also, number of variables in a linear or non-linear function has been increased. The aim of this paper was to reflect on key aspects related to the method, didactics and creative praxis in the teaching of linear equations in higher education. If implemented, it could be contribute to a better learning in mathematics area (i.e., solving simultaneous linear equations) that essential for future engineers. The focus of this study was to introduce an additional numerical computation package of Scilab as an alternative low-cost computing programming. In this paper, Scilab software was proposed some activities that related to the mathematical models. In this experiment, four numerical methods such as Gaussian Elimination, Gauss-Jordan, Inverse Matrix, and Lower-Upper Decomposition (LU) have been implemented. The results of this study showed that a routine or procedure in numerical methods have been created and explored by using Scilab procedures. Then, the routine of numerical method that could be as a teaching material course has exploited.

Neuropsychological Findings in Childhood Neglect and their Relationships to Pediatric PTSD

PubMed Central

De Bellis, Michael D.; Hooper, Stephen R.; Spratt, Eve G.; Woolley, Donald P.

2011-01-01

Statement of the problem Although child neglect is the most prevalent form of child maltreatment, the neurocognitive effects of neglect is understudied. Methods We examined IQ, reading, mathematics, and neurocognitive domains of fine-motor skills, language, visual-spatial, memory/learning, and attention/executive functions in two groups of non-sexually abused medically healthy neglected children, one with DSM-IV posttraumatic stress disorder (PTSD) and one without, and a demographically similar healthy non-maltreated control group. Key findings Significantly lower IQ, reading, mathematics, and selected differences in complex visual attention, visual memory, language, verbal memory and learning, planning, problem solving, and speeded naming were seen in Neglect Groups. The Neglect with PTSD Group performed worse than controls on NEPSY Design Copying, NEPSY Tower, and Mathematics; and performed worse than controls and Neglect without PTSD on NEPSY Memory for Faces-Delayed. Negative correlations were seen between PTSD symptoms, PTSD severity, and maltreatment variables, and IQ, Academic Achievement, and neurocognitive domains. Conclusions Neglected children demonstrated significantly lower neurocognitive outcomes and academic achievement than controls. Lower IQ, neurocognitive functions, and achievement may be associated with more PTSD symptoms (particularly re-experiencing symptoms), greater PTSD severity, and a greater number of maltreatment experiences. Trauma experiences may additionally contribute to subsequent neurodevelopmental risk in neglected children. PMID:19703321

Problem Solvers: Problem--How Long Can You Stand?

ERIC Educational Resources Information Center

Teaching Children Mathematics, 2010

2010-01-01

Healthy lifestyles are increasingly emphasized these days. This month the authors begin a series of mathematical problems that also address physical activity. They hope that these problems offer opportunities to investigate mathematics and also reinforce the desire to lead a healthy life. In their first problem of the academic year, students…