Prospective Mathematics Teachers' Opinions about Mathematical Modeling Method and Applicability of This Method

ERIC Educational Resources Information Center

Akgün, Levent

2015-01-01

The aim of this study is to identify prospective secondary mathematics teachers' opinions about the mathematical modeling method and the applicability of this method in high schools. The case study design, which is among the qualitative research methods, was used in the study. The study was conducted with six prospective secondary mathematics…

Advancing K-8 Teachers' STEM Education for Teaching Interdisciplinary Science and Mathematics with Technologies

ERIC Educational Resources Information Center

Niess, Margaret; Gillow-Wiles, Henry

2013-01-01

This primarily online Master's degree program focused on advancing K-8 teachers' interdisciplinary mathematical and science content knowledge while integrating appropriate digital technologies as learning and teaching tools. The mixed-method, interpretive study examined in-service teachers' technological, pedagogical, and content knowledge (TPACK)…

Secondary School Advanced Mathematics, Chapter 8, Systems of Equations. Student's Text.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This text is the last of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. In this volume the solution of systems of linear and quadratic equations and inequalities in…

Informal Content and Student Note-Taking in Advanced Mathematics Classes

ERIC Educational Resources Information Center

Fukawa-Connelly, Timothy; Weber, Keith; Mejía-Ramos, Juan Pablo

2017-01-01

This study investigates 3 hypotheses about proof-based mathematics instruction: (a) that lectures include informal content (ways of thinking and reasoning about advanced mathematics that are not captured by formal symbolic statements), (b) that informal content is usually presented orally but not written on the board, and (c) that students do not…

The Impact of Advanced Curriculum on the Achievement of Mathematically Promising Elementary Students

ERIC Educational Resources Information Center

Gavin, M. Katherine; Casa, Tutita M.; Adelson, Jill L.; Carroll, Susan R.; Sheffield, Linda Jensen

2009-01-01

The primary aim of Project M[superscript 3]: Mentoring Mathematical Minds was to develop and field test advanced units for mathematically promising elementary students based on exemplary practices in gifted and mathematics education. This article describes the development of the units and reports on mathematics achievement results for students in…

Advanced Mathematics 305--Optional Half Credit. Interim Guide.

ERIC Educational Resources Information Center

Manitoba Dept. of Education, Winnipeg.

This manual outlines an advanced mathematics course for secondary school students in Manitoba (Canada). Included are eight different topics for a total of ten modules, with each module accounting for 18 40-minute periods. Teachers, or teachers and students cooperatively, should select the equivalent of five modules from the eight topics covered.…

Advanced mathematics communication beyond modality of\\xA0sight

NASA Astrophysics Data System (ADS)

Sedaghatjou, Mina

2018-01-01

This study illustrates how mathematical communication and learning are inherently multimodal and embodied; hence, sight-disabled students are also able to conceptualize visuospatial information and mathematical concepts through tactile and auditory activities. Adapting a perceptuomotor integration approach, the study shows that the lack of access to visual fields in an advanced mathematics course does not obstruct a blind student's ability to visualize, but transforms it. The goal of this study is not to compare the visually impaired student with non-visually impaired students to address the 'differences' in understanding; instead, I discuss the challenges that a blind student, named Anthony, has encountered and the ways that we tackled those problems. I also demonstrate how the proper and precisely crafted tactile materials empowered Anthony to learn mathematical functions.

An Improved Mathematical Scheme for LTE-Advanced Coexistence with FM Broadcasting Service

PubMed Central

Al-hetar, Abdulaziz M.

2016-01-01

Power spectral density (PSD) overlapping analysis is considered the surest approach to evaluate feasibility of compatibility between wireless communication systems. In this paper, a new closed-form for the Interference Signal Power Attenuation (ISPA) is mathematically derived to evaluate interference caused from Orthogonal Frequency Division Multiplexing (OFDM)-based Long Term Evolution (LTE)-Advanced into Frequency Modulation (FM) broadcasting service. In this scheme, ISPA loss due to PSD overlapping of both OFDM-based LTE-Advanced and FM broadcasting service is computed. The proposed model can estimate power attenuation loss more precisely than the Advanced Minimum Coupling Loss (A-MCL) and approximate-ISPA methods. Numerical results demonstrate that the interference power is less than that obtained using the A-MCL and approximate ISPA methods by 2.8 and 1.5 dB at the co-channel and by 5.2 and 2.2 dB at the adjacent channel with null guard band, respectively. The outperformance of this scheme over the other methods leads to more diminishing in the required physical distance between the two systems which ultimately supports efficient use of the radio frequency spectrum. PMID:27855216

An Improved Mathematical Scheme for LTE-Advanced Coexistence with FM Broadcasting Service.

PubMed

Shamsan, Zaid Ahmed; Al-Hetar, Abdulaziz M

2016-01-01

Power spectral density (PSD) overlapping analysis is considered the surest approach to evaluate feasibility of compatibility between wireless communication systems. In this paper, a new closed-form for the Interference Signal Power Attenuation (ISPA) is mathematically derived to evaluate interference caused from Orthogonal Frequency Division Multiplexing (OFDM)-based Long Term Evolution (LTE)-Advanced into Frequency Modulation (FM) broadcasting service. In this scheme, ISPA loss due to PSD overlapping of both OFDM-based LTE-Advanced and FM broadcasting service is computed. The proposed model can estimate power attenuation loss more precisely than the Advanced Minimum Coupling Loss (A-MCL) and approximate-ISPA methods. Numerical results demonstrate that the interference power is less than that obtained using the A-MCL and approximate ISPA methods by 2.8 and 1.5 dB at the co-channel and by 5.2 and 2.2 dB at the adjacent channel with null guard band, respectively. The outperformance of this scheme over the other methods leads to more diminishing in the required physical distance between the two systems which ultimately supports efficient use of the radio frequency spectrum.

Technologies Used in the Study of Advanced Mathematics by Students Who Are Visually Impaired in Classrooms: Teachers' Perspectives

ERIC Educational Resources Information Center

DePountis, Vicki M.; Pogrund, Rona L.; Griffin-Shirley, Nora; Lan, William Y.

2015-01-01

Introduction: This research examined the perspectives of teachers of students who are visually impaired regarding the use and effectiveness of high-tech assistive technology purported to assist visually impaired students in advanced mathematics. Methods: The data for this study were collected via a mixed-methods online survey distributed through…

Basic and Advanced Numerical Performances Relate to Mathematical Expertise but Are Fully Mediated by Visuospatial Skills

PubMed Central

2016-01-01

Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. PMID:26913930

Origins of the brain networks for advanced mathematics in expert mathematicians

PubMed Central

Amalric, Marie; Dehaene, Stanislas

2016-01-01

The origins of human abilities for mathematics are debated: Some theories suggest that they are founded upon evolutionarily ancient brain circuits for number and space and others that they are grounded in language competence. To evaluate what brain systems underlie higher mathematics, we scanned professional mathematicians and mathematically naive subjects of equal academic standing as they evaluated the truth of advanced mathematical and nonmathematical statements. In professional mathematicians only, mathematical statements, whether in algebra, analysis, topology or geometry, activated a reproducible set of bilateral frontal, Intraparietal, and ventrolateral temporal regions. Crucially, these activations spared areas related to language and to general-knowledge semantics. Rather, mathematical judgments were related to an amplification of brain activity at sites that are activated by numbers and formulas in nonmathematicians, with a corresponding reduction in nearby face responses. The evidence suggests that high-level mathematical expertise and basic number sense share common roots in a nonlinguistic brain circuit. PMID:27071124

Origins of the brain networks for advanced mathematics in expert mathematicians.

PubMed

Amalric, Marie; Dehaene, Stanislas

2016-05-03

The origins of human abilities for mathematics are debated: Some theories suggest that they are founded upon evolutionarily ancient brain circuits for number and space and others that they are grounded in language competence. To evaluate what brain systems underlie higher mathematics, we scanned professional mathematicians and mathematically naive subjects of equal academic standing as they evaluated the truth of advanced mathematical and nonmathematical statements. In professional mathematicians only, mathematical statements, whether in algebra, analysis, topology or geometry, activated a reproducible set of bilateral frontal, Intraparietal, and ventrolateral temporal regions. Crucially, these activations spared areas related to language and to general-knowledge semantics. Rather, mathematical judgments were related to an amplification of brain activity at sites that are activated by numbers and formulas in nonmathematicians, with a corresponding reduction in nearby face responses. The evidence suggests that high-level mathematical expertise and basic number sense share common roots in a nonlinguistic brain circuit.

How Syntactic Reasoners Can Develop Understanding, Evaluate Conjectures, and Generate Counterexamples in Advanced Mathematics

ERIC Educational Resources Information Center

Weber, Keith

2009-01-01

This paper presents a case study of a highly successful student whose exploration of an advanced mathematical concept relies predominantly on syntactic reasoning, such as developing formal representations of mathematical ideas and making logical deductions. This student is observed as he learns a new mathematical concept and then completes…

Some observations on the interdigitation of advances in medical science and mathematics.

PubMed

Glamore, Michael James; West, James L; O'leary, James Patrick

2013-12-01

The immense advancement of our understanding of disease processes has not been a uniform progression related to the passage of time. Advances have been made in "lurches" and "catches" since the advent of the written word. There has been a remarkable interdependency between such advances in medicine and advances in mathematics that has proved beneficial to both. This work explores some of these critical relationships and documents how the individuals involved contributed to advances in each.

Basic and advanced numerical performances relate to mathematical expertise but are fully mediated by visuospatial skills.

PubMed

Sella, Francesco; Sader, Elie; Lolliot, Simon; Cohen Kadosh, Roi

2016-09-01

Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Applying Mathematical Optimization Methods to an ACT-R Instance-Based Learning Model.

PubMed

Said, Nadia; Engelhart, Michael; Kirches, Christian; Körkel, Stefan; Holt, Daniel V

2016-01-01

Computational models of cognition provide an interface to connect advanced mathematical tools and methods to empirically supported theories of behavior in psychology, cognitive science, and neuroscience. In this article, we consider a computational model of instance-based learning, implemented in the ACT-R cognitive architecture. We propose an approach for obtaining mathematical reformulations of such cognitive models that improve their computational tractability. For the well-established Sugar Factory dynamic decision making task, we conduct a simulation study to analyze central model parameters. We show how mathematical optimization techniques can be applied to efficiently identify optimal parameter values with respect to different optimization goals. Beyond these methodological contributions, our analysis reveals the sensitivity of this particular task with respect to initial settings and yields new insights into how average human performance deviates from potential optimal performance. We conclude by discussing possible extensions of our approach as well as future steps towards applying more powerful derivative-based optimization methods.

Symbolic Drawings Reveal Changes in Preservice Teacher Mathematics Attitudes after a Mathematics Methods Course

ERIC Educational Resources Information Center

Rule, Audrey C.; Harrell, Mary H.

2006-01-01

A new method of analyzing mathematics attitudes through symbolic drawings, situated within the field of Jungian-oriented analytical psychology, was applied to 52 preservice elementary teachers before and after a mathematics methods course. In this triangulation mixed methods design study, pretest images related to past mathematics experiences…

Gender Differences in the Use and Benefit of Advanced Learning Technologies for Mathematics

ERIC Educational Resources Information Center

Arroyo, Ivon; Burleson, Winslow; Tai, Minghui; Muldner, Kasia; Woolf, Beverly Park

2013-01-01

We provide evidence of persistent gender effects for students using advanced adaptive technology while learning mathematics. This technology improves each gender's learning and affective predispositions toward mathematics, but specific features in the software help either female or male students. Gender differences were seen in the students' style…

Advanced Mathematical Study and the Development of Conditional Reasoning Skills

PubMed Central

Attridge, Nina; Inglis, Matthew

2013-01-01

Since the time of Plato, philosophers and educational policy-makers have assumed that the study of mathematics improves one's general ‘thinking skills’. Today, this argument, known as the ‘Theory of Formal Discipline’ is used in policy debates to prioritize mathematics in school curricula. But there is no strong research evidence which justifies it. We tested the Theory of Formal Discipline by tracking the development of conditional reasoning behavior in students studying post-compulsory mathematics compared to post-compulsory English literature. In line with the Theory of Formal Discipline, the mathematics students did develop their conditional reasoning to a greater extent than the literature students, despite them having received no explicit tuition in conditional logic. However, this development appeared to be towards the so-called defective conditional understanding, rather than the logically normative material conditional understanding. We conclude by arguing that Plato may have been correct to claim that studying advanced mathematics is associated with the development of logical reasoning skills, but that the nature of this development may be more complex than previously thought. PMID:23869241

Innovations in Science and Mathematics Education: Advanced Designs for Technologies of Learning.

ERIC Educational Resources Information Center

Jacobson, Michael J., Ed.; Kozma, Robert B., Ed.

This collection of essays consists of current work that addresses the challenge not just to put the newest technologies in schools, but to identify advanced ways to design and use these new technologies to advance learning. These essays are intended for science and mathematics educators, educational and cognitive researchers, instructional…

Mathematical methods in systems biology.

PubMed

Kashdan, Eugene; Duncan, Dominique; Parnell, Andrew; Schattler, Heinz

2016-12-01

The editors of this Special Issue of Mathematical Biosciences and Engineering were the organizers for the Third International Workshop "Mathematical Methods in System Biology" that took place on June 15-18, 2015 at the University College Dublin in Ireland. As stated in the workshop goals, we managed to attract a good mix of mathematicians and statisticians working on biological and medical applications with biologists and clinicians interested in presenting their challenging problems and looking to find mathematical and statistical tools for their solutions.

PREFACE: International Conference on Advancement in Science and Technology 2012 (iCAST): Contemporary Mathematics, Mathematical Physics and their Applications

NASA Astrophysics Data System (ADS)

Ganikhodjaev, Nasir; Mukhamedov, Farrukh; Hee, Pah Chin

2013-04-01

The 4th International Conference on the Advancement of Science and Technology 2012 (iCAST 2012), with theme 'Contemporary Mathematics, Mathematical Physics and their Applications', took place in Kuantan, Malaysia, from Wednesday 7 to Friday 9 November 2012. The conference was attended by more than 100 participants, and hosted about 160 oral and poster papers by more than 140 pre-registered authors. The key topics of the 4th iCAST 2012 include Pure Mathematics, Applied Mathematics, Theoretical/Mathematical Physics, Dynamical Systems, Statistics and Financial Mathematics. The scientific program was rather full since after the Keynote and Invited Talks in the morning, four parallel sessions ran every day. However, according to all attendees, the program was excellent with a high level of talks and the scientific environment was fruitful; thus all attendees had a creative time. The conference aimed to promote the knowledge and development of high-quality research in mathematical fields concerned with the application of other scientific fields as well as modern technological trends in physics, chemistry, biology, medicine, economics, sociology and environmental sciences. We would like to thank the Keynote and the Invited Speakers for their significant contributions to 4th iCAST 2012. We would also like to thank the members of the International Scientific Committee and the members of the Organizing Committee. We cannot end without expressing our many thanks to International Islamic University Malaysia and our sponsors for their financial support . This volume presents selected papers which have been peer-reviewed. The editors hope that it may be useful and fruitful for scholars, researchers, and advanced technical members of the industrial laboratory facilities for developing new tools and products. Guest Editors Nasir Ganikhodjaev, Farrukh Mukhamedov and Pah Chin Hee The PDF contains the committee lists, board list and biographies of the plenary speakers.

Advanced Algebra and Calculus. High School Mathematics Curricula. Instructor's Guide.

ERIC Educational Resources Information Center

Natour, Denise M.

This manual is an instructor's guide for the utilization of the "CCA High School Mathematics Curricula: Advanced Algebra and Calculus" courseware developed by the Computer-based Education Research Laboratory (CERL). The curriculum comprises 34 algebra lessons within 12 units and 15 calculus lessons that are computer-based and require…

Mathematical modelling and quantitative methods.

PubMed

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

2002-01-01

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

Moving toward Positive Mathematics Beliefs and Developing Socio-Mathematical Authority: Urban Preservice Teachers in Mathematics Methods Courses

ERIC Educational Resources Information Center

Saran, Rupam; Gujarati, Joan

2013-01-01

This article explores how preservice elementary teachers change their negative beliefs toward mathematics into positive ones after taking a mathematics methods course that follows the Concrete-Pictorial-Abstract (CPA) instructional method. Also explored is the relationship between those beliefs and sociomathematical authority. By administering…

Computational and mathematical methods in brain atlasing.

PubMed

Nowinski, Wieslaw L

2017-12-01

Brain atlases have a wide range of use from education to research to clinical applications. Mathematical methods as well as computational methods and tools play a major role in the process of brain atlas building and developing atlas-based applications. Computational methods and tools cover three areas: dedicated editors for brain model creation, brain navigators supporting multiple platforms, and atlas-assisted specific applications. Mathematical methods in atlas building and developing atlas-aided applications deal with problems in image segmentation, geometric body modelling, physical modelling, atlas-to-scan registration, visualisation, interaction and virtual reality. Here I overview computational and mathematical methods in atlas building and developing atlas-assisted applications, and share my contribution to and experience in this field.

Authentic Teaching Experiences in Secondary Mathematics Methods

ERIC Educational Resources Information Center

Stickles, Paula R.

2015-01-01

Often secondary mathematics methods courses include classroom peer teaching, but many pre-service teachers find it challenging to teach their classmate peers as there are no discipline issues and little mathematical discourse as the "students" know the content. We will share a recent change in our methods course where pre-service…

Preparing and Supporting Black Students to Enroll and Achieve in Advanced Mathematics Classes in Middle School: A Case Study

ERIC Educational Resources Information Center

Cobbs, Joyce Bernice

2014-01-01

The literature on minority student achievement indicates that Black students are underrepresented in advanced mathematics courses. Advanced mathematics courses offer students the opportunity to engage with challenging curricula, experience rigorous instruction, and interact with quality teachers. The middle school years are particularly…

Lectures in Advanced Mathematics: Why Students Might Not Understand What the Mathematics Professor Is Trying to Convey

ERIC Educational Resources Information Center

Lew, Kristen; Fukawa-Connelly, Timothy Patrick; Mejía-Ramos , Juan Pablo; Weber, Keith

2016-01-01

We describe a case study in which we investigate the effectiveness of a lecture in advanced mathematics. We first videorecorded a lecture delivered by an experienced professor who had a reputation for being an outstanding instructor. Using video recall, we then interviewed the professor to determine the ideas that he intended to convey and how he…

Advancement via Individual Determination: A Model for Equity in Secondary Mathematics

ERIC Educational Resources Information Center

Hodges, Cynthia D.

2013-01-01

This study examined the impact of Advancement Via Individual Determination (AVID) methodologies on the mathematics achievement of African American, European American, and Hispanic students as measured by the State of Texas Assessment of Academic Readiness (STAAR) End of Course (EOC) for Algebra I. This quantitative nonexperimental ex post facto…

Which Advanced Mathematics Courses Influence ACT Score? A State Level Analysis of the Iowa Class of 2012

ERIC Educational Resources Information Center

Grinstead, Mary L.

2013-01-01

This study explores the relationship between specific advanced mathematics courses and college readiness (as determined by ACT score). The ACT organization has found a consistent relationship between taking a minimum core number of mathematics courses and higher ACT scores (mathematics and composite) (ACT, Inc., 2012c). However, the extent to…

MATHEMATICAL METHODS IN MEDICAL IMAGE PROCESSING

PubMed Central

ANGENENT, SIGURD; PICHON, ERIC; TANNENBAUM, ALLEN

2013-01-01

In this paper, we describe some central mathematical problems in medical imaging. The subject has been undergoing rapid changes driven by better hardware and software. Much of the software is based on novel methods utilizing geometric partial differential equations in conjunction with standard signal/image processing techniques as well as computer graphics facilitating man/machine interactions. As part of this enterprise, researchers have been trying to base biomedical engineering principles on rigorous mathematical foundations for the development of software methods to be integrated into complete therapy delivery systems. These systems support the more effective delivery of many image-guided procedures such as radiation therapy, biopsy, and minimally invasive surgery. We will show how mathematics may impact some of the main problems in this area, including image enhancement, registration, and segmentation. PMID:23645963

Science and Mathematics Advanced Placement Exams: Growth and Achievement over Time

ERIC Educational Resources Information Center

Judson, Eugene

2017-01-01

Rapid growth of Advanced Placement (AP) exams in the last 2 decades has been paralleled by national enthusiasm to promote availability and rigor of science, technology, engineering, and mathematics (STEM). Trends were examined in STEM AP to evaluate and compare growth and achievement. Analysis included individual STEM subjects and disaggregation…

Incentivizing Advanced Mathematics Study at Upper Secondary Level: The Case of Bonus Points in Ireland

ERIC Educational Resources Information Center

Treacy, Páraic Thomas

2018-01-01

Secondary level mathematics education in Ireland has recently experienced a period of significant change with the introduction of new curricula and the addition of an incentive to study upper secondary mathematics at the most advanced level (Higher Level). This incentive, typically referred to as 'bonus points', appears to have aided a significant…

Secondary School Advanced Mathematics, Chapter 4, Equations, Inequalities, and Radicals, Chapter 5, Circles and Spheres. Teacher's Commentary.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This manual was designed for use with the third of five texts in the Secondary School Advanced Mathematics (SSAM) series. Developed for students who have completed the Secondary School Mathematics (SSM) program and wish to continue their studies in mathematics, this series is designed to review, strengthen, and fill gaps in the material covered in…

Secondary School Advanced Mathematics, Chapter 4, Equations, Inequalities, and Radicals, Chapter 5, Circles and Spheres. Student's Text.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This text is the third of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. The first of the two chapters in this text deals with equations, inequalities and radicals.…

Method and Effectiveness of an Individualized Exercise of Fundamental Mathematics.

ERIC Educational Resources Information Center

Yoshioka, Takayoshi; Nishizawa, Hitoshi; Tsukamoto Takehiko

2001-01-01

Describes a method used to provide mathematics students in Japanese colleges of engineering with supplementary exercises to aid their learning. Outlines the online operation of individualized exercises that help the students to understand mathematical methods used to solve problems and also mathematical ideas or concepts upon which methods are…

Research Methods in Healthcare Epidemiology and Antimicrobial Stewardship-Mathematical Modeling.

PubMed

Barnes, Sean L; Kasaie, Parastu; Anderson, Deverick J; Rubin, Michael

2016-11-01

Mathematical modeling is a valuable methodology used to study healthcare epidemiology and antimicrobial stewardship, particularly when more traditional study approaches are infeasible, unethical, costly, or time consuming. We focus on 2 of the most common types of mathematical modeling, namely compartmental modeling and agent-based modeling, which provide important advantages-such as shorter developmental timelines and opportunities for extensive experimentation-over observational and experimental approaches. We summarize these advantages and disadvantages via specific examples and highlight recent advances in the methodology. A checklist is provided to serve as a guideline in the development of mathematical models in healthcare epidemiology and antimicrobial stewardship. Infect Control Hosp Epidemiol 2016;1-7.

What's Working: Program Factors Influencing California Community College Basic Skills Mathematics Students' Advancement to Transfer Level

ERIC Educational Resources Information Center

Fiero, Diane M.

2013-01-01

Purpose: The purpose of this study was to determine which basic skills program factors were exhibited by successful basic skills programs that helped students advance to transfer-level mathematics. This study specifically examined California community college basic skills programs that assist students who place in mathematics courses 2 levels…

Mathematical methods in medicine: neuroscience, cardiology and pathology

PubMed Central

Amigó, José M.

2017-01-01

The application of mathematics, natural sciences and engineering to medicine is gaining momentum as the mutual benefits of this collaboration become increasingly obvious. This theme issue is intended to highlight the trend in the case of mathematics. Specifically, the scope of this theme issue is to give a general view of the current research in the application of mathematical methods to medicine, as well as to show how mathematics can help in such important aspects as understanding, prediction, treatment and data processing. To this end, three representative specialties have been selected: neuroscience, cardiology and pathology. Concerning the topics, the 12 research papers and one review included in this issue cover biofluids, cardiac and virus dynamics, computational neuroscience, functional magnetic resonance imaging data processing, neural networks, optimization of treatment strategies, time-series analysis and tumour growth. In conclusion, this theme issue contains a collection of fine contributions at the intersection of mathematics and medicine, not as an exercise in applied mathematics but as a multidisciplinary research effort that interests both communities and our society in general. This article is part of the themed issue ‘Mathematical methods in medicine: neuroscience, cardiology and pathology’. PMID:28507240

Mathematical methods in medicine: neuroscience, cardiology and pathology.

PubMed

Amigó, José M; Small, Michael

2017-06-28

The application of mathematics, natural sciences and engineering to medicine is gaining momentum as the mutual benefits of this collaboration become increasingly obvious. This theme issue is intended to highlight the trend in the case of mathematics. Specifically, the scope of this theme issue is to give a general view of the current research in the application of mathematical methods to medicine, as well as to show how mathematics can help in such important aspects as understanding, prediction, treatment and data processing. To this end, three representative specialties have been selected: neuroscience, cardiology and pathology. Concerning the topics, the 12 research papers and one review included in this issue cover biofluids, cardiac and virus dynamics, computational neuroscience, functional magnetic resonance imaging data processing, neural networks, optimization of treatment strategies, time-series analysis and tumour growth. In conclusion, this theme issue contains a collection of fine contributions at the intersection of mathematics and medicine, not as an exercise in applied mathematics but as a multidisciplinary research effort that interests both communities and our society in general.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'. © 2017 The Author(s).

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

ERIC Educational Resources Information Center

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

2016-01-01

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

Secondary School Advanced Mathematics, Chapter 1, Organizing Geometric Knowledge, Chapter 2, Concepts and Skills in Algebra. Student's Text.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This text is the first of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. The first chapter, devoted to organizing geometric knowledge, deals with the distinction…

Proceedings of the 2013 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering - M and C 2013

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

NONE

2013-07-01

The Mathematics and Computation Division of the American Nuclear (ANS) and the Idaho Section of the ANS hosted the 2013 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M and C 2013). This proceedings contains over 250 full papers with topics ranging from reactor physics; radiation transport; materials science; nuclear fuels; core performance and optimization; reactor systems and safety; fluid dynamics; medical applications; analytical and numerical methods; algorithms for advanced architectures; and validation verification, and uncertainty quantification.

A Mixed Methods Study of Teach for America Teachers' Mathematical Beliefs, Knowledge, and Classroom Teaching Practices during a Reform-Based University Mathematics Methods Course

ERIC Educational Resources Information Center

Swars, Susan Lee

2015-01-01

This mixed methods study examined the mathematical preparation of elementary teachers in a Teach for America (TFA) program, focal participants for whom there is scant extant research. Data collection occurred before and after a university mathematics methods course, with a particular focus on the participants' (n = 22) mathematical beliefs,…

Secondary School Advanced Mathematics, Chapter 1, Organizing Geometric Knowledge, Chapter 2, Concepts and Skills in Algebra. Teacher's Commentary.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This manual was designed for use with the first of five texts in the Secondary School Advanced Mathematics (SSAM) series. Developed for students who have completed the Secondary School Mathematics (SSM) program and wish to continue their studies in mathematics, this series is designed to review, strengthen, and fill gaps in the material covered in…

Mathematical methods of studying physical phenomena

NASA Astrophysics Data System (ADS)

Man'ko, Margarita A.

2013-03-01

In recent decades, substantial theoretical and experimental progress was achieved in understanding the quantum nature of physical phenomena that serves as the foundation of present and future quantum technologies. Quantum correlations like the entanglement of the states of composite systems, the phenomenon of quantum discord, which captures other aspects of quantum correlations, quantum contextuality and, connected with these phenomena, uncertainty relations for conjugate variables and entropies, like Shannon and Rényi entropies, and the inequalities for spin states, like Bell inequalities, reflect the recently understood quantum properties of micro and macro systems. The mathematical methods needed to describe all quantum phenomena mentioned above were also the subject of intense studies in the end of the last, and beginning of the new, century. In this section of CAMOP 'Mathematical Methods of Studying Physical Phenomena' new results and new trends in the rapidly developing domain of quantum (and classical) physics are presented. Among the particular topics under discussion there are some reviews on the problems of dynamical invariants and their relations with symmetries of the physical systems. In fact, this is a very old problem of both classical and quantum systems, e.g. the systems of parametric oscillators with time-dependent parameters, like Ermakov systems, which have specific constants of motion depending linearly or quadratically on the oscillator positions and momenta. Such dynamical invariants play an important role in studying the dynamical Casimir effect, the essence of the effect being the creation of photons from the vacuum in a cavity with moving boundaries due to the presence of purely quantum fluctuations of the electromagnetic field in the vacuum. It is remarkable that this effect was recently observed experimentally. The other new direction in developing the mathematical approach in physics is quantum tomography that provides a new vision of

Factors Contributing to Rural High School Students' Participation in Advanced Mathematics Courses. Working Paper No. 34

ERIC Educational Resources Information Center

Anderson, Rick

2006-01-01

The focus of this paper is a group of rural high school students and the factors that contributed to their participation in mathematics classes beyond those minimally required for high school graduation. The author follows Gutierrez (2002) in referring to participation as course taking, particularly in elective and advanced mathematics classes.…

(Re)Envisioning Mathematics Education: Examining Equity and Social Justice in an Elementary Mathematics Methods Course

ERIC Educational Resources Information Center

Koestler, Courtney

2010-01-01

In this dissertation, I present my attempts at designing an elementary mathematics methods course to support prospective teachers in developing an understanding of how to teach all students in learning powerful mathematics. To do this, I introduced them to teaching mathematics for equity and social justice by discussing ways to support students'…

Keystone Method: A Learning Paradigm in Mathematics

ERIC Educational Resources Information Center

Siadat, M. Vali; Musial, Paul M.; Sagher, Yoram

2008-01-01

This study reports the effects of an integrated instructional program (the Keystone Method) on the students' performance in mathematics and reading, and tracks students' persistence and retention. The subject of the study was a large group of students in remedial mathematics classes at the college, willing to learn but lacking basic educational…

Incentivizing advanced mathematics study at upper secondary level: the case of bonus points in Ireland

NASA Astrophysics Data System (ADS)

Treacy, Páraic Thomas

2018-04-01

Secondary level mathematics education in Ireland has recently experienced a period of significant change with the introduction of new curricula and the addition of an incentive to study upper secondary mathematics at the most advanced level (Higher Level). This incentive, typically referred to as 'bonus points', appears to have aided a significant increase in the number of students studying upper secondary mathematics at Higher Level. However, thematic analysis of interviews with experienced upper secondary mathematics examiners and exploration of mathematics diagnostic test data outlined in this paper suggest that the difficulty of the Higher Level upper secondary mathematics final examination in Ireland has reduced since the introduction of the bonus points initiative. The sharp increase in students attempting this examination coupled with a policy of maintaining a consistent proportion of students achieving passing grades was identified as a key reason for this possible reduction in standards.

Mathematics Underground

ERIC Educational Resources Information Center

Luther, Kenneth H.

2012-01-01

Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…

Contradictions between and within School and University Activity Systems Helping to Explain Students' Difficulty with Advanced Mathematics

ERIC Educational Resources Information Center

Jooganah, Kamila; Williams, Julian S.

2016-01-01

This article explores how contradictions, as framed by activity theory (Engeström, 1987), can explain first-year undergraduate students' experiences of learning advanced mathematics. Analysing qualitative interview and observational data of students and lecturers based in one university mathematics department, we argue that contradictions between…

A study of direct moxibustion using mathematical methods.

PubMed

Liu, Miao; Kauh, Sang Ken; Lim, Sabina

2012-01-01

Direct moxibustion is an important and widely used treatment method in traditional medical science. The use of a mathematical method to analyse direct moxibustion treatment is necessary and helpful in exploring the new direct moxibustion instruments and their standardisation. Thus, this paper aims to use a mathematical method to study direct moxibustion in skin to demonstrate a direct relationship between direct moxibustion and skin stimuli. In this paper, the transient thermal response of skin layers is analysed to study direct moxibustion using the data got from standardised method to measure the temperature of a burning moxa cone. Numerical simulations based on an appropriate finite element model are developed to predict the heat transfer, thermal damage and thermal stress distribution of barley moxa cones and jujube moxa cones in the skin tissue. The results are verified by the ancient literatures of traditional Chinese medicine and clinical application, and showed that mathematical method can be a good interface between moxa cone and skin tissue providing the numerical value basis for moxibustion.

Silent method for mathematics instruction: An overview of teaching subsets

NASA Astrophysics Data System (ADS)

Sugiman, Apino, Ezi

2017-05-01

Generally, teachers use oral communication for teaching mathematics. Taking an opposite perspective, this paper describes how instructional practices for mathematics can be carried out namely a silent method. Silent method uses body language, written, and oral communication for classroom interaction. This research uses a design research approach consisting of four phases: preliminary, prototyping and developing the instruction, and assessment. There are four stages of silent method. The first stage is conditioning stage in which the teacher introduces the method and makes agreement about the `rule of the game'. It is followed by the second one, elaborating stage, where students guess and explore alternative answers. The third stage is developing mathematical thinking by structuring and symbolizing. Finally, the method is ended by reinforcing stage which aims at strengthening and reflecting student's understanding. In this paper, every stage is described on the basis of practical experiences in a real mathematics classroom setting.

Editorial: Mathematical Methods and Modeling in Machine Fault Diagnosis

DOE PAGES

Yan, Ruqiang; Chen, Xuefeng; Li, Weihua; ...

2014-12-18

Modern mathematics has commonly been utilized as an effective tool to model mechanical equipment so that their dynamic characteristics can be studied analytically. This will help identify potential failures of mechanical equipment by observing change in the equipment’s dynamic parameters. On the other hand, dynamic signals are also important and provide reliable information about the equipment’s working status. Modern mathematics has also provided us with a systematic way to design and implement various signal processing methods, which are used to analyze these dynamic signals, and to enhance intrinsic signal components that are directly related to machine failures. This special issuemore » is aimed at stimulating not only new insights on mathematical methods for modeling but also recently developed signal processing methods, such as sparse decomposition with potential applications in machine fault diagnosis. Finally, the papers included in this special issue provide a glimpse into some of the research and applications in the field of machine fault diagnosis through applications of the modern mathematical methods.« less

Selecting and Using Mathematics Methods Texts: Nontrivial Tasks

ERIC Educational Resources Information Center

Harkness, Shelly Sheats; Brass, Amy

2017-01-01

Mathematics methods textbooks/texts are important components of many courses for preservice teachers. Researchers should explore how these texts are selected and used. Within this paper we report the findings of a survey administered electronically to 132 members of the Association of Mathematics Teacher Educators (AMTE) in order to answer the…

Mathematical methods for protein science

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

Hart, W.; Istrail, S.; Atkins, J.

1997-12-31

Understanding the structure and function of proteins is a fundamental endeavor in molecular biology. Currently, over 100,000 protein sequences have been determined by experimental methods. The three dimensional structure of the protein determines its function, but there are currently less than 4,000 structures known to atomic resolution. Accordingly, techniques to predict protein structure from sequence have an important role in aiding the understanding of the Genome and the effects of mutations in genetic disease. The authors describe current efforts at Sandia to better understand the structure of proteins through rigorous mathematical analyses of simple lattice models. The efforts have focusedmore » on two aspects of protein science: mathematical structure prediction, and inverse protein folding.« less

The Equity Education. Fostering the Advancement of Women in the Sciences, Mathematics, and Engineering.

ERIC Educational Resources Information Center

Davis, Cinda-Sue; And Others

This volume includes 10 reports that present findings and recommendations for advancing women in science, mathematics and engineering. Critical issues facing women in these disciplines are addressed, including demographic myths and realities at various educational levels; the educational pipeline for girls and women; involvement in education and…

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

NASA Astrophysics Data System (ADS)

Varsavsky, Cristina

2010-12-01

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

Infusing Mathematics Content into a Methods Course: Impacting Content Knowledge for Teaching

ERIC Educational Resources Information Center

Burton, Megan; Daane, C. J.; Giesen, Judy

2008-01-01

This study compared content knowledge for teaching mathematics differences between elementary pre-service teachers in a traditional versus an experimental mathematics methods course. The experimental course replaced 20 minutes of traditional methods, each class, with an intervention of elementary mathematics content. The difference between groups…

Perception of mathematics teachers on cooperative learning method in the 21st century

NASA Astrophysics Data System (ADS)

Taufik, Nurshahira Alwani Mohd; Maat, Siti Mistima

2017-05-01

Mathematics education is one of the branches to be mastered by students to help them compete with the upcoming challenges that are very challenging. As such, all parties should work together to help increase student achievement in Mathematics education in line with the Malaysian Education Blueprint (MEB) 2010-2025. Teaching methods play a very important role in attracting and fostering student understanding and interested in learning Mathematics. Therefore, this study was conducted to identify the perceptions of teachers in carrying out cooperative methods in the teaching and learning of mathematics. Participants of this study involving 4 teachers who teach Mathematics in primary schools around the state of Negeri Sembilan. Interviews are used as a method for gathering data. The findings indicate that cooperative methods help increasing interest and understanding in the teaching and learning of mathematics. In conclusion, the teaching methods affect the interest and understanding of students in the learning of Mathematics in the classroom.

Research in Mathematics Education: Multiple Methods for Multiple Uses

ERIC Educational Resources Information Center

Battista, Michael; Smith, Margaret S.; Boerst, Timothy; Sutton, John; Confrey, Jere; White, Dorothy; Knuth, Eric; Quander, Judith

2009-01-01

Recent federal education policies and reports have generated considerable debate about the meaning, methods, and goals of "scientific research" in mathematics education. Concentrating on the critical problem of determining which educational programs and practices reliably improve students' mathematics achievement, these policies and reports focus…

Mathematical Modeling in the Undergraduate Curriculum

ERIC Educational Resources Information Center

Toews, Carl

2012-01-01

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

Recent Advances of Malaria Parasites Detection Systems Based on Mathematical Morphology

PubMed Central

Di Ruberto, Cecilia; Kocher, Michel

2018-01-01

Malaria is an epidemic health disease and a rapid, accurate diagnosis is necessary for proper intervention. Generally, pathologists visually examine blood stained slides for malaria diagnosis. Nevertheless, this kind of visual inspection is subjective, error-prone and time-consuming. In order to overcome the issues, numerous methods of automatic malaria diagnosis have been proposed so far. In particular, many researchers have used mathematical morphology as a powerful tool for computer aided malaria detection and classification. Mathematical morphology is not only a theory for the analysis of spatial structures, but also a very powerful technique widely used for image processing purposes and employed successfully in biomedical image analysis, especially in preprocessing and segmentation tasks. Microscopic image analysis and particularly malaria detection and classification can greatly benefit from the use of morphological operators. The aim of this paper is to present a review of recent mathematical morphology based methods for malaria parasite detection and identification in stained blood smears images. PMID:29419781

Recent Advances of Malaria Parasites Detection Systems Based on Mathematical Morphology.

PubMed

Loddo, Andrea; Di Ruberto, Cecilia; Kocher, Michel

2018-02-08

Malaria is an epidemic health disease and a rapid, accurate diagnosis is necessary for proper intervention. Generally, pathologists visually examine blood stained slides for malaria diagnosis. Nevertheless, this kind of visual inspection is subjective, error-prone and time-consuming. In order to overcome the issues, numerous methods of automatic malaria diagnosis have been proposed so far. In particular, many researchers have used mathematical morphology as a powerful tool for computer aided malaria detection and classification. Mathematical morphology is not only a theory for the analysis of spatial structures, but also a very powerful technique widely used for image processing purposes and employed successfully in biomedical image analysis, especially in preprocessing and segmentation tasks. Microscopic image analysis and particularly malaria detection and classification can greatly benefit from the use of morphological operators. The aim of this paper is to present a review of recent mathematical morphology based methods for malaria parasite detection and identification in stained blood smears images.

Technologies That Facilitate the Study of Advanced Mathematics by Students Who Are Blind: Teachers' Perspectives

ERIC Educational Resources Information Center

DePountis, Vicki M.; Pogrund, Rona L.; Griffin-Shirley, Nora; Lan, William Y.

2015-01-01

This research examined the perspectives of teachers of students with visual impairments (TVIs) regarding the use and effectiveness of electronic assistive technology (EAT) purported to assist students who are blind in advanced mathematics subjects. The data for this study were collected via an online survey distributed to a convenience sample of…

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

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

PubMed

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

2010-01-01

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

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

PubMed Central

Davies, Robin; Hodge, Terrell; Enyedi, Alexander

2010-01-01

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

Career Advancement Outcomes in Academic Science, Technology, Engineering and Mathematics (STEM): Gender, Mentoring Resources, and Homophily

ERIC Educational Resources Information Center

Lee, Sang Eun

2017-01-01

This dissertation examines gender differences in career advancement outcomes among academic science, technology, engineering and mathematics (STEM) scientists. In particular, this research examines effects of gender, PhD advisors and postdoctoral supervisors mentoring resources and gender homophily in the mentoring dyads on the career advancement…

In-Situ Assays Using a New Advanced Mathematical Algorithm - 12400

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

Oginni, B.M.; Bronson, F.L.; Field, M.B.

2012-07-01

Current mathematical efficiency modeling software for in-situ counting, such as the commercially available In-Situ Object Calibration Software (ISOCS), typically allows the description of measurement geometries via a list of well-defined templates which describe regular objects, such as boxes, cylinder, or spheres. While for many situations, these regular objects are sufficient to describe the measurement conditions, there are occasions in which a more detailed model is desired. We have developed a new all-purpose geometry template that can extend the flexibility of current ISOCS templates. This new template still utilizes the same advanced mathematical algorithms as current templates, but allows the extensionmore » to a multitude of shapes and objects that can be placed at any location and even combined. In addition, detectors can be placed anywhere and aimed at any location within the measurement scene. Several applications of this algorithm to in-situ waste assay measurements, as well as, validations of this template using Monte Carlo calculations and experimental measurements are studied. Presented in this paper is a new template of the mathematical algorithms for evaluating efficiencies. This new template combines all the advantages of the ISOCS and it allows the use of very complex geometries, it also allows stacking of geometries on one another in the same measurement scene and it allows the detector to be placed anywhere in the measurement scene and pointing in any direction. We have shown that the template compares well with the previous ISOCS software within the limit of convergence of the code, and also compare well with the MCNPX and measured data within the joint uncertainties for the code and the data. The new template agrees with ISOCS to within 1.5% at all energies. It agrees with the MCNPX to within 10% at all energies and it agrees with most geometries within 5%. It finally agrees with measured data to within 10%. This mathematical algorithm can

Metric Education in Mathematics Methods Classes.

ERIC Educational Resources Information Center

Trent, John H.

A pre-test on knowledge of the metric system was administered to elementary mathematics methods classes at the University of Nevada at the beginning of the 1975 Spring Semester. A one-hour lesson was prepared and taught regarding metric length, weight, volume, and temperature. At the end of the semester the original test was given as the…

Effects of Mathematics Integration in a Teaching Methods Course on Mathematics Ability of Preservice Agricultural Education Teachers

ERIC Educational Resources Information Center

Stripling, Christopher T.; Roberts, T. Grady

2014-01-01

The purpose of this study was to determine the effects of incorporating mathematics teaching and integration strategies (MTIS) in a teaching methods course on preservice agricultural teachers' mathematics ability. The research design was quasi-experimental and utilized a nonequivalent control group. The MTIS treatment had a positive effect on the…

What Math Matters? Types of Mathematics Knowledge and Relationships to Methods Course Performance

ERIC Educational Resources Information Center

Kajander, Ann; Holm, Jennifer

2016-01-01

This study investigated the effect of a departmental focus on enhanced mathematics knowledge for teaching on overall performance in upper elementary mathematics methods courses. The study examined the effect of performance on a new course in mathematics for teaching on performance at the methods course level. In addition, the effect of performance…

Integration of Technology, Curriculum, and Professional Development for Advancing Middle School Mathematics: Three Large-Scale Studies

ERIC Educational Resources Information Center

Roschelle, Jeremy; Shechtman, Nicole; Tatar, Deborah; Hegedus, Stephen; Hopkins, Bill; Empson, Susan; Knudsen, Jennifer; Gallagher, Lawrence P.

2010-01-01

The authors present three studies (two randomized controlled experiments and one embedded quasi-experiment) designed to evaluate the impact of replacement units targeting student learning of advanced middle school mathematics. The studies evaluated the SimCalc approach, which integrates an interactive representational technology, paper curriculum,…

The Monte Carlo Method. Popular Lectures in Mathematics.

ERIC Educational Resources Information Center

Sobol', I. M.

The Monte Carlo Method is a method of approximately solving mathematical and physical problems by the simulation of random quantities. The principal goal of this booklet is to suggest to specialists in all areas that they will encounter problems which can be solved by the Monte Carlo Method. Part I of the booklet discusses the simulation of random…

Tracing the Construction of Mathematical Activity with an Advanced Graphing Calculator to Understand the Roles of Technology Developers, Teachers and Students

ERIC Educational Resources Information Center

Hillman, Thomas

2014-01-01

This article examines mathematical activity with digital technology by tracing it from its development through its use in classrooms. Drawing on material-semiotic approaches from the field of Science and Technology Studies, it examines the visions of mathematical activity that developers had for an advanced graphing calculator. It then follows the…

A Mathematics Software Database Update.

ERIC Educational Resources Information Center

Cunningham, R. S.; Smith, David A.

1987-01-01

Contains an update of an earlier listing of software for mathematics instruction at the college level. Topics are: advanced mathematics, algebra, calculus, differential equations, discrete mathematics, equation solving, general mathematics, geometry, linear and matrix algebra, logic, statistics and probability, and trigonometry. (PK)

Investigating Mathematics Self-Efficacy Beliefs of Elementary Pre-Service Teachers in a Reform-Based Mathematics Methods Course

ERIC Educational Resources Information Center

Setra, Abdelghani

2017-01-01

For the last thirty years research has unfailingly shown that teacher efficacy has a positive impact on student outcomes, making teacher efficacy an critical element in quality mathematics instruction. The purpose of this study is to examine the impact of a math methods course on the mathematics teaching efficacy beliefs of elementary pre-service…

Mathematical models used in segmentation and fractal methods of 2-D ultrasound images

NASA Astrophysics Data System (ADS)

Moldovanu, Simona; Moraru, Luminita; Bibicu, Dorin

2012-11-01

Mathematical models are widely used in biomedical computing. The extracted data from images using the mathematical techniques are the "pillar" achieving scientific progress in experimental, clinical, biomedical, and behavioural researches. This article deals with the representation of 2-D images and highlights the mathematical support for the segmentation operation and fractal analysis in ultrasound images. A large number of mathematical techniques are suitable to be applied during the image processing stage. The addressed topics cover the edge-based segmentation, more precisely the gradient-based edge detection and active contour model, and the region-based segmentation namely Otsu method. Another interesting mathematical approach consists of analyzing the images using the Box Counting Method (BCM) to compute the fractal dimension. The results of the paper provide explicit samples performed by various combination of methods.

A Comparison of Pre- and Post- Levels of Mathematics Anxiety among Preservice Teacher Candidates Enrolled in a Mathematics Methods Course.

ERIC Educational Resources Information Center

Sloan, Tina Rye; Vinson, Beth; Haynes, Jonita; Gresham, Regina

This study examined the effectiveness of a methods course in the reduction of mathematics anxiety levels among three groups of preservice teachers majoring in elementary education. The sample included 61 novices enrolled in a course entitled Mathematics for the Young Child. This methods course utilized concrete manipulatives and active learning…

Mathematics Achievement: Traditional Instruction and Technology-Assisted Course Delivery Methods

ERIC Educational Resources Information Center

Vilardi, Robert; Rice, Margaret L.

2014-01-01

The purpose of this study was to analyze technology-assisted course delivery methods to determine their overall effectiveness as it pertains to mathematics courses. This study analyzed both current and historical data in the areas of achievement, retention, and grade distribution for mathematics classes. The study included 14,562 students enrolled…

Student Teachers' Views about Assessment and Evaluation Methods in Mathematics

ERIC Educational Resources Information Center

Dogan, Mustafa

2011-01-01

This study aimed to find out assessment and evaluation approaches in a Mathematics Teacher Training Department based on the views and experiences of student teachers. The study used a descriptive survey method, with the research sample consisting of 150 third- and fourth-year Primary Mathematics student teachers. Data were collected using a…

Mathematics Achievement: Traditional Instruction and Technology-Assisted Course Delivery Methods

ERIC Educational Resources Information Center

Vilardi, Robert

2013-01-01

The purpose of this study was to analyze technology-assisted course delivery methods to determine their overall effectiveness as it pertains to mathematics courses. This study analyzed both current and historical data in mathematics classes in the areas of achievement, retention, and grade distribution. The goal of this study was to determine if…

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

ERIC Educational Resources Information Center

Crowe, Cheryll E.; Ma, Xin

2010-01-01

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

Secondary School Advanced Mathematics, Chapter 6, The Complex Number System, Chapter 7, Equations of the First and Second Degree in Two Variables. Student's Text.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This text is the fourth of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. This text begins with a brief discussion of quadratic equations which motivates the…

Secondary School Advanced Mathematics, Chapter 6, The Complex Number System, Chapter 7, Equations of the First and Second Degree in Two Variables. Teacher's Commentary.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This manual was designed for use with the fourth of five texts in the Secondary School Advanced Mathematics (SSAM) series. Developed for students who have completed the Secondary School Mathematics (SSM) program and wish to continue their studies in mathematics, this series is designed to review, strengthen, and fill gaps in the material covered…

Reframing Research on Methods Courses to Inform Mathematics Teacher Educators' Practice

ERIC Educational Resources Information Center

Kastberg, Signe E.; Tyminski, Andrew M.; Sanchez, Wendy B.

2017-01-01

Calls have been made for the creation of a shared knowledge base in mathematics teacher education with the power to inform the design of scholarly inquiry and mathematics teacher educators' (MTEs) scholarly practices. Focusing on mathematics methods courses, we summarize and contribute to literature documenting activities MTEs use in mathematics…

Encouraging Young Women to Stay in the Mathematics Pipeline: Mathematics Camps for Young Women

ERIC Educational Resources Information Center

Chacon, Paul; Soto-Johnson, Hortensia

2003-01-01

For two summers, week-long residential mathematics programs were held for high school women, with the primary goal of encouraging them to continue their study of mathematics. The activities were designed to rekindle their excitement about mathematics and to support the idea that women should learn advanced mathematics. This paper reports the…

TIMSS Advanced 2008 Assessment Frameworks

ERIC Educational Resources Information Center

Garden, Robert A.; Lie, Svein; Robitaille, David F.; Angell, Carl; Martin, Michael O.; Mullis, Ina V.S.; Foy, Pierre; Arora, Alka

2006-01-01

Developing the Trends in International Mathematics and Science Study (TIMSS) Advanced 2008 Assessment Frameworks was a collaborative venture involving mathematics and physics experts from around the world. The document contains two frameworks for implementing TIMSS Advanced 2008--one for advanced mathematics and one for physics. It also contains…

Advanced High School Biology in an Era of Rapid Change: A Summary of the Biology Panel Report from the NRC Committee on Programs for Advanced Study of Mathematics and Science in American High Schools

ERIC Educational Resources Information Center

Wood, William B.

2002-01-01

A recently released National Research Council (NRC) report, "Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools", evaluated and recommended changes in the Advanced Placement (AP), International Baccalaureate (IB), and other advanced secondary school science programs. As part of this study,…

Mathematical models of cell motility.

PubMed

Flaherty, Brendan; McGarry, J P; McHugh, P E

2007-01-01

Cell motility is an essential biological action in the creation, operation and maintenance of our bodies. Developing mathematical models elucidating cell motility will greatly advance our understanding of this fundamental biological process. With accurate models it is possible to explore many permutations of the same event and concisely investigate their outcome. While great advancements have been made in experimental studies of cell motility, it now has somewhat fallen on mathematical models to taking a leading role in future developments. The obvious reason for this is the complexity of cell motility. Employing the processing power of today's computers will give researches the ability to run complex biophysical and biochemical scenarios, without the inherent difficulty and time associated with in vitro investigations. Before any great advancement can be made, the basics of cell motility will have to be well-defined. Without this, complicated mathematical models will be hindered by their inherent conjecture. This review will look at current mathematical investigations of cell motility, explore the reasoning behind such work and conclude with how best to advance this interesting and challenging research area.

Using the Scientific Method to Engage Mathematical Modeling: An Investigation of pi

ERIC Educational Resources Information Center

Archer, Lester A. C.; Ng, Karen E.

2016-01-01

The purpose of this paper is to explain how to use the scientific method as the framework to introduce mathematical model. Two interdisciplinary activities, targeted for students in grade 6 or grade 7, are explained to show the application of the scientific method while building a mathematical model to investigate the relationship between the…

Social activity method (SAM): A fractal language for mathematics

NASA Astrophysics Data System (ADS)

Dowling, Paul

2013-09-01

In this paper I shall present and develop my organisational language, social activity method (SAM), and illustrate some of its applications. I shall introduce a new scheme for modes of recontextualisation that enables the analysis of the ways in which one activity - which might be school mathematics or social research or any empirically observed regularity of practice - recontextualises the practice of another and I shall also present, deploy, and develop an existing scheme - domains of action - in an analysis of school mathematics examination papers and in the structuring of what I refer to as the esoteric domain. This domain is here conceived as a hybrid domain of, first, linguistic and extralinguistic resources that are unambiguously mathematical in terms of both expression and content and, second, pedagogic theory - often tacit - that enables the mathematical gaze onto other practices and so recontextualises them. A second and more general theme that runs through the paper is the claim that there is nothing that is beyond semiosis, that there is nothing to which we have direct access, unmediated by interpretation. This state of affairs has implications for mathematics education. Specifically, insofar as an individual's mathematical semiotic system is under continuous development - the curriculum never being graspable all at once - understanding - as a stable semiotic moment - of any aspect or object of mathematics is always localised to the individual and is at best transient, and the sequencing of such moments may well also be more individualised than consistent in some correspondence with the sequencing of the curriculum. This being the case, a concentration on understanding as a goal may well serve to inhibit the pragmatic acquisition and deployment of mathematical technologies, which should be the principal aim of mathematics teaching and learning. The paper is primarily concerned with mathematics education. SAM, however, is a language that is available for

Structural and Conceptual Interweaving of Mathematics Methods Coursework and Field Practica

ERIC Educational Resources Information Center

Bahr, Damon L.; Monroe, Eula Ewing; Eggett, Dennis

2014-01-01

This paper describes a study of observed relationships between the design of a preservice elementary mathematics methods course with accompanying field practicum and changes in the extent to which participating prospective teachers identified themselves with the mathematics reform movement after becoming practicing teachers. The curriculum of the…

A Multi-Method Investigation of Mathematics Motivation for Elementary Age Students

ERIC Educational Resources Information Center

Linder, Sandra M.; Smart, Julie B.; Cribbs, Jennifer

2015-01-01

This paper presents the results of a multi-method study examining elementary students with high self-reported levels of mathematics motivation. Second- through fifth-grade students at a Title One school in the southeastern United States completed the Elementary Mathematics Motivation Instrument (EMMI), which examines levels of mathematics…

One-Year Integrated Mathematics and Mathematics Methods Course for Prospective Elementary School Teachers.

ERIC Educational Resources Information Center

Springer, George

This guide describes the content of a proposed mathematics course for prospective elementary school teachers. It is the result of a two-year study at Indiana University in which three existing courses were integrated and coordinated. For each unit of instruction, there are (1) remarks for motivation of study, (2) remarks on methods of teaching,…

How Preservice Teachers Make Meaning of Mathematics Methods Texts

ERIC Educational Resources Information Center

Harkness, Shelly Sheats; Brass, Amy

2017-01-01

Mathematics methods texts are important resources for supporting preservice teachers' learning. Methods instructors routinely assign readings from texts. Yet, anecdotally and also based on reading compliance literature, many students report that they do not read assigned readings. Within this paper we briefly describe the findings from a survey of…

Driven by History: Mathematics Education Reform

ERIC Educational Resources Information Center

Permuth, Steve; Dalzell, Nicole

2013-01-01

The advancement of modern societies is fueled by mathematics, and mathematics education provides the foundation upon which future scientists and engineers will build. Society dictates how mathematics will be taught through the development and implementation of mathematics standards. When examining the progression of these standards, it is…

Strategic Alliance to Advanced Technological Education through Enhanced Mathematics, Science, Technology, and English Education at the Secondary Level

ERIC Educational Resources Information Center

Scarborough, Jule Dee

2004-01-01

This document (book) reports on the Strategic Alliance to Advance Technological Education through Enhanced Mathematics, Science, Technology, and English Education at the Secondary Level, funded by National Science Foundation. It was a collaborative partnership involving the Rockford Public Schools, Rock Valley College, and Northern Illinois…

Advanced Mathematics Communication beyond Modality of Sight

ERIC Educational Resources Information Center

Sedaghatjou, Mina

2018-01-01

This study illustrates how mathematical communication and learning are inherently multimodal and embodied; hence, sight-disabled students are also able to conceptualize visuospatial information and mathematical concepts through tactile and auditory activities. Adapting a perceptuomotor integration approach, the study shows that the lack of access…

Problems of Mathematical Finance by Stochastic Control Methods

NASA Astrophysics Data System (ADS)

Stettner, Łukasz

The purpose of this paper is to present main ideas of mathematics of finance using the stochastic control methods. There is an interplay between stochastic control and mathematics of finance. On the one hand stochastic control is a powerful tool to study financial problems. On the other hand financial applications have stimulated development in several research subareas of stochastic control in the last two decades. We start with pricing of financial derivatives and modeling of asset prices, studying the conditions for the absence of arbitrage. Then we consider pricing of defaultable contingent claims. Investments in bonds lead us to the term structure modeling problems. Special attention is devoted to historical static portfolio analysis called Markowitz theory. We also briefly sketch dynamic portfolio problems using viscosity solutions to Hamilton-Jacobi-Bellman equation, martingale-convex analysis method or stochastic maximum principle together with backward stochastic differential equation. Finally, long time portfolio analysis for both risk neutral and risk sensitive functionals is introduced.

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

PubMed

Robeva, Raina

2009-01-01

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

Applied Mathematical Methods in Theoretical Physics

NASA Astrophysics Data System (ADS)

Masujima, Michio

2005-04-01

All there is to know about functional analysis, integral equations and calculus of variations in a single volume. This advanced textbook is divided into two parts: The first on integral equations and the second on the calculus of variations. It begins with a short introduction to functional analysis, including a short review of complex analysis, before continuing a systematic discussion of different types of equations, such as Volterra integral equations, singular integral equations of Cauchy type, integral equations of the Fredholm type, with a special emphasis on Wiener-Hopf integral equations and Wiener-Hopf sum equations. After a few remarks on the historical development, the second part starts with an introduction to the calculus of variations and the relationship between integral equations and applications of the calculus of variations. It further covers applications of the calculus of variations developed in the second half of the 20th century in the fields of quantum mechanics, quantum statistical mechanics and quantum field theory. Throughout the book, the author presents over 150 problems and exercises -- many from such branches of physics as quantum mechanics, quantum statistical mechanics, and quantum field theory -- together with outlines of the solutions in each case. Detailed solutions are given, supplementing the materials discussed in the main text, allowing problems to be solved making direct use of the method illustrated. The original references are given for difficult problems. The result is complete coverage of the mathematical tools and techniques used by physicists and applied mathematicians Intended for senior undergraduates and first-year graduates in science and engineering, this is equally useful as a reference and self-study guide.

Clickers and Classroom Voting in a Transition to Advanced Mathematics Course

ERIC Educational Resources Information Center

Lockard, Shannon R.; Metcalf, Rebecca C.

2015-01-01

Clickers and classroom voting are used across a number of disciplines in a variety of institutions. There are several papers that describe the use of clickers in mathematics classrooms such as precalculus, calculus, statistics, and even differential equations. This paper describes a method of incorporating clickers and classroom voting in a…

Advanced Methods of Protein Crystallization.

PubMed

Moreno, Abel

2017-01-01

This chapter provides a review of different advanced methods that help to increase the success rate of a crystallization project, by producing larger and higher quality single crystals for determination of macromolecular structures by crystallographic methods. For this purpose, the chapter is divided into three parts. The first part deals with the fundamentals for understanding the crystallization process through different strategies based on physical and chemical approaches. The second part presents new approaches involved in more sophisticated methods not only for growing protein crystals but also for controlling the size and orientation of crystals through utilization of electromagnetic fields and other advanced techniques. The last section deals with three different aspects: the importance of microgravity, the use of ligands to stabilize proteins, and the use of microfluidics to obtain protein crystals. All these advanced methods will allow the readers to obtain suitable crystalline samples for high-resolution X-ray and neutron crystallography.

Advanced high school biology in an era of rapid change: a summary of the biology panel report from the NRC Committee on Programs for Advanced Study of Mathematics and Science in American High Schools.

PubMed

Wood, William B

2002-01-01

A recently released National Research Council (NRC) report, Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools, evaluated and recommended changes in the Advanced Placement (AP), International Baccalaureate (IB), and other advanced secondary school science programs. As part of this study, discipline-specific panels were formed to evaluate advanced programs in biology, chemistry, physics, and mathematics. Among the conclusions of the Content Panel for Biology were that AP courses in particular suffer from inadequate quality control as well as excessive pressure to fulfill their advanced placement function, which encourages teachers to attempt coverage of all areas of biology and emphasize memorization of facts rather than in-depth understanding. In this essay, the Panel's principal findings are discussed, with an emphasis on its recommendation that colleges and universities should be strongly discouraged from using performance on either the AP examination or the IB examination as the sole basis for automatic placement out of required introductory courses for biology majors and distribution requirements for nonmajors.

Advanced High School Biology in an Era of Rapid Change: A Summary of the Biology Panel Report from the NRC Committee on Programs for Advanced Study of Mathematics and Science in American High Schools

PubMed Central

2002-01-01

A recently released National Research Council (NRC) report, Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools, evaluated and recommended changes in the Advanced Placement (AP), International Baccalaureate (IB), and other advanced secondary school science programs. As part of this study, discipline-specific panels were formed to evaluate advanced programs in biology, chemistry, physics, and mathematics. Among the conclusions of the Content Panel for Biology were that AP courses in particular suffer from inadequate quality control as well as excessive pressure to fulfill their advanced placement function, which encourages teachers to attempt coverage of all areas of biology and emphasize memorization of facts rather than in-depth understanding. In this essay, the Panel's principal findings are discussed, with an emphasis on its recommendation that colleges and universities should be strongly discouraged from using performance on either the AP examination or the IB examination as the sole basis for automatic placement out of required introductory courses for biology majors and distribution requirements for nonmajors. PMID:12669097

Conceptual metaphors and mathematical practice: on cognitive studies of historical developments in mathematics.

PubMed

Schlimm, Dirk

2013-04-01

This article looks at recent work in cognitive science on mathematical cognition from the perspective of history and philosophy of mathematical practice. The discussion is focused on the work of Lakoff and Núñez, because this is the first comprehensive account of mathematical cognition that also addresses advanced mathematics and its history. Building on a distinction between mathematics as it is presented in textbooks and as it presents itself to the researcher, it is argued that the focus of cognitive analyses of historical developments of mathematics has been primarily on the former, even if they claim to be about the latter. Copyright © 2013 Cognitive Science Society, Inc.

The Relationship of Mathematics Anxiety and Mathematical Knowledge to the Learning of Mathematical Pedagogy by Preservice Elementary Teachers.

ERIC Educational Resources Information Center

Battista, Michael T.

1986-01-01

Examined how preservice elementary teachers' (N=38) mathematical knowledge and mathematics anxiety affect their success in a mathematics methods course. Also examined the hypothesis that a mathematics methods course can reduce the mathematics anxiety of these teachers. One finding is that mathematics anxiety does not inhibit their learning of…

TIMSS Advanced 2015 Assessment Frameworks

ERIC Educational Resources Information Center

Mullis, Ina V. S., Ed.; Martin, Michael O., Ed.

2014-01-01

The "TIMSS Advanced 2015 Assessment Frameworks" provides the foundation for the two international assessments to take place as part of the International Association for the Evaluation of Educational Achievement's TIMSS (Trends in International Mathematics and Science Study) Advanced 2015--Advanced Mathematics and Physics. Chapter 1 (Liv…

Mathematics and the surgeon.

PubMed Central

Crank, J.

1976-01-01

The surgeon uses elementary mathematics just as much as any other educated layman. In his professional life, however, much of the knowledge and skill on which he relies has had a mathematical strand in its development, possibly woven into the supporting disciplines such as physics, chemistry, biology, and bioengineering. The valves and limitations of mathematical models are examined briefly in the general medical field and particularly in relation to the surgeon. Arithmetic and statistics are usually regarded as the most immediately useful parts of mathematics. Examples are cited, however, of medical postgraduate work which uses other highly advanced mathematical techniques. The place of mathematics in postgraduate and postexperience teaching courses is touched on. The role of a mathematical consultant in the medical team is discussed. PMID:942167

Prevalence of Mixed Methods Research in Mathematics Education

ERIC Educational Resources Information Center

Ross, Amanda A.; Onwuegbuzie, Anthony J.

2012-01-01

In wake of federal legislation such as the No Child Left Behind Act of 2001 that have called for "scientifically based research in education," this study examined the possible trends in mixed methods research articles published in 2 peer-reviewed mathematics education journals (n = 87) from 2002 to 2006. The study also illustrates how…

Preferences of Teaching Methods and Techniques in Mathematics with Reasons

ERIC Educational Resources Information Center

Ünal, Menderes

2017-01-01

In this descriptive study, the goal was to determine teachers' preferred pedagogical methods and techniques in mathematics. Qualitative research methods were employed, primarily case studies. 40 teachers were randomly chosen from various secondary schools in Kirsehir during the 2015-2016 educational terms, and data were gathered via…

Theoretical Explanations in Mathematical Physics

NASA Astrophysics Data System (ADS)

Rivadulla, Andrés

Many physicists wonder at the usefulness of mathematics in physics. According Madrid to Einstein mathematics is admirably appropriate to the objects of reality. Wigner asserts that mathematics plays an unreasonable important role in physics. James Jeans affirms that God is a mathematician, and that the first aim of physics is to discover the laws of nature, which are written in mathematical language. Dirac suggests that God may have used very advanced mathematics in constructing the universe. And Barrow adheres himself to Wigner's claim about the unreasonable effectiveness of mathematics for the workings of the physical world.

Mathematics Content Coverage and Student Learning in Kindergarten

PubMed Central

Engel, Mimi; Claessens, Amy; Watts, Tyler; Farkas, George

2017-01-01

Analyzing data from two nationally representative kindergarten cohorts, we examine the mathematics content teachers cover in kindergarten. We expand upon prior research, finding that kindergarten teachers report emphasizing basic mathematics content. Although teachers reported increased coverage of advanced content between the 1998–99 and 2010–11 school years, they continued to place more emphasis on basic content. We find that time on advanced content is positively associated with student learning, whereas time on basic content has a negative association with learning. We argue that increased exposure to more advanced mathematics content could benefit the vast majority of kindergartners. PMID:29353913

Examinations in the Final Year of Transition to Mathematical Methods Computer Algebra System (CAS)

ERIC Educational Resources Information Center

Leigh-Lancaster, David; Les, Magdalena; Evans, Michael

2010-01-01

2009 was the final year of parallel implementation for Mathematical Methods Units 3 and 4 and Mathematical Methods (CAS) Units 3 and 4. From 2006-2009 there was a common technology-free short answer examination that covered the same function, algebra, calculus and probability content for both studies with corresponding expectations for key…

Pre-service Mathematics Teachers' Knowledge of History of Mathematics and Their Attitudes and Beliefs Towards Using History of Mathematics in Mathematics Education

NASA Astrophysics Data System (ADS)

Alpaslan, Mustafa; Işıksal, Mine; Haser, Çiğdem

2014-01-01

This study examined pre-service mathematics teachers' knowledge of history of mathematics and their attitudes and beliefs towards using history of mathematics in mathematics education based on year level in teacher education program and gender. The sample included 1,593 freshman, sophomore, junior, and senior pre-service middle school (grades 4-8) mathematics teachers from nine universities in Turkey. Data were collected through Knowledge of History of Mathematics Test and Attitudes and Beliefs towards the Use of History of Mathematics in Mathematics Education Questionnaire. Results indicate that pre-service teachers have moderate knowledge of history of mathematics and positive attitudes and beliefs towards using history of mathematics. Their knowledge scores increase as the year level in teacher education program advanced. Males' knowledge scores are significantly higher than females' scores in the first 2 years. This situation reverses in the last 2 years, but it is not statistically significant. Pre-service teachers have more positive attitudes and availing beliefs towards using history of mathematics as they progress in their teacher education program. Females have greater attitudes and beliefs mean scores than males in each of the years. The results indicate that the teacher education program may have enhanced the pre-service teachers' knowledge of history of mathematics by related courses. However, the moderate knowledge scores indicate that there is a need for revision of these courses. The pre-service teachers' positive attitudes and beliefs towards using history of mathematics stress the importance of teacher education program in order to prepare them for implementing this alternative strategy in the future.

The link between middle school mathematics course placement and achievement.

PubMed

Domina, Thurston

2014-01-01

The proportion of eighth graders in United States public schools enrolled in algebra or a more advanced mathematics course doubled between 1990 and 2011. This article uses Early Childhood Longitudinal Study's Kindergarten Cohort data to consider the selection process into advanced middle school mathematics courses and estimate the effects of advanced courses on students' mathematics achievement (n = 6,425; mean age at eighth grade = 13.7). Eighth-grade algebra and geometry course placements are academically selective, but considerable between-school variation exists in students' odds of taking these advanced courses. While analyses indicate that advanced middle school mathematics courses boost student achievement, these effects are most pronounced in content areas closely related to class content and may be contingent on student academic readiness. © 2014 The Author. Child Development © 2014 Society for Research in Child Development, Inc.

[Applications of mathematical statistics methods on compatibility researches of traditional Chinese medicines formulae].

PubMed

Mai, Lan-Yin; Li, Yi-Xuan; Chen, Yong; Xie, Zhen; Li, Jie; Zhong, Ming-Yu

2014-05-01

The compatibility of traditional Chinese medicines (TCMs) formulae containing enormous information, is a complex component system. Applications of mathematical statistics methods on the compatibility researches of traditional Chinese medicines formulae have great significance for promoting the modernization of traditional Chinese medicines and improving clinical efficacies and optimizations of formulae. As a tool for quantitative analysis, data inference and exploring inherent rules of substances, the mathematical statistics method can be used to reveal the working mechanisms of the compatibility of traditional Chinese medicines formulae in qualitatively and quantitatively. By reviewing studies based on the applications of mathematical statistics methods, this paper were summarized from perspective of dosages optimization, efficacies and changes of chemical components as well as the rules of incompatibility and contraindication of formulae, will provide the references for further studying and revealing the working mechanisms and the connotations of traditional Chinese medicines.

Mathematical Discovery and "Affect": The "Effect" of Aha! Experiences on Undergraduate Mathematics Students

ERIC Educational Resources Information Center

Liljedahl, Peter G.

2005-01-01

The AHA! experience-the moment of illumination on the heels of lengthy, and seemingly fruitless, intentional effort-has long been the basis for lore in mathematics. Unfortunately, such lore is often restricted to the discussion of these phenomena in the context of great mathematicians and great mathematical advancement. But are such experiences…

Avoiding Mathematics Trauma: Alternative Teaching Methods.

ERIC Educational Resources Information Center

Ufuktepe, Unal; Ozel, Claire Thomas

Children in primary education often encounter mathematics having picked up a general fear of mathematics from the society around them. This results in lack of confidence, avoidance of non-standard thought processes, weakness in problem solving strategies, and other negative consequences. This study offers an alternative approach: presenting…

Clinical Assessment in Mathematics: Learning the Craft.

ERIC Educational Resources Information Center

Hunting, Robert P.; Doig, Brian A.

1997-01-01

Discusses a professional development program called Clinical Approaches to Mathematics Assessment. Argues for the advanced training of mathematics teachers who understand knowledge construction processes of students; can use clinical tools for evaluating a student's unique mathematical "fingerprint"; and can create or adapt problems, tasks, or…

Mathematical Creativity: Psychology, Progress and Caveats

ERIC Educational Resources Information Center

Sriraman, Bharath

2017-01-01

The aim of this paper is to provide a concise survey of advances in the study of the psychology of creativity, with an emphasis on literature that is typically not cited in mathematics education. In spite of claims that mathematical creativity is an ill-defined area of inquiry in mathematics education, the literature from psychology can serve as…

Efficacy of the Cooperative Learning Method on Mathematics Achievement and Attitude: A Meta-Analysis Research

ERIC Educational Resources Information Center

Capar, Gulfer; Tarim, Kamuran

2015-01-01

This research compiles experimental studies from 1988 to 2010 that examined the influence of the cooperative learning method, as compared with that of traditional methods, on mathematics achievement and on attitudes towards mathematics. The related field was searched using the following key words in Turkish "matematik ve isbirlikli ögrenme,…

Teaching by Open-Approach Method in Japanese Mathematics Classroom.

ERIC Educational Resources Information Center

Nohda, Nobuhiko

Mathematics educators in Japan have traditionally emphasized mathematical perspectives in research and practice. This paper features an account of changes in mathematics education in Japan that focus on the possibilities of individual students as well as their mathematical ways of thinking. Students' mathematical thinking, mathematical…

Social Activity Method (SAM): A Fractal Language for Mathematics

ERIC Educational Resources Information Center

Dowling, Paul

2013-01-01

In this paper I shall present and develop my organisational language, "social activity method" (SAM), and illustrate some of its applications. I shall introduce a new scheme for "modes of recontextualisation" that enables the analysis of the ways in which one activity--which might be school mathematics or social research or any…

The Application of Montessori Method in Learning Mathematics: An Experimental Research

ERIC Educational Resources Information Center

Faryadi, Qais

2017-01-01

The prime objective of this research was to investigate whether the Montessori method of learning helped kindergarten pupils improve their mathematical proficiency, critical thinking and problem-solving skills, besides training them to be responsible learners. Quantitative, qualitative, and observational methods were employed in the investigation.…

Evaluate E-loyalty of sales website: a Fuzzy mathematics method

NASA Astrophysics Data System (ADS)

Yi, Ying; Liu, Zhen-Yu; Xiong, Ying-Zi

The study about online consumer loyalty is limited, but how to evaluate the customers' E-loyalty to a sales website is always a noticeable question. By using some methods of fuzzy mathematics, we provide a more accurate way to evaluate E-loyalty of sales website. Moreover, this method can differentiate level and degree of each factor that influences E-loyalty.

Advanced Mathematical Tools in Metrology III

NASA Astrophysics Data System (ADS)

Ciarlini, P.

The Table of Contents for the book is as follows: * Foreword * Invited Papers * The ISO Guide to the Expression of Uncertainty in Measurement: A Bridge between Statistics and Metrology * Bootstrap Algorithms and Applications * The TTRSs: 13 Oriented Constraints for Dimensioning, Tolerancing & Inspection * Graded Reference Data Sets and Performance Profiles for Testing Software Used in Metrology * Uncertainty in Chemical Measurement * Mathematical Methods for Data Analysis in Medical Applications * High-Dimensional Empirical Linear Prediction * Wavelet Methods in Signal Processing * Software Problems in Calibration Services: A Case Study * Robust Alternatives to Least Squares * Gaining Information from Biomagnetic Measurements * Full Papers * Increase of Information in the Course of Measurement * A Framework for Model Validation and Software Testing in Regression * Certification of Algorithms for Determination of Signal Extreme Values during Measurement * A Method for Evaluating Trends in Ozone-Concentration Data and Its Application to Data from the UK Rural Ozone Monitoring Network * Identification of Signal Components by Stochastic Modelling in Measurements of Evoked Magnetic Fields from Peripheral Nerves * High Precision 3D-Calibration of Cylindrical Standards * Magnetic Dipole Estimations for MCG-Data * Transfer Functions of Discrete Spline Filters * An Approximation Method for the Linearization of Tridimensional Metrology Problems * Regularization Algorithms for Image Reconstruction from Projections * Quality of Experimental Data in Hydrodynamic Research * Stochastic Drift Models for the Determination of Calibration Intervals * Short Communications * Projection Method for Lidar Measurement * Photon Flux Measurements by Regularised Solution of Integral Equations * Correct Solutions of Fit Problems in Different Experimental Situations * An Algorithm for the Nonlinear TLS Problem in Polynomial Fitting * Designing Axially Symmetric Electromechanical Systems of

New method for calculating a mathematical expression for streamflow recession

USGS Publications Warehouse

Rutledge, Albert T.

1991-01-01

An empirical method has been devised to calculate the master recession curve, which is a mathematical expression for streamflow recession during times of negligible direct runoff. The method is based on the assumption that the storage-delay factor, which is the time per log cycle of streamflow recession, varies linearly with the logarithm of streamflow. The resulting master recession curve can be nonlinear. The method can be executed by a computer program that reads a data file of daily mean streamflow, then allows the user to select several near-linear segments of streamflow recession. The storage-delay factor for each segment is one of the coefficients of the equation that results from linear least-squares regression. Using results for each recession segment, a mathematical expression of the storage-delay factor as a function of the log of streamflow is determined by linear least-squares regression. The master recession curve, which is a second-order polynomial expression for time as a function of log of streamflow, is then derived using the coefficients of this function.

Mathematics in Finance and Economics: Importance of Teaching Higher Order Mathematical Thinking Skills in Finance

ERIC Educational Resources Information Center

Tularam, Gurudeo Anand

2013-01-01

This paper addresses the importance of teaching mathematics in business and finance schools of tertiary institutions of Australia. The paper explores the nature of thinking and reasoning required for advancement financial or economic studies involves the use of higher order thinking and creativity skills (HOTS) for teaching in mathematics classes.…

Smooth Transition for Advancement to Graduate Education (STAGE) for Underrepresented Groups in the Mathematical Sciences Pilot Project: Broadening Participation through Mentoring

ERIC Educational Resources Information Center

Eubanks-Turner, Christina; Beaulieu, Patricia; Pal, Nabendu

2018-01-01

The Smooth Transition for Advancement to Graduate Education (STAGE) project was a three-year pilot project designed to mentor undergraduate students primarily from under-represented groups in the mathematical sciences. The STAGE pilot project focused on mentoring students as they transitioned from undergraduate education to either graduate school…

All Students Need Advanced Mathematics. Math Works

ERIC Educational Resources Information Center

Achieve, Inc., 2013

2013-01-01

This fact sheet explains that to thrive in today's world, all students will need to graduate with very strong math skills. That can only mean one thing: advanced math courses are now essential math courses. Highlights of this paper include: (1) Advanced math equals college success; (2) Advanced math equals career opportunity; and (3) Advanced math…

The Effectiveness of Robotics as a Manipulative in Mathematics Instruction: A Mixed Method Study

ERIC Educational Resources Information Center

Sheehy, Leonard

2017-01-01

Addition of fractions is an important foundation for students to experience success in mathematics. This mixed-methods study was conducted to measure the effectiveness of robotics as a mathematics manipulative with seventh grade students. Two groups of students were established: control and treatment. The control group received teacher-centered…

Predicting Mathematical Aptitude for Higher Education

ERIC Educational Resources Information Center

McDonald, Betty

2008-01-01

This present study seeks to predict mathematical aptitude for higher education by examining the relationship between mathematics results from the Caribbean Examinations Council (CXC) general proficiency examination and the results from the General Certificate of Education (GCE) advanced level examination. This present study arose from a more…

Engineering Undergraduates' Views of A-Level Mathematics and Further Mathematics as Preparation for Their Degree

ERIC Educational Resources Information Center

Darlington, Ellie; Bowyer, Jessica

2017-01-01

An ongoing reform programme of the post-16 Advanced "A"-level qualifications in England and Wales means that pre-university mathematics content and assessment will change from 2017. Undergraduate engineering is a subject that relies heavily on mathematics, and applicants to engineering degree programmes in the UK are required to have…

Advanced Math? Write!

ERIC Educational Resources Information Center

Brandenburg, Sister M. Luka

2002-01-01

High-school mathematics teacher in Rock Island, Illinois, describes plan for using writing assignment to improve student understanding of advanced mathematics. Plan includes the following elements: Start small, be firm with students, make writing assignments count, and inform colleagues. (PKP)

Mathematical modeling in realistic mathematics education

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Mathematics in Literature and Cinema: An Interdisciplinary Course

ERIC Educational Resources Information Center

Chabrán, H. Rafael; Kozek, Mark

2016-01-01

We describe our team-taught, interdisciplinary course "Numb3rs in Lett3rs & Fi1ms: Mathematics in Literature and Cinema," which explores mathematics in the context of modern literature and cinema. Our goal with this course is to advance collaborations between mathematics and the written/theatre-based creative arts.

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

PubMed

Zhang, Gang; Wang, Ai-Fang

2007-07-01

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

Application of differential transformation method for solving dengue transmission mathematical model

NASA Astrophysics Data System (ADS)

Ndii, Meksianis Z.; Anggriani, Nursanti; Supriatna, Asep K.

2018-03-01

The differential transformation method (DTM) is a semi-analytical numerical technique which depends on Taylor series and has application in many areas including Biomathematics. The aim of this paper is to employ the differential transformation method (DTM) to solve system of non-linear differential equations for dengue transmission mathematical model. Analytical and numerical solutions are determined and the results are compared to that of Runge-Kutta method. We found a good agreement between DTM and Runge-Kutta method.

Technology in K-12 Mathematics Classrooms

ERIC Educational Resources Information Center

Ozel, Serkan; Yetkiner, Zeynep Ebrar; Capraro, Robert M.

2008-01-01

Technology integration in mathematics classrooms is important to the field of education, not only because today's society is becoming more and more advanced and reliant upon technology but also because schools are beginning to embrace technology as an essential part of their curricula. The Principles and Standards for School Mathematics (National…

Cognitive assessment in mathematics with the least squares distance method.

PubMed

Ma, Lin; Çetin, Emre; Green, Kathy E

2012-01-01

This study investigated the validation of comprehensive cognitive attributes of an eighth-grade mathematics test using the least squares distance method and compared performance on attributes by gender and region. A sample of 5,000 students was randomly selected from the data of the 2005 Turkish national mathematics assessment of eighth-grade students. Twenty-five math items were assessed for presence or absence of 20 cognitive attributes (content, cognitive processes, and skill). Four attributes were found to be misspecified or nonpredictive. However, results demonstrated the validity of cognitive attributes in terms of the revised set of 17 attributes. The girls had similar performance on the attributes as the boys. The students from the two eastern regions significantly underperformed on the most attributes.

Sharing the Treats of Mathematics in a Senior Capstone Course

ERIC Educational Resources Information Center

Shifflet, Daniel R.

2013-01-01

In this paper we discuss why a senior capstone course is the perfect setting to reward graduating seniors with some of the more fun and interesting aspects of advanced mathematics. We provide a beginner's list of topics to consider as well as a method of implementing these tidbits outside of the classroom if time is an issue.

Mathematical Difficulty: Does Early Intervention Enhance Mathematical Performance?

ERIC Educational Resources Information Center

Graham, Jennifer

2008-01-01

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

Mathematical Visualization

ERIC Educational Resources Information Center

Rogness, Jonathan

2011-01-01

Advances in computer graphics have provided mathematicians with the ability to create stunning visualizations, both to gain insight and to help demonstrate the beauty of mathematics to others. As educators these tools can be particularly important as we search for ways to work with students raised with constant visual stimulation, from video games…

Exploring mathematics anxiety and attitude: Mathematics students' experiences

NASA Astrophysics Data System (ADS)

Sahri, Nurul Ashikin; Kamaruzaman, Wan Nur Farahdalila Wan; Jamil, Jastini Mohd.; Shaharanee, Izwan Nizal Mohd.

2017-11-01

A quantitative and correlational, survey methods were used to investigate the relationships among mathematical anxiety and attitude toward student's mathematics performance. Participants were 100 students volunteer to enroll in undergraduate Industrial Statistics, Decision Sciences and Business Mathematics at one of northern university in Malaysia. Survey data consisted of demographic items and Likert scale items. The collected data was analyzed by using the idea of correlation and regression analysis. The results indicated that there was a significant positive relationship between students' attitude and mathematics anxiety. Results also indicated that a substantial positive effect of students' attitude and mathematics anxiety in students' achievement. Further study can be conducted on how mathematical anxiety and attitude toward mathematics affects can be used to predict the students' performance in the class.

Handwritten mathematical symbols dataset.

PubMed

Chajri, Yassine; Bouikhalene, Belaid

2016-06-01

Due to the technological advances in recent years, paper scientific documents are used less and less. Thus, the trend in the scientific community to use digital documents has increased considerably. Among these documents, there are scientific documents and more specifically mathematics documents. In this context, we present our own dataset of handwritten mathematical symbols composed of 10,379 images. This dataset gathers Arabic characters, Latin characters, Arabic numerals, Latin numerals, arithmetic operators, set-symbols, comparison symbols, delimiters, etc.

Mathematical Rigor in the Common Core

ERIC Educational Resources Information Center

Hull, Ted H.; Balka, Don S.; Miles, Ruth Harbin

2013-01-01

A whirlwind of activity surrounds the topic of teaching and learning mathematics. The driving forces are a combination of changes in assessment and advances in technology that are being spurred on by the introduction of content in the Common Core State Standards for Mathematical Practice. Although the issues are certainly complex, the same forces…

Analyzing the Teaching of Advanced Mathematics Courses via the Enacted Example Space

ERIC Educational Resources Information Center

Fukawa-Connelly, Timothy Patrick; Newton, Charlene

2014-01-01

Examples are believed to be very important in developing conceptual understanding of mathematical ideas, useful both in mathematics research and instruction (Bills & Watson in "Educational Studies in Mathematics" 69:77-79, 2008; Mason & Watson, 2008; Bills & Tall, 1998; Tall & Vinner, 1981). In this study, we draw on the…

A new adaptive estimation method of spacecraft thermal mathematical model with an ensemble Kalman filter

NASA Astrophysics Data System (ADS)

Akita, T.; Takaki, R.; Shima, E.

2012-04-01

An adaptive estimation method of spacecraft thermal mathematical model is presented. The method is based on the ensemble Kalman filter, which can effectively handle the nonlinearities contained in the thermal model. The state space equations of the thermal mathematical model is derived, where both temperature and uncertain thermal characteristic parameters are considered as the state variables. In the method, the thermal characteristic parameters are automatically estimated as the outputs of the filtered state variables, whereas, in the usual thermal model correlation, they are manually identified by experienced engineers using trial-and-error approach. A numerical experiment of a simple small satellite is provided to verify the effectiveness of the presented method.

Preservice Teachers' Reconciliation of an Epistemological Issue in an Integrated Mathematics/Science Methods Course

ERIC Educational Resources Information Center

Cormas, Peter C.

2017-01-01

Preservice teachers in six sections (n = 87) of a sequenced, methodological and process-integrated elementary mathematics/science methods course were able to reconcile an issue centered on a similar area of epistemology. Preservice teachers participated in a science inquiry lesson on biological classification and a mathematics problem-solving…

Pedagogical Applications from Real Analysis for Secondary Mathematics Teachers

ERIC Educational Resources Information Center

Wasserman, Nicholas; Weber, Keith

2017-01-01

In this article, we consider the potential influences of the study of proofs in advanced mathematics on secondary mathematics teaching. Thus far, the literature has highlighted the benefits of applying the conclusions of particular proofs to secondary content and of developing a more general sense of disciplinary practices in mathematics in…

The impact of rigorous mathematical thinking as learning method toward geometry understanding

NASA Astrophysics Data System (ADS)

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

2018-05-01

To reach higher order thinking skill, needed to be mastered the conceptual understanding. RMT is a unique realization of the cognitive conceptual construction approach based on Mediated Learning Experience (MLE) theory by Feurstein and Vygotsky’s sociocultural theory. This was quasi experimental research which was comparing the experimental class that was given Rigorous Mathematical Thinking (RMT) as learning method and control class that was given Direct Learning (DL) as the conventional learning activity. This study examined whether there was different effect of two learning method toward conceptual understanding of Junior High School students. The data was analyzed by using Independent t-test and obtained a significant difference of mean value between experimental and control class on geometry conceptual understanding. Further, by semi-structure interview known that students taught by RMT had deeper conceptual understanding than students who were taught by conventional way. By these result known that Rigorous Mathematical Thinking (RMT) as learning method have positive impact toward Geometry conceptual understanding.

What do mathematics teachers and teacher trainees know about the history of mathematics?

NASA Astrophysics Data System (ADS)

Gazit, Avikam

2013-06-01

The aim of this study is to present the findings of a study that examined the knowledge of mathematics teachers and teacher trainees, in different tracks, about the concepts, topics and characters from the history of mathematics. The findings indicate a lack of knowledge concerning most of the topics examined. Only about 40% of the participants knew about the origin of our counting system and the only item that reached above 50% was the item relating to the man who edited the book which is the basis for the plane geometry - Euclid (about 83%). Another meaningful finding was that the group with the highest score was that of mathematics teacher trainees in the accelerated track - a unique training scheme for middle school teachers (65.7%). The group with the lowest score was that of the elementary school mathematics student teachers (19.3%). One obvious conclusion is that we need to strengthen the knowledge of the history of mathematics in teacher training and in-service teachers' advanced studies.

Mathematical correlation of modal-parameter-identification methods via system-realization theory

NASA Technical Reports Server (NTRS)

Juang, Jer-Nan

1987-01-01

A unified approach is introduced using system-realization theory to derive and correlate modal-parameter-identification methods for flexible structures. Several different time-domain methods are analyzed and treated. A basic mathematical foundation is presented which provides insight into the field of modal-parameter identification for comparison and evaluation. The relation among various existing methods is established and discussed. This report serves as a starting point to stimulate additional research toward the unification of the many possible approaches for modal-parameter identification.

Handwritten mathematical symbols dataset

PubMed Central

Chajri, Yassine; Bouikhalene, Belaid

2016-01-01

Due to the technological advances in recent years, paper scientific documents are used less and less. Thus, the trend in the scientific community to use digital documents has increased considerably. Among these documents, there are scientific documents and more specifically mathematics documents. In this context, we present our own dataset of handwritten mathematical symbols composed of 10,379 images. This dataset gathers Arabic characters, Latin characters, Arabic numerals, Latin numerals, arithmetic operators, set-symbols, comparison symbols, delimiters, etc. PMID:27006975

Peirce's Philosophy of Mathematical Education: Fostering Reasoning Abilities for Mathematical Inquiry

ERIC Educational Resources Information Center

Campos, Daniel G.

2010-01-01

I articulate Charles S. Peirce's philosophy of mathematical education as related to his conception of mathematics, the nature of its method of inquiry, and especially, the reasoning abilities required for mathematical inquiry. The main thesis is that Peirce's philosophy of mathematical education primarily aims at fostering the development of the…

Equating TIMSS Mathematics Subtests with Nonlinear Equating Methods Using NEAT Design: Circle-Arc Equating Approaches

ERIC Educational Resources Information Center

Ozdemir, Burhanettin

2017-01-01

The purpose of this study is to equate Trends in International Mathematics and Science Study (TIMSS) mathematics subtest scores obtained from TIMSS 2011 to scores obtained from TIMSS 2007 form with different nonlinear observed score equating methods under Non-Equivalent Anchor Test (NEAT) design where common items are used to link two or more test…

Use of CAS in Secondary School: A Factor Influencing the Transition to University-Level Mathematics?

ERIC Educational Resources Information Center

Varsavsky, Cristina

2012-01-01

Australian secondary school systems offer three levels of senior (year 12) mathematics studies, none of them compulsory: elementary, intermediate and advanced. The intermediate and advanced studies prepare students for further mathematics studies at university level. In the state of Victoria, there are two versions of intermediate mathematics: one…

Mathematical correlation of modal parameter identification methods via system realization theory

NASA Technical Reports Server (NTRS)

Juang, J. N.

1986-01-01

A unified approach is introduced using system realization theory to derive and correlate modal parameter identification methods for flexible structures. Several different time-domain and frequency-domain methods are analyzed and treated. A basic mathematical foundation is presented which provides insight into the field of modal parameter identification for comparison and evaluation. The relation among various existing methods is established and discussed. This report serves as a starting point to stimulate additional research towards the unification of the many possible approaches for modal parameter identification.

An Introduction to Graphical and Mathematical Methods for Detecting Heteroscedasticity in Linear Regression.

ERIC Educational Resources Information Center

Thompson, Russel L.

Homoscedasticity is an important assumption of linear regression. This paper explains what it is and why it is important to the researcher. Graphical and mathematical methods for testing the homoscedasticity assumption are demonstrated. Sources of homoscedasticity and types of homoscedasticity are discussed, and methods for correction are…

Advancement of understanding in physical science and reduction of mathematical anxiety through the use of supplemental mathematics material

NASA Astrophysics Data System (ADS)

Roberson, James Chadwick

The purpose of this study was to determine if supplementary mathematics materials (created to be complementary to a physical science course) could provide a significant change in the attitudes and performance of the students involved. The supplementary text was provided in the form of a booklet. Participants were students in a physical science class. Students were given surveys to evaluate existing knowledge of physical science, mathematics skill, and mathematics anxiety in the context of a science class. Students were divided into control and experimental groups by lab section, with the experimental group receiving a supplemental booklet. At the end of the semester, another anxiety survey was given. The anxiety surveys and test grades were compared between groups. Anxiety scores were compared between the beginning and end of the semester within each group. Too few students reported using the booklets for a reliable statistical comparison (of grades) to be made. A statistically significant difference in mathematics anxiety levels was found between the groups.

A mathematical method for precisely calculating the radiographic angles of the cup after total hip arthroplasty.

PubMed

Zhao, Jing-Xin; Su, Xiu-Yun; Xiao, Ruo-Xiu; Zhao, Zhe; Zhang, Li-Hai; Zhang, Li-Cheng; Tang, Pei-Fu

2016-11-01

We established a mathematical method to precisely calculate the radiographic anteversion (RA) and radiographic inclination (RI) angles of the acetabular cup based on anterior-posterior (AP) pelvic radiographs after total hip arthroplasty. Using Mathematica software, a mathematical model for an oblique cone was established to simulate how AP pelvic radiographs are obtained and to address the relationship between the two-dimensional and three-dimensional geometry of the opening circle of the cup. In this model, the vertex was the X-ray beam source, and the generatrix was the ellipse in radiographs projected from the opening circle of the acetabular cup. Using this model, we established a series of mathematical formulas to reveal the differences between the true RA and RI cup angles and the measurements results achieved using traditional methods and AP pelvic radiographs and to precisely calculate the RA and RI cup angles based on post-operative AP pelvic radiographs. Statistical analysis indicated that traditional methods should be used with caution if traditional measurements methods are used to calculate the RA and RI cup angles with AP pelvic radiograph. The entire calculation process could be performed by an orthopedic surgeon with mathematical knowledge of basic matrix and vector equations. Copyright © 2016 IPEM. Published by Elsevier Ltd. All rights reserved.

Use of CAS in secondary school: a factor influencing the transition to university-level mathematics?

NASA Astrophysics Data System (ADS)

Varsavsky, Cristina

2012-01-01

Australian secondary school systems offer three levels of senior (year 12) mathematics studies, none of them compulsory: elementary, intermediate and advanced. The intermediate and advanced studies prepare students for further mathematics studies at university level. In the state of Victoria, there are two versions of intermediate mathematics: one where students learn and are examined with a computer algebra system (CAS) and another where students can only use scientific calculators. This study compares the performance of 1240 students as they transitioned to traditional university-level mathematics and according to whether they learned intermediate mathematics with or without the assistance of a CAS. This study concludes that students without CAS show a slight advantage, but the most important factor affecting student performance is the uptake of advanced-level mathematics studies in secondary school.

The Mathematics Education Debates: Preparing Students to Become Professionally Active Mathematics Teachers

ERIC Educational Resources Information Center

Munakata, Mika

2010-01-01

The Mathematics Education Debate is an assignment designed for and implemented in an undergraduate mathematics methods course for prospective secondary school mathematics teachers. For the assignment, students read and analyze current research and policy reports related to mathematics education, prepare and present their positions, offer…

Which Preschool Mathematics Competencies Are Most Predictive of Fifth Grade Achievement?

PubMed Central

Nguyen, Tutrang; Watts, Tyler W.; Duncan, Greg J.; Clements, Douglas H.; Sarama, Julie S.; Wolfe, Christopher; Spitler, Mary Elaine

2016-01-01

In an effort to promote best practices regarding mathematics teaching and learning at the preschool level, national advisory panels and organizations have emphasized the importance of children’s emergent counting and related competencies, such as the ability to verbally count, maintain one-to-one correspondence, count with cardinality, subitize, and count forward or backward from a given number. However, little research has investigated whether the kind of mathematical knowledge promoted by the various standards documents actually predict later mathematics achievement. The present study uses longitudinal data from a primarily low-income and minority sample of children to examine the extent to which preschool mathematical competencies, specifically basic and advanced counting, predict fifth grade mathematics achievement. Using regression analyses, we find early numeracy abilities to be the strongest predictors of later mathematics achievement, with advanced counting competencies more predictive than basic counting competencies. Our results highlight the significance of preschool mathematics knowledge for future academic achievement. PMID:27057084

Which Preschool Mathematics Competencies Are Most Predictive of Fifth Grade Achievement?

PubMed

Nguyen, Tutrang; Watts, Tyler W; Duncan, Greg J; Clements, Douglas H; Sarama, Julie S; Wolfe, Christopher; Spitler, Mary Elaine

In an effort to promote best practices regarding mathematics teaching and learning at the preschool level, national advisory panels and organizations have emphasized the importance of children's emergent counting and related competencies, such as the ability to verbally count, maintain one-to-one correspondence, count with cardinality, subitize, and count forward or backward from a given number. However, little research has investigated whether the kind of mathematical knowledge promoted by the various standards documents actually predict later mathematics achievement. The present study uses longitudinal data from a primarily low-income and minority sample of children to examine the extent to which preschool mathematical competencies, specifically basic and advanced counting, predict fifth grade mathematics achievement. Using regression analyses, we find early numeracy abilities to be the strongest predictors of later mathematics achievement, with advanced counting competencies more predictive than basic counting competencies. Our results highlight the significance of preschool mathematics knowledge for future academic achievement.

Collaborating to Improve Inquiry-Based Teaching in Elementary Science and Mathematics Methods Courses

ERIC Educational Resources Information Center

Magee, Paula A.; Flessner, Ryan

2012-01-01

This study examines the effect of promoting inquiry-based teaching (IBT) through collaboration between a science methods course and mathematics methods course in an elementary teacher education program. During the collaboration, preservice elementary teacher (PST) candidates experienced 3 different types of inquiry as a way to foster increased…

The Preparedness of Preservice Secondary Mathematics Teachers to Teach Statistics: A Cross-Institutional Mixed Methods Study

ERIC Educational Resources Information Center

Lovett, Jennifer Nickell

2016-01-01

The purpose of this study is to provide researchers, mathematics educators, and statistics educators information about the current state of preservice secondary mathematics teachers' preparedness to teach statistics. To do so, this study employed an explanatory mixed methods design to quantitatively examine the statistical knowledge and statistics…

Mathematics Content Coverage and Student Learning in Kindergarten

ERIC Educational Resources Information Center

Engel, Mimi; Claessens, Amy; Watts, Tyler; Farkas, George

2016-01-01

Analyzing data from two nationally representative kindergarten cohorts, we examine the mathematics content teachers cover in kindergarten. We expand upon prior research, finding that kindergarten teachers report emphasizing basic mathematics content. Although teachers reported increased coverage of advanced content between the 1998-1999 and…

Enhancing School Mathematics Culturally: A Path of Reconciliation

ERIC Educational Resources Information Center

Aikenhead, Glen S.

2017-01-01

Culturally responsive or place-based school mathematics that focuses on Indigenous students has an established presence in the research literature. This culture-based innovation represents a historical shift from conventional approaches to mathematics education. Moreover, it has demonstratively advanced the academic achievement for both Indigenous…

Molecular modeling: An open invitation for applied mathematics

NASA Astrophysics Data System (ADS)

Mezey, Paul G.

2013-10-01

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

Unstructured viscous grid generation by advancing-front method

NASA Technical Reports Server (NTRS)

Pirzadeh, Shahyar

1993-01-01

A new method of generating unstructured triangular/tetrahedral grids with high-aspect-ratio cells is proposed. The method is based on new grid-marching strategy referred to as 'advancing-layers' for construction of highly stretched cells in the boundary layer and the conventional advancing-front technique for generation of regular, equilateral cells in the inviscid-flow region. Unlike the existing semi-structured viscous grid generation techniques, the new procedure relies on a totally unstructured advancing-front grid strategy resulting in a substantially enhanced grid flexibility and efficiency. The method is conceptually simple but powerful, capable of producing high quality viscous grids for complex configurations with ease. A number of two-dimensional, triangular grids are presented to demonstrate the methodology. The basic elements of the method, however, have been primarily designed with three-dimensional problems in mind, making it extendible for tetrahedral, viscous grid generation.

Mathematical modeling for Phase I cancer trials: A study of metronomic vinorelbine for advanced non-small cell lung cancer (NSCLC) and mesothelioma patients.

PubMed

Barlesi, Fabrice; Imbs, Diane-Charlotte; Tomasini, Pascale; Greillier, Laurent; Galloux, Melissa; Testot-Ferry, Albane; Garcia, Mélanie; Elharrar, Xavier; Pelletier, Annick; André, Nicolas; Mascaux, Céline; Lacarelle, Bruno; Cheikh, Raouf El; Serre, Raphaël; Ciccolini, Joseph; Barbolosi, Dominique

2017-07-18

Using mathematical modelling allows to select a treatment's regimen across infinite possibilities. Here, we report the phase I assessment of a new schedule for metronomic vinorelbine in treating refractory advanced NSCLC and mesothelioma patients. Overall, 13 patients were screened and 12 were treated (50% male, median age: 68yrs), including 9 NSCLC patients. All patients received at least one week (3 doses) of treatment. At data cut-off, the median length of treatment was 6.5 weeks (1-32+). All the patients presented with at least one adverse event (AE) and six patients with a severe AE (SAE). One partial response and 5 stable diseases were observed. The median OS was 6.4 months (95% CI, 4.8 to 12 months). The median and mean vinorelbine's AUC were 122 ng/ml*h and 159 ng/ml*h, respectively, with the higher plasmatic vinorelbine exposure associated with the best ORR (difference of AUC comparison between responders and non-responders, p-value 0.017). The mathematical modelling determined the administration of vinorelbine, 60 mg on Day 1, 30 mg on Day 2 and 60 mg on Day 4 weekly until progression, as the best schedule. Advanced NSCLC or mesothelioma patients progressing after standard treatment were eligible for the trial. NCT02555007. Responses with acceptable safety profile were observed in heavily pretreated NSCLC and mesothelioma patients using oral vinorelbine at this metronomic dosage based on a mathematic modeling. This study demonstrates the feasibility of this new type of approach, as mathematical modeling may help to rationally decide the better regimen to be clinically tested across infinite possibilities.

Pre-Service Secondary Mathematics Teachers' Reflections on Good and Bad Mathematics Teaching

ERIC Educational Resources Information Center

Dayal, Hem Chand

2013-01-01

Researchers suggest that teachers' beliefs about teaching are strongly influenced by their personal experiences with mathematics. This study aimed to explore Pacific Island pre-service secondary mathematics teachers' perceptions about good and bad mathematics teachers. Thirty pre-service teachers, enrolled in a mathematics teaching methods course…

Mathematics: Report of the Project 2061 Phase I Mathematics Panel.

ERIC Educational Resources Information Center

Blackwell, David; Henkin, Leon

This is one of five panel reports that have been prepared as part of the first phase of Project 2061, a long-term multipurpose undertaking of the American Association for the Advancement of Science designed to help reform science, mathematics, and technology education in the United States. Major sections included are: (1) "Introduction";…

Do Advanced Mathematics Skills Predict Success in Biology and Chemistry Degrees?

ERIC Educational Resources Information Center

Adkins, Michael; Noyes, Andrew

2018-01-01

The mathematical preparedness of science undergraduates has been a subject of debate for some time. This paper investigates the relationship between school mathematics attainment and degree outcomes in biology and chemistry across England, a much larger scale of analysis than has hitherto been reported in the literature. A unique dataset which…

Theoretical Mathematics

NASA Astrophysics Data System (ADS)

Stöltzner, Michael

Answering to the double-faced influence of string theory on mathematical practice and rigour, the mathematical physicists Arthur Jaffe and Frank Quinn have contemplated the idea that there exists a `theoretical' mathematics (alongside `theoretical' physics) whose basic structures and results still require independent corroboration by mathematical proof. In this paper, I shall take the Jaffe-Quinn debate mainly as a problem of mathematical ontology and analyse it against the backdrop of two philosophical views that are appreciative towards informal mathematical development and conjectural results: Lakatos's methodology of proofs and refutations and John von Neumann's opportunistic reading of Hilbert's axiomatic method. The comparison of both approaches shows that mitigating Lakatos's falsificationism makes his insights about mathematical quasi-ontology more relevant to 20th century mathematics in which new structures are introduced by axiomatisation and not necessarily motivated by informal ancestors. The final section discusses the consequences of string theorists' claim to finality for the theory's mathematical make-up. I argue that ontological reductionism as advocated by particle physicists and the quest for mathematically deeper axioms do not necessarily lead to identical results.

Advanced Ablative Insulators and Methods of Making Them

NASA Technical Reports Server (NTRS)

Congdon, William M.

2005-01-01

Advanced ablative (more specifically, charring) materials that provide temporary protection against high temperatures, and advanced methods of designing and manufacturing insulators based on these materials, are undergoing development. These materials and methods were conceived in an effort to replace the traditional thermal-protection systems (TPSs) of re-entry spacecraft with robust, lightweight, better-performing TPSs that can be designed and manufactured more rapidly and at lower cost. These materials and methods could also be used to make improved TPSs for general aerospace, military, and industrial applications.

Pre-Service Teachers' Mathematics Language and Reflection in the Context of an Early Childhood Mathematics Methods Course

ERIC Educational Resources Information Center

Boyd, Soleil

2016-01-01

Preschool teachers are expected to engage young children in challenging and supportive mathematics learning. Rich and responsive language experiences in mathematics support children's language acquisition and engagement related to mathematics, however, such engaging experiences may be minimally available to many young children. Professional…

Using Mixed Methods to Analyze Video Data: A Mathematics Teacher Professional Development Example

ERIC Educational Resources Information Center

DeCuir-Gunby, Jessica T.; Marshall, Patricia L.; McCulloch, Allison W.

2012-01-01

This article uses data from 65 teachers participating in a K-2 mathematics professional development research project as an example of how to analyze video recordings of teachers' classroom lessons using mixed methods. Through their discussion, the authors demonstrate how using a mixed methods approach to classroom video analysis allows researchers…

The Implementation of APIQ Creative Mathematics Game Method in the Subject Matter of Greatest Common Factor and Least Common Multiple in Elementary School

NASA Astrophysics Data System (ADS)

Rahman, Abdul; Saleh Ahmar, Ansari; Arifin, A. Nurani M.; Upu, Hamzah; Mulbar, Usman; Alimuddin; Arsyad, Nurdin; Ruslan; Rusli; Djadir; Sutamrin; Hamda; Minggi, Ilham; Awi; Zaki, Ahmad; Ahmad, Asdar; Ihsan, Hisyam

2018-01-01

One of causal factors for uninterested feeling of the students in learning mathematics is a monotonous learning method, like in traditional learning method. One of the ways for motivating students to learn mathematics is by implementing APIQ (Aritmetika Plus Intelegensi Quantum) creative mathematics game method. The purposes of this research are (1) to describe students’ responses toward the implementation of APIQ creative mathematics game method on the subject matter of Greatest Common Factor (GCF) and Least Common Multiple (LCM) and (2) to find out whether by implementing this method, the student’s learning completeness will improve or not. Based on the results of this research, it is shown that the responses of the students toward the implementation of APIQ creative mathematics game method in the subject matters of GCF and LCM were good. It is seen in the percentage of the responses were between 76-100%. (2) The implementation of APIQ creative mathematics game method on the subject matters of GCF and LCM improved the students’ learning.

TEACHING OF ADVANCED MATHEMATICAL CONCEPTS TO CULTURALLY DISADVANTAGED ELEMENTARY SCHOOL CHILDREN.

ERIC Educational Resources Information Center

RUPLEY, WILLIAM H.

THE SUCCESS OF DISCOVERY MATHEMATICS TEACHING IN THE ELEMENTARY SCHOOL WAS TESTED OVER A 1-YEAR PERIOD. THE PROJECT WAS INTENDED TO SEE IF A TRAINED MATHEMATICIAN WORKING AT AN ELEMENTARY SCHOOL WITH DISADVANTAGED CHILDREN COULD (1) MOTIVATE THE CHILDREN TO BE INTERESTED IN SCHOOL WORK BY INTERESTING THEM IN MATHEMATICS AND (2) COMMUNICATE WITH…

Mathematics and Comprehensive Ideals

ERIC Educational Resources Information Center

Watson, Anne

2011-01-01

This article revisits methods and debates about teaching mathematics that were common in the 1980s and early 1990s, and then moves up to date with the findings from three mathematics departments that set out to make a difference for their lowest attaining students. The methods they used were distinctly focused on core mathematical ideas, and how…

Advances in Adaptive Control Methods

NASA Technical Reports Server (NTRS)

Nguyen, Nhan

2009-01-01

This poster presentation describes recent advances in adaptive control technology developed by NASA. Optimal Control Modification is a novel adaptive law that can improve performance and robustness of adaptive control systems. A new technique has been developed to provide an analytical method for computing time delay stability margin for adaptive control systems.

Mathematical Perspectives

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

Glimm, J.

2009-10-14

Progress for the past decade or so has been extraordinary. The solution of Fermat's Last Theorem [11] and of the Poincare Conjecture [1] have resolved two of the most outstanding challenges to mathematics. For both cases, deep and advanced theories and whole subfields of mathematics came into play and were developed further as part of the solutions. And still the future is wide open. Six of the original seven problems from the Clay Foundation challenge remain open, the 23 DARPA challenge problems are open. Entire new branches of mathematics have been developed, including financial mathematics and the connection between geometrymore » and string theory, proposed to solve the problems of quantized gravity. New solutions of the Einstein equations, inspired by shock wave theory, suggest a cosmology model which fits accelerating expansion of the universe possibly eliminating assumptions of 'dark matter'. Intellectual challenges and opportunities for mathematics are greater than ever. The role of mathematics in society continues to grow; with this growth comes new opportunities and some growing pains; each will be analyzed here. We see a broadening of the intellectual and professional opportunities and responsibilities for mathematicians. These trends are also occuring across all of science. The response can be at the level of the professional societies, which can work to deepen their interactions, not only within the mathematical sciences, but also with other scientific societies. At a deeper level, the choices to be made will come from individual mathematicians. Here, of course, the individual choices will be varied, and we argue for respect and support for this diversity of responses. In such a manner, we hope to preserve the best of the present while welcoming the best of the new.« less

Comparison of anaerobic threshold determined by visual and mathematical methods in healthy women.

PubMed

Higa, M N; Silva, E; Neves, V F C; Catai, A M; Gallo, L; Silva de Sá, M F

2007-04-01

Several methods are used to estimate anaerobic threshold (AT) during exercise. The aim of the present study was to compare AT obtained by a graphic visual method for the estimate of ventilatory and metabolic variables (gold standard), to a bi-segmental linear regression mathematical model of Hinkley's algorithm applied to heart rate (HR) and carbon dioxide output (VCO2) data. Thirteen young (24 +/- 2.63 years old) and 16 postmenopausal (57 +/- 4.79 years old) healthy and sedentary women were submitted to a continuous ergospirometric incremental test on an electromagnetic braking cycloergometer with 10 to 20 W/min increases until physical exhaustion. The ventilatory variables were recorded breath-to-breath and HR was obtained beat-to-beat over real time. Data were analyzed by the nonparametric Friedman test and Spearman correlation test with the level of significance set at 5%. Power output (W), HR (bpm), oxygen uptake (VO2; mL kg(-1) min(-1)), VO2 (mL/min), VCO2 (mL/min), and minute ventilation (VE; L/min) data observed at the AT level were similar for both methods and groups studied (P > 0.05). The VO2 (mL kg(-1) min(-1)) data showed significant correlation (P < 0.05) between the gold standard method and the mathematical model when applied to HR (rs = 0.75) and VCO2 (rs = 0.78) data for the subjects as a whole (N = 29). The proposed mathematical method for the detection of changes in response patterns of VCO2 and HR was adequate and promising for AT detection in young and middle-aged women, representing a semi-automatic, non-invasive and objective AT measurement.

Preservice Teachers' Video Simulations and Subsequent Noticing: A Practice-Based Method to Prepare Mathematics Teachers

ERIC Educational Resources Information Center

Amador, Julie M.

2017-01-01

The purpose of this study was to implement a Video Simulation Task in a mathematics methods teacher education course to engage preservice teachers in considering both the teaching and learning aspects of mathematics lesson delivery. Participants anticipated student and teacher thinking and created simulations, in which they acted out scenes on a…

Advanced Mathematics. Training Module 1.303.3.77.

ERIC Educational Resources Information Center

Kirkwood Community Coll., Cedar Rapids, IA.

This document is an instructional module prepared in objective form for use by an instructor familiar with mathematics as applied to water and wastewater treatment plant operation. Included are objectives, instructor guides and student handouts. This is the third level of a three module series and is concerned with statistics, total head, steady…

Advanced propulsion for LEO-Moon transport. 1: A method for evaluating advanced propulsion performance

NASA Technical Reports Server (NTRS)

Stern, Martin O.

1992-01-01

This report describes a study to evaluate the benefits of advanced propulsion technologies for transporting materials between low Earth orbit and the Moon. A relatively conventional reference transportation system, and several other systems, each of which includes one advanced technology component, are compared in terms of how well they perform a chosen mission objective. The evaluation method is based on a pairwise life-cycle cost comparison of each of the advanced systems with the reference system. Somewhat novel and economically important features of the procedure are the inclusion not only of mass payback ratios based on Earth launch costs, but also of repair and capital acquisition costs, and of adjustments in the latter to reflect the technological maturity of the advanced technologies. The required input information is developed by panels of experts. The overall scope and approach of the study are presented in the introduction. The bulk of the paper describes the evaluation method; the reference system and an advanced transportation system, including a spinning tether in an eccentric Earth orbit, are used to illustrate it.

How to begin a new topic in mathematics: does it matter to students' performance in mathematics?

PubMed

Ma, Xin; Papanastasiou, Constantinos

2006-08-01

The authors use Canadian data from the Third International Mathematics and Science Study to examine six instructional methods that mathematics teachers use to introduce new topics in mathematics on performance of eighth-grade students in six mathematical areas (mathematics as a whole, algebra, data analysis, fraction, geometry, and measurement). Results of multilevel analysis with students nested within schools show that the instructional methods of having the teacher explain the rules and definitions and looking at the textbook while the teacher talks about it had little instructional effects on student performance in any mathematical area. In contrast, the instructional method in which teachers try to solve an example related to the new topic was effective in promoting student performance across all mathematical areas.

Domain Decomposition By the Advancing-Partition Method

NASA Technical Reports Server (NTRS)

Pirzadeh, Shahyar Z.

2008-01-01

A new method of domain decomposition has been developed for generating unstructured grids in subdomains either sequentially or using multiple computers in parallel. Domain decomposition is a crucial and challenging step for parallel grid generation. Prior methods are generally based on auxiliary, complex, and computationally intensive operations for defining partition interfaces and usually produce grids of lower quality than those generated in single domains. The new technique, referred to as "Advancing Partition," is based on the Advancing-Front method, which partitions a domain as part of the volume mesh generation in a consistent and "natural" way. The benefits of this approach are: 1) the process of domain decomposition is highly automated, 2) partitioning of domain does not compromise the quality of the generated grids, and 3) the computational overhead for domain decomposition is minimal. The new method has been implemented in NASA's unstructured grid generation code VGRID.

A MATLAB-Aided Method for Teaching Calculus-Based Business Mathematics

ERIC Educational Resources Information Center

Liang, Jiajuan; Pan, William S. Y.

2009-01-01

MATLAB is a powerful package for numerical computation. MATLAB contains a rich pool of mathematical functions and provides flexible plotting functions for illustrating mathematical solutions. The course of calculus-based business mathematics consists of two major topics: 1) derivative and its applications in business; and 2) integration and its…

An Enzymatic Clinical Chemistry Laboratory Experiment Incorporating an Introduction to Mathematical Method Comparison Techniques

ERIC Educational Resources Information Center

Duxbury, Mark

2004-01-01

An enzymatic laboratory experiment based on the analysis of serum is described that is suitable for students of clinical chemistry. The experiment incorporates an introduction to mathematical method-comparison techniques in which three different clinical glucose analysis methods are compared using linear regression and Bland-Altman difference…

Career Advancement Outcomes in Academic Science, Technology, Engineering and Mathematics (STEM): Gender, Mentoring Resources, and Homophily

NASA Astrophysics Data System (ADS)

Lee, Sang Eun

This dissertation examines gender differences in career advancement outcomes among academic science, technology, engineering and mathematics (STEM) scientists. In particular, this research examines effects of gender, PhD advisors and postdoctoral supervisors mentoring resources and gender homophily in the mentoring dyads on the career advancement outcomes at early career stages. Female academic scientists have disadvantages in the career progress in the academic STEM. They tend to fall behind throughout their career paths and to leave the field compared to their male colleagues. Researchers have found that gender differences in the career advancement are shaped by gender-biased evaluations derived from gender stereotypes. Other studies demonstrate the positive impacts of mentoring and gender homophily in the mentoring dyads. To add greater insights to the current findings of female academic scientists' career disadvantages, this dissertation investigates comprehensive effects of gender, mentoring, and gender homophily in the mentoring dyads on female scientists' career advancement outcomes in academic science. Based on the Status Characteristics Theory, the concept of mentoring, Social Capital Theory, and Ingroup Bias Theory, causal path models are developed to test direct and indirect effects of gender, mentoring resources, and gender homophily on STEM faculty's career advancement. The research models were tested using structural equation modeling (SEM) with data collected from a national survey, funded by the National Science Foundation, completed in 2011 by tenured and tenure-track academic STEM faculty from higher education institutions in the United States. Findings suggest that there is no gender difference in career advancement controlling for mentoring resources and gender homophily in the mentoring dyads and other factors including research productivity and domestic caregiving responsibilities. Findings also show that the positive relationship between

[Research advances in dendrochronology].

PubMed

Fang, Ke-Yan; Chen, Qiu-Yan; Liu, Chang-Zhi; Cao, Chun-Fu; Chen, Ya-Jun; Zhou, Fei-Fei

2014-07-01

Tree-ring studies in China have achieved great advances since the 1990s, particularly for the dendroclimatological studies which have made some influence around the world. However, because of the uneven development, limited attention has been currently paid on the other branches of dendrochronology. We herein briefly compared the advances of dendrochronology in China and of the world and presented suggestions on future dendrochronological studies. Large-scale tree-ring based climate reconstructions in China are highly needed by employing mathematical methods and a high quality tree-ring network of the ring-width, density, stable isotope and wood anatomy. Tree-ring based field climate reconstructions provide potentials on explorations of climate forcings during the reconstructed periods via climate diagnosis and process simulation.

Reducible or irreducible? Mathematical reasoning and the ontological method.

PubMed

Fisher, William P

2010-01-01

Science is often described as nothing but the practice of measurement. This perspective follows from longstanding respect for the roles mathematics and quantification have played as media through which alternative hypotheses are evaluated and experience becomes better managed. Many figures in the history of science and psychology have contributed to what has been called the "quantitative imperative," the demand that fields of study employ number and mathematics even when they do not constitute the language in which investigators think together. But what makes an area of study scientific is, of course, not the mere use of number, but communities of investigators who share common mathematical languages for exchanging quantitative and quantitative value. Such languages require rigorous theoretical underpinning, a basis in data sufficient to the task, and instruments traceable to reference standard quantitative metrics. The values shared and exchanged by such communities typically involve the application of mathematical models that specify the sufficient and invariant relationships necessary for rigorous theorizing and instrument equating. The mathematical metaphysics of science are explored with the aim of connecting principles of quantitative measurement with the structures of sufficient reason.

Implementing a Flipped Classroom Approach in a University Numerical Methods Mathematics Course

ERIC Educational Resources Information Center

Johnston, Barbara M.

2017-01-01

This paper describes and analyses the implementation of a "flipped classroom" approach, in an undergraduate mathematics course on numerical methods. The approach replaced all the lecture contents by instructor-made videos and was implemented in the consecutive years 2014 and 2015. The sequential case study presented here begins with an…

Application of mathematical methods of analysis in selection of competing information technologies

NASA Astrophysics Data System (ADS)

Semenov, V. L.; Kadyshev, E. N.; Zakharova, A. N.; Patianova, A. O.; Dulina, G. S.

2018-05-01

The article discusses the use of qualimetry methods using the apparatus of mathematical analysis in the formation of the integral index that allows one to select the best option among competing information technology. The authors propose the use of affine space in the evaluation and selection of competing information technologies.

Advanced Computational Methods for Monte Carlo Calculations

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

Brown, Forrest B.

This course is intended for graduate students who already have a basic understanding of Monte Carlo methods. It focuses on advanced topics that may be needed for thesis research, for developing new state-of-the-art methods, or for working with modern production Monte Carlo codes.

Mathematical aspects of finite element methods for incompressible viscous flows

NASA Technical Reports Server (NTRS)

Gunzburger, M. D.

1986-01-01

Mathematical aspects of finite element methods are surveyed for incompressible viscous flows, concentrating on the steady primitive variable formulation. The discretization of a weak formulation of the Navier-Stokes equations are addressed, then the stability condition is considered, the satisfaction of which insures the stability of the approximation. Specific choices of finite element spaces for the velocity and pressure are then discussed. Finally, the connection between different weak formulations and a variety of boundary conditions is explored.

New Technologies in Mathematics.

ERIC Educational Resources Information Center

Sarmiento, Jorge

An understanding of past technological advancements can help educators understand the influence of new technologies in education. Inventions such as the abacus, logarithms, the slide rule, the calculating machine, computers, and electronic calculators have all found their place in mathematics education. While new technologies can be very useful,…

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.

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

NASA Technical Reports Server (NTRS)

Cruthirds, John E.

2003-01-01

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

The Language of Mathematics: The Importance of Teaching and Learning Mathematical Vocabulary

ERIC Educational Resources Information Center

Riccomini, Paul J.; Smith, Gregory W.; Hughes, Elizabeth M.; Fries, Karen M.

2015-01-01

Vocabulary understanding is a major contributor to overall comprehension in many content areas, including mathematics. Effective methods for teaching vocabulary in all content areas are diverse and long standing. Teaching and learning the language of mathematics is vital for the development of mathematical proficiency. Students' mathematical…

Mathematics. [SITE 2001 Section].

ERIC Educational Resources Information Center

Connell, Michael L., Ed.; Lowery, Norene Vail, Ed.; Harnisch, Delwyn L., Ed.

This document contains the following papers on mathematics from the SITE (Society for Information Technology & Teacher Education) 2001 conference: "Secondary Mathematics Methods Course with Technology Units: Encouraging Pre-Service Teachers To Use Technology" (Rajee Amarasinghe); "Competency Exams in College Mathematics"…

Mathematical modeling of physiological systems: an essential tool for discovery.

PubMed

Glynn, Patric; Unudurthi, Sathya D; Hund, Thomas J

2014-08-28

Mathematical models are invaluable tools for understanding the relationships between components of a complex system. In the biological context, mathematical models help us understand the complex web of interrelations between various components (DNA, proteins, enzymes, signaling molecules etc.) in a biological system, gain better understanding of the system as a whole, and in turn predict its behavior in an altered state (e.g. disease). Mathematical modeling has enhanced our understanding of multiple complex biological processes like enzyme kinetics, metabolic networks, signal transduction pathways, gene regulatory networks, and electrophysiology. With recent advances in high throughput data generation methods, computational techniques and mathematical modeling have become even more central to the study of biological systems. In this review, we provide a brief history and highlight some of the important applications of modeling in biological systems with an emphasis on the study of excitable cells. We conclude with a discussion about opportunities and challenges for mathematical modeling going forward. In a larger sense, the review is designed to help answer a simple but important question that theoreticians frequently face from interested but skeptical colleagues on the experimental side: "What is the value of a model?" Copyright © 2014 Elsevier Inc. All rights reserved.

Throw Away Your Mathematical Handbook! Undergraduate Physics with Wolfram|Alpha, a FREE(!) Internet-Based Mathematical Engine

NASA Astrophysics Data System (ADS)

Looney, Craig W.

2009-10-01

Wolfram|Alpha (http://www.wolframalpha.com/), a free internet-based mathematical engine released earlier this year, represents an orders-of magnitude advance in mathematical power freely available - without money, passwords, or downloads - on the web. Wolfram|Alpha is based on Mathematica, so it can plot functions, take derivatives, solve systems of equations, perform symbolic and numerical integration, and more. These capabilities (especially plotting and integration) will be explored in the context of topics covered in upper level undergraduate physics courses.

Becoming a Teacher Educator: A Self-Study of the Use of Inquiry in a Mathematics Methods Course

ERIC Educational Resources Information Center

Marin, Katherine Ariemma

2014-01-01

This article details the self-study of a beginning teacher educator in her first experience in teaching a mathematics methods course. The transition from teacher to teacher educator is explored through the experience of a course focused on inquiry. Inquiry is embedded within the course from two perspectives: mathematical inquiry and teaching as…

A Case against Computer Symbolic Manipulation in School Mathematics Today.

ERIC Educational Resources Information Center

Waits, Bert K.; Demana, Franklin

1992-01-01

Presented are two reasons discouraging computer symbol manipulation systems use in school mathematics at present: cost for computer laboratories or expensive pocket computers; and impracticality of exact solution representations. Although development with this technology in mathematics education advances, graphing calculators are recommended to…

Parametric synthesis of a robust controller on a base of mathematical programming method

NASA Astrophysics Data System (ADS)

Khozhaev, I. V.; Gayvoronskiy, S. A.; Ezangina, T. A.

2018-05-01

Considered paper is dedicated to deriving sufficient conditions, linking root indices of robust control quality with coefficients of interval characteristic polynomial, on the base of mathematical programming method. On the base of these conditions, a method of PI- and PID-controllers, providing aperiodic transient process with acceptable stability degree and, subsequently, acceptable setting time, synthesis was developed. The method was applied to a problem of synthesizing a controller for a depth control system of an unmanned underwater vehicle.

Total Quality Management in the Classroom: Applications to University-Level Mathematics.

ERIC Educational Resources Information Center

Williams, Frank

1995-01-01

Describes a Total Quality Management-based system of instruction that is used in a variety of undergraduate mathematics courses. The courses that incorporate this approach include mathematics appreciation, introductory calculus, and advanced applied linear algebra. (DDR)

Teaching Undergraduate Mathematics in Interactive Groups: How Does It Fit with Students' Learning?

ERIC Educational Resources Information Center

Sheryn, Louise; Ell, Fiona

2014-01-01

Debates about how undergraduate mathematics should be taught are informed by different views of what it is to learn and to do mathematics. In this qualitative study 10 students enrolled in an advanced undergraduate course in mathematics shared their views about how they best learn mathematics. After participating in a semester-long course in…

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.

Experiences of Advanced High School Students in Synchronous Online Recitations

ERIC Educational Resources Information Center

Mayer, Greg; Lingle, Jeremy; Usselman, Marion

2017-01-01

The question of how to best design an online course that promotes student-centred learning is an area of ongoing research. This mixed-methods study focused on a section of advanced high school students, in college-level mathematics courses, that used a synchronous online environment mediated over web-conferencing software, and whether the…

Mathematic models for a ray tracing method and its applications in wireless optical communications.

PubMed

Zhang, Minglun; Zhang, Yangan; Yuan, Xueguang; Zhang, Jinnan

2010-08-16

This paper presents a new ray tracing method, which contains a whole set of mathematic models, and its validity is verified by simulations. In addition, both theoretical analysis and simulation results show that the computational complexity of the method is much lower than that of previous ones. Therefore, the method can be used to rapidly calculate the impulse response of wireless optical channels for complicated systems.

Improving students’ mathematical representational ability through RME-based progressive mathematization

NASA Astrophysics Data System (ADS)

Warsito; Darhim; Herman, T.

2018-01-01

This study aims to determine the differences in the improving of mathematical representation ability based on progressive mathematization with realistic mathematics education (PMR-MP) with conventional learning approach (PB). The method of research is quasi-experiments with non-equivalent control group designs. The study population is all students of class VIII SMPN 2 Tangerang consisting of 6 classes, while the sample was taken two classes with purposive sampling technique. The experimental class is treated with PMR-MP while the control class is treated with PB. The instruments used are test of mathematical representation ability. Data analysis was done by t-test, ANOVA test, post hoc test, and descriptive analysis. The result of analysis can be concluded that: 1) there are differences of mathematical representation ability improvement between students treated by PMR-MP and PB, 2) no interaction between learning approach (PMR-MP, PB) and prior mathematics knowledge (PAM) to improve students’ mathematical representation; 3) Students’ mathematical representation improvement in the level of higher PAM is better than medium, and low PAM students. Thus, based on the process of mathematization, it is very important when the learning direction of PMR-MP emphasizes on the process of building mathematics through a mathematical model.

Chaos: A Mathematical Introduction

NASA Astrophysics Data System (ADS)

Banks, John; Dragan, Valentina; Jones, Arthur

2003-06-01

This text presents concepts on chaos in discrete time dynamics that are accessible to anyone who has taken a first course in undergraduate calculus. Retaining its commitment to mathematical integrity, the book, originating in a popular one-semester middle level undergraduate course, constitutes the first elementary presentation of a traditionally advanced subject.

TIMMS Advanced 2015 Assessment Frameworks

ERIC Educational Resources Information Center

Mullis, Ina V. S., Ed.; Martin, Michael O., Ed.

2014-01-01

It is critical for countries to ensure that capable secondary school students receive further preparation in advanced mathematics and science, so that they are ready to enter challenging university-level studies that prepare them for careers in science, technology, engineering, and mathematics (STEM) fields. This group of students will become the…

Mobile learning to improve mathematics teachers mathematical competencies

NASA Astrophysics Data System (ADS)

Hendrayana, A.; Wahyudin

2018-01-01

The role of teachers is crucial to the success of mathematics learning. One of the learning indicator is characterized by the students’ improved mathematical proficiency. In order to increase that, it is necessary to improve the teacher’s mathematical skills first. For that, it needs an innovative way to get teachers close to easily accessible learning resources through technology. The technology can facilitate teachers to access learning resources anytime and anywhere. The appropriate information technology is mobile learning. Innovations that can make teachers easy to access learning resources are mobile applications that can be accessed anytime and anywhere either online or offline. The research method was research development method. In preliminary analysis, subjects consist of teachers and lecturers in professional teacher education program. The results that the teachers ready to adopt mobile-learning for the improvement of their skills.

Improving Junior High School Students' Mathematical Analogical Ability Using Discovery Learning Method

ERIC Educational Resources Information Center

Maarif, Samsul

2016-01-01

The aim of this study was to identify the influence of discovery learning method towards the mathematical analogical ability of junior high school's students. This is a research using factorial design 2x2 with ANOVA-Two ways. The population of this research included the entire students of SMPN 13 Jakarta (State Junior High School 13 of Jakarta)…

Advanced Computational Methods in Bio-Mechanics.

PubMed

Al Qahtani, Waleed M S; El-Anwar, Mohamed I

2018-04-15

A novel partnership between surgeons and machines, made possible by advances in computing and engineering technology, could overcome many of the limitations of traditional surgery. By extending surgeons' ability to plan and carry out surgical interventions more accurately and with fewer traumas, computer-integrated surgery (CIS) systems could help to improve clinical outcomes and the efficiency of healthcare delivery. CIS systems could have a similar impact on surgery to that long since realised in computer-integrated manufacturing. Mathematical modelling and computer simulation have proved tremendously successful in engineering. Computational mechanics has enabled technological developments in virtually every area of our lives. One of the greatest challenges for mechanists is to extend the success of computational mechanics to fields outside traditional engineering, in particular to biology, the biomedical sciences, and medicine. Biomechanics has significant potential for applications in orthopaedic industry, and the performance arts since skills needed for these activities are visibly related to the human musculoskeletal and nervous systems. Although biomechanics is widely used nowadays in the orthopaedic industry to design orthopaedic implants for human joints, dental parts, external fixations and other medical purposes, numerous researches funded by billions of dollars are still running to build a new future for sports and human healthcare in what is called biomechanics era.

Advanced boundary layer transition measurement methods for flight applications

NASA Technical Reports Server (NTRS)

Holmes, B. J.; Croom, C. C.; Gail, P. D.; Manuel, G. S.; Carraway, D. L.

1986-01-01

In modern laminar flow flight research, it is important to understand the specific cause(s) of laminar to turbulent boundary-layer transition. Such information is crucial to the exploration of the limits of practical application of laminar flow for drag reduction on aircraft. The transition modes of interest in current flight investigations include the viscous Tollmien-Schlichting instability, the inflectional instability at laminar separation, and the crossflow inflectional instability, as well as others. This paper presents the results to date of research on advanced devices and methods used for the study of laminar boundary-layer transition phenomena in the flight environment. Recent advancements in the development of arrayed hot-film devices and of a new flow visualization method are discussed. Arrayed hot-film devices have been designed to detect the presence of laminar separation, and of crossflow vorticity. The advanced flow visualization method utilizes color changes in liquid-crystal coatings to detect boundary-layer transition at high altitude flight conditions. Flight and wind tunnel data are presented to illustrate the design and operation of these advanced methods. These new research tools provide information on disturbance growth and transition mode which is essential to furthering our understanding of practical design limits for applications of laminar flow technology.

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

ERIC Educational Resources Information Center

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

2016-01-01

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

A Primer In Advanced Fatigue Life Prediction Methods

NASA Technical Reports Server (NTRS)

Halford, Gary R.

2000-01-01

Metal fatigue has plagued structural components for centuries, and it remains a critical durability issue in today's aerospace hardware. This is true despite vastly improved and advanced materials, increased mechanistic understanding, and development of accurate structural analysis and advanced fatigue life prediction tools. Each advance is quickly taken advantage of to produce safer, more reliable more cost effective, and better performing products. In other words, as the envelop is expanded, components are then designed to operate just as close to the newly expanded envelop as they were to the initial one. The problem is perennial. The economic importance of addressing structural durability issues early in the design process is emphasized. Tradeoffs with performance, cost, and legislated restrictions are pointed out. Several aspects of structural durability of advanced systems, advanced materials and advanced fatigue life prediction methods are presented. Specific items include the basic elements of durability analysis, conventional designs, barriers to be overcome for advanced systems, high-temperature life prediction for both creep-fatigue and thermomechanical fatigue, mean stress effects, multiaxial stress-strain states, and cumulative fatigue damage accumulation assessment.

An Appropriate Prompts System Based on the Polya Method for Mathematical Problem-Solving

ERIC Educational Resources Information Center

Lee, Chien I.

2017-01-01

Current mathematics education emphasizes techniques, formulas, and procedures, neglecting the importance of understanding, presentation, and reasoning. This turns students into passive listeners that are well-practiced only in using formulas that they do not understand. We therefore adopted the Polya problem-solving method to provide students with…

Sampling for Patient Exit Interviews: Assessment of Methods Using Mathematical Derivation and Computer Simulations.

PubMed

Geldsetzer, Pascal; Fink, Günther; Vaikath, Maria; Bärnighausen, Till

2018-02-01

(1) To evaluate the operational efficiency of various sampling methods for patient exit interviews; (2) to discuss under what circumstances each method yields an unbiased sample; and (3) to propose a new, operationally efficient, and unbiased sampling method. Literature review, mathematical derivation, and Monte Carlo simulations. Our simulations show that in patient exit interviews it is most operationally efficient if the interviewer, after completing an interview, selects the next patient exiting the clinical consultation. We demonstrate mathematically that this method yields a biased sample: patients who spend a longer time with the clinician are overrepresented. This bias can be removed by selecting the next patient who enters, rather than exits, the consultation room. We show that this sampling method is operationally more efficient than alternative methods (systematic and simple random sampling) in most primary health care settings. Under the assumption that the order in which patients enter the consultation room is unrelated to the length of time spent with the clinician and the interviewer, selecting the next patient entering the consultation room tends to be the operationally most efficient unbiased sampling method for patient exit interviews. © 2016 The Authors. Health Services Research published by Wiley Periodicals, Inc. on behalf of Health Research and Educational Trust.

Science, technology, engineering, mathematics (STEM) as mathematics learning approach in 21st century

NASA Astrophysics Data System (ADS)

Milaturrahmah, Naila; Mardiyana, Pramudya, Ikrar

2017-08-01

This 21st century demands competent human resources in science, technology, engineering design and mathematics so that education is expected to integrate the four disciplines. This paper aims to describe the importance of STEM as mathematics learning approach in Indonesia in the 21st century. This paper uses a descriptive analysis research method, and the method reveals that STEM education growing in developed countries today can be a framework for innovation mathematics in Indonesia in the 21st century. STEM education integrate understanding of science, math skills, and the available technology with the ability to perform engineering design process. Implementation of mathematics learning with STEM approach makes graduates trained in using of mathematics knowledge that they have to create innovative products that are able to solve the problems that exist in society.

PENDISC: a simple method for constructing a mathematical model from time-series data of metabolite concentrations.

PubMed

Sriyudthsak, Kansuporn; Iwata, Michio; Hirai, Masami Yokota; Shiraishi, Fumihide

2014-06-01

The availability of large-scale datasets has led to more effort being made to understand characteristics of metabolic reaction networks. However, because the large-scale data are semi-quantitative, and may contain biological variations and/or analytical errors, it remains a challenge to construct a mathematical model with precise parameters using only these data. The present work proposes a simple method, referred to as PENDISC (Parameter Estimation in a N on- DImensionalized S-system with Constraints), to assist the complex process of parameter estimation in the construction of a mathematical model for a given metabolic reaction system. The PENDISC method was evaluated using two simple mathematical models: a linear metabolic pathway model with inhibition and a branched metabolic pathway model with inhibition and activation. The results indicate that a smaller number of data points and rate constant parameters enhances the agreement between calculated values and time-series data of metabolite concentrations, and leads to faster convergence when the same initial estimates are used for the fitting. This method is also shown to be applicable to noisy time-series data and to unmeasurable metabolite concentrations in a network, and to have a potential to handle metabolome data of a relatively large-scale metabolic reaction system. Furthermore, it was applied to aspartate-derived amino acid biosynthesis in Arabidopsis thaliana plant. The result provides confirmation that the mathematical model constructed satisfactorily agrees with the time-series datasets of seven metabolite concentrations.

Shifting Pre-Service Teachers' Beliefs about Mathematics Teaching: The Contextual Situation of a Mathematics Methods Course

ERIC Educational Resources Information Center

Jao, Limin

2017-01-01

For pre-service teachers (PSTs) who have been exposed to traditional approaches, teacher education courses can be a revelatory experience in their development as educators. This study explores if Canadian upper elementary/lower secondary (grades 4-10) PSTs change their beliefs about mathematics teaching as a result of taking a mathematics methods…

Learning Mathematics in English at Basic Schools in Ghana: A Benefit or Hindrance?

ERIC Educational Resources Information Center

Fredua-Kwarteng, Eric; Ahia, Francis

2015-01-01

Facilitating effective mathematics learning and higher mathematics achievement have long been recognized as a key to the scientific and technological advancement of the African continent. While the central role that language proficiency plays in mathematics teaching and learning has received an overwhelming research attention in the literature…

Fifty Years of A-Level Mathematics: Have Standards Changed?

ERIC Educational Resources Information Center

Jones, Ian; Wheadon, Chris; Humphries, Sara; Inglis, Matthew

2016-01-01

Advanced-level (A-level) mathematics is a high-profile qualification taken by many school leavers in England, Wales, Northern Ireland and around the world as preparation for university study. Concern has been expressed in these countries that standards in A-level mathematics have declined over time, and that school leavers enter university or the…

The Mathematical Education of Engineers.

ERIC Educational Resources Information Center

Gnedenko, B. V.; Khalil, Z.

1979-01-01

Several general aspects are discussed. These include the role of mathematics in scientific and technical progress, some deficiencies in training, the role of mathematics in engineering faculties, and methods of improving mathematical training. (MP)

Technology Adoption in Secondary Mathematics Teaching in Kenya: An Explanatory Mixed Methods Study

ERIC Educational Resources Information Center

Kamau, Leonard Mwathi

2014-01-01

This study examined the factors related to technology adoption by secondary mathematics teachers in Nyandarua and Nairobi counties in the Republic of Kenya. Using a sequential explanatory mixed methods approach, I collected qualitative data from interviews and classroom observations of six teachers to better understand statistical results from the…

Mathematical Heroes--No Longer Unsung

ERIC Educational Resources Information Center

Chin, Cynthia E.

2007-01-01

The history of Fermat's Last Theorem, recounted in the theatrical piece "Fermat's Last Tango," is a useful vehicle for introducing students to the variety of personalities, processes, and products involved in advanced mathematical investigation. The musical's accessible, informative, and positive portrayal of mathematicians and their work is…

Mathematics and academic diversity in Japan.

PubMed

Woodward, John; Ono, Yumiko

2004-01-01

Japanese education has been the subject of considerable research and educational commentary in the United States over the last 20 years. Since the early 1990s, there has been increased interest in Japanese methods for teaching mathematics, and the Third International Mathematics and Science Study has accelerated American interest in Japanese methods. Observational studies, teacher and student surveys, and analyses of classroom videotapes have provided a rich picture of how the Japanese teach the whole class. However, little has been written about how academically low-achieving math students fare in Japanese schools. This article briefly summarizes Japanese methods for teaching mathematics and describes how the educational system addresses academic diversity. It concludes with a description of a method for teaching mathematics that some Japanese mathematics educators feel has promise for students with learning disabilities.

Mathematical Observations: The Genesis of Mathematical Discovery in the Classroom

ERIC Educational Resources Information Center

Beaugris, Louis M.

2013-01-01

In his "Proofs and Refutations," Lakatos identifies the "Primitive Conjecture" as the first stage in the pattern of mathematical discovery. In this article, I am interested in ways of reaching the "Primitive Conjecture" stage in an undergraduate classroom. I adapted Realistic Mathematics Education methods in an…

Mathematic modeling of the method of measurement relative dielectric permeability

NASA Astrophysics Data System (ADS)

Plotnikova, I. V.; Chicherina, N. V.; Stepanov, A. B.

2018-05-01

The method of measuring relative permittivity’s and the position of the interface between layers of a liquid medium is considered in the article. An electric capacitor is a system consisting of two conductors that are separated by a dielectric layer. It is mathematically proven that at any given time it is possible to obtain the values of the relative permittivity in the layers of the liquid medium and to determine the level of the interface between the layers of the two-layer liquid. The estimation of measurement errors is made.

Advanced methods of structural and trajectory analysis for transport aircraft

NASA Technical Reports Server (NTRS)

Ardema, Mark D.

1995-01-01

This report summarizes the efforts in two areas: (1) development of advanced methods of structural weight estimation, and (2) development of advanced methods of trajectory optimization. The majority of the effort was spent in the structural weight area. A draft of 'Analytical Fuselage and Wing Weight Estimation of Transport Aircraft', resulting from this research, is included as an appendix.

The Chess and Mathematics Connection: More than Just a Game

ERIC Educational Resources Information Center

Berkman, Robert M.

2004-01-01

This article describes connections between chess and mathematics, including examples of activities that connect chess with set theory, patterns, algebra, geometry, combinatorics, and Pascal's triangle. The author observes that competitive games play a dual purpose in advancing the work of mathematics educators: to reinforce a specific skill and to…

Advances in Classification Methods for Military Munitions Response

DTIC Science & Technology

2010-12-01

Response Herb Nelson Objective of the Course Provide an update on the sensors , methods, and status of the classification of military munitions...advanced EMI sensors 2Advances in Classification - Introduction Report Documentation Page Form ApprovedOMB No. 0704-0188 Public reporting burden for the...Electromagnetics (EM): Fundamentals and Parameter Extraction Stephen Billings EM Module Outline ● EMI Fundamentals How EMI sensors work and what they measure

On mathematical modelling of aeroelastic problems with finite element method

NASA Astrophysics Data System (ADS)

Sváček, Petr

2018-06-01

This paper is interested in solution of two-dimensional aeroelastic problems. Two mathematical models are compared for a benchmark problem. First, the classical approach of linearized aerodynamical forces is described to determine the aeroelastic instability and the aeroelastic response in terms of frequency and damping coefficient. This approach is compared to the coupled fluid-structure model solved with the aid of finite element method used for approximation of the incompressible Navier-Stokes equations. The finite element approximations are coupled to the non-linear motion equations of a flexibly supported airfoil. Both methods are first compared for the case of small displacement, where the linearized approach can be well adopted. The influence of nonlinearities for the case of post-critical regime is discussed.

An Exploratory Study of Taiwanese Mathematics Teachers' Conceptions of School Mathematics, School Statistics, and Their Differences

ERIC Educational Resources Information Center

Yang, Kai-Lin

2014-01-01

This study used phenomenography, a qualitative method, to investigate Taiwanese mathematics teachers' conceptions of school mathematics, school statistics, and their differences. To collect data, we interviewed five mathematics teachers by open questions. They also responded to statements drawn on mathematical/statistical conceptions and…

Mathematical, Logical, and Formal Methods in Information Retrieval: An Introduction to the Special Issue.

ERIC Educational Resources Information Center

Crestani, Fabio; Dominich, Sandor; Lalmas, Mounia; van Rijsbergen, Cornelis Joost

2003-01-01

Discusses the importance of research on the use of mathematical, logical, and formal methods in information retrieval to help enhance retrieval effectiveness and clarify underlying concepts of information retrieval. Highlights include logic; probability; spaces; and future research needs. (Author/LRW)

Developing Mathematical Knowledge for Teaching in a Methods Course: The Case of Function

ERIC Educational Resources Information Center

Steele, Michael D.; Hillen, Amy F.; Smith, Margaret S.

2013-01-01

This study describes teacher learning in a teaching experiment consisting of a content-focused methods course involving the mathematical knowledge for teaching function. Prospective and practicing teachers in the course showed growth in their ability to define function, to provide examples of functions and link them to the definition, in the…

Some Considerations in Combining Traditional and Non-Traditional Methods of Instruction in a Mathematics Program.

ERIC Educational Resources Information Center

Gormley, Tyrone D.

Based on the assumption that each student learns in a unique way, this paper outlines the factors to be considered before selecting the methods of instruction for particular mathematics courses and their students. The advantages and disadvantages of the lecture/textbook and question/answer method, individualized instruction, self-pacing,…

When Traditional Won't Do: Experiences from a "Lower-Level" Mathematics Classroom

ERIC Educational Resources Information Center

Hill, Crystal

2010-01-01

As the last bell rings, students scurry to their respective classrooms, doors begin to close, and the class period begins. Imagine that you are in the hallway of the school and you look into an advanced mathematics class, into an Algebra I, Part I, mathematics class (a course designed for students who have not found success in mathematics). What…

Construction of mathematical model for measuring material concentration by colorimetric method

NASA Astrophysics Data System (ADS)

Liu, Bing; Gao, Lingceng; Yu, Kairong; Tan, Xianghua

2018-06-01

This paper use the method of multiple linear regression to discuss the data of C problem of mathematical modeling in 2017. First, we have established a regression model for the concentration of 5 substances. But only the regression model of the substance concentration of urea in milk can pass through the significance test. The regression model established by the second sets of data can pass the significance test. But this model exists serious multicollinearity. We have improved the model by principal component analysis. The improved model is used to control the system so that it is possible to measure the concentration of material by direct colorimetric method.

Using Self-Efficacy as a Construct for Evaluating Science and Mathematics Methods Courses

NASA Astrophysics Data System (ADS)

Brand, Brenda R.; Wilkins, Jesse L. M.

2007-04-01

The focus of this study was elementary preservice teachers’ development as effective teachers of science and mathematics as influenced by their participation in elementary science and mathematics methods courses. Preservice teachers’ reports of factors that influenced their perception of their teaching abilities were analyzed according to Bandura’s (1994) 4 sources of efficacy: mastery experiences, vicarious experiences, social persuasion, and stress reduction. This investigation allowed the researchers to evaluate the courses based on these sources. The analysis indicated all 4 sources influenced preservice teachers’ teaching self-efficacy beliefs, with mastery experiences considered the most influential. Embedded within discussions of mastery experiences were references to the other sources of efficacy, which suggest an interrelationship between mastery experiences and the other sources.

The Effectiveness of Technology Integration in a Metropolitan Elementary Mathematics Program: Mad Dog Math

ERIC Educational Resources Information Center

Cohen, Miriam

2012-01-01

The outcome of American students' performances during international comparisons consistently scoring inadequately in mathematics exposes the crisis of deficient mathematics achievement thus causing deep concerns. Learners who acquire a strong theoretical foundation in mathematics at the primary level thrived later in more advanced level…

Integrability: mathematical methods for studying solitary waves theory

NASA Astrophysics Data System (ADS)

Wazwaz, Abdul-Majid

2014-03-01

In recent decades, substantial experimental research efforts have been devoted to linear and nonlinear physical phenomena. In particular, studies of integrable nonlinear equations in solitary waves theory have attracted intensive interest from mathematicians, with the principal goal of fostering the development of new methods, and physicists, who are seeking solutions that represent physical phenomena and to form a bridge between mathematical results and scientific structures. The aim for both groups is to build up our current understanding and facilitate future developments, develop more creative results and create new trends in the rapidly developing field of solitary waves. The notion of the integrability of certain partial differential equations occupies an important role in current and future trends, but a unified rigorous definition of the integrability of differential equations still does not exist. For example, an integrable model in the Painlevé sense may not be integrable in the Lax sense. The Painlevé sense indicates that the solution can be represented as a Laurent series in powers of some function that vanishes on an arbitrary surface with the possibility of truncating the Laurent series at finite powers of this function. The concept of Lax pairs introduces another meaning of the notion of integrability. The Lax pair formulates the integrability of nonlinear equation as the compatibility condition of two linear equations. However, it was shown by many researchers that the necessary integrability conditions are the existence of an infinite series of generalized symmetries or conservation laws for the given equation. The existence of multiple soliton solutions often indicates the integrability of the equation but other tests, such as the Painlevé test or the Lax pair, are necessary to confirm the integrability for any equation. In the context of completely integrable equations, studies are flourishing because these equations are able to describe the

A Multifaceted Mathematical Approach for Complex Systems

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

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

2012-03-07

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

Mathematical Models for Immunology: Current State of the Art and Future Research Directions.

PubMed

Eftimie, Raluca; Gillard, Joseph J; Cantrell, Doreen A

2016-10-01

The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales. To emphasise the use of mathematics in modelling in this area, we also review some of the mathematical tools used to investigate these models. Finally, we discuss some future trends in both experimental immunology and mathematical immunology for the upcoming years.

Discrete mathematics, formal methods, the Z schema and the software life cycle

NASA Technical Reports Server (NTRS)

Bown, Rodney L.

1991-01-01

The proper role and scope for the use of discrete mathematics and formal methods in support of engineering the security and integrity of components within deployed computer systems are discussed. It is proposed that the Z schema can be used as the specification language to capture the precise definition of system and component interfaces. This can be accomplished with an object oriented development paradigm.

Examining Preservice Teacher Belief Changes in the Context of Coordinated Mathematics Methods Coursework and Classroom Experiences

ERIC Educational Resources Information Center

Bahr, Damon; Monroe, Eula E.; Shaha, Steven H.

2013-01-01

The purpose of this study was to compare changes in beliefs of two groups of preservice teachers involved in two types of opportunities to immediately apply methods for teaching accompanying an elementary mathematics methods course. Students in one group applied the methods learned in class through weekly 30-minute peer-teaching sessions, while…

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

ERIC Educational Resources Information Center

Davis, Claudine Davillier

2012-01-01

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

Physical and mathematical modeling of antimicrobial photodynamic therapy

NASA Astrophysics Data System (ADS)

Bürgermeister, Lisa; López, Fernando Romero; Schulz, Wolfgang

2014-07-01

Antimicrobial photodynamic therapy (aPDT) is a promising method to treat local bacterial infections. The therapy is painless and does not cause bacterial resistances. However, there are gaps in understanding the dynamics of the processes, especially in periodontal treatment. This work describes the advances in fundamental physical and mathematical modeling of aPDT used for interpretation of experimental evidence. The result is a two-dimensional model of aPDT in a dental pocket phantom model. In this model, the propagation of laser light and the kinetics of the chemical reactions are described as coupled processes. The laser light induces the chemical processes depending on its intensity. As a consequence of the chemical processes, the local optical properties and distribution of laser light change as well as the reaction rates. The mathematical description of these coupled processes will help to develop treatment protocols and is the first step toward an inline feedback system for aPDT users.

Blended Learning, E-Learning and Mobile Learning in Mathematics Education

ERIC Educational Resources Information Center

Borba, Marcelo C.; Askar, Petek; Engelbrecht, Johann; Gadanidis, George; Llinares, Salvador; Aguilar, Mario Sánchez

2016-01-01

In this literature survey we focus on identifying recent advances in research on digital technology in the field of mathematics education. To conduct the survey we have used internet search engines with keywords related to mathematics education and digital technology and have reviewed some of the main international journals, including the ones in…

A Framework for Mathematical Thinking: The Case of Linear Algebra

ERIC Educational Resources Information Center

Stewart, Sepideh; Thomas, Michael O. J.

2009-01-01

Linear algebra is one of the unavoidable advanced courses that many mathematics students encounter at university level. The research reported here was part of the first author's recent PhD study, where she created and applied a theoretical framework combining the strengths of two major mathematics education theories in order to investigate the…

University of Chicago School Mathematics Project 6-12 Curriculum. What Works Clearinghouse Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2011

2011-01-01

The "University of Chicago School Mathematics Project ("UCSMP") 6-12 Curriculum" is a series of yearlong courses--(1) Transition Mathematics; (2) Algebra; (3) Geometry; (4) Advanced Algebra; (5) Functions, Statistics, and Trigonometry; and (6) Precalculus and Discrete Mathematics--emphasizing problem solving, real-world applications, and the use…

Is There a Relationship between Pre-Service Teachers' Mathematical Values and Their Teaching Anxiety in Mathematics?

ERIC Educational Resources Information Center

Yazici, Ersen; Peker, Murat; Ertekin, Erhan; Dilmac, Bulent

2011-01-01

Introduction: The aim of this study is to investigate the relation between the pre-service teachers' mathematical values and teaching anxieties in mathematics. Method: The research was carried out on 359 teacher candidates attending the elementary school mathematics, secondary school mathematics and primary school teaching programs. To this end,…

Transitioning to the Common Core State Standards for Mathematics: A Mixed Methods Study of Elementary Teachers' Experiences and Perspectives

ERIC Educational Resources Information Center

Swars, Susan Lee; Chestnutt, Cliff

2016-01-01

This mixed methods study explored elementary teachers' (n = 73) experiences with and perspectives on the recently implemented Common Core State Standards for Mathematics (CCSS-Mathematics) at a high-needs, urban school. Analysis of the survey, questionnaire, and interview data reveals the findings cluster around: familiarity with and preparation…

Profile of Metacognition of Mathematics and Mathematics Education Students in Understanding the Concept of Integral Calculus

NASA Astrophysics Data System (ADS)

Misu, La; Ketut Budayasa, I.; Lukito, Agung

2018-03-01

This study describes the metacognition profile of mathematics and mathematics education students in understanding the concept of integral calculus. The metacognition profile is a natural and intact description of a person’s cognition that involves his own thinking in terms of using his knowledge, planning and monitoring his thinking process, and evaluating his thinking results when understanding a concept. The purpose of this study was to produce the metacognition profile of mathematics and mathematics education students in understanding the concept of integral calculus. This research method is explorative method with the qualitative approach. The subjects of this study are mathematics and mathematics education students who have studied integral calculus. The results of this study are as follows: (1) the summarizing category, the mathematics and mathematics education students can use metacognition knowledge and metacognition skills in understanding the concept of indefinite integrals. While the definite integrals, only mathematics education students use metacognition skills; and (2) the explaining category, mathematics students can use knowledge and metacognition skills in understanding the concept of indefinite integrals, while the definite integrals only use metacognition skills. In addition, mathematics education students can use knowledge and metacognition skills in understanding the concept of both indefinite and definite integrals.

Interest in mathematics and science among students having high mathematics aptitude

NASA Astrophysics Data System (ADS)

Ely, Jane Alice

The study investigates why men and women differ in their interest in mathematics and science and in the pursuit of careers in mathematics and science. The most persistent gender differential in educational standard testing is the scores in mathematics achievement. The mean Scholastic Aptitude Test (Mathematics) scores for women are consistently below that of men by about 40 points. One result of this gender differential in mathematics is that few women entertain a career requiring a robust knowledge of higher mathematics (i.e. engineering, computing, or the physical sciences). A large body of literature has been written attempting to explain why this is happening. Biological, cultural, structural and psychological explanations have been suggested and empirically examined. Controlling for mathematical ability is one method of sorting out these explanations. Eliminating mathematical ability as a factor, this dissertation reports the results of a study of men and women college students who all had high mathematics ability. Thus, any differences we found among them would have to be a result of other variables. Using a Mathematics Placement Exam and the SAT-M, forty-two students (12 males and 30 females) with high scores in both were interviewed. Student were asked about their experiences in high school and college mathematics, their career choices, and their attitudes toward mathematics. The findings, that there were no gender differences in the course selection, attitudes towards mathematics, and career choice, differed from my initial expectations. This negative finding suggests that women with high ability in mathematics are just as likely as men to pursue interests in mathematics and related courses in college and in selecting careers.

For the Technologically Challenged: Four Free Online Tools to Liven up a Mathematics Classroom

ERIC Educational Resources Information Center

Northcote, Maria

2015-01-01

Use of technology in the mathematics classroom has the potential to advance children's learning of mathematics and enhance their attitudes about mathematics. When used in conjunction with purposeful planning, teachers can use technological tools to reinforce their pedagogical intentions and to facilitate relevant learning activities for students.…

Mathematics is always invisible, Professor Dowling

NASA Astrophysics Data System (ADS)

Cable, John

2015-09-01

This article provides a critical evaluation of a technique of analysis, the Social Activity Method, recently offered by Dowling (2013) as a `gift' to mathematics education. The method is found to be inadequate, firstly, because it employs a dichotomy (between `expression' and `content') instead of a finer analysis (into symbols, concepts and setting or phenomena), and, secondly, because the distinction between `public' and `esoteric' mathematics, although interesting, is allowed to obscure the structure of the mathematics itself. There is also criticism of what Dowling calls the `myth of participation', which denies the intimate links between mathematics and the rest of the universe that lie at the heart of mathematical pedagogy. Behind all this lies Dowling's `essentially linguistic' conception of mathematics, which is criticised on the dual ground that it ignores the chastening experience of formalism in mathematical philosophy and that linguistics itself has taken a wrong turn and ignores lessons that might be learnt from mathematics education.

Advancements in Research on Creativity and Giftedness in Mathematics Education: Introduction to the Special Issue

ERIC Educational Resources Information Center

Singer, Florence Mihaela; Sheffield, Linda Jensen; Leikin, Roza

2017-01-01

Creativity and giftedness in mathematics education research are topics of an increased interest in the education community during recent years. This introductory paper to the special issue on Mathematical Creativity and Giftedness in Mathematics Education has a twofold purpose: to offer a brief historical perspective on the study of creativity and…

The Mathematics--Children's-Literature Connection.

ERIC Educational Resources Information Center

Gailey, Stavroula K.

1993-01-01

Describes three types of children's books for use in developing mathematical concepts. Discusses the characteristics of a good mathematical concept book, methods of incorporating reading into the mathematics class, and three examples of children's books. Includes a bibliography of 159 children's trade books selected for integration into…

A Phenomenological Exploration of Mathematical Engagement: Approaching an Old Metaphor Anew.

ERIC Educational Resources Information Center

Handa, Yuichi

2003-01-01

Investigates the heart of the experience of mathematical engagement and the meaning derived from such activities. Analyzes dialogue between five people, two of whom are professional mathematicians, another two who are graduate students in either engineering or education, and one who lacks advanced mathematical training but maintains a positive…

TIMSS Advanced 2015 and Advanced Placement Calculus & Physics. A Framework Analysis. Research in Review 2016-1

ERIC Educational Resources Information Center

Lazzaro, Christopher; Jones, Lee; Webb, David C.; Grover, Ryan; Di Giacomo, F. Tony; Marino, Katherine Adele

2016-01-01

This report will determine to what degree the AP Physics 1 and 2 and AP Calculus AB and BC frameworks are aligned with the Trends in International Mathematics and Science Study (TIMSS) Advanced Physics and Mathematics frameworks. This will enable an exploration of any differences in content coverage and levels of complexity, and will set the stage…

Listening to Early Career Teachers: How Can Elementary Mathematics Methods Courses Better Prepare Them to Utilize Standards-Based Practices in Their Classrooms?

ERIC Educational Resources Information Center

Coester, Lee Anne

2010-01-01

This study was designed to gather input from early career elementary teachers with the goal of finding ways to improve elementary mathematics methods courses. Multiple areas were explored including the degree to which respondents' elementary mathematics methods course focused on the NCTM Process Standards, the teachers' current standards-based…

Mathematical Methods of System Analysis in Construction Materials

NASA Astrophysics Data System (ADS)

Garkina, Irina; Danilov, Alexander

2017-10-01

modules and their levels (the mathematical description, a decision algorithm) are defined. Adequacy is established (compliance of results of modelling to experimental data; is defined by the level of knowledge of process and validity of the accepted assumptions). The global criterion of quality of material is considered as a set of private criteria (properties). Synthesis of material is carried out on the basis of one-criteria optimization on each of the chosen private criteria. Results of one-criteria optimization are used at multicriteria optimization. The methods of developing materials as single-purpose, multi-purpose, including contradictory, systems are indicated. The scheme of synthesis of composite materials as difficult systems is developed. The specified system approach effectively was used in case of synthesis of composite materials with special properties.

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

ERIC Educational Resources Information Center

Liang, Jiajuan; Martin, Linda

2008-01-01

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

Two Meanings of Algorithmic Mathematics.

ERIC Educational Resources Information Center

Maurer, Stephen B.

1984-01-01

Two mathematical topics are interpreted from the viewpoints of traditional (performing algorithms) and contemporary (creating algorithms and thinking in terms of them for solving problems and developing theory) algorithmic mathematics. The two topics are Horner's method for evaluating polynomials and Gauss's method for solving systems of linear…

Mathematical description of drug-target interactions: application to biologics that bind to targets with two binding sites.

PubMed

Gibiansky, Leonid; Gibiansky, Ekaterina

2018-02-01

The emerging discipline of mathematical pharmacology occupies the space between advanced pharmacometrics and systems biology. A characteristic feature of the approach is application of advance mathematical methods to study the behavior of biological systems as described by mathematical (most often differential) equations. One of the early application of mathematical pharmacology (that was not called this name at the time) was formulation and investigation of the target-mediated drug disposition (TMDD) model and its approximations. The model was shown to be remarkably successful, not only in describing the observed data for drug-target interactions, but also in advancing the qualitative and quantitative understanding of those interactions and their role in pharmacokinetic and pharmacodynamic properties of biologics. The TMDD model in its original formulation describes the interaction of the drug that has one binding site with the target that also has only one binding site. Following the framework developed earlier for drugs with one-to-one binding, this work aims to describe a rigorous approach for working with similar systems and to apply it to drugs that bind to targets with two binding sites. The quasi-steady-state, quasi-equilibrium, irreversible binding, and Michaelis-Menten approximations of the model are also derived. These equations can be used, in particular, to predict concentrations of the partially bound target (RC). This could be clinically important if RC remains active and has slow internalization rate. In this case, introduction of the drug aimed to suppress target activity may lead to the opposite effect due to RC accumulation.

Heuristic Biases in Mathematical Reasoning

ERIC Educational Resources Information Center

Inglis, Matthew; Simpson, Adrian

2005-01-01

In this paper we briefly describe the dual process account of reasoning, and explain the role of heuristic biases in human thought. Concentrating on the so-called matching bias effect, we describe a piece of research that indicates a correlation between success at advanced level mathematics and an ability to override innate and misleading…

Assessment and Learning of Mathematics.

ERIC Educational Resources Information Center

Leder, Gilah C., Ed.

This book addresses the link between student learning of mathematics, the teaching method adopted in the mathematics classroom, and the assessment procedures used to determine and measure student knowledge. Fifteen chapters address issues that include a review of different models of mathematics learning and assessment practices, three contrasting…

Various Solution Methods, Accompanied by Dynamic Investigation, for the Same Problem as a Means for Enriching the Mathematical Toolbox

ERIC Educational Resources Information Center

Oxman, Victor; Stupel, Moshe

2018-01-01

A geometrical task is presented with multiple solutions using different methods, in order to show the connection between various branches of mathematics and to highlight the importance of providing the students with an extensive 'mathematical toolbox'. Investigation of the property that appears in the task was carried out using a computerized tool.

Various solution methods, accompanied by dynamic investigation, for the same problem as a means for enriching the mathematical toolbox

NASA Astrophysics Data System (ADS)

Oxman, Victor; Stupel, Moshe

2018-04-01

A geometrical task is presented with multiple solutions using different methods, in order to show the connection between various branches of mathematics and to highlight the importance of providing the students with an extensive 'mathematical toolbox'. Investigation of the property that appears in the task was carried out using a computerized tool.

Advances in multi-scale modeling of solidification and casting processes

NASA Astrophysics Data System (ADS)

Liu, Baicheng; Xu, Qingyan; Jing, Tao; Shen, Houfa; Han, Zhiqiang

2011-04-01

The development of the aviation, energy and automobile industries requires an advanced integrated product/process R&D systems which could optimize the product and the process design as well. Integrated computational materials engineering (ICME) is a promising approach to fulfill this requirement and make the product and process development efficient, economic, and environmentally friendly. Advances in multi-scale modeling of solidification and casting processes, including mathematical models as well as engineering applications are presented in the paper. Dendrite morphology of magnesium and aluminum alloy of solidification process by using phase field and cellular automaton methods, mathematical models of segregation of large steel ingot, and microstructure models of unidirectionally solidified turbine blade casting are studied and discussed. In addition, some engineering case studies, including microstructure simulation of aluminum casting for automobile industry, segregation of large steel ingot for energy industry, and microstructure simulation of unidirectionally solidified turbine blade castings for aviation industry are discussed.

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

PubMed

Chen, Liang-Hsuan; Hsueh, Chan-Ching

2007-06-01

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

Widening and Increasing Post-16 Mathematics Participation: Pathways, Pedagogies and Politics

ERIC Educational Resources Information Center

Noyes, Andrew; Wake, Geoff; Drake, Pat

2011-01-01

This paper explores the potential impact of a national pilot initiative in England aimed at increasing and widening participation in advanced mathematical study through the creation of a new qualification for 16- to 18-year-olds. This proposed qualification pathway--"Use of Mathematics"--sits in parallel with long-established,…

Fostering Teacher Learning of Conjecturing, Generalising and Justifying through Mathematics Studio

ERIC Educational Resources Information Center

Lesseig, Kristin

2016-01-01

Calls to advance students' ability to engage in mathematical reasoning practices including conjecturing, generalising and justifying (CGJ) place significant new demands on teachers. This case study examines how Mathematics Studio provided opportunities for a team of U.S. middle school teachers to learn about these practices and ways to promote…

Developing Culturally Responsive Mathematics Teachers: Secondary Teachers' Evolving Conceptions of Knowing Students

ERIC Educational Resources Information Center

Parker, Frieda; Bartell, Tonya Gau; Novak, Jodie D.

2017-01-01

Research advances in teaching, learning, curriculum, and assessment have not changed the continued underperformance of marginalized students in mathematics education. Culturally responsive teaching is a means of addressing the needs of these students. It is sometimes challenging, however, to convince secondary mathematics teachers about the…

Experimental Mathematics and Computational Statistics

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

Bailey, David H.; Borwein, Jonathan M.

2009-04-30

The field of statistics has long been noted for techniques to detect patterns and regularities in numerical data. In this article we explore connections between statistics and the emerging field of 'experimental mathematics'. These includes both applications of experimental mathematics in statistics, as well as statistical methods applied to computational mathematics.

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.

Characteristics and Impact of the Further Mathematics Knowledge Networks: Analysis of an English Professional Development Initiative on the Teaching of Advanced Mathematics

ERIC Educational Resources Information Center

Ruthven, Kenneth

2014-01-01

Reports from 13 Further Mathematics Knowledge Networks supported by the National Centre for Excellence in the Teaching of Mathematics [NCETM] are analysed. After summarizing basic characteristics of the networks regarding leadership, composition and pattern of activity, each of the following aspects is examined in greater depth: Developmental aims…

Mathematical Literacy Teachers' Engagement with Contextual Tasks Based on Personal Finance

ERIC Educational Resources Information Center

Bansilal, Sarah; Mkhwanazi, Thokozani; Mahlabela, Patisizwe

2012-01-01

This article reports on a study carried out with a group of 108 practising Mathematical Literacy (ML) teachers who participated in an Advanced Certificate in Education (ACE) programme. The purpose of the qualitative study was to identify and describe the teachers' varying levels of engagement with mathematics tools and resources. The teachers were…

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

ERIC Educational Resources Information Center

Mumcu, Hayal Yavuz

2016-01-01

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

Accelerating Mathematics Achievement Using Heterogeneous Grouping

ERIC Educational Resources Information Center

Burris, Carol Corbett; Heubert, Jay P.; Levin, Henry M.

2006-01-01

This longitudinal study examined the effects of providing an accelerated mathematics curriculum in heterogeneously grouped middle school classes in a diverse suburban school district. A quasi-experimental cohort design was used to evaluate subsequent completion of advanced high school math courses as well as academic achievement. Results showed…

Collegiate Mathematics Teaching: An Unexamined Practice

ERIC Educational Resources Information Center

Speer, Natasha M.; Smith, John P., III; Horvath, Aladar

2010-01-01

Though written accounts of collegiate mathematics teaching exist (e.g., mathematicians' reflections and analyses of learning and teaching in innovative courses), research on collegiate teachers' actual classroom teaching practice is virtually non-existent. We advance this claim based on a thorough review of peer-reviewed journals where scholarship…

Methods and Applications for Advancing Distance Education Technologies: International Issues and Solutions

ERIC Educational Resources Information Center

Syed, Mahbubur Rahman, Ed.

2009-01-01

The emerging field of advanced distance education delivers academic courses across time and distance, allowing educators and students to participate in a convenient learning method. "Methods and Applications for Advancing Distance Education Technologies: International Issues and Solutions" demonstrates communication technologies, intelligent…

Advances in Statistical Methods for Substance Abuse Prevention Research

PubMed Central

MacKinnon, David P.; Lockwood, Chondra M.

2010-01-01

The paper describes advances in statistical methods for prevention research with a particular focus on substance abuse prevention. Standard analysis methods are extended to the typical research designs and characteristics of the data collected in prevention research. Prevention research often includes longitudinal measurement, clustering of data in units such as schools or clinics, missing data, and categorical as well as continuous outcome variables. Statistical methods to handle these features of prevention data are outlined. Developments in mediation, moderation, and implementation analysis allow for the extraction of more detailed information from a prevention study. Advancements in the interpretation of prevention research results include more widespread calculation of effect size and statistical power, the use of confidence intervals as well as hypothesis testing, detailed causal analysis of research findings, and meta-analysis. The increased availability of statistical software has contributed greatly to the use of new methods in prevention research. It is likely that the Internet will continue to stimulate the development and application of new methods. PMID:12940467

General advancing front packing algorithm for the discrete element method

NASA Astrophysics Data System (ADS)

Morfa, Carlos A. Recarey; Pérez Morales, Irvin Pablo; de Farias, Márcio Muniz; de Navarra, Eugenio Oñate Ibañez; Valera, Roberto Roselló; Casañas, Harold Díaz-Guzmán

2018-01-01

A generic formulation of a new method for packing particles is presented. It is based on a constructive advancing front method, and uses Monte Carlo techniques for the generation of particle dimensions. The method can be used to obtain virtual dense packings of particles with several geometrical shapes. It employs continuous, discrete, and empirical statistical distributions in order to generate the dimensions of particles. The packing algorithm is very flexible and allows alternatives for: 1—the direction of the advancing front (inwards or outwards), 2—the selection of the local advancing front, 3—the method for placing a mobile particle in contact with others, and 4—the overlap checks. The algorithm also allows obtaining highly porous media when it is slightly modified. The use of the algorithm to generate real particle packings from grain size distribution curves, in order to carry out engineering applications, is illustrated. Finally, basic applications of the algorithm, which prove its effectiveness in the generation of a large number of particles, are carried out.

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.

Dispersive traveling wave solutions of the Equal-Width and Modified Equal-Width equations via mathematical methods and its applications

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

2018-06-01

The Equal-Width and Modified Equal-Width equations are used as a model in partial differential equations for the simulation of one-dimensional wave transmission in nonlinear media with dispersion processes. In this article we have employed extend simple equation method and the exp(-varphi(ξ)) expansion method to construct the exact traveling wave solutions of equal width and modified equal width equations. The obtained results are novel and have numerous applications in current areas of research in mathematical physics. It is exposed that our method, with the help of symbolic computation, provides a effective and powerful mathematical tool for solving different kind nonlinear wave problems.

Philosophy and mathematics: interactions.

PubMed

Rashed, Roshdi

From Plato to the beginnings of the last century, mathematics provided philosophers with methods of exposition, procedures of demonstration, and instruments of analysis. The unprecedented development of mathematics on the one hand, and the mathematicians' appropriation of Logic from the philosophers on the other hand, have given rise to two problems with which the philosophers have to contend: (1) Is there still a place for the philosophy of mathematics? and (2) To what extent is a philosophy of mathematics still possible? This article offers some reflections on these questions, which have preoccupied a good many philosophers and continue to do so.

Implications of Eighth Grade Algebra I on High School Mathematics Achievement

ERIC Educational Resources Information Center

Bayard, Robert

2012-01-01

As of 2008, approximately 40% of eighth grade students in the United States enroll in Algebra I (National Council of Teachers of Mathematics, 2008). Although research has shown that students have more opportunities to take advanced mathematics courses by taking eighth grade Algebra I, in the United States, approximately only one-third to one-half…

Mathematics Readiness of First-Year University Students

ERIC Educational Resources Information Center

Atuahene, Francis; Russell, Tammy A.

2016-01-01

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

The Effect of Instruction through Mathematical Modelling on Modelling Skills of Prospective Elementary Mathematics Teachers

ERIC Educational Resources Information Center

Ciltas, Alper; Isik, Ahmet

2013-01-01

The aim of this study was to examine the modelling skills of prospective elementary mathematics teachers who were studying the mathematical modelling method. The research study group was composed of 35 prospective teachers. The exploratory case analysis method was used in the study. The data were obtained via semi-structured interviews and a…

Influence of a Mathematics Teachers' Circle on Elementary Teachers' Use of Problem Solving

ERIC Educational Resources Information Center

Garner, Mary L.; Watson, Virginia; Rogers, Beth; Head, Catherine

2017-01-01

Math teachers' circles are a form of professional development that is recommended by the Conference Board of the Mathematical Sciences in their publication Mathematical Education of Teachers II (2012). However, little research has been published on how effective math teachers' circles are in advancing the mathematical knowledge of teachers and…

Undergraduate Mathematics Majors' Writing Performance Producing Proofs and Counterexamples about Continuous Functions

ERIC Educational Resources Information Center

Ko, Yi-Yin; Knuth, Eric

2009-01-01

In advanced mathematical thinking, proving and refuting are crucial abilities to demonstrate whether and why a proposition is true or false. Learning proofs and counterexamples within the domain of continuous functions is important because students encounter continuous functions in many mathematics courses. Recently, a growing number of studies…

Consumer Economics and Consumer Mathematics Textbooks.

ERIC Educational Resources Information Center

Eastern Michigan Univ., Ypsilanti. National Inst. for Consumer Education.

This publication lists a selection of consumer economics and consumer mathematics textbooks available for review from the National Institute for Consumer Education. Twenty-six textbooks for the secondary level are cited. Nine advanced level texts are also listed. These texts are generally considered college level texts but could be adapted for…

A model of professional competences in mathematics to update mathematical and didactic knowledge of teachers

NASA Astrophysics Data System (ADS)

Díaz, Verónica; Poblete, Alvaro

2017-07-01

This paper describes part of a research and development project carried out in public elementary schools. Its objective was to update the mathematical and didactic knowledge of teachers in two consecutive levels in urban and rural public schools of Region de Los Lagos and Region de Los Rios of southern Chile. To that effect, and by means of an advanced training project based on a professional competences model, didactic interventions based on types of problems and types of mathematical competences with analysis of contents and learning assessment were designed. The teachers' competence regarding the didactic strategy used and its results, as well as the students' learning achievements are specified. The project made possible to validate a strategy of lifelong improvement in mathematics, based on the professional competences of teachers and their didactic transposition in the classroom, as an alternative to consolidate learning in areas considered vulnerable in two regions of the country.

Examining Primary Pre-Service Teachers' Difficulties of Mathematics Teaching with the Micro-Teaching Method

ERIC Educational Resources Information Center

Savas Basturk; Tastepe, Mehtap

2015-01-01

The purpose of the study was to examine primary pre-service teachers' difficulties of the teaching of mathematics with micro-teaching method. The participants of the study were 15 third grade pre-service teachers from the department of primary education in the faculty of education. In this grade which includes four sections, there were…

Cards in the Classroom: Mathematics and Methods.

ERIC Educational Resources Information Center

Baker, Robert N.

This report researches the use of a standard deck of playing cards in entry-level college mathematics classrooms. The study looks at published research on the use of cards, and reviews pedagogic concerns directly related to the implementation of playing cards in the classroom--including the appropriateness of manipulatives, the link to cooperative…

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 Use of Software in Academic Stream High School Mathematics Teaching

ERIC Educational Resources Information Center

Clay, Simon; Fotou, Nikolaos; Monaghan, John

2017-01-01

This paper reports on classroom observations of senior high school mathematics lessons with a focus on the use of digital technology. The observations were of teachers enrolled in an in-service course, Teaching Advanced Mathematics. The paper reports selected results and comments on: software that was observed to have been used; the use (or not)…

Cost estimating methods for advanced space systems

NASA Technical Reports Server (NTRS)

Cyr, Kelley

1988-01-01

The development of parametric cost estimating methods for advanced space systems in the conceptual design phase is discussed. The process of identifying variables which drive cost and the relationship between weight and cost are discussed. A theoretical model of cost is developed and tested using a historical data base of research and development projects.

Science and Mathematics in Astronomy

NASA Technical Reports Server (NTRS)

Woolack, Edward

2009-01-01

A brief historical introduction to the development of observational astronomy will be presented. The close historical relationship between the successful application of mathematical concepts and advances in astronomy will be presented. A variety of simple physical demonstrations, hands-on group activities, and puzzles will be used to understand how the properties of light can be used to understand the contents of our universe.

Mathematical Education for Geographers

ERIC Educational Resources Information Center

Wilson, Alan

1978-01-01

Outlines mathematical topics of use to college geography students identifies teaching methods for mathematical techniques in geography at the University of Leeds; and discusses problem of providing students with a framework for synthesizing all content of geography education. For journal availability, see SO 506 593. (Author/AV)

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

ERIC Educational Resources Information Center

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

2015-01-01

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

Interactive, Learner-Centered Methods of Teaching Mathematics

ERIC Educational Resources Information Center

Alsardary, Salar; Blumberg, Phyllis

2009-01-01

We describe a learner-centered upper-level mathematics course where the students present the material to the class instead of the instructor, and the students make presentations on applied topics at the regional MAA meeting. After take-home examinations the students can discuss their answers one-on-one with the instructor. The students liked the…

The Technological Enframing of Mathematics Education

ERIC Educational Resources Information Center

Thornton, Steve

2014-01-01

In this paper I seek to critique pervasive notions of what counts in mathematics education using Heidegger's notion of the technological enframing. I suggest that early childhood and schooling have become technologies in themselves, casting students and teachers as part of the standing reserve within the inexorable drive for economic advancement.…

Mathematical and information maintenance of biometric systems

NASA Astrophysics Data System (ADS)

Boriev, Z.; Sokolov, S.; Nyrkov, A.; Nekrasova, A.

2016-04-01

This article describes the different mathematical methods for processing biometric data. A brief overview of methods for personality recognition by means of a signature is conducted. Mathematical solutions of a dynamic authentication method are considered. Recommendations on use of certain mathematical methods, depending on specific tasks, are provided. Based on the conducted analysis of software and the choice made in favor of the wavelet analysis, a brief basis for its use in the course of software development for biometric personal identification is given for the purpose of its practical application.

Essential Mathematics for the Physical Sciences; Volume I: Homogeneous boundary value problems, Fourier methods, and special functions

NASA Astrophysics Data System (ADS)

Borden, Brett; Luscombe, James

2017-10-01

Physics is expressed in the language of mathematics; it is deeply ingrained in how physics is taught and how it's practiced. A study of the mathematics used in science is thus a sound intellectual investment for training as scientists and engineers. This first volume of two is centered on methods of solving partial differential equations and the special functions introduced. This text is based on a course offered at the Naval Postgraduate School (NPS) and while produced for NPS needs, it will serve other universities well.

Mathematical methods to model rodent behavior in the elevated plus-maze.

PubMed

Arantes, Rafael; Tejada, Julián; Bosco, Geraldine G; Morato, Silvio; Roque, Antonio C

2013-11-15

The elevated plus maze is a widely used experimental test to study anxiety-like rodent behavior. It is made of four arms, two open and two closed, connected at a central area forming a plus shaped maze. The whole apparatus is elevated 50 cm from the floor. The anxiety of the animal is usually assessed by the number of entries and duration of stay in each arm type during a 5-min period. Different mathematical methods have been proposed to model the mechanisms that control the animal behavior in the maze, such as factor analysis, statistical inference on Markov chains and computational modeling. In this review we discuss these methods and propose possible extensions of them as a direction for future research. Copyright © 2013 Elsevier B.V. All rights reserved.

Hua Loo-Keng and the Movement of Popularizing Mathematics in the People's Republic of China

ERIC Educational Resources Information Center

Richard, Jean W.

2010-01-01

This paper examines the mathematical and teaching practices of the renowned self-taught Chinese mathematician Hua Loo-keng in the movement of popularizing mathematics in the People's Republic of China. In this movement, Hua Loo-keng taught industrial workers and peasants with a low level of education how to use fairly advanced mathematical methods…

Effects of an Additional Mathematics Content Course on Elementary Teachers' Mathematical Beliefs and Knowledge for Teaching

ERIC Educational Resources Information Center

Smith, Marvin E.; Swars, Susan L.; Smith, Stephanie Z.; Hart, Lynn C.; Haardorfer, Regine

2012-01-01

This longitudinal study examines the effects of changes in an elementary teacher preparation program on mathematics beliefs and content knowledge for teaching of two groups of prospective teachers (N = 276): (1) those who completed a program with three mathematics content courses and two mathematics methods courses and (2) those who completed a…

Mathematically precocious and female: Self-efficacy and STEM course choices among high achieving middle grade students

NASA Astrophysics Data System (ADS)

Burt, Stacey M.

The problem addressed in this project is the lack of mathematically gifted females choosing to pursue advanced science, technology, engineering, and mathematics (STEM) courses in secondary education due to deficiencies in self-efficacy. The purpose of this project was to study the effects of a child-guided robotics program as it relates to the self-efficacy of mathematically gifted 6th grade female students and their future course choices in the advanced STEM content areas. This mixed-model study utilized a STEM attitude survey, artifacts, interviews, field notes, and standardized tests as measurement tools. Significance was found between genders in the treatment group for the standardized science scores, indicating closure in the achievement gap. Research suggests that STEM enrichment is beneficial for mathematically gifted females.

Sam's Progress with Learning Mathematics

ERIC Educational Resources Information Center

Haslam, Lynne

2007-01-01

Sam is 18 years old and has Down syndrome. He achieved a grade in the standard assessment of mathematics (GCSE) at 16 years of age. This paper describes the part played in his success in school by the Kumon method of teaching mathematics, identifies the benefits of the small steps and lots of practice built in to the method and illustrates the…

Integration of Technology in Elementary Pre-Service Teacher Education: An Examination of Mathematics Methods Courses

ERIC Educational Resources Information Center

Mitchell, Rebecca; Laski, Elida

2013-01-01

Instructors (N = 204) of elementary mathematics methods courses completed a survey assessing the extent to which they stay informed about research related to effective uses of educational technology and the kinds and numbers of educational technologies they include in their courses. Findings indicate that, while they view educational technology…

Mathematical modelling of skeletal repair.

PubMed

MacArthur, B D; Please, C P; Taylor, M; Oreffo, R O C

2004-01-23

Tissue engineering offers significant promise as a viable alternative to current clinical strategies for replacement of damaged tissue as a consequence of disease or trauma. Since mathematical modelling is a valuable tool in the analysis of complex systems, appropriate use of mathematical models has tremendous potential for advancing the understanding of the physical processes involved in such tissue reconstruction. In this review, the potential benefits, and limitations, of theoretical modelling in tissue engineering applications are examined with specific emphasis on tissue engineering of bone. A central tissue engineering approach is the in vivo implantation of a biomimetic scaffold seeded with an appropriate population of stem or progenitor cells. This review will therefore consider the theory behind a number of key factors affecting the success of such a strategy including: stem cell or progenitor population expansion and differentiation ex vivo; cell adhesion and migration, and the effective design of scaffolds; and delivery of nutrient to avascular structures. The focus will be on current work in this area, as well as on highlighting limitations and suggesting possible directions for future work to advance health-care for all.

Mathematics anxiety and mathematics achievement

NASA Astrophysics Data System (ADS)

Sherman, Brian F.; Wither (Post.), David P.

2003-09-01

This paper is a distillation of the major result from the 1998 Ph.D. thesis of the late David Wither. It details a longitudinal study over five years of the relationship between mathematics anxiety and mathematics achievement. It starts from the already well documented negative correlation between the two, and seeks to establish one of the three hypotheses—that mathematics anxiety causes an impairment of mathematics achievement; that lack of mathematics achievement causes mathematics anxiety; or that there is a third underlying cause of the two.

Giving Reason to Prospective Mathematics Teachers

ERIC Educational Resources Information Center

D'Ambrosio, Beatriz; Kastberg, Signe

2012-01-01

This article describes the development of the authors' understanding of the contradictions in their mathematics teacher education practice. This understanding emerged from contrasting analyses of the impact of the authors' practices in mathematics content courses versus mathematics methods courses. Examples of the authors' work with two students,…

Gender Differences in the Effects of a Utility-Value Intervention to Help Parents Motivate Adolescents in Mathematics and Science

ERIC Educational Resources Information Center

Rozek, Christopher S.; Hyde, Janet S.; Svoboda, Ryan C.; Hulleman, Chris S.; Harackiewicz, Judith M.

2015-01-01

A foundation in science, technology, engineering, and mathematics (STEM) education is critical for students' college and career advancement, but many U.S. students fail to take advanced mathematics and science classes in high school. Research has neglected the potential role of parents in enhancing students' motivation for pursuing STEM courses.…

The Opinions of Middle School Mathematics Teachers on the Integration of Mathematics Course and Social Issues

ERIC Educational Resources Information Center

Turhan Turkkan, Buket; Karakus, Memet

2018-01-01

The purpose of this study is to examine the opinions of middle school mathematics teachers on the integration of mathematics course and social issues. For this purpose, qualitative research method was used in this study. As for determining the participants of the research, criterion sampling among purposeful sampling methods was used. Being a…

Grounded and embodied mathematical cognition: Promoting mathematical insight and proof using action and language.

PubMed

Nathan, Mitchell J; Walkington, Candace

2017-01-01

We develop a theory of grounded and embodied mathematical cognition (GEMC) that draws on action-cognition transduction for advancing understanding of how the body can support mathematical reasoning. GEMC proposes that participants' actions serve as inputs capable of driving the cognition-action system toward associated cognitive states. This occurs through a process of transduction that promotes valuable mathematical insights by eliciting dynamic depictive gestures that enact spatio-temporal properties of mathematical entities. Our focus here is on pre-college geometry proof production. GEMC suggests that action alone can foster insight but is insufficient for valid proof production if action is not coordinated with language systems for propositionalizing general properties of objects and space. GEMC guides the design of a video game-based learning environment intended to promote students' mathematical insights and informal proofs by eliciting dynamic gestures through in-game directed actions. GEMC generates several hypotheses that contribute to theories of embodied cognition and to the design of science, technology, engineering, and mathematics (STEM) education interventions. Pilot study results with a prototype video game tentatively support theory-based predictions regarding the role of dynamic gestures for fostering insight and proof-with-insight, and for the role of action coupled with language to promote proof-with-insight. But the pilot yields mixed results for deriving in-game interventions intended to elicit dynamic gesture production. Although our central purpose is an explication of GEMC theory and the role of action-cognition transduction, the theory-based video game design reveals the potential of GEMC to improve STEM education, and highlights the complex challenges of connecting embodiment research to education practices and learning environment design.

Middle School Mathematics: 2006-07 to 2008-09. Impact Evaluation. E&R Report No. 10.11

ERIC Educational Resources Information Center

Paeplow, Colleen

2010-01-01

In 2006-07, seven Wake County Public School System (WCPSS) middle schools piloted Algebraic Thinking as an alternate approach to teaching middle school mathematics. Algebraic Thinking was developed to help students in grade 6 reach higher mathematics courses by combining the regular and advanced middle school mathematics courses into one…

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

PubMed Central

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

2011-01-01

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

Socioeconomic variation, number competence, and mathematics learning difficulties in young children.

PubMed

Jordan, Nancy C; Levine, Susan C

2009-01-01

As a group, children from disadvantaged, low-income families perform substantially worse in mathematics than their counterparts from higher-income families. Minority children are disproportionately represented in low-income populations, resulting in significant racial and social-class disparities in mathematics learning linked to diminished learning opportunities. The consequences of poor mathematics achievement are serious for daily functioning and for career advancement. This article provides an overview of children's mathematics difficulties in relation to socioeconomic status (SES). We review foundations for early mathematics learning and key characteristics of mathematics learning difficulties. A particular focus is the delays or deficiencies in number competencies exhibited by low-income children entering school. Weaknesses in number competence can be reliably identified in early childhood, and there is good evidence that most children have the capacity to develop number competence that lays the foundation for later learning.

Advancements in Research Synthesis Methods: From a Methodologically Inclusive Perspective

ERIC Educational Resources Information Center

Suri, Harsh; Clarke, David

2009-01-01

The dominant literature on research synthesis methods has positivist and neo-positivist origins. In recent years, the landscape of research synthesis methods has changed rapidly to become inclusive. This article highlights methodologically inclusive advancements in research synthesis methods. Attention is drawn to insights from interpretive,…

Advanced MRI Methods for Assessment of Chronic Liver Disease

PubMed Central

Taouli, Bachir; Ehman, Richard L.; Reeder, Scott B.

2010-01-01

MRI plays an increasingly important role for assessment of patients with chronic liver disease. MRI has numerous advantages, including lack of ionizing radiation and the possibility of performing multiparametric imaging. With recent advances in technology, advanced MRI methods such as diffusion-, perfusion-weighted MRI, MR elastography, chemical shift based fat-water separation and MR spectroscopy can now be applied to liver imaging. We will review the respective roles of these techniques for assessment of chronic liver disease. PMID:19542391

The Impact of Cooperative Learning Methods on Elementary Preservice Education Teachers' Mathematics Achievement and Anxiety

ERIC Educational Resources Information Center

Swift, Elijah Raford, Jr.

2012-01-01

The purpose of this study was to address the gap in research regarding the use of cooperative learning instructional methods in college mathematics courses to prepare future teachers. Bruner's constructivist theory and social interdependence theory guided this study. The research questions focused on the effects of the use of cooperative learning…

The Crossroads between Biology and Mathematics: The Scientific Method as the Basics of Scientific Literacy

ERIC Educational Resources Information Center

Karsai, Istvan; Kampis, George

2010-01-01

Biology is changing and becoming more quantitative. Research is creating new challenges that need to be addressed in education as well. New educational initiatives focus on combining laboratory procedures with mathematical skills, yet it seems that most curricula center on a single relationship between scientific knowledge and scientific method:…

Kindergarten Children's Interactions with Touchscreen Mathematics Virtual Manipulatives: An Innovative Mixed Methods Analysis

ERIC Educational Resources Information Center

Tucker, Stephen I.; Lommatsch, Christina W.; Moyer-Packenham, Patricia S.; Anderson-Pence, Katie L.; Symanzik, Jürgen

2017-01-01

The purpose of this study was to examine patterns of mathematical practices evident during children's interactions with touchscreen mathematics virtual manipulatives. Researchers analyzed 33 Kindergarten children's interactions during activities involving apps featuring mathematical content of early number sense or quantity in base ten, recorded…

Development of Advanced Methods of Structural and Trajectory Analysis for Transport Aircraft

NASA Technical Reports Server (NTRS)

Ardema, Mark D.

1996-01-01

In this report the author describes: (1) development of advanced methods of structural weight estimation, and (2) development of advanced methods of flight path optimization. A method of estimating the load-bearing fuselage weight and wing weight of transport aircraft based on fundamental structural principles has been developed. This method of weight estimation represents a compromise between the rapid assessment of component weight using empirical methods based on actual weights of existing aircraft and detailed, but time-consuming, analysis using the finite element method. The method was applied to eight existing subsonic transports for validation and correlation. Integration of the resulting computer program, PDCYL, has been made into the weights-calculating module of the AirCraft SYNThesis (ACSYNT) computer program. ACSYNT bas traditionally used only empirical weight estimation methods; PDCYL adds to ACSYNT a rapid, accurate means of assessing the fuselage and wing weights of unconventional aircraft. PDCYL also allows flexibility in the choice of structural concept, as well as a direct means of determining the impact of advanced materials on structural weight.

The written mathematical communication profile of prospective math teacher in mathematical proving

NASA Astrophysics Data System (ADS)

Pantaleon, K. V.; Juniati, D.; Lukito, A.; Mandur, K.

2018-01-01

Written mathematical communication is the process of expressing mathematical ideas and understanding in writing. It is one of the important aspects that must be mastered by the prospective math teacher as tool of knowledge transfer. This research was a qualitative research that aimed to describe the mathematical communication profile of the prospective mathematics teacher in mathematical proving. This research involved 48 students of Mathematics Education Study Program; one of them with moderate math skills was chosen as the main subject. Data were collected through tests, assignments, and task-based interviews. The results of this study point out that in the proof of geometry, the subject explains what is understood, presents the idea in the form of drawing and symbols, and explains the content/meaning of a representation accurately and clearly, but the subject can not convey the argument systematically and logically. Whereas in the proof of algebra, the subject describes what is understood, explains the method used, and describes the content/meaning of a symbolic representation accurately, systematically, logically, but the argument presented is not clear because it is insufficient detailed and complete.

Soundoff: Mathematics Is Getting Easier.

ERIC Educational Resources Information Center

Usiskin, Zalman

1984-01-01

Teaching mathematics in hard ways, rather than using easier methods or technology, is described. Employing the most efficient means possible to solve a problem is the essence of good mathematics, rather than wasting time in practicing obsolete skills. (MNS)

Advanced soft computing diagnosis method for tumour grading.

PubMed

Papageorgiou, E I; Spyridonos, P P; Stylios, C D; Ravazoula, P; Groumpos, P P; Nikiforidis, G N

2006-01-01

To develop an advanced diagnostic method for urinary bladder tumour grading. A novel soft computing modelling methodology based on the augmentation of fuzzy cognitive maps (FCMs) with the unsupervised active Hebbian learning (AHL) algorithm is applied. One hundred and twenty-eight cases of urinary bladder cancer were retrieved from the archives of the Department of Histopathology, University Hospital of Patras, Greece. All tumours had been characterized according to the classical World Health Organization (WHO) grading system. To design the FCM model for tumour grading, three experts histopathologists defined the main histopathological features (concepts) and their impact on grade characterization. The resulted FCM model consisted of nine concepts. Eight concepts represented the main histopathological features for tumour grading. The ninth concept represented the tumour grade. To increase the classification ability of the FCM model, the AHL algorithm was applied to adjust the weights of the FCM. The proposed FCM grading model achieved a classification accuracy of 72.5%, 74.42% and 95.55% for tumours of grades I, II and III, respectively. An advanced computerized method to support tumour grade diagnosis decision was proposed and developed. The novelty of the method is based on employing the soft computing method of FCMs to represent specialized knowledge on histopathology and on augmenting FCMs ability using an unsupervised learning algorithm, the AHL. The proposed method performs with reasonably high accuracy compared to other existing methods and at the same time meets the physicians' requirements for transparency and explicability.

Johannes Kepler and his contribution to Applied Mathematics

NASA Astrophysics Data System (ADS)

Pichler, Franz

The worldwide renown of Johannes Kepler is based above all on his contribution to astronomy. The 3 Kepler's Laws relating to the planets are well known and will ensure that his name is remembered by future generations. Besides his astronomical work, Kepler also made important contributions in the fields of theology, physics, phylosophy and mathematics. The actual paper discusses the advances by Kepler in the application of mathematics to the solution of "real life problems". The author made a concise account of some of the disciples by Kepler: Klug, Wieleitner, Caspar, Hammer, paying particular attention to works published by Kepler while he was living in Linz (1612-1628). The Kepler's contribution to applied mathematics is an example supremely worthy of emulation, the author concludes.

Mathematics for the Student Scientist

NASA Astrophysics Data System (ADS)

Lauten, A. Darien; Lauten, Gary N.

1998-03-01

The Earth Day:Forest Watch Program, introduces elementary, middle, and secondary students to field laboratory, and satellite-data analysis methods for assessing the health of Eastern White Pine ( Pinus strobus). In this Student-Scientist Partnership program, mathematics, as envisioned in the NCTM Standards, arises naturally and provides opportunities for science-mathematics interdisciplinary student learning. School mathematics becomes the vehicle for students to quantify, represent, analyze, and interpret meaningful, real data.

The Influence of a Reform-Based Mathematics Methods Course on Preservice Teachers' Beliefs

ERIC Educational Resources Information Center

Evans, Brian R.; Leonard, Jacqueline; Krier, Kathleen; Ryan, Steve

2013-01-01

Beliefs about teaching mathematics and urban students' ability to learn mathematics are often overlooked in the discourse on highly qualified teachers. Altering teacher experiences has the potential to change their beliefs. It was found in this qualitative case study that preservice teachers' beliefs about teaching mathematics to urban students…

The Acquisition of Mathematics Pedagogical Content Knowledge in University Mathematics Education Courses: Results of a Mixed Methods Study on the Effectiveness of Teacher Education in Germany

ERIC Educational Resources Information Center

Buchholtz, Nils Frederik

2017-01-01

This paper reports on a longitudinal mixed methods evaluation study on the acquisition and development of mathematical pedagogical content knowledge (MPCK) of future teachers at several German universities. The study is a German supplementary study to the international comparative TEDS-M 2008 study. Besides the pedagogical content knowledge that…

Research in Mathematics Education.

ERIC Educational Resources Information Center

Shumway, Richard J., Ed.

This volume represents an effort to develop a definitive reference work on research in mathematics education. The reference is divided into two parts. Part 1, on the research process, focuses on problems of research methods and their relevance to research in mathematics education. Part 1 also introduces the beginner to some of the issues and…

Demonstration Lessons in Mathematics Education: Teachers' Observation Foci and Intended Changes in Practice

ERIC Educational Resources Information Center

Clarke, Doug; Roche, Anne; Wilkie, Karina; Wright, Vince; Brown, Jill; Downton, Ann; Horne, Marj; Knight, Rose; McDonough, Andrea; Sexton, Matthew; Worrall, Chris

2013-01-01

As part of a teacher professional learning project in mathematics education, university mathematics educators taught demonstration lessons in project primary schools. These lessons were part of a "pre-brief, teaching, and debrief" process, in which up to eight teachers observed each lesson. Using brief questionnaires completed in advance of the…

Mathematical Games

ERIC Educational Resources Information Center

Gardner, Martin

1978-01-01

Describes the life and work of Charles Peirce, U.S. mathematician and philosopher. His accomplishments include contributions to logic, the foundations of mathematics and scientific method, and decision theory and probability theory. (MA)

METHODS ADVANCEMENT FOR MILK ANALYSIS: THE MAMA STUDY

EPA Science Inventory

The Methods Advancement for Milk Analysis (MAMA) study was designed by US EPA and CDC investigators to provide data to support the technological and study design needs of the proposed National Children=s Study (NCS). The NCS is a multi-Agency-sponsored study, authorized under the...

Role of linguistic skills in fifth-grade mathematics.

PubMed

Kleemans, Tijs; Segers, Eliane; Verhoeven, Ludo

2018-03-01

The current study investigated the direct and indirect relations between basic linguistic skills (i.e., phonological skills and grammatical ability) and advanced linguistic skills (i.e., academic vocabulary and verbal reasoning), on the one hand, and fifth-grade mathematics (i.e., arithmetic, geometry, and fractions), on the other, taking working memory and general intelligence into account and controlling for socioeconomic status, age, and gender. The results showed the basic linguistic representations of 167 fifth graders to be indirectly related to their geometric and fraction skills via arithmetic. Furthermore, advanced linguistic skills were found to be directly related to geometry and fractions after controlling for arithmetic. It can be concluded that linguistic skills directly and indirectly relate to mathematical ability in the upper grades of primary education, which highlights the importance of paying attention to such skills in the school curriculum. Copyright © 2017 Elsevier Inc. All rights reserved.

Proofs and Refutations in the Undergraduate Mathematics Classroom

ERIC Educational Resources Information Center

Larsen, Sean; Zandieh, Michelle

2008-01-01

In his 1976 book, "Proofs and Refutations," Lakatos presents a collection of case studies to illustrate methods of mathematical discovery in the history of mathematics. In this paper, we reframe these methods in ways that we have found make them more amenable for use as a framework for research on learning and teaching mathematics. We present an…

Does CAS Use Disadvantage Girls in VCE Mathematics?

ERIC Educational Resources Information Center

Forgasz, Helen; Tan, Hazel

2010-01-01

In 2009, four mathematics subjects were offered at the year 12 level in the Victorian Certificate of Education (VCE). The two subjects at the intermediate level--Mathematical Methods and Mathematical Methods CAS--run in parallel, that is, a student can be enrolled in only one or the other, the choice being made at the school level. The curricular…

The effect of Missouri mathematics project learning model on students’ mathematical problem solving ability

NASA Astrophysics Data System (ADS)

Handayani, I.; Januar, R. L.; Purwanto, S. E.

2018-01-01

This research aims to know the influence of Missouri Mathematics Project Learning Model to Mathematical Problem-solving Ability of Students at Junior High School. This research is a quantitative research and uses experimental research method of Quasi Experimental Design. The research population includes all student of grade VII of Junior High School who are enrolled in the even semester of the academic year 2016/2017. The Sample studied are 76 students from experimental and control groups. The sampling technique being used is cluster sampling method. The instrument is consisted of 7 essay questions whose validity, reliability, difficulty level and discriminating power have been tested. Before analyzing the data by using t-test, the data has fulfilled the requirement for normality and homogeneity. The result of data shows that there is the influence of Missouri mathematics project learning model to mathematical problem-solving ability of students at junior high school with medium effect.

Vistas in applied mathematics: Numerical analysis, atmospheric sciences, immunology

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

Balakrishnan, A.V.; Dorodnitsyn, A.A.; Lions, J.L.

1986-01-01

Advances in the theory and application of numerical modeling techniques are discussed in papers contributed, primarily by Soviet scientists, on the occasion of the 60th birthday of Gurii I. Marchuk. Topics examined include splitting techniques for computations of industrial flows, the mathematical foundations of the k-epsilon turbulence model, splitting methods for the solution of the incompressible Navier-Stokes equations, the approximation of inhomogeneous hyperbolic boundary-value problems, multigrid methods, and the finite-element approximation of minimal surfaces. Consideration is given to dynamic modeling of moist atmospheres, satellite observations of the earth radiation budget and the problem of energy-active ocean regions, a numerical modelmore » of the biosphere for use with GCMs, and large-scale modeling of ocean circulation. Also included are several papers on modeling problems in immunology.« less

Advanced methods for light trapping in optically thin silicon solar cells

NASA Astrophysics Data System (ADS)

Nagel, James Richard

2011-12-01

The field of light trapping is the study of how best to absorb light in a thin film of material when most light either reflects away at the surface or transmits straight through to the other side. This has tremendous application to the field of photovoltaics where thin silicon films can be manufactured cheaply, but also fail to capture all of the available photons in the solar spectrum. Advancements in light trapping therefore bring us closer to the day when photovoltaic devices may reach grid parity with traditional fossil fuels on the electrical energy market. This dissertation advances our understanding of light trapping by first modeling the effects of loss in planar dielectric waveguides. The mathematical framework developed here can be used to model any arbitrary three-layer structure with mixed gain or loss and then extract the total field solution for the guided modes. It is found that lossy waveguides possess a greater number of eigenmodes than their lossless counterparts, and that these "loss guided" modes attenuate much more rapidly than conventional modes. Another contribution from this dissertation is the exploration of light trapping through the use of dielectric nanospheres embedded directly within the active layer of a thin silicon film. The primary benefit to this approach is that the device can utilize a surface nitride layer serving as an antireflective coating while still retaining the benefits of light trapping within the film. The end result is that light trapping and light injection are effectively decoupled from each other and may be independently optimized within a single photovoltaic device. The final contribution from this work is a direct numerical comparison between multiple light trapping schemes. This allows us to quantify the relative performances of various design techniques against one another and objectively determine which ideas tend to capture the most light. Using numerical simulation, this work directly compares the absorption

Sam's progress with learning mathematics.

PubMed

Haslam, Lynne

2007-07-01

Sam is 18 years old and has Down syndrome. He achieved a grade in the standard assessment of mathematics (GCSE) at 16 years of age. This paper describes the part played in his success in school by the Kumon method of teaching mathematics, identifies the benefits of the small steps and lots of practice built in to the method and illustrates the way Sam applied his Kumon learning in school.

Advancing Inclusive Mathematics Education: Strategies and Resources for Effective IEP Practices

ERIC Educational Resources Information Center

Tan, Paulo

2017-01-01

Personal experiences promoting inclusive mathematics education for my own child have mostly been met with staunch resistance on the part of educators, and a resulting breakdown in collaborative efforts during individualized education program (IEP) meetings. However, I found that utilizing certain strategies and introducing innovative mathematics…

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

NASA Astrophysics Data System (ADS)

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

2016-02-01

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

The Association between Secondary Mathematics and First Year University Performance in Health Sciences

ERIC Educational Resources Information Center

Joyce, Christopher; Hine, Gregory; Anderton, Ryan

2017-01-01

In recent years, there has been a significant decline in the rate of participation in secondary school mathematics courses within Australia, particularly in advanced or higher level mathematics. The aim of this study was to investigate how grade point average (GPA) differed between five health science degrees at an Australian university. The…

A mathematical representation of an advanced helicopter for piloted simulator investigations of control system and display variations

NASA Technical Reports Server (NTRS)

Aiken, E. W.

1980-01-01

A mathematical model of an advanced helicopter is described. The model is suitable for use in control/display research involving piloted simulation. The general design approach for the six degree of freedom equations of motion is to use the full set of nonlinear gravitational and inertial terms of the equations and to express the aerodynamic forces and moments as the reference values and first order terms of a Taylor series expansion about a reference trajectory defined as a function of longitudinal airspeed. Provisions for several different specific and generic flight control systems are included in the model. The logic required to drive various flight control and weapon delivery symbols on a pilot's electronic display is also provided. Finally, the model includes a simplified representation of low altitude wind and turbulence effects. This model was used in a piloted simulator investigation of the effects of control system and display variations for an attack helicopter mission.

Synchronous Online Collaborative Professional Development for Elementary Mathematics Teachers

ERIC Educational Resources Information Center

Francis, Krista; Jacobsen, Michele

2013-01-01

Math is often taught poorly emphasizing rote, procedural methods rather than creativity and problem solving. Alberta Education developed a new mathematics curriculum to transform mathematics teaching to inquiry driven methods. This revised curriculum provides a new vision for mathematics and creates opportunities and requirements for professional…

EpiModel: An R Package for Mathematical Modeling of Infectious Disease over Networks.

PubMed

Jenness, Samuel M; Goodreau, Steven M; Morris, Martina

2018-04-01

Package EpiModel provides tools for building, simulating, and analyzing mathematical models for the population dynamics of infectious disease transmission in R. Several classes of models are included, but the unique contribution of this software package is a general stochastic framework for modeling the spread of epidemics on networks. EpiModel integrates recent advances in statistical methods for network analysis (temporal exponential random graph models) that allow the epidemic modeling to be grounded in empirical data on contacts that can spread infection. This article provides an overview of both the modeling tools built into EpiModel , designed to facilitate learning for students new to modeling, and the application programming interface for extending package EpiModel , designed to facilitate the exploration of novel research questions for advanced modelers.

Mapping Mathematics in Classroom Discourse

ERIC Educational Resources Information Center

Herbel-Eisenmann, Beth A.; Otten, Samuel

2011-01-01

This article offers a particular analytic method from systemic functional linguistics, "thematic analysis," which reveals the mathematical meaning potentials construed in discourse. Addressing concerns that discourse analysis is too often content-free, thematic analysis provides a way to represent semantic structures of mathematical content,…

Teaching the Mathematics of Radioactive Dating.

ERIC Educational Resources Information Center

Shea, James H.

2001-01-01

Describes a method used to teach the concept of radiometric dating using mathematical equations. Explores the lack of information in textbooks on how to solve radiometric dating problems using mathematical concepts. (SAH)

Advanced stress analysis methods applicable to turbine engine structures

NASA Technical Reports Server (NTRS)

Pian, T. H. H.

1985-01-01

Advanced stress analysis methods applicable to turbine engine structures are investigated. Constructions of special elements which containing traction-free circular boundaries are investigated. New versions of mixed variational principle and version of hybrid stress elements are formulated. A method is established for suppression of kinematic deformation modes. semiLoof plate and shell elements are constructed by assumed stress hybrid method. An elastic-plastic analysis is conducted by viscoplasticity theory using the mechanical subelement model.

Current advances in mathematical modeling of anti-cancer drug penetration into tumor tissues.

PubMed

Kim, Munju; Gillies, Robert J; Rejniak, Katarzyna A

2013-11-18

Delivery of anti-cancer drugs to tumor tissues, including their interstitial transport and cellular uptake, is a complex process involving various biochemical, mechanical, and biophysical factors. Mathematical modeling provides a means through which to understand this complexity better, as well as to examine interactions between contributing components in a systematic way via computational simulations and quantitative analyses. In this review, we present the current state of mathematical modeling approaches that address phenomena related to drug delivery. We describe how various types of models were used to predict spatio-temporal distributions of drugs within the tumor tissue, to simulate different ways to overcome barriers to drug transport, or to optimize treatment schedules. Finally, we discuss how integration of mathematical modeling with experimental or clinical data can provide better tools to understand the drug delivery process, in particular to examine the specific tissue- or compound-related factors that limit drug penetration through tumors. Such tools will be important in designing new chemotherapy targets and optimal treatment strategies, as well as in developing non-invasive diagnosis to monitor treatment response and detect tumor recurrence.

Mathematics in modern immunology

DOE PAGES

Castro, Mario; Lythe, Grant; Molina-París, Carmen; ...

2016-02-19

Mathematical and statistical methods enable multidisciplinary approaches that catalyse discovery. Together with experimental methods, they identify key hypotheses, define measurable observables and reconcile disparate results. Here, we collect a representative sample of studies in T-cell biology that illustrate the benefits of modelling–experimental collaborations and that have proven valuable or even groundbreaking. Furthermore, we conclude that it is possible to find excellent examples of synergy between mathematical modelling and experiment in immunology, which have brought significant insight that would not be available without these collaborations, but that much remains to be discovered.

Mathematics in modern immunology

PubMed Central

Castro, Mario; Lythe, Grant; Molina-París, Carmen; Ribeiro, Ruy M.

2016-01-01

Mathematical and statistical methods enable multidisciplinary approaches that catalyse discovery. Together with experimental methods, they identify key hypotheses, define measurable observables and reconcile disparate results. We collect a representative sample of studies in T-cell biology that illustrate the benefits of modelling–experimental collaborations and that have proven valuable or even groundbreaking. We conclude that it is possible to find excellent examples of synergy between mathematical modelling and experiment in immunology, which have brought significant insight that would not be available without these collaborations, but that much remains to be discovered. PMID:27051512

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

PubMed

Mori, Giuliano

2017-03-01

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

Students in Rural Schools Have Limited Access to Advanced Mathematics Courses. Issue Brief No. 7

ERIC Educational Resources Information Center

Graham, Suzanne E.

2009-01-01

This Carsey brief reveals that students in rural areas and small towns have less access to higher-level mathematics courses than students in urban settings, which results in serious educational consequences, including lower scores on assessment tests and fewer qualified students entering science, technology, engineering, and mathematics (STEM) job…

MAESTRO: Methods and Advanced Equipment for Simulation and Treatment in Radio-Oncology

NASA Astrophysics Data System (ADS)

Barthe, Jean; Hugon, Régis; Nicolai, Jean Philippe

2007-12-01

The integrated project MAESTRO (Methods and Advanced Equipment for Simulation and Treatment in Radio-Oncology) under contract with the European Commission in life sciences FP6 (LSHC-CT-2004-503564), concerns innovative research to develop and validate in clinical conditions, advanced methods and equipment needed in cancer treatment for new modalities in high-conformal external radiotherapy using electrons, photons and protons beams of high energy.

Advanced Doubling Adding Method for Radiative Transfer in Planetary Atmospheres

NASA Astrophysics Data System (ADS)

Liu, Quanhua; Weng, Fuzhong

2006-12-01

The doubling adding method (DA) is one of the most accurate tools for detailed multiple-scattering calculations. The principle of the method goes back to the nineteenth century in a problem dealing with reflection and transmission by glass plates. Since then the doubling adding method has been widely used as a reference tool for other radiative transfer models. The method has never been used in operational applications owing to tremendous demand on computational resources from the model. This study derives an analytical expression replacing the most complicated thermal source terms in the doubling adding method. The new development is called the advanced doubling adding (ADA) method. Thanks also to the efficiency of matrix and vector manipulations in FORTRAN 90/95, the advanced doubling adding method is about 60 times faster than the doubling adding method. The radiance (i.e., forward) computation code of ADA is easily translated into tangent linear and adjoint codes for radiance gradient calculations. The simplicity in forward and Jacobian computation codes is very useful for operational applications and for the consistency between the forward and adjoint calculations in satellite data assimilation.

Mathematics Curriculum Based Measurement to Predict State Test Performance: A Comparison of Measures and Methods

ERIC Educational Resources Information Center

Stevens, Olinger; Leigh, Erika

2012-01-01

Scope and Method of Study: The purpose of the study is to use an empirical approach to identify a simple, economical, efficient, and technically adequate performance measure that teachers can use to assess student growth in mathematics. The current study has been designed to expand the body of research for math CBM to further examine technical…

The relationship among mathematics anxiety, beliefs about mathematics, mathematics self-efficacy, and mathematics performance in associate degree nursing students.

PubMed

Walsh, Kathleen A

2008-01-01

This research explored nursing students' mathematics anxiety, beliefs about mathematics, and mathematics self-efficacy in relation to performance on a medication mathematics test. Results revealed that the participants experienced some mathematics anxiety and had positive beliefs about mathematics and mathematics self-efficacy. Qualitative responses indicated that participants worried about the consequences of failing the medication mathematics test and that practice helped reduce this anxiety. In addition, participants acknowledged the importance of correct dosage calculations for nursing practice. Implications for nursing education are discussed.

Examining the Impact of a Video Case-Based Mathematics Methods Course on Secondary Pre-Service Teachers' Skills at Analysing Students' Strategies

ERIC Educational Resources Information Center

Martinez, Mara Vanina; Superfine, Alison Castro; Carlton, Theresa; Dasgupta, Chandan

2015-01-01

This paper focuses on results from a study conducted with two cohorts of pre-service teachers (PSTs) in a video case-based mathematics methods course at a large Midwestern university in the US. The motivation for this study was to look beyond whether or not PSTs pay attention to mathematical thinking of students, as shown by previous studies when…

Quantifying temporal glucose variability in diabetes via continuous glucose monitoring: mathematical methods and clinical application.

PubMed

Kovatchev, Boris P; Clarke, William L; Breton, Marc; Brayman, Kenneth; McCall, Anthony

2005-12-01

Continuous glucose monitors (CGMs) collect detailed blood glucose (BG) time series, which carry significant information about the dynamics of BG fluctuations. In contrast, the methods for analysis of CGM data remain those developed for infrequent BG self-monitoring. As a result, important information about the temporal structure of the data is lost during the translation of raw sensor readings into clinically interpretable statistics and images. The following mathematical methods are introduced into the field of CGM data interpretation: (1) analysis of BG rate of change; (2) risk analysis using previously reported Low/High BG Indices and Poincare (lag) plot of risk associated with temporal BG variability; and (3) spatial aggregation of the process of BG fluctuations and its Markov chain visualization. The clinical application of these methods is illustrated by analysis of data of a patient with Type 1 diabetes mellitus who underwent islet transplantation and with data from clinical trials. Normative data [12,025 reference (YSI device, Yellow Springs Instruments, Yellow Springs, OH) BG determinations] in patients with Type 1 diabetes mellitus who underwent insulin and glucose challenges suggest that the 90%, 95%, and 99% confidence intervals of BG rate of change that could be maximally sustained over 15-30 min are [-2,2], [-3,3], and [-4,4] mg/dL/min, respectively. BG dynamics and risk parameters clearly differentiated the stages of transplantation and the effects of medication. Aspects of treatment were clearly visualized by graphs of BG rate of change and Low/High BG Indices, by a Poincare plot of risk for rapid BG fluctuations, and by a plot of the aggregated Markov process. Advanced analysis and visualization of CGM data allow for evaluation of dynamical characteristics of diabetes and reveal clinical information that is inaccessible via standard statistics, which do not take into account the temporal structure of the data. The use of such methods improves the

An Investigation of Teachers' Noticing, Cognitive Demand, and Mathematical Knowledge for Teaching: Video Reflections in an Elementary Mathematics Context

ERIC Educational Resources Information Center

Coddington, Lorelei R.

2014-01-01

In the past decade, mathematics performance by all students, especially minority students in low socioeconomic schools, has shown limited improvement nationwide (NCES, 2011). Traditionally in the United States, mathematics has consisted of arithmetic and computational fluency; however, mathematics researchers widely believe that this method of…

Predicting Relationships between Mathematics Anxiety, Mathematics Teaching Anxiety, Self-Efficacy Beliefs towards Mathematics and Mathematics Teaching

ERIC Educational Resources Information Center

Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent

2017-01-01

The purpose of the research is to investigate the relationships between self-efficacy beliefs toward mathematics, mathematics anxiety and self-efficacy beliefs toward mathematics teaching, mathematics teaching anxiety variables and testing the relationships between these variables with structural equation model. The sample of the research, which…

Advanced Computational Methods for Optimization of Non-Periodic Inspection Intervals for Aging Infrastructure

DTIC Science & Technology

2017-01-05

AFRL-AFOSR-JP-TR-2017-0002 Advanced Computational Methods for Optimization of Non-Periodic Inspection Intervals for Aging Infrastructure Manabu...Computational Methods for Optimization of Non-Periodic Inspection Intervals for Aging Infrastructure 5a.  CONTRACT NUMBER 5b.  GRANT NUMBER FA2386...UNLIMITED: PB Public Release 13. SUPPLEMENTARY NOTES 14. ABSTRACT This report for the project titled ’Advanced Computational Methods for Optimization of

Mathematics Instruction: Do Classrooms Matter?

ERIC Educational Resources Information Center

Desoete, Annemie; Stock, Pieter

2013-01-01

Counting abilities have been described as determinative precursors for a good development of later mathematical abilities. However, an important part of variance in mathematical achievement has also been associated with differences between instruction methods given in schools. In this study counting and instruction as predictors for mathematical…

On the role of visual experience in mathematical development: Evidence from blind mathematicians.

PubMed

Amalric, Marie; Denghien, Isabelle; Dehaene, Stanislas

2018-04-01

Advanced mathematical reasoning, regardless of domain or difficulty, activates a reproducible set of bilateral brain areas including intraparietal, inferior temporal and dorsal prefrontal cortex. The respective roles of genetics, experience and education in the development of this math-responsive network, however, remain unresolved. Here, we investigate the role of visual experience by studying the exceptional case of three professional mathematicians who were blind from birth (n=1) or became blind during childhood (n=2). Subjects were scanned with fMRI while they judged the truth value of spoken mathematical and nonmathematical statements. Blind mathematicians activated the classical network of math-related areas during mathematical reflection, similar to that found in a group of sighted professional mathematicians. Thus, brain networks for advanced mathematical reasoning can develop in the absence of visual experience. Additional activations were found in occipital cortex, even in individuals who became blind during childhood, suggesting that either mental imagery or a more radical repurposing of visual cortex may occur in blind mathematicians. Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.

Explorations with 142857: Connecting the Elementary with the Advanced

ERIC Educational Resources Information Center

Flores, Alfinio

2008-01-01

University mathematics education courses do not always provide the opportunity to make connections between advanced topics and the mathematics taught in middle school or high school. Activities like the ones described in this article invite such connections. Analyzing concrete or particular examples provides a better grasp of abstract concepts.…

Reform-Based-Instructional Method and Learning Styles on Students' Achievement and Retention in Mathematics: Administrative Implications

ERIC Educational Resources Information Center

Modebelu, M. N.; Ogbonna, C. C.

2014-01-01

This study aimed at determining the effect of reform-based-instructional method learning styles on students' achievement and retention in mathematics. A sample size of 119 students was randomly selected. The quasiexperimental design comprising pre-test, post-test, and randomized control group were employed. The Collin Rose learning styles…

Using Citation Analysis Methods to Assess the Influence of Science, Technology, Engineering, and Mathematics Education Evaluations

ERIC Educational Resources Information Center

Greenseid, Lija O.; Lawrenz, Frances

2011-01-01

This study explores the use of citation analysis methods to assess the influence of program evaluations conducted within the area of science, technology, engineering, and mathematics (STEM) education. Citation analysis is widely used within scientific research communities to measure the relative influence of scientific research enterprises and/or…

An Exploration into the Potential Career Effects from Middle and High School Mathematics Experiences: A Mixed Methods Investigation into STEM Career Choice

ERIC Educational Resources Information Center

DeThomas, Elizabeth M.

2017-01-01

This mixed methods research study examined the effects of middle and high school mathematics experiences on students' choice of college major, particularly whether students decided to major in a STEM field. Social cognitive career theory was used to examine potential influences of mathematics self-efficacy and how those influences and mathematics…

Strategy to Promote Active Learning of an Advanced Research Method

ERIC Educational Resources Information Center

McDermott, Hilary J.; Dovey, Terence M.

2013-01-01

Research methods courses aim to equip students with the knowledge and skills required for research yet seldom include practical aspects of assessment. This reflective practitioner report describes and evaluates an innovative approach to teaching and assessing advanced qualitative research methods to final-year psychology undergraduate students. An…

A mathematical model of microbial enhanced oil recovery (MEOR) method for mixed type rock

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

Sitnikov, A.A.; Eremin, N.A.; Ibattulin, R.R.

1994-12-31

This paper deals with the microbial enhanced oil recovery method. It covers: (1) Mechanism of microbial influence on the reservoir was analyzed; (2) The main groups of metabolites affected by the hydrodynamic characteristics of the reservoir were determined; (3) The criterions of use of microbial influence method on the reservoir are defined. The mathematical model of microbial influence on the reservoir was made on this basis. The injection of molasse water solution with Clostridium bacterias into the mixed type of rock was used in this model. And the results of calculations were compared with experimental data.

BOOK REVIEW: Advanced Topics in Computational Partial Differential Equations: Numerical Methods and Diffpack Programming

NASA Astrophysics Data System (ADS)

Katsaounis, T. D.

2005-02-01

The scope of this book is to present well known simple and advanced numerical methods for solving partial differential equations (PDEs) and how to implement these methods using the programming environment of the software package Diffpack. A basic background in PDEs and numerical methods is required by the potential reader. Further, a basic knowledge of the finite element method and its implementation in one and two space dimensions is required. The authors claim that no prior knowledge of the package Diffpack is required, which is true, but the reader should be at least familiar with an object oriented programming language like C++ in order to better comprehend the programming environment of Diffpack. Certainly, a prior knowledge or usage of Diffpack would be a great advantage to the reader. The book consists of 15 chapters, each one written by one or more authors. Each chapter is basically divided into two parts: the first part is about mathematical models described by PDEs and numerical methods to solve these models and the second part describes how to implement the numerical methods using the programming environment of Diffpack. Each chapter closes with a list of references on its subject. The first nine chapters cover well known numerical methods for solving the basic types of PDEs. Further, programming techniques on the serial as well as on the parallel implementation of numerical methods are also included in these chapters. The last five chapters are dedicated to applications, modelled by PDEs, in a variety of fields. The first chapter is an introduction to parallel processing. It covers fundamentals of parallel processing in a simple and concrete way and no prior knowledge of the subject is required. Examples of parallel implementation of basic linear algebra operations are presented using the Message Passing Interface (MPI) programming environment. Here, some knowledge of MPI routines is required by the reader. Examples solving in parallel simple PDEs using

Do Screencasts Help to Revise Prerequisite Mathematics? An Investigation of Student Performance and Perception

ERIC Educational Resources Information Center

Loch, Birgit; Jordan, Camilla R.; Lowe, Tim W.; Mestel, Ben D.

2014-01-01

Basic calculus skills that are prerequisites for advanced mathematical studies continue to be a problem for a significant proportion of higher education students. While there are many types of revision material that could be offered to students, in this paper we investigate whether short, narrated video recordings of mathematical explanations…

Advanced Combustion Numerics and Modeling - FY18 First Quarter Report

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

Whitesides, R. A.; Killingsworth, N. J.; McNenly, M. J.

This project is focused on early stage research and development of numerical methods and models to improve advanced engine combustion concepts and systems. The current focus is on development of new mathematics and algorithms to reduce the time to solution for advanced combustion engine design using detailed fuel chemistry. The research is prioritized towards the most time-consuming workflow bottlenecks (computer and human) and accuracy gaps that slow ACS program members. Zero-RK, the fast and accurate chemical kinetics solver software developed in this project, is central to the research efforts and continues to be developed to address the current and emergingmore » needs of the engine designers, engine modelers and fuel mechanism developers.« less

Advanced classical thermodynamics

NASA Astrophysics Data System (ADS)

Emanuel, George

The theoretical and mathematical foundations of thermodynamics are presented in an advanced text intended for graduate engineering students. Chapters are devoted to definitions and postulates, the fundamental equation, equilibrium, the application of Jacobian theory to thermodynamics, the Maxwell equations, stability, the theory of real gases, critical-point theory, and chemical thermodynamics. Diagrams, graphs, tables, and sample problems are provided.

The Effect of Mathematics Research on Mathematics Majors' Mathematical Beliefs

ERIC Educational Resources Information Center

Goodson, Joshua E.

2012-01-01

This is a dissertation about the beliefs that mathematics majors have about mathematics and how their beliefs are affected by the introduction of mathematics research. The mathematics research presented to the students dealt with counting regular orbits of an action. Research has shown that the beliefs that teachers hold about mathematics…

Integrating Universal Design and Response to Intervention in Methods Courses for General Education Mathematics Teachers

ERIC Educational Resources Information Center

Buchheister, Kelley; Jackson, Christa; Taylor, Cynthia E.

2014-01-01

Traditionally, teacher education programs have placed little emphasis on preparing mathematics teachers to work with students who struggle in mathematics. Therefore, it is crucial that mathematics teacher educators explicitly prepare prospective teachers to instruct students who struggle with mathematics by providing strategies and practices that…

Priority Desires of Pre-Service Mathematics Student-Teachers in Methods Courses at the University of Botswana

ERIC Educational Resources Information Center

Kesianye, Sesutho; Garegae, Kgomotso; Chakalisa, Paul; Mogotsi, Salome

2014-01-01

This study, a survey of University of Botswana mathematics pre-service student-teachers taking introductory methods courses, was conducted to find aspects of the courses they perceived to be their priority learning desires. It aimed at evaluating whether student-teachers perceived ideas could be tapped into towards improvement of the teacher…

Teaching undergraduate mathematics in interactive groups: how does it fit with students' learning?

NASA Astrophysics Data System (ADS)

Sheryn, Louise; Ell, Fiona

2014-08-01

Debates about how undergraduate mathematics should be taught are informed by different views of what it is to learn and to do mathematics. In this qualitative study 10 students enrolled in an advanced undergraduate course in mathematics shared their views about how they best learn mathematics. After participating in a semester-long course in combinatorics, taught using a non-traditional, formal group work approach, the 10 students shared their views about how such an approach fitted in with their experience of learning mathematics. A descriptive thematic analysis of the students' responses revealed that despite being very comfortable with the traditional approach to learning new mathematics, most students were open to a formal group work approach and could see benefits from it after their participation. The students' prior conceptions of the goal of undergraduate mathematics learning and their view of themselves as 'mathematicians' framed their experience of learning mathematics in a non-traditional class.

Advanced stress analysis methods applicable to turbine engine structures

NASA Technical Reports Server (NTRS)

Pian, Theodore H. H.

1991-01-01

The following tasks on the study of advanced stress analysis methods applicable to turbine engine structures are described: (1) constructions of special elements which contain traction-free circular boundaries; (2) formulation of new version of mixed variational principles and new version of hybrid stress elements; (3) establishment of methods for suppression of kinematic deformation modes; (4) construction of semiLoof plate and shell elements by assumed stress hybrid method; and (5) elastic-plastic analysis by viscoplasticity theory using the mechanical subelement model.

Teachers' Mathematics as Mathematics-at-Work

ERIC Educational Resources Information Center

Bednarz, Nadine; Proulx, Jérôme

2017-01-01

Through recognising mathematics teachers as professionals who use mathematics in their workplace, this article traces a parallel between the mathematics enacted by teachers in their practice and the mathematics used in workplaces found in studies of professionals (e.g. nurses, engineers, bankers). This parallel is developed through the five…

Competency Based Teacher Education Component. Curriculum Methods and Materials, Elementary Mathematics and Social Studies.

ERIC Educational Resources Information Center

Woodworth, William D.

Four mathematical/social studies module clusters are presented in an effort to develop proficiency in instruction and in inductive and deductive teaching procedures. Modules within the first cluster concern systems of numeration, set operations, numbers, measurement, geometry, mathematics, and reasoning. The second mathematical cluster presents…

Preface of the "Symposium on Mathematical Models and Methods to investigate Heterogeneity in Cell and Cell Population Biology"

NASA Astrophysics Data System (ADS)

Clairambault, Jean

2016-06-01

This session investigates hot topics related to mathematical representations of cell and cell population dynamics in biology and medicine, in particular, but not only, with applications to cancer. Methods in mathematical modelling and analysis, and in statistical inference using single-cell and cell population data, should contribute to focus this session on heterogeneity in cell populations. Among other methods are proposed: a) Intracellular protein dynamics and gene regulatory networks using ordinary/partial/delay differential equations (ODEs, PDEs, DDEs); b) Representation of cell population dynamics using agent-based models (ABMs) and/or PDEs; c) Hybrid models and multiscale models to integrate single-cell dynamics into cell population behaviour; d) Structured cell population dynamics and asymptotic evolution w.r.t. relevant traits; e) Heterogeneity in cancer cell populations: origin, evolution, phylogeny and methods of reconstruction; f) Drug resistance as an evolutionary phenotype: predicting and overcoming it in therapeutics; g) Theoretical therapeutic optimisation of combined drug treatments in cancer cell populations and in populations of other organisms, such as bacteria.

New techniques for the analysis of manual control systems. [mathematical models of human operator behavior

NASA Technical Reports Server (NTRS)

Bekey, G. A.

1971-01-01

Studies are summarized on the application of advanced analytical and computational methods to the development of mathematical models of human controllers in multiaxis manual control systems. Specific accomplishments include the following: (1) The development of analytical and computer methods for the measurement of random parameters in linear models of human operators. (2) Discrete models of human operator behavior in a multiple display situation were developed. (3) Sensitivity techniques were developed which make possible the identification of unknown sampling intervals in linear systems. (4) The adaptive behavior of human operators following particular classes of vehicle failures was studied and a model structure proposed.

System principles, mathematical models and methods to ensure high reliability of safety systems

NASA Astrophysics Data System (ADS)

Zaslavskyi, V.

2017-04-01

Modern safety and security systems are composed of a large number of various components designed for detection, localization, tracking, collecting, and processing of information from the systems of monitoring, telemetry, control, etc. They are required to be highly reliable in a view to correctly perform data aggregation, processing and analysis for subsequent decision making support. On design and construction phases of the manufacturing of such systems a various types of components (elements, devices, and subsystems) are considered and used to ensure high reliability of signals detection, noise isolation, and erroneous commands reduction. When generating design solutions for highly reliable systems a number of restrictions and conditions such as types of components and various constrains on resources should be considered. Various types of components perform identical functions; however, they are implemented using diverse principles, approaches and have distinct technical and economic indicators such as cost or power consumption. The systematic use of different component types increases the probability of tasks performing and eliminates the common cause failure. We consider type-variety principle as an engineering principle of system analysis, mathematical models based on this principle, and algorithms for solving optimization problems of highly reliable safety and security systems design. Mathematical models are formalized in a class of two-level discrete optimization problems of large dimension. The proposed approach, mathematical models, algorithms can be used for problem solving of optimal redundancy on the basis of a variety of methods and control devices for fault and defects detection in technical systems, telecommunication networks, and energy systems.

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

NASA Astrophysics Data System (ADS)

Walsh, Richard

2017-01-01

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

On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process.

PubMed

Flegg, Jennifer A; Menon, Shakti N; Maini, Philip K; McElwain, D L Sean

2015-01-01

Over the last 30 years, numerous research groups have attempted to provide mathematical descriptions of the skin wound healing process. The development of theoretical models of the interlinked processes that underlie the healing mechanism has yielded considerable insight into aspects of this critical phenomenon that remain difficult to investigate empirically. In particular, the mathematical modeling of angiogenesis, i.e., capillary sprout growth, has offered new paradigms for the understanding of this highly complex and crucial step in the healing pathway. With the recent advances in imaging and cell tracking, the time is now ripe for an appraisal of the utility and importance of mathematical modeling in wound healing angiogenesis research. The purpose of this review is to pedagogically elucidate the conceptual principles that have underpinned the development of mathematical descriptions of wound healing angiogenesis, specifically those that have utilized a continuum reaction-transport framework, and highlight the contribution that such models have made toward the advancement of research in this field. We aim to draw attention to the common assumptions made when developing models of this nature, thereby bringing into focus the advantages and limitations of this approach. A deeper integration of mathematical modeling techniques into the practice of wound healing angiogenesis research promises new perspectives for advancing our knowledge in this area. To this end we detail several open problems related to the understanding of wound healing angiogenesis, and outline how these issues could be addressed through closer cross-disciplinary collaboration.

On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process

PubMed Central

Flegg, Jennifer A.; Menon, Shakti N.; Maini, Philip K.; McElwain, D. L. Sean

2015-01-01

Over the last 30 years, numerous research groups have attempted to provide mathematical descriptions of the skin wound healing process. The development of theoretical models of the interlinked processes that underlie the healing mechanism has yielded considerable insight into aspects of this critical phenomenon that remain difficult to investigate empirically. In particular, the mathematical modeling of angiogenesis, i.e., capillary sprout growth, has offered new paradigms for the understanding of this highly complex and crucial step in the healing pathway. With the recent advances in imaging and cell tracking, the time is now ripe for an appraisal of the utility and importance of mathematical modeling in wound healing angiogenesis research. The purpose of this review is to pedagogically elucidate the conceptual principles that have underpinned the development of mathematical descriptions of wound healing angiogenesis, specifically those that have utilized a continuum reaction-transport framework, and highlight the contribution that such models have made toward the advancement of research in this field. We aim to draw attention to the common assumptions made when developing models of this nature, thereby bringing into focus the advantages and limitations of this approach. A deeper integration of mathematical modeling techniques into the practice of wound healing angiogenesis research promises new perspectives for advancing our knowledge in this area. To this end we detail several open problems related to the understanding of wound healing angiogenesis, and outline how these issues could be addressed through closer cross-disciplinary collaboration. PMID:26483695

Applying NAEP to Improve Mathematics Content and Methods Courses for Preservice Elementary and Middle School Teachers

ERIC Educational Resources Information Center

Goodson-Espy, Tracy; Cifarelli, Victor V.; Pugalee, David; Lynch-Davis, Kathleen; Morge, Shelby; Salinas, Tracie

2014-01-01

This study explored how mathematics content and methods courses for preservice elementary and middle school teachers could be improved through the integration of a set of instructional materials based on the National Assessment of Educational Progress (NAEP). A set of eight instructional modules was developed and tested. The study involved 7…

Advancement of Analysis Method for Electromagnetic Screening Effect of Mountain Tunnel

NASA Astrophysics Data System (ADS)

Okutani, Tamio; Nakamura, Nobuyuki; Terada, Natsuki; Fukuda, Mitsuyoshi; Tate, Yutaka; Inada, Satoshi; Itoh, Hidenori; Wakao, Shinji

In this paper we report advancement of an analysis method for electromagnetic screening effect of mountain tunnel with a multiple conductor circuit model. On A.C. electrified railways it is a great issue to manage the influence of electromagnetic induction caused by feeding circuits. Tunnels are said to have a screening effect to reduce the electromagnetic induction because a large amount of steel is used in the tunnels. But recently the screening effect is less expected because New Austrian Tunneling Method (NATM), in which the amount of steel used is less than in conventional methods, is adopted as the standard tunneling method for constructing mountain tunnels. So we measured and analyzed the actual screening effect of mountain tunnels constructed with NATM. In the process of the analysis we have advanced a method to analyze the screening effect more precisely. In this method we can adequately model tunnel structure as a part of multiple conductor circuit.

Editorial: Latest methods and advances in biotechnology.

PubMed

Lee, Sang Yup; Jungbauer, Alois

2014-01-01

The latest "Biotech Methods and Advances" special issue of Biotechnology Journal continues the BTJ tradition of featuring the latest breakthroughs in biotechnology. The special issue is edited by our Editors-in-Chief, Prof. Sang Yup Lee and Prof. Alois Jungbauer and covers a wide array of topics in biotechnology, including the perennial favorite workhorses of the biotech industry, Chinese hamster ovary (CHO) cell and Escherichia coli. Copyright © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Mathematics Teachers' Criteria of Dimension

ERIC Educational Resources Information Center

Ural, Alattin

2014-01-01

The aim of the study is to determine mathematics teachers' decisions about dimensions of the geometric figures, criteria of dimension and consistency of decision-criteria. The research is a qualitative research and the model applied in the study is descriptive method on the basis of general scanning model. 15 mathematics teachers attended the…

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

ERIC Educational Resources Information Center

Hebert, Michael A.; Powell, Sarah R.

2016-01-01

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

Advances and future directions of research on spectral methods

NASA Technical Reports Server (NTRS)

Patera, A. T.

1986-01-01

Recent advances in spectral methods are briefly reviewed and characterized with respect to their convergence and computational complexity. Classical finite element and spectral approaches are then compared, and spectral element (or p-type finite element) approximations are introduced. The method is applied to the full Navier-Stokes equations, and examples are given of the application of the technique to several transitional flows. Future directions of research in the field are outlined.

Introduction to multigrid methods

NASA Technical Reports Server (NTRS)

Wesseling, P.

1995-01-01

These notes were written for an introductory course on the application of multigrid methods to elliptic and hyperbolic partial differential equations for engineers, physicists and applied mathematicians. The use of more advanced mathematical tools, such as functional analysis, is avoided. The course is intended to be accessible to a wide audience of users of computational methods. We restrict ourselves to finite volume and finite difference discretization. The basic principles are given. Smoothing methods and Fourier smoothing analysis are reviewed. The fundamental multigrid algorithm is studied. The smoothing and coarse grid approximation properties are discussed. Multigrid schedules and structured programming of multigrid algorithms are treated. Robustness and efficiency are considered.

Overview of the SAMSI year-long program on Statistical, Mathematical and Computational Methods for Astronomy

NASA Astrophysics Data System (ADS)

Jogesh Babu, G.

2017-01-01

A year-long research (Aug 2016- May 2017) program on `Statistical, Mathematical and Computational Methods for Astronomy (ASTRO)’ is well under way at Statistical and Applied Mathematical Sciences Institute (SAMSI), a National Science Foundation research institute in Research Triangle Park, NC. This program has brought together astronomers, computer scientists, applied mathematicians and statisticians. The main aims of this program are: to foster cross-disciplinary activities; to accelerate the adoption of modern statistical and mathematical tools into modern astronomy; and to develop new tools needed for important astronomical research problems. The program provides multiple avenues for cross-disciplinary interactions, including several workshops, long-term visitors, and regular teleconferences, so participants can continue collaborations, even if they can only spend limited time in residence at SAMSI. The main program is organized around five working groups:i) Uncertainty Quantification and Astrophysical Emulationii) Synoptic Time Domain Surveysiii) Multivariate and Irregularly Sampled Time Seriesiv) Astrophysical Populationsv) Statistics, computation, and modeling in cosmology.A brief description of each of the work under way by these groups will be given. Overlaps among various working groups will also be highlighted. How the wider astronomy community can both participate and benefit from the activities, will be briefly mentioned.

Access to Mathematics: "A Possessive Investment in Whiteness"

ERIC Educational Resources Information Center

Battey, Dan

2013-01-01

While mathematics education gives access to elite universities, higher-paying jobs, and the accumulation of wealth, it continues to be framed as a neutral curricular domain. However, data continually show differential access provided to students of color and their White peers through tracking, the availability of Advance Placement courses, and…

Advanced quantitative measurement methodology in physics education research

NASA Astrophysics Data System (ADS)

Wang, Jing

The ultimate goal of physics education research (PER) is to develop a theoretical framework to understand and improve the learning process. In this journey of discovery, assessment serves as our headlamp and alpenstock. It sometimes detects signals in student mental structures, and sometimes presents the difference between expert understanding and novice understanding. Quantitative assessment is an important area in PER. Developing research-based effective assessment instruments and making meaningful inferences based on these instruments have always been important goals of the PER community. Quantitative studies are often conducted to provide bases for test development and result interpretation. Statistics are frequently used in quantitative studies. The selection of statistical methods and interpretation of the results obtained by these methods shall be connected to the education background. In this connecting process, the issues of educational models are often raised. Many widely used statistical methods do not make assumptions on the mental structure of subjects, nor do they provide explanations tailored to the educational audience. There are also other methods that consider the mental structure and are tailored to provide strong connections between statistics and education. These methods often involve model assumption and parameter estimation, and are complicated mathematically. The dissertation provides a practical view of some advanced quantitative assessment methods. The common feature of these methods is that they all make educational/psychological model assumptions beyond the minimum mathematical model. The purpose of the study is to provide a comparison between these advanced methods and the pure mathematical methods. The comparison is based on the performance of the two types of methods under physics education settings. In particular, the comparison uses both physics content assessments and scientific ability assessments. The dissertation includes three

Will the digital computer transform classical mathematics?

PubMed

Rotman, Brian

2003-08-15

Mathematics and machines have influenced each other for millennia. The advent of the digital computer introduced a powerfully new element that promises to transform the relation between them. This paper outlines the thesis that the effect of the digital computer on mathematics, already widespread, is likely to be radical and far-reaching. To articulate this claim, an abstract model of doing mathematics is introduced based on a triad of actors of which one, the 'agent', corresponds to the function performed by the computer. The model is used to frame two sorts of transformation. The first is pragmatic and involves the alterations and progressive colonization of the content and methods of enquiry of various mathematical fields brought about by digital methods. The second is conceptual and concerns a fundamental antagonism between the infinity enshrined in classical mathematics and physics (continuity, real numbers, asymptotic definitions) and the inherently real and material limit of processes associated with digital computation. An example which lies in the intersection of classical mathematics and computer science, the P=NP problem, is analysed in the light of this latter issue.

EpiModel: An R Package for Mathematical Modeling of Infectious Disease over Networks

PubMed Central

Jenness, Samuel M.; Goodreau, Steven M.; Morris, Martina

2018-01-01

Package EpiModel provides tools for building, simulating, and analyzing mathematical models for the population dynamics of infectious disease transmission in R. Several classes of models are included, but the unique contribution of this software package is a general stochastic framework for modeling the spread of epidemics on networks. EpiModel integrates recent advances in statistical methods for network analysis (temporal exponential random graph models) that allow the epidemic modeling to be grounded in empirical data on contacts that can spread infection. This article provides an overview of both the modeling tools built into EpiModel, designed to facilitate learning for students new to modeling, and the application programming interface for extending package EpiModel, designed to facilitate the exploration of novel research questions for advanced modelers. PMID:29731699

A Follow-up Study of Two Methods of Teaching Mathematics: Traditional versus New Math

ERIC Educational Resources Information Center

Walton, Gene A.; And Others

1977-01-01

When high school mathematics grades and test scores were analyzed, findings showed that high- and middle-ability students who had a modern mathematics course in the seventh grade received significantly higher grades in Algebra I, II, III, and Geometry than did students who had a traditional seventh grade mathematics course. (DT)

Teaching Mathematical Modeling in Mathematics Education

ERIC Educational Resources Information Center

Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant

2016-01-01

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

Mathematization in introductory physics

NASA Astrophysics Data System (ADS)

Brahmia, Suzanne M.

doing physics. It contrasts with their more common experience with mathematics as the practice of specified procedures to improve efficiency. This paper describes new curricular materials based on invention instruction provide students with opportunities to generate mathematical relationships in physics, and the paper presents preliminary evidence of the effectiveness of this method with mathematically underprepared engineering students.

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

NASA Astrophysics Data System (ADS)

Mead, J.; Wright, G. B.

2013-12-01

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

An Empirical Investigation of Differences between Mathematics Specialists and Non-Specialists at the High School Level in Cyprus: A Logistic Regression Approach

ERIC Educational Resources Information Center

Papanastasiou, Elena C.; Zembylas, Michalinos

2006-01-01

The data obtained from high-school seniors for the Third International Mathematics and Science Study (TIMSS) for the country of Cyprus appear to be contradictory. Although Cypriot students did not perform well in mathematics in elementary school, middle school, and in the non-advanced sectors of high school, students in advanced mathematics…

Group investigation with scientific approach in mathematics learning

NASA Astrophysics Data System (ADS)

Indarti, D.; Mardiyana; Pramudya, I.

2018-03-01

The aim of this research is to find out the effect of learning model toward mathematics achievement. This research is quasi-experimental research. The population of research is all VII grade students of Karanganyar regency in the academic year of 2016/2017. The sample of this research was taken using stratified cluster random sampling technique. Data collection was done based on mathematics achievement test. The data analysis technique used one-way ANOVA following the normality test with liliefors method and homogeneity test with Bartlett method. The results of this research is the mathematics learning using Group Investigation learning model with scientific approach produces the better mathematics learning achievement than learning with conventional model on material of quadrilateral. Group Investigation learning model with scientific approach can be used by the teachers in mathematics learning, especially in the material of quadrilateral, which is can improve the mathematics achievement.

Advanced aircraft service life monitoring method via flight-by-flight load spectra

NASA Astrophysics Data System (ADS)

Lee, Hongchul

This research is an effort to understand current method and to propose an advanced method for Damage Tolerance Analysis (DTA) for the purpose of monitoring the aircraft service life. As one of tasks in the DTA, the current indirect Individual Aircraft Tracking (IAT) method for the F-16C/D Block 32 does not properly represent changes in flight usage severity affecting structural fatigue life. Therefore, an advanced aircraft service life monitoring method based on flight-by-flight load spectra is proposed and recommended for IAT program to track consumed fatigue life as an alternative to the current method which is based on the crack severity index (CSI) value. Damage Tolerance is one of aircraft design philosophies to ensure that aging aircrafts satisfy structural reliability in terms of fatigue failures throughout their service periods. IAT program, one of the most important tasks of DTA, is able to track potential structural crack growth at critical areas in the major airframe structural components of individual aircraft. The F-16C/D aircraft is equipped with a flight data recorder to monitor flight usage and provide the data to support structural load analysis. However, limited memory of flight data recorder allows user to monitor individual aircraft fatigue usage in terms of only the vertical inertia (NzW) data for calculating Crack Severity Index (CSI) value which defines the relative maneuver severity. Current IAT method for the F-16C/D Block 32 based on CSI value calculated from NzW is shown to be not accurate enough to monitor individual aircraft fatigue usage due to several problems. The proposed advanced aircraft service life monitoring method based on flight-by-flight load spectra is recommended as an improved method for the F-16C/D Block 32 aircraft. Flight-by-flight load spectra was generated from downloaded Crash Survival Flight Data Recorder (CSFDR) data by calculating loads for each time hack in selected flight data utilizing loads equations. From

Methods to Determine Recommended Feeder-Wide Advanced Inverter Settings for Improving Distribution System Performance

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

Rylander, Matthew; Reno, Matthew J.; Quiroz, Jimmy E.

This paper describes methods that a distribution engineer could use to determine advanced inverter settings to improve distribution system performance. These settings are for fixed power factor, volt-var, and volt-watt functionality. Depending on the level of detail that is desired, different methods are proposed to determine single settings applicable for all advanced inverters on a feeder or unique settings for each individual inverter. Seven distinctly different utility distribution feeders are analyzed to simulate the potential benefit in terms of hosting capacity, system losses, and reactive power attained with each method to determine the advanced inverter settings.

Methods of Mathematical and Computational Physics for Industry, Science, and Technology

NASA Astrophysics Data System (ADS)

Melnik, Roderick V. N.; Voss, Frands

2006-11-01

the problem. Under both outlined scenarios, scientists and mathematicians are provided with an opportunity to challenge themselves with real-world problems and to work together in a team on important industrial issues. This issue is a result of selected contributions by participants of the meeting that took place in the Sønderborg area of Denmark, one of the most important centers for information technology, telecommunication and electronics in the country. The meeting was hosted by the University of Southern Denmark in a picturesque area of Southern Jutland. It brought together about 65 participants, among whom were professional mathematicians, engineers, physicists, and industrial participants. The meeting was a truly international one, with delegates from four major Danish Universities, the UK, Norway, Italy, Czech Republic, Turkey, China, Germany, Latvia, Canada, the United States, and Finland. Five challenging projects were presented by leading industrial companies, including Grundfos, Danfoss Industrial Control, Unisensor, and Danfoss Flow Division (now Siemens). The meeting featured also the Mathematics for Industry Workshop with several distinguished international speakers. This volume of Journal of Physics: Conference Series on `Methods of Mathematical and Computational Physics for Industry, Science, and Technology' contains contributions from some of the participants of the workshop as well as the papers produced as a result of collaborative efforts with the above mentioned industrial companies. We would like to thank all authors and participants for their contributions and for bearing with us during the review process and preparation of this issue. We thank also all our referees for their timely and detailed reports. The publication of the proceedings of this meeting in Denmark was delayed due to problems with a previous publisher. We are very grateful that Journal of Physics: Conference Series kindly agreed to publish the proceedings rapidly at this late

Mathematical Modeling and Pure Mathematics

ERIC Educational Resources Information Center

Usiskin, Zalman

2015-01-01

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

Consequences, Characteristics, and Causes of Mathematical Learning Disabilities and Persistent Low Achievement in Mathematics

PubMed Central

Geary, David C.

2011-01-01

Objective The goals of the review are threefold; a) to highlight the educational and employment consequences of poorly developed mathematical competencies; b) overview the characteristics of the children with persistently low achievement in mathematics; and c) provide a primer on cognitive science research that is aimed at identifying the cognitive mechanisms underlying these learning disabilities and associated cognitive interventions. Method Literatures on the educational and economic consequences of poor mathematics achievement were reviewed and integrated with reviews of epidemiological, behavioral genetic, and cognitive science studies of poor mathematics achievement. Results Poor mathematical competencies are common among adults and result in employment difficulties and difficulties in many common day-to-day activities. Among students, about 7% of children and adolescents have a mathematical learning disability (MLD) and another 10% show persistent low achievement (LA) in mathematics despite average abilities in most other areas. Children with MLD and their LA peers have deficits in understanding and representing numerical magnitude, difficulties retrieving basic arithmetic facts from long-term memory, and delays in learning mathematical procedures. These deficits and delays cannot be attributed to intelligence, but are related to working memory deficits for children with MLD, but not LA children. Interventions that target these cognitive deficits are in development and preliminary results are promising. Conclusion Mathematical learning disabilities and learning difficulties associated with persistent low achievement in mathematics are common and not attributable to intelligence. These individuals have identifiable number and memory delays and deficits that appear to be specific to mathematics learning. The most promising interventions are those that target these specific deficits and, in addition, for children with MLD interventions that target their low

A Quantitative Analysis of Methods Used for Avoidance and Acceleration of Developmental Mathematics Sequences in Community College

ERIC Educational Resources Information Center

Travers, Steven T.

2017-01-01

Many developmental mathematics programs at community colleges in recent years have undergone a process of redesign in an attempt increase the historical poor rate of student successful completion of required developmental coursework. Various curriculum and instructional design models that incorporate methods of avoiding and accelerating the…

Basic and Advanced Numerical Performances Relate to Mathematical Expertise but Are Fully Mediated by Visuospatial Skills

ERIC Educational Resources Information Center

Sella, Francesco; Sader, Elie; Lolliot, Simon; Cohen Kadosh, Roi

2016-01-01

Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic…

Mathematical Methods of Subjective Modeling in Scientific Research: I. The Mathematical and Empirical Basis

NASA Astrophysics Data System (ADS)

Pyt'ev, Yu. P.

2018-01-01

mathematical formalism for subjective modeling, based on modelling of uncertainty, reflecting unreliability of subjective information and fuzziness that is common for its content. The model of subjective judgments on values of an unknown parameter x ∈ X of the model M( x) of a research object is defined by the researcher-modeler as a space1 ( X, p( X), P{I^{\\bar x}}, Be{l^{\\bar x}}) with plausibility P{I^{\\bar x}} and believability Be{l^{\\bar x}} measures, where x is an uncertain element taking values in X that models researcher—modeler's uncertain propositions about an unknown x ∈ X, measures P{I^{\\bar x}}, Be{l^{\\bar x}} model modalities of a researcher-modeler's subjective judgments on the validity of each x ∈ X: the value of P{I^{\\bar x}}(\\tilde x = x) determines how relatively plausible, in his opinion, the equality (\\tilde x = x) is, while the value of Be{l^{\\bar x}}(\\tilde x = x) determines how the inequality (\\tilde x = x) should be relatively believed in. Versions of plausibility Pl and believability Bel measures and pl- and bel-integrals that inherit some traits of probabilities, psychophysics and take into account interests of researcher-modeler groups are considered. It is shown that the mathematical formalism of subjective modeling, unlike "standard" mathematical modeling, •enables a researcher-modeler to model both precise formalized knowledge and non-formalized unreliable knowledge, from complete ignorance to precise knowledge of the model of a research object, to calculate relative plausibilities and believabilities of any features of a research object that are specified by its subjective model M(\\tilde x), and if the data on observations of a research object is available, then it: •enables him to estimate the adequacy of subjective model to the research objective, to correct it by combining subjective ideas and the observation data after testing their consistency, and, finally, to empirically recover the model of a research

Students’ logical-mathematical intelligence profile

NASA Astrophysics Data System (ADS)

Arum, D. P.; Kusmayadi, T. A.; Pramudya, I.

2018-04-01

One of students’ characteristics which play an important role in learning mathematics is logical-mathematical intelligence. This present study aims to identify profile of students’ logical-mathematical intelligence in general and specifically in each indicator. It is also analyzed and described based on students’ sex. This research used qualitative method with case study strategy. The subjects involve 29 students of 9th grade that were selected by purposive sampling. Data in this research involve students’ logical-mathematical intelligence result and interview. The results show that students’ logical-mathematical intelligence was identified in the moderate level with the average score is 11.17 and 51.7% students in the range of the level. In addition, the level of both male and female students are also mostly in the moderate level. On the other hand, both male and female students’ logical-mathematical intelligence is strongly influenced by the indicator of ability to classify and understand patterns and relationships. Furthermore, the ability of comparison is the weakest indicator. It seems that students’ logical-mathematical intelligence is still not optimal because more than 50% students are identified in moderate and low level. Therefore, teachers need to design a lesson that can improve students’ logical-mathematical intelligence level, both in general and on each indicator.

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.…

Recent advances in mathematical modeling of nitrous oxides emissions from wastewater treatment processes.

PubMed

Ni, Bing-Jie; Yuan, Zhiguo

2015-12-15

Nitrous oxide (N2O) can be emitted from wastewater treatment contributing to its greenhouse gas footprint significantly. Mathematical modeling of N2O emissions is of great importance toward the understanding and reduction of the environmental impact of wastewater treatment systems. This article reviews the current status of the modeling of N2O emissions from wastewater treatment. The existing mathematical models describing all the known microbial pathways for N2O production are reviewed and discussed. These included N2O production by ammonia-oxidizing bacteria (AOB) through the hydroxylamine oxidation pathway and the AOB denitrification pathway, N2O production by heterotrophic denitrifiers through the denitrification pathway, and the integration of these pathways in single N2O models. The calibration and validation of these models using lab-scale and full-scale experimental data is also reviewed. We conclude that the mathematical modeling of N2O production, while is still being enhanced supported by new knowledge development, has reached a maturity that facilitates the estimation of site-specific N2O emissions and the development of mitigation strategies for a wastewater treatment plant taking into the specific design and operational conditions of the plant. Copyright © 2015 Elsevier Ltd. All rights reserved.

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.

Linking Preservice Teachers' Mathematics Self-Efficacy and Mathematics Teaching Efficacy to Their Mathematical Performance

ERIC Educational Resources Information Center

Bates, Alan B.; Latham, Nancy; Kim, Jin-ah

2011-01-01

This study examined preservice teachers' mathematics self-efficacy and mathematics teaching efficacy and compared them to their mathematical performance. Participants included 89 early childhood preservice teachers at a Midwestern university. Instruments included the Mathematics Self-Efficacy Scale (MSES), Mathematics Teaching Efficacy Beliefs…

Mathematical Methods for Studying DNA and Protein Interactions

NASA Astrophysics Data System (ADS)

LeGresley, Sarah

Deoxyribnucleic Acid (DNA) damage can lead to health related issues such as developmental disorders, aging, and cancer. It has been estimated that damage rates may be as high as 100,000 per cell per day. Because of the devastating effects that DNA damage can have, DNA repair mechanisms are of great interest yet are not completely understood. To gain a better understanding of possible DNA repair mechanisms, my dissertation focused on mathematical methods for understanding the interactions between DNA and proteins. I developed a damaged DNA model to estimate the probabilities of damaged DNA being located at specific positions. Experiments were then performed that suggested that the damaged DNA may be repositioned. These experimental results were consistent with the model's prediction that damaged DNA has preferred locations. To study how proteins might be moving along the DNA, I studied the use of the uniform motion "n-step" model. The n-step model has been used to determine the kinetics parameters (e.g. rates at which a protein moves along the DNA, how much energy is required to move a protein along a specified amount of DNA, etc.) of proteins moving along the DNA. Monte Carlo methods were used to simulate proteins moving with different types of non-uniform motion (e.g. backward, jumping, etc.) along the DNA. Estimates for the kinetics parameters in the n-step model were found by fitting of the Monte Carlo simulation data. Analysis indicated that non-uniform motion of the protein may lead to over or underestimation of the kinetic parameters of this n-step model.

Sparse QSAR modelling methods for therapeutic and regenerative medicine

NASA Astrophysics Data System (ADS)

Winkler, David A.

2018-02-01

The quantitative structure-activity relationships method was popularized by Hansch and Fujita over 50 years ago. The usefulness of the method for drug design and development has been shown in the intervening years. As it was developed initially to elucidate which molecular properties modulated the relative potency of putative agrochemicals, and at a time when computing resources were scarce, there is much scope for applying modern mathematical methods to improve the QSAR method and to extending the general concept to the discovery and optimization of bioactive molecules and materials more broadly. I describe research over the past two decades where we have rebuilt the unit operations of the QSAR method using improved mathematical techniques, and have applied this valuable platform technology to new important areas of research and industry such as nanoscience, omics technologies, advanced materials, and regenerative medicine. This paper was presented as the 2017 ACS Herman Skolnik lecture.

The Impact of Institutional Factors on the Relationship Between High School Mathematics Curricula and College Mathematics Course-Taking and Achievement

ERIC Educational Resources Information Center

Harwell, Michael

2013-01-01

Meta-analytic methods were used to examine the moderating effect of institutional factors on the relationship between high school mathematics curricula and college mathematics course-taking and achievement from a sample of 32 colleges. The findings suggest that the impact of curriculum on college mathematics outcomes is not generally moderated by…

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.