2012-03-06
Marsha Berger, NYU) Inclusion of the Adaptation/Adjoint module, Embedded Boundary Methods in the software package Cart3D --- Transition to NASA...ONR, DOE, AFRL, DIA Cart3D used for computing Formation Flight to reduce drag and improve energy efficiency Application to Explosively Formed
Computer Mathematics: An Introduction.
ERIC Educational Resources Information Center
New York City Board of Education, Brooklyn, NY. Div. of Curriculum and Instruction.
This document describes a mathematics course that uses the computer to solve mathematics problems. It was developed to be used with students who have completed at least one year of general mathematics or are not achieving success in the traditional mathematics program. The course is intended to review, reinforce, and extend concepts included in…
Computers in the Mathematics Curriculum.
ERIC Educational Resources Information Center
Ediger, Marlow
This paper examines ways that mathematics teachers and supervisors can use computers in a quality mathematics curriculum in a school setting. Teachers and supervisors continually need to appraise the present mathematics curriculum and make necessary changes. A modern mathematics curriculum makes much use of technology. Society emphasizes heavy use…
Experimental Mathematics and Computational Statistics
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.
1989-01-01
of irreducible factors of p(A), and s is the largest Jordan block for Ail. Each pj(bj(Aij)) is nilpotent . The t-powers of this matrix have column (d...Universit6 du Quebec 4 Montreal ....................................... 140 Exact Algorithms for the Matrix -Triangularization Subresultant PRS...algorithm for computing the Smith form for integer nonsingular matrices, of cost O(n4 log2 (n)), for a matrix of dimen- sion n. The algorithm relies on
Computer Mathematics: An Introduction. Part II.
ERIC Educational Resources Information Center
New York City Board of Education, Brooklyn, NY. Div. of Curriculum and Instruction.
This document describes a mathematics course that uses the computer to solve mathematics problems. It was developed to be used with students who have completed at least one year of general mathematics or are not achieving success in the traditional mathematics program. The course is intended to review, reinforce, and extend concepts included in…
Mathematics Teachers' Attitudes toward the Computers
ERIC Educational Resources Information Center
Ocak, Mehmet A.
2005-01-01
This study reports an investigation of the effects of gender, age, and racial and ethnicity on the attitudes of mathematics teachers towards computer use. The participants of the study were mathematics teachers working in a wide range of New York public schools (n = 50). A Confidence with Computers in Mathematics Teachers (CCMT) rating scale was…
Computer Aided Learning of Mathematics: Software Evaluation
ERIC Educational Resources Information Center
Yushau, B.; Bokhari, M. A.; Wessels, D. C. J.
2004-01-01
Computer Aided Learning of Mathematics (CALM) has been in use for some time in the Prep-Year Mathematics Program at King Fahd University of Petroleum & Minerals. Different kinds of software (both locally designed and imported) have been used in the quest of optimizing the recitation/problem session hour of the mathematics classes. This paper…
Algorithms in Modern Mathematics and Computer Science.
1980-01-01
A069 912 STANFORD UNIV CA DEPT OF COMPUTER SCIENCE F/6 12/1 ALGORITHMS IN MODERN MATHEMATICS AND COMPUTER SCIENCE .(U) JAN 80 D E KNUTH N00014-76-C...8217 Stanford Department of Computer Scienos aur 1980 Report No. STAN-CS-80-788 LEYEL~ rm ALGORITHMS IN MODERN MATHEMATICS AND COMPUTER SCIENCE by Donald L...Knuth 0 Oct Research sponsored by \\ ~ National Science Foun dation and Office of Naval Rlesearch COMPUTER SCIENCE DEPARlTMENT Stanford University
Computer Tutorial "Higher Mathematics" for Engineering Specialties.
ERIC Educational Resources Information Center
Slivina, Natalia A.; Krivosheev, Anatoly O.; Fomin, Sergey S.
This paper presents a CD-ROM computer tutorial titled "Higher Mathematics," that contains 17 educational mathematical programs and is intended for use in Russian university engineering education. The first section introduces the courseware climate in Russia and outlines problems with commercially available universal mathematical…
Mathematics for Computer Scientists: Problems and Solutions
ERIC Educational Resources Information Center
Alexander, Sylvia; Bishop, Pam; Crawford, Ewan; McCartney, Mark
2006-01-01
The results of a survey of the mathematics provision within UK university computer science departments are presented. In particular it is found that many academics are dissatisfied with the level of "mathematical preparedness" of their students. A number of recommendations and resources are suggested to address this. (Contains 6 figures.)
Computer-Game-Based Tutoring of Mathematics
ERIC Educational Resources Information Center
Ke, Fengfeng
2013-01-01
This in-situ, descriptive case study examined the potential of implementing computer mathematics games as an anchor for tutoring of mathematics. Data were collected from middle school students at a rural pueblo school and an urban Hispanic-serving school, through in-field observation, content analysis of game-based tutoring-learning interactions,…
A mathematical formulation of DNA computation.
Zhang, Mingjun; Cheng, Maggie X; Tarn, Tzyh-Jong
2006-03-01
DNA computation is to use DNA molecules for information storing and processing. The task is accomplished by encoding and interpreting DNA molecules in suspended solutions before and after the complementary binding reactions. DNA computation is attractive, due to its fast parallel information processing, remarkable energy efficiency, and high storing capacity. Challenges currently faced by DNA computation are: 1) lack of theoretical computational models for applications and 2) high error rate for implementation. This paper attempts to address these problems from mathematical modeling and genetic coding aspects. The first part of this paper presents a mathematical formulation of DNA computation. The model may serve as a theoretical framework for DNA computation. In the second part, a genetic code based DNA computation approach is presented to reduce error rate for implementation, which has been a major concern for DNA computation. The method provides a promising alternative to reduce error rate for DNA computation.
Future Prospects for Computer-Assisted Mathematics
Bailey, David H.; Borwein, Jonathan M.
2005-10-26
The recent rise of ''computer-assisted'' and ''experimental'' mathematics raises intriguing questions as to the future role of computation in mathematics. These results also draw into question the traditional distinctions that have been drawn between formal proof and computationally-assisted proof. This article explores these questions in the context of the growing consensus among computer technologists that Moore's Law is likely to continue unabated for quite some time into the future, producing hardware and software much more powerful than what is available today.
Verifying a Computer Algorithm Mathematically.
ERIC Educational Resources Information Center
Olson, Alton T.
1986-01-01
Presents an example of mathematics from an algorithmic point of view, with emphasis on the design and verification of this algorithm. The program involves finding roots for algebraic equations using the half-interval search algorithm. The program listing is included. (JN)
Will the digital computer transform classical mathematics?
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.
Mathematical computer programs: A compilation
NASA Technical Reports Server (NTRS)
1972-01-01
Computer programs, routines, and subroutines for aiding engineers, scientists, and mathematicians in direct problem solving are presented. Also included is a group of items that affords the same users greater flexibility in the use of software.
Computer programs: Operational and mathematical, a compilation
NASA Technical Reports Server (NTRS)
1973-01-01
Several computer programs which are available through the NASA Technology Utilization Program are outlined. Presented are: (1) Computer operational programs which can be applied to resolve procedural problems swiftly and accurately. (2) Mathematical applications for the resolution of problems encountered in numerous industries. Although the functions which these programs perform are not new and similar programs are available in many large computer center libraries, this collection may be of use to centers with limited systems libraries and for instructional purposes for new computer operators.
Teaching Mathematics Using a Computer Algebra.
ERIC Educational Resources Information Center
Westermann, Thomas
2001-01-01
Demonstrates the principal concept and the application of MAPLE in mathematical education in various examples. Discusses lengthy and abstract topics like the convergence of Fourier series to a given function, performs the visualization of the wave equation in the case of a vibrating string, and computes the oscillations of an idealized skyscraper…
Enhancing Mathematics Education through Computer Integration.
ERIC Educational Resources Information Center
Friedman, Edward A., And Others
1991-01-01
The director of the three-year-old Stevens project, which addresses the implementation and use of computers for middle and secondary mathematics instruction, offers a progress report. Time for preparation, teacher training, and defining the changing role of the teacher are cited as key variables. Future activities are also previewed. (Author/JJK)
Teaching Mental Computation Strategies in Early Mathematics
ERIC Educational Resources Information Center
Heirdsfield, Ann Margaret
2011-01-01
Mental computation--that is, calculating in the head--is a relatively new topic in mathematics curricula for primary-age children. It is an important skill because it enables children to learn more deeply how numbers work, make decisions about procedures, and create strategies for calculating, thus promoting number sense--a well-developed…
Mathematical challenges from theoretical/computational chemistry
1995-12-31
The committee believes that this report has relevance and potentially valuable suggestions for a wide range of readers. Target audiences include: graduate departments in the mathematical and chemical sciences; federal and private agencies that fund research in the mathematical and chemical sciences; selected industrial and government research and development laboratories; developers of software and hardware for computational chemistry; and selected individual researchers. Chapter 2 of this report covers some history of computational chemistry for the nonspecialist, while Chapter 3 illustrates the fruits of some past successful cross-fertilization between mathematical scientists and computational/theoretical chemists. In Chapter 4 the committee has assembled a representative, but not exhaustive, survey of research opportunities. Most of these are descriptions of important open problems in computational/theoretical chemistry that could gain much from the efforts of innovative mathematical scientists, written so as to be accessible introductions to the nonspecialist. Chapter 5 is an assessment, necessarily subjective, of cultural differences that must be overcome if collaborative work is to be encouraged between the mathematical and the chemical communities. Finally, the report ends with a brief list of conclusions and recommendations that, if followed, could promote accelerated progress at this interface. Recognizing that bothersome language issues can inhibit prospects for collaborative research at the interface between distinctive disciplines, the committee has attempted throughout to maintain an accessible style, in part by using illustrative boxes, and has included at the end of the report a glossary of technical terms that may be familiar to only a subset of the target audiences listed above.
Computational mathematics and physics of fusion reactors
Garabedian, Paul R.
2003-01-01
Theory has contributed significantly to recent advances in magnetic fusion research. New configurations have been found for a stellarator experiment by computational methods. Solutions of a free-boundary problem are applied to study the performance of the plasma and look for islands in the magnetic surfaces. Mathematical analysis and numerical calculations have been used to study equilibrium, stability, and transport of optimized fusion reactors. PMID:14614129
Computer Mathematical Tools: Practical Experience of Learning to Use Them
ERIC Educational Resources Information Center
Semenikhina, Elena; Drushlyak, Marina
2014-01-01
The article contains general information about the use of specialized mathematics software in the preparation of math teachers. The authors indicate the reasons to study the mathematics software. In particular, they analyze the possibility of presenting basic mathematical courses using mathematical computer tools from both a teacher and a student,…
ERIC Educational Resources Information Center
Ardiç, Mehmet Alper; Isleyen, Tevfik
2017-01-01
This study aimed at determining the secondary school mathematics teachers' and students' views on computer-assisted mathematics instruction (CAMI) conducted via Mathematica. Accordingly, three mathematics teachers in Adiyaman and nine 10th-grade students participated in the research. Firstly, the researchers trained the mathematics teachers in the…
ERIC Educational Resources Information Center
Harris, Gary A.
2000-01-01
Discusses the use of a computer algebra system in a capstone mathematics course for undergraduate mathematics majors preparing to teach secondary school mathematics. Provides sample exercises intended to demonstrate how the power of a computer algebra system such as MAPLE can contribute to desired outcomes including reinforcing and strengthening…
ERIC Educational Resources Information Center
Bukova-Guzel, Esra; Canturk-Gunhan, Berna
2011-01-01
The purpose of the study is to determine prospective mathematics teachers' views about using computer-based instructional materials in constructing mathematical concepts and to reveal how the sample computer-based instructional materials for different mathematical concepts altered their views. This is a qualitative study involving twelve…
High-Precision Computation and Mathematical Physics
Bailey, David H.; Borwein, Jonathan M.
2008-11-03
At the present time, IEEE 64-bit floating-point arithmetic is sufficiently accurate for most scientific applications. However, for a rapidly growing body of important scientific computing applications, a higher level of numeric precision is required. Such calculations are facilitated by high-precision software packages that include high-level language translation modules to minimize the conversion effort. This paper presents a survey of recent applications of these techniques and provides some analysis of their numerical requirements. These applications include supernova simulations, climate modeling, planetary orbit calculations, Coulomb n-body atomic systems, scattering amplitudes of quarks, gluons and bosons, nonlinear oscillator theory, Ising theory, quantum field theory and experimental mathematics. We conclude that high-precision arithmetic facilities are now an indispensable component of a modern large-scale scientific computing environment.
Research Area 3: Mathematical Sciences: 3.4, Discrete Mathematics and Computer Science
2015-06-10
Aug-2009 28-Aug-2013 Approved for Public Release; Distribution Unlimited Final Report: Research Area 3: Mathematical Sciences: 3.4, Discrete... Mathematics and Computer Science The views, opinions and/or findings contained in this report are those of the author(s) and should not contrued as an...ABSTRACT Final Report: Research Area 3: Mathematical Sciences: 3.4, Discrete Mathematics and Computer Science Report Title Many modern applications
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…
Defining Computational Thinking for Mathematics and Science Classrooms
ERIC Educational Resources Information Center
Weintrop, David; Beheshti, Elham; Horn, Michael; Orton, Kai; Jona, Kemi; Trouille, Laura; Wilensky, Uri
2016-01-01
Science and mathematics are becoming computational endeavors. This fact is reflected in the recently released Next Generation Science Standards and the decision to include "computational thinking" as a core scientific practice. With this addition, and the increased presence of computation in mathematics and scientific contexts, a new…
Recommendations for an Undergraduate Program in Computational Mathematics.
ERIC Educational Resources Information Center
Committee on the Undergraduate Program in Mathematics, Berkeley, CA.
This report describes an undergraduate program designed to produce mathematicians who will know how to use and to apply computers. There is a core of 12 one-semester courses: five in mathematics, four in computational mathematics and three in computer science, leaving the senior year for electives. The content and spirit of these courses are…
ERIC Educational Resources Information Center
Michigan Council of Teachers of Mathematics.
This monograph is intended to be a practical introduction to computers for K-12 mathematics teachers, describing and illustrating ways in which computer technology can be used in the teaching of mathematics. It is organized according to the major ways computers are used in classrooms, and includes activities with suggested lesson outlines, BASIC…
ERIC Educational Resources Information Center
Garcia-Santillán, Arturo; Moreno-Garcia, Elena; Escalera-Chávez, Milka E.; Rojas-Kramer, Carlos A.; Pozos-Texon, Felipe
2016-01-01
Most mathematics students show a definite tendency toward an attitudinal deficiency, which can be primarily understood as intolerance to the matter, affecting their scholar performance adversely. In addition, information and communication technologies have been gradually included within the process of teaching mathematics. Such adoption of…
Defining Computational Thinking for Mathematics and Science Classrooms
NASA Astrophysics Data System (ADS)
Weintrop, David; Beheshti, Elham; Horn, Michael; Orton, Kai; Jona, Kemi; Trouille, Laura; Wilensky, Uri
2016-02-01
Science and mathematics are becoming computational endeavors. This fact is reflected in the recently released Next Generation Science Standards and the decision to include "computational thinking" as a core scientific practice. With this addition, and the increased presence of computation in mathematics and scientific contexts, a new urgency has come to the challenge of defining computational thinking and providing a theoretical grounding for what form it should take in school science and mathematics classrooms. This paper presents a response to this challenge by proposing a definition of computational thinking for mathematics and science in the form of a taxonomy consisting of four main categories: data practices, modeling and simulation practices, computational problem solving practices, and systems thinking practices. In formulating this taxonomy, we draw on the existing computational thinking literature, interviews with mathematicians and scientists, and exemplary computational thinking instructional materials. This work was undertaken as part of a larger effort to infuse computational thinking into high school science and mathematics curricular materials. In this paper, we argue for the approach of embedding computational thinking in mathematics and science contexts, present the taxonomy, and discuss how we envision the taxonomy being used to bring current educational efforts in line with the increasingly computational nature of modern science and mathematics.
[Research activities in applied mathematics, fluid mechanics, and computer science
NASA Technical Reports Server (NTRS)
1995-01-01
This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period April 1, 1995 through September 30, 1995.
Research in Applied Mathematics, Fluid Mechanics and Computer Science
NASA Technical Reports Server (NTRS)
1999-01-01
This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period October 1, 1998 through March 31, 1999.
Some Aspects of Mathematics and Computer Science in Japan,
Japan. In fact, he learned about a rather wide variety of research in various aspects of applied mathematics and computer science . The readers...Mathematics . Those interested in computer science and applications software will be most interested in the work at Fujitsu Limited and the work at the
The Effects of Modern Mathematics Computer Games on Mathematics Achievement and Class Motivation
ERIC Educational Resources Information Center
Kebritchi, Mansureh; Hirumi, Atsusi; Bai, Haiyan
2010-01-01
This study examined the effects of a computer game on students' mathematics achievement and motivation, and the role of prior mathematics knowledge, computer skill, and English language skill on their achievement and motivation as they played the game. A total of 193 students and 10 teachers participated in this study. The teachers were randomly…
ADD/ADHD: Effects on Mathematics and Mathematical Computations
ERIC Educational Resources Information Center
Brooks, Michael D.
2007-01-01
This study evaluates research that provides an understanding about mathematical results which can be determined independently from contributing factors. The relevance of the findings is important because there are many different reasons hypothesized by researchers as to why Attention Deficit Disorder/Attentions Deficit Hyperactive Disorder…
ERIC Educational Resources Information Center
Hatfield, Larry Lee
Reported are the results of an investigation of the effects of programing a computer in a seventh grade mathematics class. Two treatments were conducted during two successive years. The students in the treatment group used the programing language BASIC to write computer algorithms following supplemental instruction. The mathematical content was…
Computer-Based Mathematics Instructions for Engineering Students
NASA Technical Reports Server (NTRS)
Khan, Mustaq A.; Wall, Curtiss E.
1996-01-01
Almost every engineering course involves mathematics in one form or another. The analytical process of developing mathematical models is very important for engineering students. However, the computational process involved in the solution of some mathematical problems may be very tedious and time consuming. There is a significant amount of mathematical software such as Mathematica, Mathcad, and Maple designed to aid in the solution of these instructional problems. The use of these packages in classroom teaching can greatly enhance understanding, and save time. Integration of computer technology in mathematics classes, without de-emphasizing the traditional analytical aspects of teaching, has proven very successful and is becoming almost essential. Sample computer laboratory modules are developed for presentation in the classroom setting. This is accomplished through the use of overhead projectors linked to graphing calculators and computers. Model problems are carefully selected from different areas.
Computation and graphics in mathematical research
Hoffman, D.A.; Spruck, J.
1992-08-13
This report discusses: The description of the GANG Project and results for prior research; the center for geometry, analysis, numerics and graphics; description of GANG Laboratory; software development at GANG; and mathematical and scientific research activities.
Evaluation of Computer Games for Learning about Mathematical Functions
ERIC Educational Resources Information Center
Tüzün, Hakan; Arkun, Selay; Bayirtepe-Yagiz, Ezgi; Kurt, Funda; Yermeydan-Ugur, Benlihan
2008-01-01
In this study, researchers evaluated the usability of game environments for teaching and learning about mathematical functions. A 3-Dimensional multi-user computer game called as "Quest Atlantis" has been used, and an educational game about mathematical functions has been developed in parallel to the Quest Atlantis' technical and…
Experiences of Student Mathematics-Teachers in Computer-Based Mathematics Learning Environment
ERIC Educational Resources Information Center
Karatas, Ilhan
2011-01-01
Computer technology in mathematics education enabled the students find many opportunities for investigating mathematical relationships, hypothesizing, and making generalizations. These opportunities were provided to pre-service teachers through a faculty course. At the end of the course, the teachers were assigned project tasks involving…
Girls Back Off Mathematics Again: The Views and Experiences of Girls in Computer-Based Mathematics.
ERIC Educational Resources Information Center
Vale, Colleen
2002-01-01
Presents the views and experiences of six girls in two co-educational mathematics classrooms in which computers were regularly used. Indicates a diversity of experiences and views and multiple gender identities. Discusses implications for social justice in mathematics in the age of the information super highway. (Author/KHR)
Mathematical String Sculptures: A Case Study in Computationally-Enhanced Mathematical Crafts
ERIC Educational Resources Information Center
Eisenberg, Michael
2007-01-01
Mathematical string sculptures constitute an extremely beautiful realm of mathematical crafts. This snapshot begins with a description of a marvelous (and no longer manufactured) toy called Space Spider, which provided a framework with which children could experiment with string sculptures. Using a computer-controlled laser cutter to create frames…
Computer Shift Chemistry to More Mathematical Basis.
ERIC Educational Resources Information Center
Haggin, Joseph
1983-01-01
Discusses use and applications of computer technology in chemistry, indicating that the importance of the computer has not been fully realized in the realm of organic synthesis. Includes discussions of various computer programs and systems currently used, supplemented by tables highlighting, for example, features of major computer-aided synthesis…
Basic mathematical function libraries for scientific computation
NASA Technical Reports Server (NTRS)
Galant, David C.
1989-01-01
Ada packages implementing selected mathematical functions for the support of scientific and engineering applications were written. The packages provide the Ada programmer with the mathematical function support found in the languages Pascal and FORTRAN as well as an extended precision arithmetic and a complete complex arithmetic. The algorithms used are fully described and analyzed. Implementation assumes that the Ada type FLOAT objects fully conform to the IEEE 754-1985 standard for single binary floating-point arithmetic, and that INTEGER objects are 32-bit entities. Codes for the Ada packages are included as appendixes.
Applied analysis/computational mathematics. Final report 1993
Lax, P.; Berger, M.
1993-12-01
This is the final report for the Courant Mathematics and Computing Laboratory (CMCL) research program for the years 1991--1993. Our research efforts encompass the formulation of physical problems in terms of mathematical models (both old and new), the mathematical analysis of such models, and their numerical resolution. This last step involves the development and implementation of efficient methods for large scale computation. Our analytic and numerical work often go hand in hand; new theoretical approaches often have numerical counterparts, while numerical experimentation often suggests avenues for analytical investigation.
Students, Computers and Mathematics the Golden Trilogy in the Teaching-Learning Process
ERIC Educational Resources Information Center
García-Santillán, Arturo; Escalera-Chávez, Milka Elena; López-Morales, José Satsumi; Córdova Rangel, Arturo
2014-01-01
In this paper we examine the relationships between students' attitudes towards mathematics and technology, therefore, we take a Galbraith and Hines' scale (1998, 2000) about mathematics confidence, computer confidence, computer and mathematics interaction, mathematics motivation, computer motivation, and mathematics engagement. 164 questionnaires…
Computers in Undergraduate Education: Mathematics, Physics, Statistics, and Chemistry.
ERIC Educational Resources Information Center
Lockard, J. David
This is the report of a conference which was initiated by the National Science Foundation's Office of Computing Activities and which explored and summarized current thinking about the role of the computer for undergraduate curricula in the physical and mathematical sciences. The conference focused on deciding which goals of the existing…
Output Devices, Computation, and the Future of Mathematical Crafts.
ERIC Educational Resources Information Center
Eisenberg, Michael
2002-01-01
The advent of powerful, affordable output devices offers the potential for a vastly expanded landscape of computationally-enriched mathematical craft activities in education. Craft activities have both intellectual and emotional affordances that are relatively lacking in "traditional" computer-based education. Describes three software applications…
Teaching Mathematics with Computers: K-8.
ERIC Educational Resources Information Center
Ropes, George H.; Swett, Shiela
Recent developments in computer technology have resulted in the increasing presence of computers throughout society. As a consequence, schools must prepare students to make effective use of this technology. The purpose of this document is to provide administrators and teachers in the state of New York with guidelines for developing and…
Mathematically Equivalent, Computationally Non-equivalent Formulas and Software Comprehensibility
2016-06-07
bears little resemblance to it for computational reasons. Therefore, although the flow of control of the coded algorithm may be visible to a...software. The computational algorithm used is often mathematically equivalent to the defining formula, but bears little resemblence to it for...computational considera- tions, and often bears little resemblence to the formulas that were used to define the transaction originally. Therefore, although the
Research in applied mathematics, numerical analysis, and computer science
NASA Technical Reports Server (NTRS)
1984-01-01
Research conducted at the Institute for Computer Applications in Science and Engineering (ICASE) in applied mathematics, numerical analysis, and computer science is summarized and abstracts of published reports are presented. The major categories of the ICASE research program are: (1) numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; (2) control and parameter identification; (3) computational problems in engineering and the physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and (4) computer systems and software, especially vector and parallel computers.
Mathematical modelling in the computer-aided process planning
NASA Astrophysics Data System (ADS)
Mitin, S.; Bochkarev, P.
2016-04-01
This paper presents new approaches to organization of manufacturing preparation and mathematical models related to development of the computer-aided multi product process planning (CAMPP) system. CAMPP system has some peculiarities compared to the existing computer-aided process planning (CAPP) systems: fully formalized developing of the machining operations; a capacity to create and to formalize the interrelationships among design, process planning and process implementation; procedures for consideration of the real manufacturing conditions. The paper describes the structure of the CAMPP system and shows the mathematical models and methods to formalize the design procedures.
Computed tomographic beam-hardening artefacts: mathematical characterization and analysis.
Park, Hyoung Suk; Chung, Yong Eun; Seo, Jin Keun
2015-06-13
This paper presents a mathematical characterization and analysis of beam-hardening artefacts in X-ray computed tomography (CT). In the field of dental and medical radiography, metal artefact reduction in CT is becoming increasingly important as artificial prostheses and metallic implants become more widespread in ageing populations. Metal artefacts are mainly caused by the beam-hardening of polychromatic X-ray photon beams, which causes mismatch between the actual sinogram data and the data model being the Radon transform of the unknown attenuation distribution in the CT reconstruction algorithm. We investigate the beam-hardening factor through a mathematical analysis of the discrepancy between the data and the Radon transform of the attenuation distribution at a fixed energy level. Separation of cupping artefacts from beam-hardening artefacts allows causes and effects of streaking artefacts to be analysed. Various computer simulations and experiments are performed to support our mathematical analysis.
An Innovative Learning Model for Computation in First Year Mathematics
ERIC Educational Resources Information Center
Tonkes, E. J.; Loch, B. I.; Stace, A. W.
2005-01-01
MATLAB is a sophisticated software tool for numerical analysis and visualization. The University of Queensland has adopted Matlab as its official teaching package across large first year mathematics courses. In the past, the package has met severe resistance from students who have not appreciated their computational experience. Several main…
Application of Computer Aided Mathematics Teaching in a Secondary School
ERIC Educational Resources Information Center
Yenitepe, Mehmet Emin; Karadag, Zekeriya
2003-01-01
This is a case study that examines the effect of using presentations developed by teacher in addition to using commercially produced educational software CD-ROM in Audio-Visual Room/Computer Laboratory after classroom teaching, on students' academic achievement, as a method of Teaching Mathematics compared with only classroom teaching or after…
Computational Modeling and Mathematics Applied to the Physical Sciences.
ERIC Educational Resources Information Center
National Academy of Sciences - National Research Council, Washington, DC.
One aim of this report is to show and emphasize that in the computational approaches to most of today's pressing and challenging scientific and technological problems, the mathematical aspects cannot and should not be considered in isolation. Following an introductory chapter, chapter 2 discusses a number of typical problems leading to…
Proceedings, Conference on the Computing Environment for Mathematical Software
NASA Technical Reports Server (NTRS)
1981-01-01
Recent advances in software and hardware technology which make it economical to create computing environments appropriate for specialized applications are addressed. Topics included software tools, FORTRAN standards activity, and features of languages, operating systems, and hardware that are important for the development, testing, and maintenance of mathematical software.
Does Computer Use Promote the Mathematical Proficiency of ELL Students?
ERIC Educational Resources Information Center
Kim, Sunha; Chang, Mido
2010-01-01
The study explored the effects of computer use on the mathematical performance of students with special attention to ELL students. To achieve a high generalizability of findings, the study used a U.S. nationally representative database, the Early Childhood Longitudinal Survey Kindergarten Cohort (ECLS-K), and adopted proper weights. The study…
Developing Interactive Learning Objects for a Computing Mathematics Module
ERIC Educational Resources Information Center
Lim, Cher Ping; Lee, Siew Lie; Richards, Cameron
2006-01-01
Based on a case study of the online component of a Computing Mathematics module at a local polytechnic in Singapore, this article provides a descriptive account of the development and employment of interactive learning objects to enhance the learning experiences of the students in the course. The experimented learning objects were branded as…
NASA Astrophysics Data System (ADS)
Babich, M. D.; Zadiraka, V. K.; Lyudvichenko, V. A.; Sergienko, I. V.
2010-12-01
The use of various opportunities for computation optimization in computer technologies for applied and computational mathematics problems with prescribed quality characteristics is investigated. More precisely, the choice and determination of computational resources and methods of their efficient use for finding an approximate solution of problems up to prescribed accuracy in a limited amount of processor time are investigated.
Research in mathematical theory of computation. [computer programming applications
NASA Technical Reports Server (NTRS)
Mccarthy, J.
1973-01-01
Research progress in the following areas is reviewed: (1) new version of computer program LCF (logic for computable functions) including a facility to search for proofs automatically; (2) the description of the language PASCAL in terms of both LCF and in first order logic; (3) discussion of LISP semantics in LCF and attempt to prove the correctness of the London compilers in a formal way; (4) design of both special purpose and domain independent proving procedures specifically program correctness in mind; (5) design of languages for describing such proof procedures; and (6) the embedding of ideas in the first order checker.
Girls back off mathematics again: the views and experiences of girls in computer-based mathematics
NASA Astrophysics Data System (ADS)
Vale, Colleen
2002-12-01
The views and experiences of girls in two co-educational mathematics classrooms in which computers were regularly used were researched. Data were collected by observation and videotaping of lessons, questionnaire, and interviews of students and the teachers. In this paper case studies of six girls are presented. Their `stories' reveal a diversity of experiences and views and multiple gender identities. High achieving girls persisted as "outsiders within," other girls "backed off", and exceptional girls challenged gender stereotypes. Implications for social justice in mathematics in the age of the super highway are discussed.
Prospective Turkish Primary Teachers' Views about the Use of Computers in Mathematics Education
ERIC Educational Resources Information Center
Dogan, Mustafa
2012-01-01
The use of computers and technology in mathematics education affects students' learning, achievements, and affective dimensions. This study explores prospective Turkish primary mathematics teachers' views about the use of computers in mathematics education. The sample comprised of 129 fourth-year prospective primary mathematics teachers from two…
Mathematical and computer modeling of component surface shaping
NASA Astrophysics Data System (ADS)
Lyashkov, A.
2016-04-01
The process of shaping technical surfaces is an interaction of a tool (a shape element) and a component (a formable element or a workpiece) in their relative movements. It was established that the main objects of formation are: 1) a discriminant of a surfaces family, formed by the movement of the shape element relatively the workpiece; 2) an enveloping model of the real component surface obtained after machining, including transition curves and undercut lines; 3) The model of cut-off layers obtained in the process of shaping. When modeling shaping objects there are a lot of insufficiently solved or unsolved issues that make up a single scientific problem - a problem of qualitative shaping of the surface of the tool and then the component surface produced by this tool. The improvement of known metal-cutting tools, intensive development of systems of their computer-aided design requires further improvement of the methods of shaping the mating surfaces. In this regard, an important role is played by the study of the processes of shaping of technical surfaces with the use of the positive aspects of analytical and numerical mathematical methods and techniques associated with the use of mathematical and computer modeling. The author of the paper has posed and has solved the problem of development of mathematical, geometric and algorithmic support of computer-aided design of cutting tools based on computer simulation of the shaping process of surfaces.
ERIC Educational Resources Information Center
Zahner, William; Moschkovich, Judit
2010-01-01
Students often voice computations during group discussions of mathematics problems. Yet, this type of private speech has received little attention from mathematics educators or researchers. In this article, we use excerpts from middle school students' group mathematical discussions to illustrate and describe "computational private…
War of Ontology Worlds: Mathematics, Computer Code, or Esperanto?
Rzhetsky, Andrey; Evans, James A.
2011-01-01
The use of structured knowledge representations—ontologies and terminologies—has become standard in biomedicine. Definitions of ontologies vary widely, as do the values and philosophies that underlie them. In seeking to make these views explicit, we conducted and summarized interviews with a dozen leading ontologists. Their views clustered into three broad perspectives that we summarize as mathematics, computer code, and Esperanto. Ontology as mathematics puts the ultimate premium on rigor and logic, symmetry and consistency of representation across scientific subfields, and the inclusion of only established, non-contradictory knowledge. Ontology as computer code focuses on utility and cultivates diversity, fitting ontologies to their purpose. Like computer languages C++, Prolog, and HTML, the code perspective holds that diverse applications warrant custom designed ontologies. Ontology as Esperanto focuses on facilitating cross-disciplinary communication, knowledge cross-referencing, and computation across datasets from diverse communities. We show how these views align with classical divides in science and suggest how a synthesis of their concerns could strengthen the next generation of biomedical ontologies. PMID:21980276
[AERA. Dream machines and computing practices at the Mathematical Center].
Alberts, Gerard; De Beer, Huub T
2008-01-01
Dream machines may be just as effective as the ones materialised. Their symbolic thrust can be quite powerful. The Amsterdam 'Mathematisch Centrum' (Mathematical Center), founded February 11, 1946, created a Computing Department in an effort to realise its goal of serving society. When Aad van Wijngaarden was appointed as head of the Computing Department, however, he claimed space for scientific research and computer construction, next to computing as a service. Still, the computing service following the five stage style of Hartree's numerical analysis remained a dominant characteristic of the work of the Computing Department. The high level of ambition held by Aad van Wijngaarden lead to ever renewed projections of big automatic computers, symbolised by the never-built AERA. Even a machine that was actually constructed, the ARRA which followed A.D. Booth's design of the ARC, never made it into real operation. It did serve Van Wijngaarden to bluff his way into the computer age by midsummer 1952. Not until January 1954 did the computing department have a working stored program computer, which for reasons of policy went under the same name: ARRA. After just one other machine, the ARMAC, had been produced, a separate company, Electrologica, was set up for the manufacture of computers, which produced the rather successful X1 computer. The combination of ambition and absence of a working machine lead to a high level of work on programming, way beyond the usual ideas of libraries of subroutines. Edsger W. Dijkstra in particular led the way to an emphasis on the duties of the programmer within the pattern of numerical analysis. Programs generating programs, known elsewhere as autocoding systems, were at the 'Mathematisch Centrum' called 'superprograms'. Practical examples were usually called a 'complex', in Dutch, where in English one might say 'system'. Historically, this is where software begins. Dekker's matrix complex, Dijkstra's interrupt system, Dijkstra and
A Computational and Mathematical Model for Device Induced Thrombosis
NASA Astrophysics Data System (ADS)
Wu, Wei-Tao; Aubry, Nadine; Massoudi, Mehrdad; Antaki, James
2015-11-01
Based on the Sorenson's model of thrombus formation, a new mathematical model describing the process of thrombus growth is developed. In this model the blood is treated as a Newtonian fluid, and the transport and reactions of the chemical and biological species are modeled using CRD (convection-reaction-diffusion) equations. A computational fluid dynamic (CFD) solver for the mathematical model is developed using the libraries of OpenFOAM. Applying the CFD solver, several representative benchmark problems are studied: rapid thrombus growth in vivo by injecting Adenosine diphosphate (ADP) using iontophoretic method and thrombus growth in rectangular microchannel with a crevice which usually appears as a joint between components of devices and often becomes nidus of thrombosis. Very good agreements between the numerical and the experimental results validate the model and indicate its potential to study a host of complex and practical problems in the future, such as thrombosis in blood pumps and artificial lungs.
Mathematical and Computational Challenges in Population Biology and Ecosystems Science
NASA Technical Reports Server (NTRS)
Levin, Simon A.; Grenfell, Bryan; Hastings, Alan; Perelson, Alan S.
1997-01-01
Mathematical and computational approaches provide powerful tools in the study of problems in population biology and ecosystems science. The subject has a rich history intertwined with the development of statistics and dynamical systems theory, but recent analytical advances, coupled with the enhanced potential of high-speed computation, have opened up new vistas and presented new challenges. Key challenges involve ways to deal with the collective dynamics of heterogeneous ensembles of individuals, and to scale from small spatial regions to large ones. The central issues-understanding how detail at one scale makes its signature felt at other scales, and how to relate phenomena across scales-cut across scientific disciplines and go to the heart of algorithmic development of approaches to high-speed computation. Examples are given from ecology, genetics, epidemiology, and immunology.
ERIC Educational Resources Information Center
Piel, John A.; And Others
1994-01-01
Describes a summer mathematics institute designed for the professional development of practicing elementary teachers who need to implement NCTM (National Council of Teachers of Mathematics) standards in mathematics education. Highlights include task analysis, manipulated mathematics, computer transition activities, curriculum-based assessment, and…
Mathematical and Computational Modeling in Complex Biological Systems
Li, Wenyang; Zhu, Xiaoliang
2017-01-01
The biological process and molecular functions involved in the cancer progression remain difficult to understand for biologists and clinical doctors. Recent developments in high-throughput technologies urge the systems biology to achieve more precise models for complex diseases. Computational and mathematical models are gradually being used to help us understand the omics data produced by high-throughput experimental techniques. The use of computational models in systems biology allows us to explore the pathogenesis of complex diseases, improve our understanding of the latent molecular mechanisms, and promote treatment strategy optimization and new drug discovery. Currently, it is urgent to bridge the gap between the developments of high-throughput technologies and systemic modeling of the biological process in cancer research. In this review, we firstly studied several typical mathematical modeling approaches of biological systems in different scales and deeply analyzed their characteristics, advantages, applications, and limitations. Next, three potential research directions in systems modeling were summarized. To conclude, this review provides an update of important solutions using computational modeling approaches in systems biology. PMID:28386558
ERIC Educational Resources Information Center
Collis, Betty
1987-01-01
Attitudes toward mathematics and attitudes toward computers were examined for 1,018 grade 8 students and 800 grade 12 students. The female students were more likely than the male students to associate negative attitudes toward mathematics with negative attitudes toward computers. Participation in an eighth-grade mathematics course with a computer…
Influence of Writing Ability and Computation Skill on Mathematics Writing
ERIC Educational Resources Information Center
Powell, Sarah R.; Hebert, Michael A.
2016-01-01
Mathematics standards expect students to communicate about mathematics using oral and written methods, and some high-stakes assessments ask students to answer mathematics questions by writing. Assumptions about mathematics communication via writing include (a) students possess writing skill, (b) students can transfer this writing skill to…
NASA Technical Reports Server (NTRS)
1987-01-01
Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science during the period April, 1986 through September 30, 1986 is summarized.
NASA Technical Reports Server (NTRS)
1988-01-01
This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science during the period April l, 1988 through September 30, 1988.
NASA Technical Reports Server (NTRS)
1987-01-01
Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science during the period October 1, 1986 through March 31, 1987 is summarized.
High-Precision Computation: Mathematical Physics and Dynamics
Bailey, D. H.; Barrio, R.; Borwein, J. M.
2010-04-01
At the present time, IEEE 64-bit oating-point arithmetic is suficiently accurate for most scientic applications. However, for a rapidly growing body of important scientic computing applications, a higher level of numeric precision is required. Such calculations are facilitated by high-precision software packages that include high-level language translation modules to minimize the conversion e ort. This pa- per presents a survey of recent applications of these techniques and provides someanalysis of their numerical requirements. These applications include supernova simulations, climate modeling, planetary orbit calculations, Coulomb n-body atomic systems, studies of the one structure constant, scattering amplitudes of quarks, glu- ons and bosons, nonlinear oscillator theory, experimental mathematics, evaluation of orthogonal polynomials, numerical integration of ODEs, computation of periodic orbits, studies of the splitting of separatrices, detection of strange nonchaotic at- tractors, Ising theory, quantum held theory, and discrete dynamical systems. We conclude that high-precision arithmetic facilities are now an indispensable compo- nent of a modern large-scale scientic computing environment.
ERIC Educational Resources Information Center
Karatas, Ilhan
2014-01-01
This study examines the effect of three different computer integration models on pre-service mathematics teachers' beliefs about using computers in mathematics education. Participants included 104 pre-service mathematics teachers (36 second-year students in the Computer Oriented Model group, 35 fourth-year students in the Integrated Model (IM)…
Computer Assisted Instruction in Mathematics Can Improve Students' Test Scores: A Study.
ERIC Educational Resources Information Center
Brown, Frank
This research assessed the academic impact of a computer-assisted instructional (CAI) software program to teach mathematics. The research hypothesis states that the use of the CAI program will produce superior academic achievement in mathematics for students who use the program compared to students instructed in mathematics without the program.…
Using a Computer Algebra System to Facilitate the Learning of Mathematical Induction
ERIC Educational Resources Information Center
McAndrew, Alasdair
2010-01-01
Mathematical induction is one of the major proof techniques taught to mathematics students in the first years of their undergraduate degrees. In addition to its importance to mathematics, induction is also required for computer science and related disciplines. However, even if the concepts of a proof by induction are taught and understood, many…
ERIC Educational Resources Information Center
Sinkinson, Anne J.
2006-01-01
The research examines the range of effects of obtaining Specialist School status in two contrasting mathematics and computing colleges, concentrating on the mathematics department. The positive impact of a wider range of technology was evident in both schools although the inherent pedagogical perspectives within each mathematics department…
Reasoning with Computer Code: a new Mathematical Logic
NASA Astrophysics Data System (ADS)
Pissanetzky, Sergio
2013-01-01
A logic is a mathematical model of knowledge used to study how we reason, how we describe the world, and how we infer the conclusions that determine our behavior. The logic presented here is natural. It has been experimentally observed, not designed. It represents knowledge as a causal set, includes a new type of inference based on the minimization of an action functional, and generates its own semantics, making it unnecessary to prescribe one. This logic is suitable for high-level reasoning with computer code, including tasks such as self-programming, objectoriented analysis, refactoring, systems integration, code reuse, and automated programming from sensor-acquired data. A strong theoretical foundation exists for the new logic. The inference derives laws of conservation from the permutation symmetry of the causal set, and calculates the corresponding conserved quantities. The association between symmetries and conservation laws is a fundamental and well-known law of nature and a general principle in modern theoretical Physics. The conserved quantities take the form of a nested hierarchy of invariant partitions of the given set. The logic associates elements of the set and binds them together to form the levels of the hierarchy. It is conjectured that the hierarchy corresponds to the invariant representations that the brain is known to generate. The hierarchies also represent fully object-oriented, self-generated code, that can be directly compiled and executed (when a compiler becomes available), or translated to a suitable programming language. The approach is constructivist because all entities are constructed bottom-up, with the fundamental principles of nature being at the bottom, and their existence is proved by construction. The new logic is mathematically introduced and later discussed in the context of transformations of algorithms and computer programs. We discuss what a full self-programming capability would really mean. We argue that self
1987-10-01
This was an instrumentation grant to purchase equipment of support of research in neural networks, information science , artificial intelligence, and applied mathematics. Computer lab equipment, motor control and robotics lab equipment, speech analysis equipment and computational vision equipment were purchased.
Incorporation of Monte-Carlo Computer Techniques into Science and Mathematics Education.
ERIC Educational Resources Information Center
Danesh, Iraj
1987-01-01
Described is a Monte-Carlo method for modeling physical systems with a computer. Also discussed are ways to incorporate Monte-Carlo simulation techniques for introductory science and mathematics teaching and also for enriching computer and simulation courses. (RH)
Mathematical Methods in Operations Research and Computer Science
1992-06-01
Journal of Mathematical Analysis and Applications . Also submitted to Journal of Mathematical Analysis and Applications . SOL...November 1989. To appear in Journal of Mathematical Analysis and Applications . SOL 89-17 ENTRIKEN, Robert E. (Ph.D. thesis) The Parallel Decomposition of...to Variational Inequality Problems, December 1989. SOL 89-19 YAO, Jen-Chih. Fixed Points by Ishikawa
Mathematical and Computational Modeling of Polymer Exchange Membrane Fuel Cells
NASA Astrophysics Data System (ADS)
Ulusoy, Sehribani
In this thesis a comprehensive review of fuel cell modeling has been given and based on the review, a general mathematical fuel cell model has been developed in order to understand the physical phenomena governing the fuel cell behavior and in order to contribute to the efforts investigating the optimum performance at different operating conditions as well as with different physical parameters. The steady state, isothermal model presented here accounts for the combined effects of mass and species transfer, momentum conservation, electrical current distribution through the gas channels, the electrodes and the membrane, and the electrochemical kinetics of the reactions in the anode and cathode catalyst layers. One of the important features of the model is that it proposes a simpler modified pseudo-homogeneous/agglomerate catalyst layer model which takes the advantage of the simplicity of pseudo-homogenous modeling while taking into account the effects of the agglomerates in the catalyst layer by using experimental geometric parameters published. The computation of the general mathematical model can be accomplished in 3D, 2D and 1D with the proper assumptions. Mainly, there are two computational domains considered in this thesis. The first modeling domain is a 2D Membrane Electrode Assembly (MEA) model including the modified agglomerate/pseudo-homogeneous catalyst layer modeling with consistent treatment of water transport in the MEA while the second domain presents a 3D model with different flow filed designs: straight, stepped and tapered. COMSOL Multiphysics along with Batteries and Fuel Cell Module have been used for 2D & 3D model computations while ANSYS FLUENT PEMFC Module has been used for only 3D two-phase computation. Both models have been validated with experimental data. With 2D MEA model, the effects of temperature and water content of the membrane as well as the equivalent weight of the membrane on the performance have been addressed. 3D COMSOL simulation
Computational and Mathematical Modeling of Coupled Superconducting Quantum Interference Devices
NASA Astrophysics Data System (ADS)
Berggren, Susan Anne Elizabeth
This research focuses on conducting an extensive computational investigation and mathematical analysis into the average voltage response of arrays of Superconducting Quantum Interference Devices (SQUIDs). These arrays will serve as the basis for the development of a sensitive, low noise, significantly lower Size, Weight and Power (SWaP) antenna integrated with Low-Noise Amplifier (LNA) using the SQUID technology. The goal for this antenna is to be capable of meeting all requirements for Guided Missile Destroyers (DDG) 1000 class ships for Information Operations/Signals Intelligence (IO/SIGINT) applications in Very High Frequency/Ultra High Frequency (V/UHF) bands. The device will increase the listening capability of receivers by moving technology into a new regime of energy detection allowing wider band, smaller size, more sensitive, stealthier systems. The smaller size and greater sensitivity will allow for ships to be “de-cluttered” of their current large dishes and devices, replacing everything with fewer and smaller SQUID antenna devices. The fewer devices present on the deck of a ship, the more invisible the ship will be to enemy forces. We invent new arrays of SQUIDs, optimized for signal detection with very high dynamic range and excellent spur-free dynamic range, while maintaining extreme small size (and low radar cross section), wide bandwidth, and environmentally noise limited sensitivity, effectively shifting the bottle neck of receiver systems forever away from the antenna itself deeper into the receiver chain. To accomplish these goals we develop and validate mathematical models for different designs of SQUID arrays and use them to invent a new device and systems design. This design is capable of significantly exceeding, per size weight and power, state-of-the-art receiver system measures of performance, such as bandwidth, sensitivity, dynamic range, and spurious-free dynamic range.
Using Mathematics to Make Computing on Encrypted Data Secure and Practical
2015-12-01
USING MATHEMATICS TO MAKE COMPUTING ON ENCRYPTED DATA SECURE AND PRACTICAL UNIVERSITY OF CALIFORNIA, IRVINE DECEMBER 2015 FINAL TECHNICAL REPORT...3. DATES COVERED (From - To) DEC 2012 – JUN 2015 4. TITLE AND SUBTITLE USING MATHEMATICS TO MAKE COMPUTING ON ENCRYPTED DATA SECURE AND PRACTICAL...which it is based and the mathematics that can be used to attack it. The security of homomorphic encryption schemes is based on the presumed diculty of
Evaluation of Computer-Assisted Instruction in Elementary Mathematics for Hearing-Impaired Students.
ERIC Educational Resources Information Center
Suppes, Patrick; And Others
A sample of approximately 385 hearing-impaired elementary and secondary school students whose mathematical achievement ranged from second to sixth grades were examined to determine the effectiveness of a computer assisted elementary mathematics program on the acquisition of computational skills. The students selected were from a population of over…
Students' Activity in Computer-Supported Collaborative Problem Solving in Mathematics
ERIC Educational Resources Information Center
Hurme, Tarja-riitta; Jarvela, Sanna
2005-01-01
The purpose of this study was to analyse secondary school students' (N = 16) computer-supported collaborative mathematical problem solving. The problem addressed in the study was: What kinds of metacognitive processes appear during computer-supported collaborative learning in mathematics? Another aim of the study was to consider the applicability…
Effects of Attitudes and Behaviours on Learning Mathematics with Computer Tools
ERIC Educational Resources Information Center
Reed, Helen C.; Drijvers, Paul; Kirschner, Paul A.
2010-01-01
This mixed-methods study investigates the effects of student attitudes and behaviours on the outcomes of learning mathematics with computer tools. A computer tool was used to help students develop the mathematical concept of function. In the whole sample (N = 521), student attitudes could account for a 3.4 point difference in test scores between…
Examining Student Opinions on Computer Use Based on the Learning Styles in Mathematics Education
ERIC Educational Resources Information Center
Ozgen, Kemal; Bindak, Recep
2012-01-01
The purpose of this study is to identify the opinions of high school students, who have different learning styles, related to computer use in mathematics education. High school students' opinions on computer use in mathematics education were collected with both qualitative and quantitative approaches in the study conducted with a survey model. For…
ERIC Educational Resources Information Center
Demir, Seda; Basol, Gülsah
2014-01-01
The aim of the current study is to determine the overall effects of Computer-Assisted Mathematics Education (CAME) on academic achievement. After an extensive review of the literature, studies using Turkish samples and observing the effects of Computer-Assisted Education (CAE) on mathematics achievement were examined. As a result of this…
ERIC Educational Resources Information Center
Hall, Keith A.; And Others
A second field test of a computer-based, mobile, in-service teacher education program in modern mathematics for elementary school teachers is reported here. Evaluations of the students' achievement and of their attitudes towards mathematics and computer-assisted instruction, as well as an analysis of the relationships among achievement, attitudes,…
Correlation Educational Model in Primary Education Curriculum of Mathematics and Computer Science
ERIC Educational Resources Information Center
Macinko Kovac, Maja; Eret, Lidija
2012-01-01
This article gives insight into methodical correlation model of teaching mathematics and computer science. The model shows the way in which the related areas of computer science and mathematics can be supplemented, if it transforms the way of teaching and creates a "joint" lessons. Various didactic materials are designed, in which all…
Using the Tower of Hanoi Puzzle to Infuse Your Mathematics Classroom with Computer Science Concepts
ERIC Educational Resources Information Center
Marzocchi, Alison S.
2016-01-01
This article suggests that logic puzzles, such as the well-known Tower of Hanoi puzzle, can be used to introduce computer science concepts to mathematics students of all ages. Mathematics teachers introduce their students to computer science concepts that are enacted spontaneously and subconsciously throughout the solution to the Tower of Hanoi…
Roles of Computer Technology in the Mathematics Education of the Gifted.
ERIC Educational Resources Information Center
Grandgenett, Neal
1991-01-01
This article reviews technological advances in educational computer use and discusses applications for computers as tools, tutors, and tutees in mathematics education of gifted students. Computer-assisted instruction, artificial intelligence, multimedia, numeric processing, computer-aided design, LOGO, robotics, and hypercard software packages are…
NASA Astrophysics Data System (ADS)
Bogdanov, Alexander; Khramushin, Vasily
2016-02-01
The architecture of a digital computing system determines the technical foundation of a unified mathematical language for exact arithmetic-logical description of phenomena and laws of continuum mechanics for applications in fluid mechanics and theoretical physics. The deep parallelization of the computing processes results in functional programming at a new technological level, providing traceability of the computing processes with automatic application of multiscale hybrid circuits and adaptive mathematical models for the true reproduction of the fundamental laws of physics and continuum mechanics.
Computational Technique for Teaching Mathematics (CTTM): Visualizing the Polynomial's Resultant
ERIC Educational Resources Information Center
Alves, Francisco Regis Vieira
2015-01-01
We find several applications of the Dynamic System Geogebra--DSG related predominantly to the basic mathematical concepts at the context of the learning and teaching in Brasil. However, all these works were developed in the basic level of Mathematics. On the other hand, we discuss and explore, with DSG's help, some applications of the polynomial's…
Applied Mathematics via Student-Created Computer Graphics.
ERIC Educational Resources Information Center
Sloyer, Clifford; Smith, Lynn H.
1983-01-01
Describes topics and applications of five lessons dealing with applied mathematics (solving sequential optimization problems, queuing theory, graph theory, glyphs (pictorial techniques for displaying relationships among variables, medical mathematics). Design and evaluation of these materials which employ interactive graphics are also described.…
Using Mental Computation Training to Improve Complex Mathematical Performance
ERIC Educational Resources Information Center
Liu, Allison S.; Kallai, Arava Y.; Schunn, Christian D.; Fiez, Julie A.
2015-01-01
Mathematical fluency is important for academic and mathematical success. Fluency training programs have typically focused on fostering retrieval, which leads to math performance that does not reliably transfer to non-trained problems. More recent studies have focused on training number understanding and representational precision, but few have…
From Manipulatives to Computation: Making the Mathematical Connection.
ERIC Educational Resources Information Center
Lewis, Karen Elaine
1985-01-01
Discusses students' inability to make the connection between manipulative materials and pencil-and-paper calculations in mathematics instruction. Outlines the development of mathematical ideas through the concrete, representational, and abstract phases of instruction. An annotated bibliography listing teacher resources for representational-level…
1996-11-01
This document is intended to serve two purposes. Its first purpose is that of a program status report of the considerable progress that the Department of Energy (DOE) has made since 1993, the time of the last such report (DOE/ER-0536, The DOE Program in HPCC), toward achieving the goals of the High Performance Computing and Communications (HPCC) Program. The second purpose is that of a summary report of the many research programs administered by the Mathematical, Information, and Computational Sciences (MICS) Division of the Office of Energy Research under the auspices of the HPCC Program and to provide, wherever relevant, easy access to pertinent information about MICS-Division activities via universal resource locators (URLs) on the World Wide Web (WWW).
1996-06-01
This document is intended to serve two purposes. Its first purpose is that of a program status report of the considerable progress that the Department of Energy (DOE) has made since 1993, the time of the last such report (DOE/ER-0536, {open_quotes}The DOE Program in HPCC{close_quotes}), toward achieving the goals of the High Performance Computing and Communications (HPCC) Program. The second purpose is that of a summary report of the many research programs administered by the Mathematical, Information, and Computational Sciences (MICS) Division of the Office of Energy Research under the auspices of the HPCC Program and to provide, wherever relevant, easy access to pertinent information about MICS-Division activities via universal resource locators (URLs) on the World Wide Web (WWW). The information pointed to by the URL is updated frequently, and the interested reader is urged to access the WWW for the latest information.
ERIC Educational Resources Information Center
Jaji, Gail
This document summarizes the findings of the Second International Mathematics Study relative to calculator and computer usage by students in 20 countries. Two target populations were identified. The data on these two populations were provided by three basic questionnaires: (1) a school questionnaire; (2) a teacher questionnaire; and (3) a student…
ERIC Educational Resources Information Center
Jaji, Gail
Presents a detailed discussion of the data collected on calculator and computer use in schools in 20 countries. The document includes discussion of: (1) school policy on calculator use; (2) description of populations A (8th grade students) and B (12th grade students) in the United States; (3) uses of calculators in subjects other than mathematics;…
ERIC Educational Resources Information Center
Rosenstein, Joseph G., Ed.; Franzblau, Deborah S., Ed.; Roberts, Fred S., Ed.
This book is a collection of articles by experienced educators and explains why and how discrete mathematics should be taught in K-12 classrooms. It includes evidence for "why" and practical guidance for "how" and also discusses how discrete mathematics can be used as a vehicle for achieving the broader goals of the major…
2014-09-13
specialists in mathematics , logic, and computer science with diverse backgrounds rang- ing from homotopical algebra and category theory to theoretical and...AFRL-OSR-VA-TR-2014-0227 New Mathematics of Information Homotopical Steven Awodey CARNEGIE MELLON UNIVERSITY Final Report 09/24/2014 DISTRIBUTION A...RESPONSIBLE PERSON 19b. TELEPHONE NUMBER (Include area code) 13-09-2014 FINAL 15 JUNE 2011 - 30 APR 2014 FINAL REPORT FOR AWARD: "NEW MATHEMATICS OF
Electrical Circuits in the Mathematics/Computer Science Classroom.
ERIC Educational Resources Information Center
McMillan, Robert D.
1988-01-01
Shows how, with little or no electrical background, students can apply Boolean algebra concepts to design and build integrated electrical circuits in the classroom that will reinforce important ideas in mathematics. (PK)
Getting from x to y without Crashing: Computer Syntax in Mathematics Education
ERIC Educational Resources Information Center
Jeffrey, David J.
2010-01-01
When we use technology to teach mathematics, we hope to focus on the mathematics, restricting the computer software systems to providing support for our pedagogy. It is a matter of common experience, however, that students can become distracted or frustrated by the quirks of the particular software system being used. Here, experience using the…
A Study of the Use of a Handheld Computer Algebra System in Discrete Mathematics
ERIC Educational Resources Information Center
Powers, Robert A.; Allison, Dean E.; Grassl, Richard M.
2005-01-01
This study investigated the impact of the TI-92 handheld Computer Algebra System (CAS) on student achievement in a discrete mathematics course. Specifically, the researchers examined the differences between a CAS section and a control section of discrete mathematics on students' in-class examinations. Additionally, they analysed student approaches…
ERIC Educational Resources Information Center
Lai, Shu-Ling; Repman, Judith L.
1996-01-01
Purposes of this study were to determine: (1) if analogies and elaboration and placement of the analogies help novices learning a computer-programming language; (2) if students' mathematics ability influences programming learning; and (3) the interaction effects between analogy and mathematics ability. Subjects were 156 college students. Results…
Disentangling the Nexus: Attitudes to Mathematics and Technology in a Computer Learning Environment.
ERIC Educational Resources Information Center
Galbraith, Peter; Haines, Chris
1998-01-01
Reviews research into the impact of technology on teaching and learning in mathematics. Discusses the relationship between affective variables and performance, and having constructed appropriate measures of attitude. Presents the results from an extensive initial study that disentangles affects related to mathematics and computing, and in doing so…
Effects of Computer Assisted Instruction on Mathematics and Locus of Control.
ERIC Educational Resources Information Center
Reglin, Gary L.
South Carolina requires that prospective teachers pass an Education Entrance Examination (EEE) consisting of three parts--writing, reading, and mathematics. Minorities are having difficulty passing the mathematics portion of this test. This study investigated the effects of computer-assisted instruction (CAI) on basic skills mathematics…
ERIC Educational Resources Information Center
Holahan, Patricia J.; Jurkat, M. Peter; Friedman, Edward A.
2000-01-01
Describes the development of the Mentor Teacher Model that trained middle school and high school mathematics teachers in New Jersey as mentor teachers in the effective use of computer-based technologies for teaching mathematics. Highlights include student-centered teaching methods; cooperative learning; problem-solving activities; and technology…
ERIC Educational Resources Information Center
Yenilmez, Kursat; Ersoy, Mehmet
2008-01-01
The purpose of this study was to determine opinions of mathematics teacher candidates towards applying 7E instructional model on computer aided instruction environments. The descriptive case study model was used in this study. The sample of the study consists of 52 mathematics teacher candidates which were selected randomly from Eskisehir…
Partnership in Being a Specialist Mathematics and Computing College--Who Gains What, How and Why?
ERIC Educational Resources Information Center
Sinkinson, Anne J.
2007-01-01
The research took place in a mathematics and computing specialist school. The article reports on part of a case study of the mathematics department's experience of being a major contributor to the requirements of being a specialist school. This article aims to explore and describe one model of partnership within the "community" remit of…
ERIC Educational Resources Information Center
Mwei, Philip K.; Wando, Dave; Too, Jackson K.
2012-01-01
This paper reports the results of research conducted in six classes (Form IV) with 205 students with a sample of 94 respondents. Data represent students' statements that describe (a) the role of Mathematics teachers in a computer-assisted instruction (CAI) environment and (b) effectiveness of CAI in Mathematics instruction. The results indicated…
Examining the Use of Computer Algebra Systems in University-Level Mathematics Teaching
ERIC Educational Resources Information Center
Lavicza, Zsolt
2009-01-01
The use of Computer Algebra Systems (CAS) is becoming increasingly important and widespread in mathematics research and teaching. In this paper, I will report on a questionnaire study enquiring about mathematicians' use of CAS in mathematics teaching in three countries; the United States, the United Kingdom, and Hungary. Based on the responses…
ERIC Educational Resources Information Center
Buteau, Chantal; Marshall, Neil; Jarvis, Daniel; Lavicza, Zsolt
2010-01-01
We present results of a literature review pilot study (326 papers) regarding the use of Computer Algebra Systems (CAS) in tertiary mathematics education. Several themes that have emerged from the review are discussed: diverse uses of CAS, benefits to student learning, issues of integration and mathematics learning, common and innovative usage of…
Improving Mathematics Learning of Kindergarten Students through Computer-Assisted Instruction
ERIC Educational Resources Information Center
Foster, Matthew E.; Anthony, Jason L.; Clements, Doug H.; Sarama, Julie; Williams, Jeffrey M.
2016-01-01
This study evaluated the effects of a mathematics software program, the Building Blocks software suite, on young children's mathematics performance. Participants included 247 Kindergartners from 37 classrooms in 9 schools located in low-income communities. Children within classrooms were randomly assigned to receive 21 weeks of computer-assisted…
ERIC Educational Resources Information Center
Marshall, Neil; Buteau, Chantal
2014-01-01
As part of their undergraduate mathematics curriculum, students at Brock University learn to create and use computer-based tools with dynamic, visual interfaces, called Exploratory Objects, developed for the purpose of conducting pure or applied mathematical investigations. A student's Development Process Model of creating and using an Exploratory…
Research in progress in applied mathematics, numerical analysis, and computer science
NASA Technical Reports Server (NTRS)
1990-01-01
Research conducted at the Institute in Science and Engineering in applied mathematics, numerical analysis, and computer science is summarized. The Institute conducts unclassified basic research in applied mathematics in order to extend and improve problem solving capabilities in science and engineering, particularly in aeronautics and space.
The Gap between Expectations and Reality: Integrating Computers into Mathematics Classrooms
ERIC Educational Resources Information Center
Guven, Bulent; Cakiroglu, Unal; Akkan, Yasar
2009-01-01
As a result of dramatic changes in mathematics education around the world, in Turkey both elementary and secondary school mathematics curriculums have changed in the light of new demands since 2005. In order to perform the expected change in newly developed curriculum, computer should be integrated into learning and teaching process. Teachers'…
ERIC Educational Resources Information Center
Stultz, Sherry L.
2013-01-01
Using computers to teach students is not a new idea. Computers have been utilized for educational purposes for over 80 years. However, the effectiveness of these programs for teaching mathematics to students with specific learning disability is unclear. This study was undertaken to determine if computer-assisted instruction was as effective as…
Implementing Computer Algebra Enabled Questions for the Assessment and Learning of Mathematics
ERIC Educational Resources Information Center
Sangwin, Christopher J.; Naismith, Laura
2008-01-01
We present principles for the design of an online system to support computer algebra enabled questions for use within the teaching and learning of mathematics in higher education. The introduction of a computer algebra system (CAS) into a computer aided assessment (CAA) system affords sophisticated response processing of student provided answers.…
Students' Mathematics Word Problem-Solving Achievement in a Computer-Based Story
ERIC Educational Resources Information Center
Gunbas, N.
2015-01-01
The purpose of this study was to investigate the effect of a computer-based story, which was designed in anchored instruction framework, on sixth-grade students' mathematics word problem-solving achievement. Problems were embedded in a story presented on a computer as computer story, and then compared with the paper-based version of the same story…
Physics, Computer Science and Mathematics Division. Annual report, 1 January-31 December 1979
Lepore, J.V.
1980-09-01
This annual report describes the research work carried out by the Physics, Computer Science and Mathematics Division during 1979. The major research effort of the Division remained High Energy Particle Physics with emphasis on preparing for experiments to be carried out at PEP. The largest effort in this field was for development and construction of the Time Projection Chamber, a powerful new particle detector. This work took a large fraction of the effort of the physics staff of the Division together with the equivalent of more than a hundred staff members in the Engineering Departments and shops. Research in the Computer Science and Mathematics Department of the Division (CSAM) has been rapidly expanding during the last few years. Cross fertilization of ideas and talents resulting from the diversity of effort in the Physics, Computer Science and Mathematics Division contributed to the software design for the Time Projection Chamber, made by the Computer Science and Applied Mathematics Department.
Incorporating Computer Literacy into a Mathematics Course for Preservice Elementary Teachers.
ERIC Educational Resources Information Center
Dewar, Jacqueline M.
1986-01-01
Teaching computer literacy to preservice teachers is advocated. How such a component was added to a mathematics course for preservice elementary teachers at Loyola Marymount University in Los Angeles is described. (MNS)
NASA Technical Reports Server (NTRS)
1994-01-01
This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period October 1, 1993 through March 31, 1994. The major categories of the current ICASE research program are: (1) applied and numerical mathematics, including numerical analysis and algorithm development; (2) theoretical and computational research in fluid mechanics in selected areas of interest to LaRC, including acoustics and combustion; (3) experimental research in transition and turbulence and aerodynamics involving LaRC facilities and scientists; and (4) computer science.
Mathematical and computational modeling simulation of solar drying Systems
Technology Transfer Automated Retrieval System (TEKTRAN)
Mathematical modeling of solar drying systems has the primary aim of predicting the required drying time for a given commodity, dryer type, and environment. Both fundamental (Fickian diffusion) and semi-empirical drying models have been applied to the solar drying of a variety of agricultural commo...
ERIC Educational Resources Information Center
Heimer, Ralph T., Ed.
The preface to this book notes the relationship of its contents to the 1968 conference "to appraise mathematics educators of the present status and future prospects of computer-assisted instruction (CAI) and its implications for the teaching of mathematics." The introduction, "Computers in Mathematics and Other Education," was the keynote address…
Trigonometry--Mathematical Curricular Areas and Instructional Computing.
ERIC Educational Resources Information Center
Frandsen, Henry
1981-01-01
The computer has enormous potential for enhancing the secondary trigonometry curriculum. Areas that can be improved through use of the computer include: solutions of triangles, inductive investigations of functions, graphs of functions, and solution of trigonometric identities. (JN)
Ideal and computer mathematics applied to meshfree methods
NASA Astrophysics Data System (ADS)
Kansa, E.
2016-10-01
Early numerical methods to solve ordinary and partial differential relied upon human computers who used mechanical devices. The algorithms used changed little over the evolution of electronic computers having only low order convergence rates. A meshfree scheme was developed for problems that converges exponentially using the latest computational science toolkit.
Using the Tower of Hanoi puzzle to infuse your mathematics classroom with computer science concepts
NASA Astrophysics Data System (ADS)
Marzocchi, Alison S.
2016-07-01
This article suggests that logic puzzles, such as the well-known Tower of Hanoi puzzle, can be used to introduce computer science concepts to mathematics students of all ages. Mathematics teachers introduce their students to computer science concepts that are enacted spontaneously and subconsciously throughout the solution to the Tower of Hanoi puzzle. These concepts include, but are not limited to, conditionals, iteration, and recursion. Lessons, such as the one proposed in this article, are easily implementable in mathematics classrooms and extracurricular programmes as they are good candidates for 'drop in' lessons that do not need to fit into any particular place in the typical curriculum sequence. As an example for readers, the author describes how she used the puzzle in her own Number Sense and Logic course during the federally funded Upward Bound Math/Science summer programme for college-intending low-income high school students. The article explains each computer science term with real-life and mathematical examples, applies each term to the Tower of Hanoi puzzle solution, and describes how students connected the terms to their own solutions of the puzzle. It is timely and important to expose mathematics students to computer science concepts. Given the rate at which technology is currently advancing, and our increased dependence on technology in our daily lives, it has become more important than ever for children to be exposed to computer science. Yet, despite the importance of exposing today's children to computer science, many children are not given adequate opportunity to learn computer science in schools. In the United States, for example, most students finish high school without ever taking a computing course. Mathematics lessons, such as the one described in this article, can help to make computer science more accessible to students who may have otherwise had little opportunity to be introduced to these increasingly important concepts.
Physics, Computer Science and Mathematics Division annual report, 1 January-31 December 1983
Jackson, J.D.
1984-08-01
This report summarizes the research performed in the Physics, Computer Science and Mathematics Division of the Lawrence Berkeley Laboratory during calendar year 1983. The major activity of the Division is research in high-energy physics, both experimental and theoretical, and research and development in associated technologies. A smaller, but still significant, program is in computer science and applied mathematics. During 1983 there were approximately 160 people in the Division active in or supporting high-energy physics research, including about 40 graduate students. In computer science and mathematics, the total staff, including students and faculty, was roughly 50. Because of the creation in late 1983 of a Computing Division at LBL and the transfer of the Computer Science activities to the new Division, this annual report is the last from the Physics, Computer Science and Mathematics Division. In December 1983 the Division reverted to its historic name, the Physics Division. Its future annual reports will document high energy physics activities and also those of its Mathematics Department.
Why Mathematical Computer Simulations Are the New Laboratory for Scientists.
Buscema, Massimo
2015-01-01
In this paper, we introduce a new powerful scientific paradigm to understand natural and cultural processes. This new paradigm is based on two fundamental keywords: Data, as representative sample of the process we need to analyze, and Artificial Adaptive Systems, as a new mathematical technique able to make explicit the nonlinearity embedded in the process. We will try to make explicit these concepts analyzing how the distribution of events into the physical space may reveal the hidden logic connecting these events together.
ERIC Educational Resources Information Center
Lin, Chi-Hui
2002-01-01
Describes a study that determined the implications of computer graphics types and epistemological beliefs with regard to the design of computer-based mathematical concept learning with elementary school students in Taiwan. Discusses the factor structure of the epistemological belief questionnaire, student performance, and students' attitudes…
A Comparison of Equality in Computer Algebra and Correctness in Mathematical Pedagogy (II)
ERIC Educational Resources Information Center
Bradford, Russell; Davenport, James H.; Sangwin, Chris
2010-01-01
A perennial problem in computer-aided assessment is that "a right answer", pedagogically speaking, is not the same thing as "a mathematically correct expression", as verified by a computer algebra system, or indeed other techniques such as random evaluation. Paper I in this series considered the difference in cases where there was "the right…
Computer-Aided Instruction in Mathematics Remediation at a Community College
ERIC Educational Resources Information Center
Brocato, Mary Anne
2009-01-01
Over the past ten years, traditional lecture style delivery has given way to computer-aided instruction (CAI) in post-secondary education. Developmental mathematics courses have been one of the most widely used applications. At a small community college in the Mississippi Delta, a computer assisted version of Intermediate Algebra was implemented.…
Projects Using a Computer Algebra System in First-Year Undergraduate Mathematics
ERIC Educational Resources Information Center
Rosenzweig, Martin
2007-01-01
This paper illustrates the use of computer-based projects in two one-semester first-year undergraduate mathematics classes. Developed over a period of years, the approach is one in which the classes are organised into work-groups, with computer-based projects being undertaken periodically to illustrate the class material. These projects are…
ERIC Educational Resources Information Center
Chen, Chiu-Jung; Liu, Pei-Lin
2007-01-01
This study evaluated the effects of a personalized computer-assisted mathematics problem-solving program on the performance and attitude of Taiwanese fourth grade students. The purpose of this study was to determine whether the personalized computer-assisted program improved student performance and attitude over the nonpersonalized program.…
Effects of Computer-Based Programs on Mathematical Achievement Scores for Fourth-Grade Students
ERIC Educational Resources Information Center
Ravenel, Jessica; Lambeth, Dawn T.; Spires, Bob
2014-01-01
The purpose of the research study was to identify the effects of computer-based programs on mathematical achievement, perceptions, and engagement of fourth-grade students. The 31 student participants were divided into two intervention groups, as a hands-on group and a computer-based group. Student achievement was measured by comparing the pretest…
Physics, Computer Science and Mathematics Division. Annual report, January 1-December 31, 1980
Birge, R.W.
1981-12-01
Research in the physics, computer science, and mathematics division is described for the year 1980. While the division's major effort remains in high energy particle physics, there is a continually growing program in computer science and applied mathematics. Experimental programs are reported in e/sup +/e/sup -/ annihilation, muon and neutrino reactions at FNAL, search for effects of a right-handed gauge boson, limits on neutrino oscillations from muon-decay neutrinos, strong interaction experiments at FNAL, strong interaction experiments at BNL, particle data center, Barrelet moment analysis of ..pi..N scattering data, astrophysics and astronomy, earth sciences, and instrument development and engineering for high energy physics. In theoretical physics research, studies included particle physics and accelerator physics. Computer science and mathematics research included analytical and numerical methods, information analysis techniques, advanced computer concepts, and environmental and epidemiological studies. (GHT)
Going Around On Circles: Mathematics and Computer Art. Part 2.
ERIC Educational Resources Information Center
Gordon, Sheldon P.; Gordon, Florence S.
1984-01-01
Discusses properties of epicycloids. (The easiest way to picture them is to think of a piece of radioactive bubble gum attached to a wheel which is rolling around the outside of a larger wheel.) Includes a computer program (TRS-80 color computer) that will graph any epicycloid with integer values for the radii. (JN)
Fractal Explorations in Secondary Mathematics, Science, and Computer Science.
ERIC Educational Resources Information Center
Egnatoff, William J.
1991-01-01
Fractal geometry is introduced through examples of computational exploration of coastlines, self-similar curves, random walks, and population growth. These explorations, which include the construction of algorithms and the subsequent development and application of simple computer programs, lend themselves to self-directed study and advanced…
Studies in Mathematics, Volume 22. Studies in Computer Science.
ERIC Educational Resources Information Center
Pollack, Seymour V., Ed.
The nine articles in this collection were selected because they represent concerns central to computer science, emphasize topics of particular interest to mathematicians, and underscore the wide range of areas deeply and continually affected by computer science. The contents consist of: "Introduction" (S. V. Pollack), "The…
1990-03-01
Final Report D T IC The Clemson University A LECTE University Research Initiative Program APR 0 2 1990 in Discrete Mathematics & D Computational...Analsis AIOOlVI-2-- q3 March 1990 - Clemson University created in September 1986 a University Research Initiative Program in Discrete Mathematics and...year the Steering Committee selected outstanding visiting faculty who were supported by funds supplied by Clemson University with reduced teaching
NASA Technical Reports Server (NTRS)
Arnold, S. M.; Tan, H. Q.; Dong, X.
1989-01-01
Development of new material models for describing the high temperature constitutive behavior of real materials represents an important area of research in engineering disciplines. Derivation of mathematical expressions (constitutive equations) which describe this high temperature material behavior can be quite time consuming, involved and error prone; thus intelligent application of symbolic systems to facilitate this tedious process can be of significant benefit. A computerized procedure (SDICE) capable of efficiently deriving potential based constitutive models, in analytical form is presented. This package, running under MACSYMA, has the following features: partial differentiation, tensor computations, automatic grouping and labeling of common factors, expression substitution and simplification, back substitution of invariant and tensorial relations and a relational data base. Also limited aspects of invariant theory were incorporated into SDICE due to the utilization of potentials as a starting point and the desire for these potentials to be frame invariant (objective). Finally not only calculation of flow and/or evolutionary laws were accomplished but also the determination of history independent nonphysical coefficients in terms of physically measurable parameters, e.g., Young's modulus, was achieved. The uniqueness of SDICE resides in its ability to manipulate expressions in a general yet predefined order and simplify expressions so as to limit expression growth. Results are displayed when applicable utilizing index notation.
NASA Astrophysics Data System (ADS)
Neves, Rui Gomes; Teodoro, Vítor Duarte
2012-09-01
A teaching approach aiming at an epistemologically balanced integration of computational modelling in science and mathematics education is presented. The approach is based on interactive engagement learning activities built around computational modelling experiments that span the range of different kinds of modelling from explorative to expressive modelling. The activities are designed to make a progressive introduction to scientific computation without requiring prior development of a working knowledge of programming, generate and foster the resolution of cognitive conflicts in the understanding of scientific and mathematical concepts and promote performative competency in the manipulation of different and complementary representations of mathematical models. The activities are supported by interactive PDF documents which explain the fundamental concepts, methods and reasoning processes using text, images and embedded movies, and include free space for multimedia enriched student modelling reports and teacher feedback. To illustrate, an example from physics implemented in the Modellus environment and tested in undergraduate university general physics and biophysics courses is discussed.
Research in mathematics and computer science, March 1, 1991--September 30, 1992
Pieper, G.W.
1992-10-01
This report discusses the following topics in mathematics and computer science at Argonne National Laboratory: Harnessing the Power; Modeling Piezoelectric Crystals; A Two-Way Street; The Challenge Is On; A True Molecular Engineering Capability; CHAMMPions Attack Climate Issues; Studying Vortex Dynamics; Studying Vortex Structure; Providing Reliable and Fast Derivatives; Automating Reasoning for Scientific Problem Solving; Optimization and Mathematical Programming; Scalable Algorithms for Linear Algebra; Reliable Core Software; Computing Phylogenetic Trees; Managing Life-Critical Systems; Interacting with Data through Visualization; New Tools for New Technologies.
Computer Facilitated Mathematical Methods in Chemical Engineering--Similarity Solution
ERIC Educational Resources Information Center
Subramanian, Venkat R.
2006-01-01
High-performance computers coupled with highly efficient numerical schemes and user-friendly software packages have helped instructors to teach numerical solutions and analysis of various nonlinear models more efficiently in the classroom. One of the main objectives of a model is to provide insight about the system of interest. Analytical…
Computation, Mathematics and Logistics Department Report for Fiscal Year 1978.
1980-03-01
ENCODING CONSTRAINTS PROGRAM SYSTEMS UER INN INFORMATION FILE DESIGN ANALYST FIELDY IES S M ANALYZER ADATA BASE ROUTINE DESIGNER RECORD COMPUTER...NTIPS automation is considered feasible. Prototypes for all the functions can be built. The big payoff areas are in improved TI update capability and
Mathematics in the Needle Trades. Computing Piecework. Module 2.
ERIC Educational Resources Information Center
South Carolina State Dept. of Education, Columbia. Office of Vocational Education.
This module on computing piecework, one in a series on the needle trades, contains the following components: an introduction, directions, an objective, learning activities, student information, student self-check, check-out activities, and an instructor's final checklist. The module presents information on the piecework pay plan, such as…
Introducing Computer Algebra to School Teachers of Mathematics
ERIC Educational Resources Information Center
Man, Yiu-Kwong
2007-01-01
Since the last decade, the use of computer algebra systems at the Hong Kong school level is still very limited. Among various reasons behind, the lack of exposure of this kind of software to local school teachers should be taken into account. In this article, we describe how to introduce MAPLE in a BEd module of a local teacher-training programme.…
Computational Psychiatry: towards a mathematically informed understanding of mental illness
Huys, Quentin J M; Roiser, Jonathan P
2016-01-01
Computational Psychiatry aims to describe the relationship between the brain's neurobiology, its environment and mental symptoms in computational terms. In so doing, it may improve psychiatric classification and the diagnosis and treatment of mental illness. It can unite many levels of description in a mechanistic and rigorous fashion, while avoiding biological reductionism and artificial categorisation. We describe how computational models of cognition can infer the current state of the environment and weigh up future actions, and how these models provide new perspectives on two example disorders, depression and schizophrenia. Reinforcement learning describes how the brain can choose and value courses of actions according to their long-term future value. Some depressive symptoms may result from aberrant valuations, which could arise from prior beliefs about the loss of agency (‘helplessness’), or from an inability to inhibit the mental exploration of aversive events. Predictive coding explains how the brain might perform Bayesian inference about the state of its environment by combining sensory data with prior beliefs, each weighted according to their certainty (or precision). Several cortical abnormalities in schizophrenia might reduce precision at higher levels of the inferential hierarchy, biasing inference towards sensory data and away from prior beliefs. We discuss whether striatal hyperdopaminergia might have an adaptive function in this context, and also how reinforcement learning and incentive salience models may shed light on the disorder. Finally, we review some of Computational Psychiatry's applications to neurological disorders, such as Parkinson's disease, and some pitfalls to avoid when applying its methods. PMID:26157034
Motivating Computer Engineering Freshmen through Mathematical and Logical Puzzles
ERIC Educational Resources Information Center
Parhami, B.
2009-01-01
As in many other fields of science and technology, college students in computer engineering do not come into full contact with the key ideas and challenges of their chosen discipline until the third year of their studies. This situation poses a problem in terms of keeping the students motivated as they labor through their foundational, basic…
ERIC Educational Resources Information Center
Austin, Gilbert R.
The purpose of this study was to evaluate the effects of using different mathematics textbooks on the mathematical computational ability of students as a method of assessing the effectiveness of different mathematics instruction. This study resulted from a 1963 report which discussed the results of the New Hampshire Statewide Eighth Grade Testing…
ERIC Educational Resources Information Center
Cornu, Bernard, Ed.; Ralston, Anthony, Ed.
In 1985 the International Commission on Mathematical Instruction (ICMI) published the first edition of a book of studies on the topic of the influence of computers on mathematics and the teaching of mathematics. This document is an updated version of that book and includes five articles from the 1985 ICMI conference at Strasbourg, France; reports…
ERIC Educational Resources Information Center
Seo, You-Jin; Bryant, Diane Pedrotty
2009-01-01
The purpose of this study was to conduct a meta-study of computer-assisted instruction (CAI) studies in mathematics for students with learning disabilities (LD) focusing on examining the effects of CAI on the mathematics performance of students with LD. This study examined a total of 11 mathematics CAI studies, which met the study selection…
Mathematical model partitioning and packing for parallel computer calculation
NASA Technical Reports Server (NTRS)
Arpasi, Dale J.; Milner, Edward J.
1986-01-01
This paper deals with the development of multiprocessor simulations from a serial set of ordinary differential equations describing a physical system. The identification of computational parallelism within the model equations is discussed. A technique is presented for identifying this parallelism and for partitioning the equations for parallel solution on a multiprocessor. Next, an algorithm which packs the equations into a minimum number of processors is described. The results of applying the packing algorithm to a turboshaft engine model are presented.
Mathematical Analysis and Computer Program Development for Electromagnetic Science Studies.
1981-11-01
interest that needed to be computed was the far-field power pattern of a planar array of electrodes . The derivation of it is carried out belnw. Fig. 3...shows, for a double- electrode array and relevant geometry. As several inve3tigators have shown, radiation into an isotropic medium is often a reasonable...physical approximation to make. and certainly makes the analysis simpler. For the double- electrode array shown in Fig. 3 , we note that Y" + L -1 2. (2
Symbolic Computation in a Constructive Approach to Methods of Mathematical Physics
NASA Astrophysics Data System (ADS)
Lopez, Robert
2001-10-01
Mastery of the discipline of physics requires not only expertise and intuition in science, but also a measure of competence in mathematical understanding and technique. In fact, courses in methods of mathematical physics are important stepping-stones to progress in physics education. In this talk, we shall illustrate the role that a computer algebra system can play in a more efficient and effective mastery of mathematical techniques needed in the physics curriculum. To do this, we will present a series of examples taken from the undergraduate math curriculum at RHIT where the author has just published Advanced Engineering Mathematics, a new applied math book based on the availability of a computer algebra system. We will discuss the solution of boundary value problems, including the wave equation on the finite string, the heat equation in a finite rod and cylinder, and the potential equation in rectangles, disks, and spheres. We will also discuss coupled oscillators and normal modes. Finally, we will discuss the calculus of variations and Hamilton's principle, setting up and solving the single and double plane pendulum problems, and the spherical pendulum problem. Throughout, we will show how the use of modern computer tools makes so much more mathematics available to the student, and makes it so much easier to obtain physical insights.
Mathematical modeling and computation of the optical response from nanostructures
NASA Astrophysics Data System (ADS)
Sun, Yuanchang
This dissertation studies the computational modeling for nanostructures in response to external electromagnetic fields. Light-matter interactions on nanoscale are at the heart of nano-optics. To fully characterize the optical interactions with nanostructures quantum electrodynamics (QED) must be invoked, however, the required extremely intense computation and analysis prohibit QED from applications in nano-optics. To avoid the expensive computations and be able to seize the essential quantum effects a semiclassical model is developed. The wellposedness of the model partial differential equations is established. Emphasis is placed on the optical interactions with an individual nanostructure, excitons and biexcitons effects and finite-size effects are investigated. The crucial step of our model is to couple the electromagnetic fields with the motion of the excited particles to yield a new dielectric constant which contains quantum effects of interest. A novel feature of the dielectric constant is the wavevector-dependence which leads to a multi-wave propagation inside the medium. Additional boundary conditions are proposed to deal with this situation. We proceed with incorporating this dielectric constant to Maxwell's equations, and by solving a scattering problem the quantum effects can be captured in the scattered spectra.
Group theory and biomolecular conformation: I. Mathematical and computational models
Chirikjian, Gregory S
2010-01-01
Biological macromolecules, and the complexes that they form, can be described in a variety of ways ranging from quantum mechanical and atomic chemical models, to coarser grained models of secondary structure and domains, to continuum models. At each of these levels, group theory can be used to describe both geometric symmetries and conformational motion. In this survey, a detailed account is provided of how group theory has been applied across computational structural biology to analyze the conformational shape and motion of macromolecules and complexes. PMID:20827378
NASA Technical Reports Server (NTRS)
1989-01-01
Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science during the period October 1, 1988 through March 31, 1989 is summarized.
NASA Technical Reports Server (NTRS)
1984-01-01
Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis and computer science during the period October 1, 1983 through March 31, 1984 is summarized.
A Comparative Study of Partial Credit Assessment and Computer-Based Testing for Mathematics
ERIC Educational Resources Information Center
Darrah, Marjorie; Fuller, Edgar; Miller, David
2010-01-01
This paper discusses a possible solution to a problem frequently encountered by educators seeking to use computer-based or multiple choice-based exams for mathematics. These assessment methodologies force a discrete grading system on students and do not allow for the possibility of partial credit. The research presented in this paper investigates…
ERIC Educational Resources Information Center
Wei, Fang-Yi Flora; Hendrix, Katherine Grace
2009-01-01
This study investigated whether competitive and noncompetitive educational mathematics computer games influence four- to seven-year-old boys' and girls' recall of game-playing experience. A qualitative analysis was performed to investigate what preschool children may have learned through their selective recall of game-playing experience. A…
ERIC Educational Resources Information Center
Shotsberger, Paul G.
This report describes the need for a state-level inservice education program for secondary mathematics public school teachers in North Carolina, in order to enable them to effectively implement computer use in classrooms. A decision model for policy analysis was used to determine optimal strategy for the program. Following a review of the…
ERIC Educational Resources Information Center
King, James M.; And Others
The materials described here represent the conversion of a highly popular student workbook "Sets, Probability and Statistics: The Mathematics of Life Insurance" into a computer program. The program is designed to familiarize students with the concepts of sets, probability, and statistics, and to provide practice using real life examples. It also…
A Relational Frame and Artificial Neural Network Approach to Computer-Interactive Mathematics
ERIC Educational Resources Information Center
Ninness, Chris; Rumph, Robin; McCuller, Glen; Vasquez III, Eleazar; Harrison, Carol; Ford, Angela M.; Capt, Ashley; Ninness, Sharon K.; Bradfield, Anna
2005-01-01
Fifteen participants unfamiliar with mathematical operations relative to reflections and vertical and horizontal shifts were exposed to an introductory lecture regarding the fundamentals of the rectangular coordinate system and the relationship between formulas and their graphed analogues. The lecture was followed immediately by computer-assisted…
ERIC Educational Resources Information Center
Hastings, Harold M.; And Others
This booklet is the ninth in a series of nine from the Teacher Training Institute at Hofstra University (New York) and describes the content and the approach of an institute course in which the participants use the personal computer as a personal tool within the mathematical discovery process of making conjectures, testing those conjectures, and…
ERIC Educational Resources Information Center
Sahin, Alpaslan; Adiguzel, Tufan
2014-01-01
The purpose of this study is to investigate how international teachers, who were from overseas but taught in the United States, rate effective teacher qualities in three domains; personal, professional, and classroom management skills. The study includes 130 international mathematics, science, and computer teachers who taught in a multi-school…
Science-Technology Coupling: The Case of Mathematical Logic and Computer Science.
ERIC Educational Resources Information Center
Wagner-Dobler, Roland
1997-01-01
In the history of science, there have often been periods of sudden rapprochements between pure science and technology-oriented branches of science. Mathematical logic as pure science and computer science as technology-oriented science have experienced such a rapprochement, which is studied in this article in a bibliometric manner. (Author)
ERIC Educational Resources Information Center
Senechal, Lester
This document promotes a better awareness of available technological tools, their implementation, and their advantages and applications in teaching and learning mathematics. Principles for successful implementation are: (1) computation should be an integral part of instruction; (2) software and curriculum development should go hand-in-hand; (3)…
Improving Mathematical Skills Assessed on the High School Proficiency Test: Computation of Percents.
ERIC Educational Resources Information Center
Hills, Catherine A.
This monograph aims to provide teachers of grades 7, 8, and 9 with a variety of instructional activities and strategies that identify student difficulties in computing percents and teaching the skills needed for that cluster on the mathematics part of the New Jersey High School Proficiency Test (HSPT). Sections include: (1) "Concepts"…
Effective Computer-Aided Assessment of Mathematics; Principles, Practice and Results
ERIC Educational Resources Information Center
Greenhow, Martin
2015-01-01
This article outlines some key issues for writing effective computer-aided assessment (CAA) questions in subjects with substantial mathematical or statistical content, especially the importance of control of random parameters and the encoding of wrong methods of solution (mal-rules) commonly used by students. The pros and cons of using CAA and…
ERIC Educational Resources Information Center
Bruce-Simmons, Christine
2013-01-01
This study examined the impact of computer-assisted instruction on the mathematics performance of underachieving fifth-grade students in a rural school district in South Carolina. The instructional technology program ([IF) is South Carolina's response to addressing the needs of its young, struggling math students. The 449 fifth-grade students in…
ERIC Educational Resources Information Center
Jackson, Karen Latrice Terrell
2014-01-01
Students' perceptions influence their expectations and values. According to Expectations and Values Theory of Achievement Motivation (EVT-AM), students' expectations and values impact their behaviors (Eccles & Wigfield, 2002). This study seeks to find students' perceptions of developmental mathematics in a mastery learning computer-based…
ERIC Educational Resources Information Center
Psycharis, Sarantos
2016-01-01
Computational experiment approach considers models as the fundamental instructional units of Inquiry Based Science and Mathematics Education (IBSE) and STEM Education, where the model take the place of the "classical" experimental set-up and simulation replaces the experiment. Argumentation in IBSE and STEM education is related to the…
ERIC Educational Resources Information Center
Rich, Peter J.; Bly, Neil; Leatham, Keith R.
2014-01-01
This study aimed to provide first-hand accounts of the perceived long-term effects of learning computer programming on a learner's approach to mathematics. These phenomenological accounts, garnered from individual interviews of seven different programmers, illustrate four specific areas of interest: (1) programming provides context for many…
ERIC Educational Resources Information Center
Heck, Andre; Kedzierska, Ewa; Ellermeijer, Ton
2009-01-01
In this paper we report on the sustained research and development work at the AMSTEL Institute of the University of Amsterdam to improve mathematics and science education at primary and secondary school level, which has lead amongst other things to the development of the integrated computer working environment Coach 6. This environment consists of…
Computer-Assisted Teaching and Mathematical Learning in Down Syndrome Children
ERIC Educational Resources Information Center
Ortega-Tudela, J. M.; Gomez-Ariza, C. J.
2006-01-01
The present study aims to explore the extent to which computer-assisted teaching facilitates the learning of basic mathematical concepts and skills in children with Down Syndrome (DS). Thus, the effectiveness of a multimedia teaching method is compared with a traditional one in the teaching of counting and cardinality abilities and concepts. In…
Teachers' Use of Computational Tools to Construct and Explore Dynamic Mathematical Models
ERIC Educational Resources Information Center
Santos-Trigo, Manuel; Reyes-Rodriguez, Aaron
2011-01-01
To what extent does the use of computational tools offer teachers the possibility of constructing dynamic models to identify and explore diverse mathematical relations? What ways of reasoning or thinking about the problems emerge during the model construction process that involves the use of the tools? These research questions guided the…
ERIC Educational Resources Information Center
Gadalla, Tahany M.
The equivalence of multiple-choice (MC) and constructed response (discrete) (CR-D) response formats as applied to mathematics computation at grade levels two to six was tested. The difference between total scores from the two response formats was tested for statistical significance, and the factor structure of items in both response formats was…
ERIC Educational Resources Information Center
Educational Technology Center, Cambridge, MA.
Developed to guide the research of the Educational Technology Center, a consortium based at Harvard Graduate School of Education, this report addresses the use of new information technologies to enrich, extend, and transform current instructional practice in science, mathematics, and computer education. A discussion of the basic elements required…
ERIC Educational Resources Information Center
Wanjala, Martin M. S.; Aurah, Catherine M.; Symon, Koros C.
2015-01-01
The paper reports findings of a study which sought to examine the pedagogical factors that affect the integration of computers in mathematics instruction as perceived by teachers in secondary schools in Kenya. This study was based on the Technology Acceptance Model (TAM). A descriptive survey design was used for this study. Stratified and simple…
NASA Technical Reports Server (NTRS)
1992-01-01
Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, fluid mechanics including fluid dynamics, acoustics, and combustion, aerodynamics, and computer science during the period 1 Apr. 1992 - 30 Sep. 1992 is summarized.
ERIC Educational Resources Information Center
Mautone, Jennifer A.; DuPaul, George J.; Jitendra, Asha K.
2005-01-01
The present study examines the effects of computer-assisted instruction (CAI) on the mathematics performance and classroom behavior of three second-through fourth-grade students with ADHD. A controlled case study is used to evaluate the effects of the computer software on participants' mathematics performance and on-task behavior. Participants'…
Birgin, Osman; Catlioğlu, Hakan; Gürbüz, Ramazan; Aydin, Serhat
2010-10-01
This study aimed to investigate the experiences of pre-service mathematics (PSM) teachers with computers and their attitudes toward them. The Computer Attitude Scale, Computer Competency Survey, and Computer Use Information Form were administered to 180 Turkish PSM teachers. Results revealed that most PSM teachers used computers at home and at Internet cafes, and that their competency was generally intermediate and upper level. The study concludes that PSM teachers' attitudes about computers differ according to their years of study, computer ownership, level of computer competency, frequency of computer use, computer experience, and whether they had attended a computer-aided instruction course. However, computer attitudes were not affected by gender.
1997-12-31
The conference focused on computational and modeling issues in the geosciences. Of the geosciences, problems associated with phenomena occurring in the earth`s subsurface were best represented. Topics in this area included petroleum recovery, ground water contamination and remediation, seismic imaging, parameter estimation, upscaling, geostatistical heterogeneity, reservoir and aquifer characterization, optimal well placement and pumping strategies, and geochemistry. Additional sessions were devoted to the atmosphere, surface water and oceans. The central mathematical themes included computational algorithms and numerical analysis, parallel computing, mathematical analysis of partial differential equations, statistical and stochastic methods, optimization, inversion, homogenization and renormalization. The problem areas discussed at this conference are of considerable national importance, with the increasing importance of environmental issues, global change, remediation of waste sites, declining domestic energy sources and an increasing reliance on producing the most out of established oil reservoirs.
Computational oncology--mathematical modelling of drug regimens for precision medicine.
Barbolosi, Dominique; Ciccolini, Joseph; Lacarelle, Bruno; Barlési, Fabrice; André, Nicolas
2016-04-01
Computational oncology is a generic term that encompasses any form of computer-based modelling relating to tumour biology and cancer therapy. Mathematical modelling can be used to probe the pharmacokinetics and pharmacodynamics relationships of the available anticancer agents in order to improve treatment. As a result of the ever-growing numbers of druggable molecular targets and possible drug combinations, obtaining an optimal toxicity-efficacy balance is an increasingly complex task. Consequently, standard empirical approaches to optimizing drug dosing and scheduling in patients are now of limited utility; mathematical modelling can substantially advance this practice through improved rationalization of therapeutic strategies. The implementation of mathematical modelling tools is an emerging trend, but remains largely insufficient to meet clinical needs; at the bedside, anticancer drugs continue to be prescribed and administered according to standard schedules. To shift the therapeutic paradigm towards personalized care, precision medicine in oncology requires powerful new resources for both researchers and clinicians. Mathematical modelling is an attractive approach that could help to refine treatment modalities at all phases of research and development, and in routine patient care. Reviewing preclinical and clinical examples, we highlight the current achievements and limitations with regard to computational modelling of drug regimens, and discuss the potential future implementation of this strategy to achieve precision medicine in oncology.
ERIC Educational Resources Information Center
Costellano, Janet; Scaffa, Matthew
The product of a Special Studies Institute, this teacher developed resource guide for the emotionally handicapped (K-6) presents 37 activities designed to develop mathematics concepts and skills utilizing the urban out-of-doors. Focus is on experiencing math models, patterns, problems, and relationships found in an urban environment. Activities…
Derivation and computation of discrete-delay and continuous-delay SDEs in mathematical biology.
Allen, Edward J
2014-06-01
Stochastic versions of several discrete-delay and continuous-delay differential equations, useful in mathematical biology, are derived from basic principles carefully taking into account the demographic, environmental, or physiological randomness in the dynamic processes. In particular, stochastic delay differential equation (SDDE) models are derived and studied for Nicholson's blowflies equation, Hutchinson's equation, an SIS epidemic model with delay, bacteria/phage dynamics, and glucose/insulin levels. Computational methods for approximating the SDDE models are described. Comparisons between computational solutions of the SDDEs and independently formulated Monte Carlo calculations support the accuracy of the derivations and of the computational methods.
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.
Modelling skin disease: lessons from the worlds of mathematics, physics and computer science.
Gilmore, Stephen
2005-05-01
Theoretical biology is a field that attempts to understand the complex phenomena of life in terms of mathematical and physical principles. Likewise, theoretical medicine employs mathematical arguments and models as a methodology in approaching the complexities of human disease. Naturally, these concepts can be applied to dermatology. There are many possible methods available in the theoretical investigation of skin disease. A number of examples are presented briefly. These include the mathematical modelling of pattern formation in congenital naevi and erythema gyratum repens, an information-theoretic approach to the analysis of genetic networks in autoimmunity, and computer simulations of early melanoma growth. To conclude, an analogy is drawn between the behaviour of well-known physical processes, such as earthquakes, and the spatio-temporal evolution of skin disease. Creating models in skin disease can lead to predictions that can be investigated experimentally or by observation and offer the prospect of unexpected or important insights into pathogenesis.
ERIC Educational Resources Information Center
Pamuk, Savas; Peker, Deniz
2009-01-01
The purpose of this study was to investigate Turkish pre-service science and mathematics teachers' computer self-efficacies (CSEs) and computer attitude (CA) considering gender, year in program, and computer ownership as independent variables. Additionally the study aimed to examine the relationship between CSE and CA. Computer Self-efficacy Scale…
Research on Mega-Math: Discrete mathematics and computer science for children. Final report
Fellows, M.R.
1995-06-26
The objective of the subcontract was to provide further research on the approach to mathematics education embodied in the workbook ``This is Mega-Mathematics!`` essentially produced under the subcontract and its preceding informal (alas!) cooperative arrangements. The workbook is now widely and freely distributed on the Internet under the copyright of the Los Alamos National Labs. This research was to consist of: (1) the development and dissemination of materials, (2) experimentation with use of the materials in classroom visits and other events, (3) communication of the ideas embodied in the materials to various forums concerned with mathematics education reform, (4) the development of connections to the computer games industry, (5) the development of new workbook-type materials, (6) publications, (7) the development of connections to Science Museums, (8) the development of uses of the Internet to make MegaMath materials and ideas available through that medium, (9) the stimulation of and coordination with other projects in mathematics education reform. All of these objectives have been accomplished in what should be regarded as one of the most interesting and cost-effective projects ever undertaken in mathematics education, a testimony to the vision and creative imagination of the Los Alamos Labs.
NASA Astrophysics Data System (ADS)
Akkoç, Hatice
2015-11-01
This paper focuses on a specific aspect of formative assessment, namely questioning. Given that computers have gained widespread use in learning and teaching, specific attention should be made when organizing formative assessment in computer learning environments (CLEs). A course including various workshops was designed to develop knowledge and skills of questioning in CLEs. This study investigates how pre-service mathematics teachers used formative questioning with technological tools such as Geogebra and Graphic Calculus software. Participants are 35 pre-service mathematics teachers. To analyse formative questioning, two types of questions are investigated: mathematical questions and technical questions. Data were collected through lesson plans, teaching notes, interviews and observations. Descriptive statistics of the number of questions in the lesson plans before and after the workshops are presented. Examples of two types of questions are discussed using the theoretical framework. One pre-service teacher was selected and a deeper analysis of the way he used questioning during his three lessons was also investigated. The findings indicated an improvement in using technical questions for formative purposes and that the course provided a guideline in planning and using mathematical and technical questions in CLEs.
Concentrator optical characterization using computer mathematical modelling and point source testing
NASA Technical Reports Server (NTRS)
Dennison, E. W.; John, S. L.; Trentelman, G. F.
1984-01-01
The optical characteristics of a paraboloidal solar concentrator are analyzed using the intercept factor curve (a format for image data) to describe the results of a mathematical model and to represent reduced data from experimental testing. This procedure makes it possible not only to test an assembled concentrator, but also to evaluate single optical panels or to conduct non-solar tests of an assembled concentrator. The use of three-dimensional ray tracing computer programs to calculate the mathematical model is described. These ray tracing programs can include any type of optical configuration from simple paraboloids to array of spherical facets and can be adapted to microcomputers or larger computers, which can graphically display real-time comparison of calculated and measured data.
NASA Technical Reports Server (NTRS)
Palusinski, O. A.; Allgyer, T. T.
1979-01-01
The elimination of Ampholine from the system by establishing the pH gradient with simple ampholytes is proposed. A mathematical model was exercised at the level of the two-component system by using values for mobilities, diffusion coefficients, and dissociation constants representative of glutamic acid and histidine. The constants assumed in the calculations are reported. The predictions of the model and computer simulation of isoelectric focusing experiments are in direct importance to obtain Ampholine-free, stable pH gradients.
2013-03-04
FSI): – Oscillatory interactions in engineering systems (e.g. aircraft, turbines , and bridges) can lead to failure – The blood flow in arteries...propagation: infer global heterogeneous wave speed from surface observations of seismic waveforms • 1.07 million uncertain parameters • 630M states
[Geometry, analysis, and computation in mathematics and applied science]. Progress report
Hoffman, D.
1994-02-01
The principal investigators` work on a variety of pure and applied problems in Differential Geometry, Calculus of Variations and Mathematical Physics has been done in a computational laboratory and been based on interactive scientific computer graphics and high speed computation created by the principal investigators to study geometric interface problems in the physical sciences. We have developed software to simulate various physical phenomena from constrained plasma flow to the electron microscope imaging of the microstructure of compound materials, techniques for the visualization of geometric structures that has been used to make significant breakthroughs in the global theory of minimal surfaces, and graphics tools to study evolution processes, such as flow by mean curvature, while simultaneously developing the mathematical foundation of the subject. An increasingly important activity of the laboratory is to extend this environment in order to support and enhance scientific collaboration with researchers at other locations. Toward this end, the Center developed the GANGVideo distributed video software system and software methods for running lab-developed programs simultaneously on remote and local machines. Further, the Center operates a broadcast video network, running in parallel with the Center`s data networks, over which researchers can access stored video materials or view ongoing computations. The graphical front-end to GANGVideo can be used to make ``multi-media mail`` from both ``live`` computing sessions and stored materials without video editing. Currently, videotape is used as the delivery medium, but GANGVideo is compatible with future ``all-digital`` distribution systems. Thus as a byproduct of mathematical research, we are developing methods for scientific communication. But, most important, our research focuses on important scientific problems; the parallel development of computational and graphical tools is driven by scientific needs.
ERIC Educational Resources Information Center
Calhoun, James M., Jr.
2011-01-01
Student achievement is not progressing on mathematics as measured by state, national, and international assessments. Much of the research points to mathematics curriculum and instruction as the root cause of student failure to achieve at levels comparable to other nations. Since mathematics is regarded as a gate keeper to many educational…
Saturday Academay of Computing and Mathematics (SACAM) at the Oak Ridge National Laboratory
Clark, D.N. )
1991-01-01
To be part of the impending Information Age, our students and teachers must be trained in the use of computers, logic, and mathematics. The Saturday Academy of Computing and Mathematics (SACAM) represents one facet of Oak Ridge National Laboratory's (ORNL) response to meet the challenge. SACAM attempts to provide the area's best high school students with a creative program that illustrates how researchers are using computing and mathematics tools to help solve nationally recognized problems in virtually all scientific fields. Each SACAM program is designed as eight 3-hour sessions. Each session outlines a current scientific question or research area. Sessions are presented on a Saturday morning by a speaker team of two to four ORNL scientists (mentors) working in that particular field. Approximately four students and one teacher from each of ten area high schools attend the eight sessions. Session topics cover diverse problems such as climate modeling cryptography and cryptology, high-energy physics, human genome sequencing, and even the use of probability in locating people lost in a national forest. Evaluations from students, teachers, and speakers indicate that the program has been well received, and a tracking program is being undertaken to determine long-range benefits. An analysis of the program's successes and lessons learned is presented as well as resources required for the program.
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.
Physics, computer science and mathematics division. Annual report, 1 January - 31 December 1982
Jackson, J.D.
1983-08-01
Experimental physics research activities are described under the following headings: research on e/sup +/e/sup -/ annihilation; research at Fermilab; search for effects of a right-handed gauge boson; the particle data center; high energy astrophysics and interdisciplinary experiments; detector and other research and development; publications and reports of other research; computation and communication; and engineering, evaluation, and support operations. Theoretical particle physics research and heavy ion fusion research are described. Also, activities of the Computer Science and Mathematics Department are summarized. Publications are listed. (WHK)
Computational experiment on the numerical solution of some inverse problems of mathematical physics
NASA Astrophysics Data System (ADS)
Vasil'ev, V. I.; Kardashevsky, A. M.; Sivtsev, PV
2016-11-01
In this article the computational experiment on the numerical solution of the most popular linear inverse problems for equations of mathematical physics are presented. The discretization of retrospective inverse problem for parabolic equation is performed using difference scheme with non-positive weight multiplier. Similar difference scheme is also used for the numerical solution of Cauchy problem for two-dimensional Laplace equation. The results of computational experiment, performed on model problems with exact solution, including ones with randomly perturbed input data are presented and discussed.
NASA Technical Reports Server (NTRS)
Palusinski, O. A.; Allgyer, T. T.; Mosher, R. A.; Bier, M.; Saville, D. A.
1981-01-01
A mathematical model of isoelectric focusing at the steady state has been developed for an M-component system of electrochemically defined ampholytes. The model is formulated from fundamental principles describing the components' chemical equilibria, mass transfer resulting from diffusion and electromigration, and electroneutrality. The model consists of ordinary differential equations coupled with a system of algebraic equations. The model is implemented on a digital computer using FORTRAN-based simulation software. Computer simulation data are presented for several two-component systems showing the effects of varying the isoelectric points and dissociation constants of the constituents.
Mathematic-computational modeling for the calculations involved in the Stern-Volmer theory
NASA Astrophysics Data System (ADS)
Thadeu, Felipe C.; Silva, Juliana A.; Silva, Dilson
2016-12-01
The present work consists of the description of a mathematic-computational routine to process the calculation, statistics, plotting graphs and then show binding constants of ligands to transport proteins, as described by the Stern-Volmer Theory. The quenching of fluorescence technique used to analyze samples produces a great amount of data to build spectral plots. The aim of the work is to develop a computational tool which simplify, turn confident and make agile to deal with the great mass of data generated by the fluorescence spectroscopy equipment.
ERIC Educational Resources Information Center
Celedón-Pattichis, Sylvia; LópezLeiva, Carlos Alfonso; Pattichis, Marios S.; Llamocca, Daniel
2013-01-01
There is a strong need in the United States to increase the number of students from underrepresented groups who pursue careers in Science, Technology, Engineering, and Mathematics. Drawing from sociocultural theory, we present approaches to establishing collaborations between computer engineering and mathematics/bilingual education faculty to…
ERIC Educational Resources Information Center
Ziya, Engin; Dogan, Nuri; Kelecioglu, Hulya
2010-01-01
This study aims at determining the extent to which computer using skills specified in Project for International Students Evaluation (PISA) 2006 predict Turkish students' achievement in mathematics. Apart from questions on mathematics, science and reading competencies, a student questionnaire, a school questionnaire and a parent questionnaire were…
ERIC Educational Resources Information Center
Afzal, Muhammad Tanveer; Gondal, Bashir; Fatima, Nuzhat
2014-01-01
The major objective of the study was to elicit the effect of three instructional methods for teaching of mathematics on low, average and high achiever elementary school students. Three methods: traditional instructional method, computer assisted instruction (CAI) and teacher facilitated mathematics learning software were employed for the teaching…
ERIC Educational Resources Information Center
Kanive, Rebecca; Nelson, Peter M.; Burns, Matthew K.; Ysseldyke, James
2014-01-01
The authors' purpose was to determine the effects of computer-based practice and conceptual interventions on computational fluency and word-problem solving of fourth- and fifth-grade students with mathematics difficulties. A randomized pretest-posttest control group design found that students assigned to the computer-based practice intervention…
NASA Astrophysics Data System (ADS)
Celedón-Pattichis, Sylvia; LópezLeiva, Carlos Alfonso; Pattichis, Marios S.; Llamocca, Daniel
2013-12-01
There is a strong need in the United States to increase the number of students from underrepresented groups who pursue careers in Science, Technology, Engineering, and Mathematics. Drawing from sociocultural theory, we present approaches to establishing collaborations between computer engineering and mathematics/bilingual education faculty to address this need. We describe our work through the Advancing Out-of-School Learning in Mathematics and Engineering project by illustrating how an integrated curriculum that is based on mathematics with applications in image and video processing can be designed and how it can be implemented with middle school students from underrepresented groups.
NASA Astrophysics Data System (ADS)
Li, Yiming
2007-12-01
This symposium is an open forum for discussion on the current trends and future directions of physical modeling, mathematical theory, and numerical algorithm in electrical and electronic engineering. The goal is for computational scientists and engineers, computer scientists, applied mathematicians, physicists, and researchers to present their recent advances and exchange experience. We welcome contributions from researchers of academia and industry. All papers to be presented in this symposium have carefully been reviewed and selected. They include semiconductor devices, circuit theory, statistical signal processing, design optimization, network design, intelligent transportation system, and wireless communication. Welcome to this interdisciplinary symposium in International Conference of Computational Methods in Sciences and Engineering (ICCMSE 2007). Look forward to seeing you in Corfu, Greece!
Neural mechanisms underlying the computation of hierarchical tree structures in mathematics.
Nakai, Tomoya; Sakai, Kuniyoshi L
2014-01-01
Whether mathematical and linguistic processes share the same neural mechanisms has been a matter of controversy. By examining various sentence structures, we recently demonstrated that activations in the left inferior frontal gyrus (L. IFG) and left supramarginal gyrus (L. SMG) were modulated by the Degree of Merger (DoM), a measure for the complexity of tree structures. In the present study, we hypothesize that the DoM is also critical in mathematical calculations, and clarify whether the DoM in the hierarchical tree structures modulates activations in these regions. We tested an arithmetic task that involved linear and quadratic sequences with recursive computation. Using functional magnetic resonance imaging, we found significant activation in the L. IFG, L. SMG, bilateral intraparietal sulcus (IPS), and precuneus selectively among the tested conditions. We also confirmed that activations in the L. IFG and L. SMG were free from memory-related factors, and that activations in the bilateral IPS and precuneus were independent from other possible factors. Moreover, by fitting parametric models of eight factors, we found that the model of DoM in the hierarchical tree structures was the best to explain the modulation of activations in these five regions. Using dynamic causal modeling, we showed that the model with a modulatory effect for the connection from the L. IPS to the L. IFG, and with driving inputs into the L. IFG, was highly probable. The intrinsic, i.e., task-independent, connection from the L. IFG to the L. IPS, as well as that from the L. IPS to the R. IPS, would provide a feedforward signal, together with negative feedback connections. We indicate that mathematics and language share the network of the L. IFG and L. IPS/SMG for the computation of hierarchical tree structures, and that mathematics recruits the additional network of the L. IPS and R. IPS.
The mathematics of a quantum Hamiltonian computing half adder Boolean logic gate
NASA Astrophysics Data System (ADS)
Dridi, G.; Julien, R.; Hliwa, M.; Joachim, C.
2015-08-01
The mathematics behind the quantum Hamiltonian computing (QHC) approach of designing Boolean logic gates with a quantum system are given. Using the quantum eigenvalue repulsion effect, the QHC AND, NAND, OR, NOR, XOR, and NXOR Hamiltonian Boolean matrices are constructed. This is applied to the construction of a QHC half adder Hamiltonian matrix requiring only six quantum states to fullfil a half Boolean logical truth table. The QHC design rules open a nano-architectronic way of constructing Boolean logic gates inside a single molecule or atom by atom at the surface of a passivated semi-conductor.
The mathematics of a quantum Hamiltonian computing half adder Boolean logic gate.
Dridi, G; Julien, R; Hliwa, M; Joachim, C
2015-08-28
The mathematics behind the quantum Hamiltonian computing (QHC) approach of designing Boolean logic gates with a quantum system are given. Using the quantum eigenvalue repulsion effect, the QHC AND, NAND, OR, NOR, XOR, and NXOR Hamiltonian Boolean matrices are constructed. This is applied to the construction of a QHC half adder Hamiltonian matrix requiring only six quantum states to fullfil a half Boolean logical truth table. The QHC design rules open a nano-architectronic way of constructing Boolean logic gates inside a single molecule or atom by atom at the surface of a passivated semi-conductor.
Geometry, analysis, and computation in mathematics and applied sciences. Final report
Kusner, R.B.; Hoffman, D.A.; Norman, P.; Pedit, F.; Whitaker, N.; Oliver, D.
1995-12-31
Since 1993, the GANG laboratory has been co-directed by David Hoffman, Rob Kusner and Peter Norman. A great deal of mathematical research has been carried out here by them and by GANG faculty members Franz Pedit and Nate Whitaker. Also new communication tools, such as the GANG Webserver have been developed. GANG has trained and supported nearly a dozen graduate students, and at least half as many undergrads in REU projects.The GANG Seminar continues to thrive, making Amherst a site for short and long term visitors to come to work with the GANG. Some of the highlights of recent or ongoing research at GANG include: CMC surfaces, minimal surfaces, fluid dynamics, harmonic maps, isometric immersions, knot energies, foam structures, high dimensional soap film singularities, elastic curves and surfaces, self-similar curvature evolution, integrable systems and theta functions, fully nonlinear geometric PDE, geometric chemistry and biology. This report is divided into the following sections: (1) geometric variational problems; (2) soliton geometry; (3) embedded minimal surfaces; (4) numerical fluid dynamics and mathematical modeling; (5) GANG graphics and mathematical software; (6) description of the computational and visual analysis facility; and (7) research by undergraduates and GANG graduate seminar.
NASA Astrophysics Data System (ADS)
Fogarty, Gerry; Cretchley, Patricia; Harman, Chris; Ellerton, Nerida; Konki, Nissam
2001-09-01
This study reports on the validation of a questionnaire designed to measure general mathematics confidence, general confidence with using technology, and attitudes towards the use of technology for mathematics learning. A questionnaire was administered to 289 students commencing a tertiary level course on linear algebra and calculus. Scales formed on the basis of factor analysis demonstrated high internal consistency reliability and divergent validity. A repeat administration confirmed the earlier psychometric findings as well as establishing good test-retest reliability. The resulting instrument can be used to measure attitudinal factors that mediate the effective use of technology in mathematics learning.
ERIC Educational Resources Information Center
Feng, Chuan C.
Reported is the Cooperative College-School Science Program in Computing Science Education which was conducted by the University of Colorado Department of Civil Engineering in the summer of 1967. The program consisted of two five-week terms. The course work was composed of two formal lecture courses in Computer Related Mathematics and Computer…
Bendixsen, C L
1982-11-01
A computer-based mathematical program, ICPSEF, was developed for the first-cycle extraction system at the Idaho Chemical Processing Plant (ICPP). At the ICPP, spent nuclear fuels are processed to recover unfissioned uranium. The uranium is recovered from aqueous solutions in a pulse column, solvent extraction system using tributyl phosphate (TBP) solvent (purex process). A previously developed SEPHIS-MOD4 computer program was added to and modified to provide a model for the ICPP system. Major modifications included addition of: (1) partial theoretical stages to permit more accurate modeling of ICPP columns, (2) modeling ammonium hydroxide neutralization of nitric acid in a scrubbing column, and (3) equilibrium data for 5 to 10 vol % TBP. The model was verified by comparison with actual operating data. Detailed instructions for using the ICPSEF model and sample results of the model are included.
Mabbott, Donald J; Bisanz, Jeffrey
2008-01-01
Knowledge and skill in multiplication were investigated for late elementary-grade students with mathematics learning disabilities (MLD), typically achieving age-matched peers, low-achieving age-matched peers, and ability-matched peers by examining multiple measures of computational skill, working memory, and conceptual knowledge. Poor multiplication fact mastery and calculation fluency and general working memory discriminated children with MLD from typically achieving age-matched peers. Furthermore, children with MLD were slower in executing backup procedures than typically achieving age-matched peers. The performance of children with MLD on multiple measures of multiplication skill and knowledge was most similar to that of ability-matched younger children. MLD may be due to difficulties in computational skills and working memory. Implications for the diagnosis and remediation of MLD are discussed.
ERIC Educational Resources Information Center
de Kock, Willem D.; Harskamp, Egbert G.
2014-01-01
Teachers in primary education experience difficulties in teaching word problem solving in their mathematics classes. However, during controlled experiments with a metacognitive computer programme, students' problem-solving skills improved. Also without the supervision of researchers, metacognitive computer programmes can be beneficial in a natural…
ERIC Educational Resources Information Center
Sanders, Jo
From 1990 to 1993, 200 educators, primarily classroom teachers of computers, mathematics, and science, participated in the Computer Equity Expert Project. After a seminar on gender equity in these fields, the educators returned to their schools and taught workshops to their colleagues. Together, workshop participants and their colleagues developed…
ERIC Educational Resources Information Center
Riccomini, Paul J.
2008-01-01
This paper is an analysis of published research on computer-assisted instruction (CAI) for mathematics involving students with learning disabilities. A systematic search of the literature on computer-assisted instructional interventions for students with learning disabilities yielded 25 studies that met the criteria for inclusion in this analysis.…
Uncertainty and variability in computational and mathematical models of cardiac physiology
Mirams, Gary R.; Pathmanathan, Pras; Gray, Richard A.; Challenor, Peter
2016-01-01
Key points Mathematical and computational models of cardiac physiology have been an integral component of cardiac electrophysiology since its inception, and are collectively known as the Cardiac Physiome.We identify and classify the numerous sources of variability and uncertainty in model formulation, parameters and other inputs that arise from both natural variation in experimental data and lack of knowledge.The impact of uncertainty on the outputs of Cardiac Physiome models is not well understood, and this limits their utility as clinical tools.We argue that incorporating variability and uncertainty should be a high priority for the future of the Cardiac Physiome.We suggest investigating the adoption of approaches developed in other areas of science and engineering while recognising unique challenges for the Cardiac Physiome; it is likely that novel methods will be necessary that require engagement with the mathematics and statistics community. Abstract The Cardiac Physiome effort is one of the most mature and successful applications of mathematical and computational modelling for describing and advancing the understanding of physiology. After five decades of development, physiological cardiac models are poised to realise the promise of translational research via clinical applications such as drug development and patient‐specific approaches as well as ablation, cardiac resynchronisation and contractility modulation therapies. For models to be included as a vital component of the decision process in safety‐critical applications, rigorous assessment of model credibility will be required. This White Paper describes one aspect of this process by identifying and classifying sources of variability and uncertainty in models as well as their implications for the application and development of cardiac models. We stress the need to understand and quantify the sources of variability and uncertainty in model inputs, and the impact of model structure and complexity and
ERIC Educational Resources Information Center
Lopez-Morteo, Gabriel; Lopez, Gilberto
2007-01-01
In this paper, we introduce an electronic collaborative learning environment based on Interactive Instructors of Recreational Mathematics (IIRM), establishing an alternative approach for motivating students towards mathematics. The IIRM are educational software components, specializing in mathematical concepts, presented through recreational…
Using computer algebra and SMT-solvers to analyze a mathematical model of cholera propagation
NASA Astrophysics Data System (ADS)
Trujillo Arredondo, Mariana
2014-06-01
We analyze a mathematical model for the transmission of cholera. The model is already defined and involves variables such as the pathogen agent, which in this case is the bacterium Vibrio cholera, and the human population. The human population is divided into three classes: susceptible, infectious and removed. Using Computer Algebra, specifically Maple we obtain two equilibrium states: the disease free state and the endemic state. Using Maple it is possible to prove that the disease free state is locally asymptotically stable if and only if R0 < 1. Using Maple it is possible to prove that the endemic equilibrium state is locally stable when it exists, it is to say when R0 > 1. Using the package Red-Log of the Computer algebra system Reduce and the SMT-Solver Z3Py it is possible to obtain numerical conditions for the model. The formula for the basic reproductive number makes a synthesis with all epidemic parameters in the model. Also it is possible to make numerical simulations which are very illustrative about the epidemic patters that are expected to be observed in real situations. We claim that these kinds of software are very useful in the analysis of epidemic models given that the symbolic computation provides algebraic formulas for the basic reproductive number and such algebraic formulas are very useful to derive control measures. For other side, computer algebra software is a powerful tool to make the stability analysis for epidemic models given that the all steps in the stability analysis can be made automatically: finding the equilibrium points, computing the jacobian, computing the characteristic polynomial for the jacobian, and applying the Routh-Hurwitz theorem to the characteristic polynomial. Finally, using SMT-Solvers is possible to make automatically checks of satisfiability, validity and quantifiers elimination being these computations very useful to analyse complicated epidemic models.
Physics, Computer Science and Mathematics Division annual report, 1 January-31 December 1981
Birge, R.W.
1982-12-01
This report summarizes the research performed in the Physics, Computer Science and Mathematics Division of the Lawrence Berkeley Laboratory during calendar year 1981. During the year under review the Division devoted roughly half its effort to the final construction stages of the Time Projection Chamber and other equipment for the PEP-4 facility at SLAC. The year was marked by the successful passage of milestone after milestone - the two-sector test of the TPC with cosmic rays in July 1981, the full TPC test in November 1981, and the roll-in onto the PEP beam line on 6 January 1982. In other e/sup +/e/sup -/ experiments, the Mark II detector continued its productive data-taking at PEP. In other areas, the final stages of data analysis, particularly for the structure functions, proceeded for the inelastic muon scattering experiment performed at Fermilab, a muon polarimeter experiment was developed and mounted at TRIUMF to probe for the presence of right-handed currents in muon decay, and the design and then construction began of fine-grained hadron calorimeters for the end caps of the Colliding Detector Facility at Fermilab. The Particle Data Group intensified its activities, despite financial constraints, as it proceeded toward production of a new edition of its authoritative Review of Particle Properties early in 1982. During 1981 the Theoretical Physics Group pursued a diverse spectrum of research in its own right and also interacted effectively with the experimental program. Research and development continued on the segmented mirror for the ten-meter telescope proposed by the University of California. Activities in the Computer Science and Mathematics Department encompassed networking, database management, software engineering, and computer graphics, as well as basic research in nonlinear phenomena in combustion and fluid flow.
Applied & Computational MathematicsChallenges for the Design and Control of Dynamic Energy Systems
Brown, D L; Burns, J A; Collis, S; Grosh, J; Jacobson, C A; Johansen, H; Mezic, I; Narayanan, S; Wetter, M
2011-03-10
The Energy Independence and Security Act of 2007 (EISA) was passed with the goal 'to move the United States toward greater energy independence and security.' Energy security and independence cannot be achieved unless the United States addresses the issue of energy consumption in the building sector and significantly reduces energy consumption in buildings. Commercial and residential buildings account for approximately 40% of the U.S. energy consumption and emit 50% of CO{sub 2} emissions in the U.S. which is more than twice the total energy consumption of the entire U.S. automobile and light truck fleet. A 50%-80% improvement in building energy efficiency in both new construction and in retrofitting existing buildings could significantly reduce U.S. energy consumption and mitigate climate change. Reaching these aggressive building efficiency goals will not happen without significant Federal investments in areas of computational and mathematical sciences. Applied and computational mathematics are required to enable the development of algorithms and tools to design, control and optimize energy efficient buildings. The challenge has been issued by the U.S. Secretary of Energy, Dr. Steven Chu (emphasis added): 'We need to do more transformational research at DOE including computer design tools for commercial and residential buildings that enable reductions in energy consumption of up to 80 percent with investments that will pay for themselves in less than 10 years.' On July 8-9, 2010 a team of technical experts from industry, government and academia were assembled in Arlington, Virginia to identify the challenges associated with developing and deploying newcomputational methodologies and tools thatwill address building energy efficiency. These experts concluded that investments in fundamental applied and computational mathematics will be required to build enabling technology that can be used to realize the target of 80% reductions in energy consumption. In addition the
Mathematical model and dynamic computer simulation on free flow zone electrophoresis.
Zhang, Jie; Yan, Jian; Li, Si; Pang, Bo; Guo, Cheng-Gang; Cao, Cheng-Xi; Jin, Xin-Qiao
2013-10-07
In this paper, a mathematical model was proposed for calculating physico-chemical parameters and simulating the separation process of solutes in free-flow zone electrophoresis (FFZE). Computer software was developed and implemented in a Delphi XE2 environment based on the model, which comprises zone electrophoresis, electrolyte solution, hydrodynamics and diffusion as well as conversion equations. The simulation results reveal that (i) the software is capable of simulating a dynamic process of FFZE properly; (ii) the software can simulate operation parameters (e.g., electric field, flow rate and pH value) for experimental optimization; (iii) the simulator is able to display the final electropherogram of numerous analytes in FFZE; and (iv) the electropherogram of FFZE can be automatically converted to that of capillary zone electrophoresis. In order to verify the rationality and reliability of this software, the relevant experiments were conducted and further compared with the simulations. The comparisons demonstrated the high agreement between the simulations and the experiments as well as those cited from the relevant references. In addition, effective mobility, diffusion coefficient and concentration of solutes can be conveniently gained via the software. The developed mathematical model and designed software have evident significance for the optimization of experimental conditions and basic physico-chemical parameters in FFZE.
ERIC Educational Resources Information Center
Athappilly, Kuriakose; And Others
1983-01-01
The aggregate findings of experiments with modern mathematics for the last 30 years show that there have not been many detrimental effects of "new math" either on achievement or attitude. Instead, the evidence points toward beneficial effects in terms of improvement in overall achievement and attitude. (Author/BW)
NASA Astrophysics Data System (ADS)
Kaski, K.; Salomaa, M.
1990-01-01
These are Proceedings of the Third Nordic Symposium on Computer Simulation in Physics, Chemistry, Biology, and Mathematics, held August 25-26, 1989, at Lahti (Finland). The Symposium belongs to an annual series of Meetings, the first one of which was arranged in 1987 at Lund (Sweden) and the second one in 1988 at Kolle-Kolle near Copenhagen (Denmark). Although these Symposia have thus far been essentially Nordic events, their international character has increased significantly; the trend is vividly reflected through contributions in the present Topical Issue. The interdisciplinary nature of Computational Science is central to the activity; this fundamental aspect is also responsible, in an essential way, for its rapidly increasing impact. Crucially important to a wide spectrum of superficially disparate fields is the common need for extensive - and often quite demanding - computational modelling. For such theoretical models, no closed-form (analytical) solutions are available or they would be extremely difficult to find; hence one must rather resort to the Art of performing computational investigations. Among the unifying features in the computational research are the methods of simulation employed; methods which frequently are quite closely related with each other even for faculties of science that are quite unrelated. Computer simulation in Natural Sciences is presently apprehended as a discipline on its own right, occupying a broad region somewhere between the experimental and theoretical methods, but also partially overlapping with and complementing them. - Whichever its proper definition may be, the computational approach serves as a novel and an extremely versatile tool with which one can equally well perform "pure" experimental modelling and conduct "computational theory". Computational studies that have earlier been made possible only through supercomputers have opened unexpected, as well as exciting, novel frontiers equally in mathematics (e.g., fractals
ERIC Educational Resources Information Center
Hartley, M. Shaheed; Treagust, David F.
2014-01-01
This study responded to a national call to improve the outcomes in mathematics in the Grade 12 matriculation examination in South Africa by reporting learners' perceptions of the introduction of computer-assisted learning in their mathematics classrooms. Three Grade 12 mathematics classes in a peri-urban school in South Africa were visited over a…
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
Many industrial problems provide scientists with important and challenging problems that need to be solved today rather than tomorrow. The key role of mathematical physics, modelling, and computational methodologies in addressing such problems continues to increase. Science has never been exogenous to applied research. Gigantic ships and steam engines, repeating catapult of Dionysius and the Antikythera `computer' invented around 80BC are just a few examples demonstrating a profound link between theoretical and applied science in the ancient world. Nowadays, many industrial problems are typically approached by groups of researchers who are working as a team bringing their expertise to the success of the entire enterprise. Since the late 1960s several groups of European mathematicians and scientists have started organizing regular meetings, seeking new challenges from industry and contributing to the solution of important industrial problems. In particular, this often took the format of week-long workshops originally initiated by the Oxford Study Groups with Industry in 1968. Such workshops are now held in many European countries (typically under the auspices of the European Study Groups with Industry - ESGI), as well as in Australia, Canada, the United States, and other countries around the world. Problems given by industrial partners are sometimes very difficult to complete within a week. However, during a week of brainstorming activities these problems inevitably stimulate developing fruitful new ideas, new approaches, and new collaborations. At the same time, there are cases where as soon as the problem is formulated mathematically, it is relatively easy to solve. Hence, putting the industrial problem into a mathematical framework, based on physical laws, often provides a key element to the success. In addition to this important first step, the value in such cases is the real, practical applicability of the results obtained for an industrial partner who presents
Patra, Subir; Banerjee, Sourav; Terejanu, Gabriel; Chanda, Anindya
2015-01-01
Colony expansion is an essential feature of fungal infections. Although mechanisms that regulate hyphal forces on the substrate during expansion have been reported previously, there is a critical need of a methodology that can compute the pressure profiles exerted by fungi on substrates during expansion; this will facilitate the validation of therapeutic efficacy of novel antifungals. Here, we introduce an analytical decoding method based on Biot’s incremental stress model, which was used to map the pressure distribution from an expanding mycelium of a popular plant pathogen, Aspergillus parasiticus. Using our recently developed Quantitative acoustic contrast tomography (Q-ACT) we detected that the mycelial growth on the solid agar created multiple surface and subsurface wrinkles with varying wavelengths across the depth of substrate that were computable with acousto-ultrasonic waves between 50 MHz–175 MHz. We derive here the fundamental correlation between these wrinkle wavelengths and the pressure distribution on the colony subsurface. Using our correlation we show that A. parasiticus can exert pressure as high as 300 KPa on the surface of a standard agar growth medium. The study provides a novel mathematical foundation for quantifying fungal pressures on substrate during hyphal invasions under normal and pathophysiological growth conditions. PMID:26262897
NASA Astrophysics Data System (ADS)
Saldarriaga Vargas, Clarita
When there are diseases affecting large populations where the social, economic and cultural diversity is significant within the same region, the biological parameters that determine the behavior of the dispersion disease analysis are affected by the selection of different individuals. Therefore and because of the variety and magnitude of the communities at risk of contracting dengue disease around all over the world, suggest defining differentiated populations with individual contributions in the results of the dispersion dengue disease analysis. In this paper those conditions were taken in account when several epidemiologic models were analyzed. Initially a stability analysis was done for a SEIR mathematical model of Dengue disease without differential susceptibility. Both free disease and endemic equilibrium states were found in terms of the basic reproduction number and were defined in the Theorem (3.1). Then a DSEIR model was solved when a new susceptible group was introduced to consider the effects of important biological parameters of non-homogeneous populations in the spreading analysis. The results were compiled in the Theorem (3.2). Finally Theorems (3.3) and (3.4) resumed the basic reproduction numbers for three and n different susceptible groups respectively, giving an idea of how differential susceptibility affects the equilibrium states. The computations were done using an algorithmic method implemented in Maple 11, a general-purpose computer algebra system.
ERIC Educational Resources Information Center
Dotson, Daniel S.; Franks, Tina P.
2015-01-01
More than 53,000 citations from 609 dissertations published at The Ohio State University between 1998-2012 representing four science disciplines--civil engineering, computer science, mathematics and physics--were examined to determine what, if any, preferences or trends exist. This case study seeks to identify whether or not researcher preferences…
ERIC Educational Resources Information Center
Dogan, Mustafa
2010-01-01
This study explores Turkish primary mathematics trainee teachers' attitudes to computer and technology. A survey was conducted with a self constructed questionnaire. Piloting, factor and reliability ([alpha] = 0.94) analyses were performed. The final version of the questionnaire has three parts with a total of 48 questions including a Likert type…
ERIC Educational Resources Information Center
Leng, Ng Wee; Choo, Kwee Tiow; Soon, Lau Hock; Yi-Huak, Koh; Sun, Yap Yew
2005-01-01
This study examines the effects of using Texas Instruments' Voyage 200 calculator (V200), a graphing calculator with a built-in computer algebra system (CAS), on attitudes towards CAS and achievement in mathematics of junior college students (17 year olds). Students' attitudes towards CAS were examined using a 40-item Likert-type instrument…
ERIC Educational Resources Information Center
Nejem, Khamis Mousa; Muhanna, Wafa
2013-01-01
The purpose of this study was to investigate the effect of using computer games in teaching mathematics on developing the number sense of fourth grade students. To achieve this purpose a study sample of (81) students was selected from the fourth grade. This sample was divided into two groups. One group was randomly chosen to be the experimental…
ERIC Educational Resources Information Center
Gambari, A. I.; Falode, C. O.; Adegbenro, D. A.
2014-01-01
This study investigated the effectiveness of computer animation and geometry instructional model on mathematics achievement and retention on Junior Secondary School Students in Minna, Nigeria. It also examined the influence of gender on students' achievement and retention. The research was a pre-test post-test experimental and control group…
ERIC Educational Resources Information Center
Promraksa, Siwarak; Sangaroon, Kiat; Inprasitha, Maitree
2014-01-01
The objectives of this research were to study and analyze the characteristics of computational thinking about the estimation of the students in mathematics classroom applying lesson study and open approach. Members of target group included 4th grade students of 2011 academic year of Choomchon Banchonnabot School. The Lesson plan used for data…
ERIC Educational Resources Information Center
Hickendorff, Marian
2013-01-01
The results of an exploratory study into measurement of elementary mathematics ability are presented. The focus is on the abilities involved in solving standard computation problems on the one hand and problems presented in a realistic context on the other. The objectives were to assess to what extent these abilities are shared or distinct, and…
ERIC Educational Resources Information Center
Aksu, Hasan Hüseyin
2014-01-01
This study aims to investigate, in terms of different variables, the views of prospective Mathematics teachers on tablet computers to be used in schools as an outcome of the Fatih Project, which was initiated by the Ministry of National Education. In the study, scanning model, one of the quantitative research methods, was used. In the population…
ERIC Educational Resources Information Center
Yushau, Balarabe
2006-01-01
As the pedagogical-effectiveness of information technology (IT) in mathematics education is carefully established the topic of discourse among mathematicians and mathematics educators is no longer a dispute about whether or not to use IT in the teaching and learning of mathematics but a shift to some debate about the when and how of its usage.…
NASA Astrophysics Data System (ADS)
Schäfer, Andreas; Holz, Jan; Leonhardt, Thiemo; Schroeder, Ulrik; Brauner, Philipp; Ziefle, Martina
2013-06-01
In this study, we address the problem of low retention and high dropout rates of computer science university students in early semesters of the studies. Complex and high abstract mathematical learning materials have been identified as one reason for the dropout rate. In order to support the understanding and practicing of core mathematical concepts, we developed a game-based multitouch learning environment in which the need for a suitable learning environment for mathematical logic was combined with the ability to train cooperation and collaboration in a learning scenario. As application domain, the field of mathematical logic had been chosen. The development process was accomplished along three steps: First, ethnographic interviews were run with 12 students of computer science revealing typical problems with mathematical logic. Second, a multitouch learning environment was developed. The game consists of multiple learning and playing modes in which teams of students can collaborate or compete against each other. Finally, a twofold evaluation of the environment was carried out (user study and cognitive walk-through). Overall, the evaluation showed that the game environment was easy to use and rated as helpful: The chosen approach of a multiplayer game supporting competition, collaboration, and cooperation is perceived as motivating and "fun."
Computational physics and applied mathematics capability review June 8-10, 2010
Lee, Stephen R
2010-01-01
Los Alamos National Laboratory will review its Computational Physics and Applied Mathematics (CPAM) capabilities in 2010. The goals of capability reviews are to assess the quality of science, technology, and engineering (STE) performed by the capability, evaluate the integration of this capability across the Laboratory and within the scientific community, examine the relevance of this capability to the Laboratory's programs, and provide advice on the current and future directions of this capability. This is the first such review for CPAM, which has a long and unique history at the Laboratory, starting from the inception of the Laboratory in 1943. The CPAM capability covers an extremely broad technical area at Los Alamos, encompassing a wide array of disciplines, research topics, and organizations. A vast array of technical disciplines and activities are included in this capability, from general numerical modeling, to coupled multi-physics simulations, to detailed domain science activities in mathematics, methods, and algorithms. The CPAM capability involves over 12 different technical divisions and a majority of our programmatic and scientific activities. To make this large scope tractable, the CPAM capability is broken into the following six technical 'themes.' These themes represent technical slices through the CPAM capability and collect critical core competencies of the Laboratory, each of which contributes to the capability (and each of which is divided into multiple additional elements in the detailed descriptions of the themes in subsequent sections), as follows. Theme 1: Computational Fluid Dynamics - This theme speaks to the vast array of scientific capabilities for the simulation of fluids under shocks, low-speed flow, and turbulent conditions - which are key, historical, and fundamental strengths of the Laboratory. Theme 2: Partial Differential Equations - The technical scope of this theme is the applied mathematics and numerical solution of partial
Kirschner, Denise E; Linderman, Jennifer J
2009-04-01
In addition to traditional and novel experimental approaches to study host-pathogen interactions, mathematical and computer modelling have recently been applied to address open questions in this area. These modelling tools not only offer an additional avenue for exploring disease dynamics at multiple biological scales, but also complement and extend knowledge gained via experimental tools. In this review, we outline four examples where modelling has complemented current experimental techniques in a way that can or has already pushed our knowledge of host-pathogen dynamics forward. Two of the modelling approaches presented go hand in hand with articles in this issue exploring fluorescence resonance energy transfer and two-photon intravital microscopy. Two others explore virtual or 'in silico' deletion and depletion as well as a new method to understand and guide studies in genetic epidemiology. In each of these examples, the complementary nature of modelling and experiment is discussed. We further note that multi-scale modelling may allow us to integrate information across length (molecular, cellular, tissue, organism, population) and time (e.g. seconds to lifetimes). In sum, when combined, these compatible approaches offer new opportunities for understanding host-pathogen interactions.
Kirschner, Denise E.; Linderman, Jennifer J.
2009-01-01
SUMMARY In addition to traditional and novel experimental approaches to study host-pathogen interactions, mathematical and computer modeling has recently been applied to address open questions in this area. These modeling tools not only offer an additional avenue for exploring disease dynamics at multiple biological scales, but also complement and extend knowledge gained via experimental tools. In this review, we outline four examples where modeling has complemented current experimental techniques in a way that can or has already pushed our knowledge of host-pathogen dynamics forward. Two of the modeling approaches presented go hand-in-hand with articles in this issue exploring FRET and two-photon intra-vital microscopy. Two others explore virtual or “in silico” deletion and depletion as well as a new method to understand and guide studies in genetic epidemiology. In each of these examples, the complementary nature of modeling and experiment is discussed. We further note that multi-scale modeling may allow us to integrate information across length (molecular, cellular, tissue, organism, population) and time (e.g. seconds to lifetimes). In sum, when combined, these compatible approaches offer new opportunities for understanding host-pathogen interactions. PMID:19134115
Yang, Anxiong; Stingl, Michael; Berry, David A.; Lohscheller, Jörg; Voigt, Daniel; Eysholdt, Ulrich; Döllinger, Michael
2011-01-01
With the use of an endoscopic, high-speed camera, vocal fold dynamics may be observed clinically during phonation. However, observation and subjective judgment alone may be insufficient for clinical diagnosis and documentation of improved vocal function, especially when the laryngeal disease lacks any clear morphological presentation. In this study, biomechanical parameters of the vocal folds are computed by adjusting the corresponding parameters of a three-dimensional model until the dynamics of both systems are similar. First, a mathematical optimization method is presented. Next, model parameters (such as pressure, tension and masses) are adjusted to reproduce vocal fold dynamics, and the deduced parameters are physiologically interpreted. Various combinations of global and local optimization techniques are attempted. Evaluation of the optimization procedure is performed using 50 synthetically generated data sets. The results show sufficient reliability, including 0.07 normalized error, 96% correlation, and 91% accuracy. The technique is also demonstrated on data from human hemilarynx experiments, in which a low normalized error (0.16) and high correlation (84%) values were achieved. In the future, this technique may be applied to clinical high-speed images, yielding objective measures with which to document improved vocal function of patients with voice disorders. PMID:21877808
ERIC Educational Resources Information Center
Hennes, James D.; And Others
In recent years the graduation requirements in mathematics and science have increased in response to state and national goals calling for increased competency by U.S. graduates in those areas. Data on course enrollment in science, mathematics, and computer science in grades 7-12 were collected from 89 percent of the schools in Colorado in October,…
1992-07-24
opportunity to see "mathematics at work" in every day life through films , videos. etc. and to visit the workplace of and to interact directly with...the tours, students viewed video tapes and a film , and discussed career opportunities in mathematics-based fields. The students viewed the video...Solve It." The students also viewed the film "Donald in Mathemagic Land" which shows how mathematics grows from simple ideas. This component also
Yuan, Jing-Ping; Chen, Chuang; Sun, Sheng-Rong; Hu, Ming-Bai; Liu, Juan; Li, Yan
2013-01-01
Background The expending and invasive features of tumor nests could reflect the malignant biological behaviors of breast invasive ductal carcinoma. Useful information on cancer invasiveness hidden within tumor nests could be extracted and analyzed by computer image processing and big data analysis. Methods Tissue microarrays from invasive ductal carcinoma (n = 202) were first stained with cytokeratin by immunohistochemical method to clearly demarcate the tumor nests. Then an expert-aided computer analysis system was developed to study the mathematical and geometrical features of the tumor nests. Computer recognition system and imaging analysis software extracted tumor nests information, and mathematical features of tumor nests were calculated. The relationship between tumor nests mathematical parameters and patients' 5-year disease free survival was studied. Results There were 8 mathematical parameters extracted by expert-aided computer analysis system. Three mathematical parameters (number, circularity and total perimeter) with area under curve >0.5 and 4 mathematical parameters (average area, average perimeter, total area/total perimeter, average (area/perimeter)) with area under curve <0.5 in ROC analysis were combined into integrated parameter 1 and integrated parameter 2, respectively. Multivariate analysis showed that integrated parameter 1 (P = 0.040) was independent prognostic factor of patients' 5-year disease free survival. The hazard risk ratio of integrated parameter 1 was 1.454 (HR 95% CI [1.017–2.078]), higher than that of N stage (HR 1.396, 95% CI [1.125–1.733]) and hormone receptor status (HR 0.575, 95% CI [0.353–0.936]), but lower than that of histological grading (HR 3.370, 95% CI [1.125–5.364]) and T stage (HR 1.610, 95% CI [1.026 –2.527]). Conclusions This study indicated integrated parameter 1 of mathematical features (number, circularity and total perimeter) of tumor nests could be a useful parameter to predict the prognosis
My Entirely Plausible Fantasy: Early Mathematics Education in the Age of the Touchscreen Computer
ERIC Educational Resources Information Center
Ginsburg, Herbert P.
2014-01-01
This paper offers an account of what early mathematics education could look like in an age of young digital natives. Each "Tubby," as the tablets are called, presents Nicole (our generic little child) with stimulating mathematics microworlds, from which, beginning at age 3, she can learn basic math concepts, as well as methods of…
ERIC Educational Resources Information Center
Yang, Euphony F. Y.; Chang, Ben; Cheng, Hercy N. H.; Chan, Tak-Wai
2016-01-01
This study examined how to foster pupils' mathematical communication abilities by using tablet PCs. Students were encouraged to generate math creations (including mathematical representation, solution, and solution explanation of word problems) as their teaching materials and reciprocally tutor classmates to increase opportunities for mathematical…
ERIC Educational Resources Information Center
Exner, Robert; And Others
The sixteen chapters of this book provide the core material for the Elements of Mathematics Program, a secondary sequence developed for highly motivated students with strong verbal abilities. The sequence is based on a functional-relational approach to mathematics teaching, and emphasizes teaching by analysis of real-life situations. This text is…
Polyhedral Sculpture: The Path from Computational Artifact to Real-World Mathematical Object.
ERIC Educational Resources Information Center
Eisenberg, Michael; Nishioka, Ann
Mathematics educators often despair at math's austere, "abstract" reputation. This paper describes recent work in developing an application named "HyperGami," which is designed to integrate both the abstract and"real-world" aspects of mathematics by allowing children to design and construct polyhedral models and…
ERIC Educational Resources Information Center
Clarke, Pier Junor
2009-01-01
This article presents a case study of one pre-service secondary school mathematics (PSSM) teacher taken from a larger study within an English-speaking Caribbean context. The major goal of the larger study was to investigate the experiences and perceptions of the PSSM teachers as they explored the graphing calculator and mathematics software in…
The Influence of Computer-Assisted Instruction on Eighth Grade Mathematics Achievement
ERIC Educational Resources Information Center
Tienken, Christopher H.; Maher, James A.
2008-01-01
The issue of lower than expected mathematics achievement is a concern to education leaders and policymakers at all levels of the U.S. PK-12 education system. The purpose of this quantitative, quasi-experimental study was to determine if there was a measurable difference in achievement on the mathematics section of the state test for students (n =…
Tennant, Marc; Kruger, Estie
2013-02-01
This study developed a Monte Carlo simulation approach to examining the prevalence and incidence of dental decay using Australian children as a test environment. Monte Carlo simulation has been used for a half a century in particle physics (and elsewhere); put simply, it is the probability for various population-level outcomes seeded randomly to drive the production of individual level data. A total of five runs of the simulation model for all 275,000 12-year-olds in Australia were completed based on 2005-2006 data. Measured on average decayed/missing/filled teeth (DMFT) and DMFT of highest 10% of sample (Sic10) the runs did not differ from each other by more than 2% and the outcome was within 5% of the reported sampled population data. The simulations rested on the population probabilities that are known to be strongly linked to dental decay, namely, socio-economic status and Indigenous heritage. Testing the simulated population found DMFT of all cases where DMFT<>0 was 2.3 (n = 128,609) and DMFT for Indigenous cases only was 1.9 (n = 13,749). In the simulation population the Sic25 was 3.3 (n = 68,750). Monte Carlo simulations were created in particle physics as a computational mathematical approach to unknown individual-level effects by resting a simulation on known population-level probabilities. In this study a Monte Carlo simulation approach to childhood dental decay was built, tested and validated.
Computation and graphics in mathematical research. Progress report, June 1, 1991--May 31, 1992
Hoffman, D.A.; Spruck, J.
1992-08-13
This report discusses: The description of the GANG Project and results for prior research; the center for geometry, analysis, numerics and graphics; description of GANG Laboratory; software development at GANG; and mathematical and scientific research activities.
ERIC Educational Resources Information Center
Cai, Jinfa
1995-01-01
This document is 7th in the Journal for Research in Mathematics Education monograph series. The mathematical performance of (n=250) U.S. 6th-grade students from both private and public schools and (n=425) Chinese 6th-graders from both key and common schools was examined on multiple-choice tasks assessing computation and simple problem solving, and…
Improved mathematical and computational tools for modeling photon propagation in tissue
NASA Astrophysics Data System (ADS)
Calabro, Katherine Weaver
Light interacts with biological tissue through two predominant mechanisms: scattering and absorption, which are sensitive to the size and density of cellular organelles, and to biochemical composition (ex. hemoglobin), respectively. During the progression of disease, tissues undergo a predictable set of changes in cell morphology and vascularization, which directly affect their scattering and absorption properties. Hence, quantification of these optical property differences can be used to identify the physiological biomarkers of disease with interest often focused on cancer. Diffuse reflectance spectroscopy is a diagnostic tool, wherein broadband visible light is transmitted through a fiber optic probe into a turbid medium, and after propagating through the sample, a fraction of the light is collected at the surface as reflectance. The measured reflectance spectrum can be analyzed with appropriate mathematical models to extract the optical properties of the tissue, and from these, a set of physiological properties. A number of models have been developed for this purpose using a variety of approaches -- from diffusion theory, to computational simulations, and empirical observations. However, these models are generally limited to narrow ranges of tissue and probe geometries. In this thesis, reflectance models were developed for a much wider range of measurement parameters, and influences such as the scattering phase function and probe design were investigated rigorously for the first time. The results provide a comprehensive understanding of the factors that influence reflectance, with novel insights that, in some cases, challenge current assumptions in the field. An improved Monte Carlo simulation program, designed to run on a graphics processing unit (GPU), was built to simulate the data used in the development of the reflectance models. Rigorous error analysis was performed to identify how inaccuracies in modeling assumptions can be expected to affect the accuracy
Experimental Mathematics and Mathematical Physics
Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David; Zudilin, Wadim
2009-06-26
One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.
ERIC Educational Resources Information Center
McCammon, Richard B.
1979-01-01
The year 1978 marked a continued trend toward practical applications in mathematical geology. Developments included work in interactive computer graphics, factor analysis, the vanishing tons problem, universal kriging, and resource estimating. (BB)
ERIC Educational Resources Information Center
Van Eck, Richard
2006-01-01
Many students enter mathematics courses with a poor attitude toward mathematics (Gal & Ginsburg, 1994), making attitude as important a consideration as achievement in mathematics (Cognition and Technology Group at Vanderbilt (CTGV), 1992; Marsh, Cairns, Relich, Barnes, & Debus, 1984; Sedighian & Sedighian, 1996). Pedagogical agents are often…
Computation, Exploration, Visualisation: Reaction to MATLAB in First-Year Mathematics.
ERIC Educational Resources Information Center
Cretchley, Patricia; Harman, Chris; Ellerton, Nerida; Fogarty, Gerard
This paper describes a model for effective incorporation of technology into the learning experience of a large and diverse group of students in first-semester first-year tertiary mathematics. It describes the introduction of elementary use of MATLAB, in a course offered both on-campus and at a distance. The diversity of the student group is…
ERIC Educational Resources Information Center
Beardslee, Edward C.; Jerman, Max E.
Five structural, four linguistic and twelve topic variables are used in regression analyses on results of a 50-item achievement test. The test items are related to 12 topics from the third-grade mathematics curriculum. The items reflect one of two cases of the structural variable, cognitive level; the two levels are characterized, inductive…
A Constructivist Computational Platform to Support Mathematics Education in Elementary School
ERIC Educational Resources Information Center
Garcia, I.; Pacheco, C.
2013-01-01
Many courses for elementary school are based upon teacher presentation and explanation of basic topics, rather than allowing students to develop their own knowledge. This traditional model may turn elementary-level lessons into an extremely theoretical, boring and non-effective process. In this context, research in mathematics elementary education…
Effects of Computer-Based Visual Representation on Mathematics Learning and Cognitive Load
ERIC Educational Resources Information Center
Yung, Hsin I.; Paas, Fred
2015-01-01
Visual representation has been recognized as a powerful learning tool in many learning domains. Based on the assumption that visual representations can support deeper understanding, we examined the effects of visual representations on learning performance and cognitive load in the domain of mathematics. An experimental condition with visual…
Peer-Led Team Learning in Mathematics Courses for Freshmen Engineering and Computer Science Students
ERIC Educational Resources Information Center
Reisel, John R.; Jablonski, Marissa R.; Munson, Ethan; Hosseini, Hossein
2014-01-01
Peer-led Team Learning (PLTL) is an instructional method reported to increase student learning in STEM courses. As mathematics is a significant hurdle for many freshmen engineering students, a PLTL program was implemented for students to attempt to improve their course performance. Here, an analysis of PLTL for freshmen engineering students in…
ERIC Educational Resources Information Center
Piburn, Michael D.; Middleton, James A.
Teacher Education for Arizona Mathematics and Science (TEAMS) is a technology-based program for preparing scientists and mathematicians for a career in middle school teaching. The metaphor of "reflective practitioner" guided the design and delivery of this program. Students did not respond well to journal keeping and many failed to…
Learning Mathematics with Interactive Whiteboards and Computer-Based Graphing Utility
ERIC Educational Resources Information Center
Erbas, Ayhan Kursat; Ince, Muge; Kaya, Sukru
2015-01-01
The purpose of this study was to explore the effect of a technology-supported learning environment utilizing an interactive whiteboard (IWB) and NuCalc graphing software compared to a traditional direct instruction-based environment on student achievement in graphs of quadratic functions and attitudes towards mathematics and technology. Sixty-five…
Computer-Aided Assessment Questions in Engineering Mathematics Using "MapleTA"[R
ERIC Educational Resources Information Center
Jones, I. S.
2008-01-01
The use of "MapleTA"[R] in the assessment of engineering mathematics at Liverpool John Moores University (JMU) is discussed with particular reference to the design of questions. Key aspects in the formulation and coding of questions are considered. Problems associated with the submission of symbolic answers, the use of randomly generated numbers…
ERIC Educational Resources Information Center
Lee, Chun-Yi; Chen, Ming-Puu
2008-01-01
In many mathematical problems, students can feel that the universality of a conjecture or a formula is validated by their experiment and experience. In contrast, students generally do not feel that deductive explanations strengthen their conviction that a conjecture or a formula is true. In order to cope up with students' conviction based only on…
ERIC Educational Resources Information Center
Salminen, Jonna; Koponen, Tuire; Räsänen, Pekka; Aro, Mikko
2015-01-01
Weaknesses in early number skills have been found to be a risk factor for later difficulties in mathematical performance. Nevertheless, only a few intervention studies with young children have been published. In this study, the responsiveness to early support in kindergarteners with most severe difficulties was examined with two different computer…
ERIC Educational Resources Information Center
Vogel, Freydis; Kollar, Ingo; Ufer, Stefan; Reichersdorfer, Elisabeth; Reiss, Kristina; Fischer, Frank
2016-01-01
Collaboration scripts and heuristic worked examples are effective means to scaffold university freshmen's mathematical argumentation skills. Yet, which collaborative learning processes are responsible for these effects has remained unclear. Learners presumably will gain the most out of collaboration if the collaborators refer to each other's…
ERIC Educational Resources Information Center
Bakker, Marjoke; van den Heuvel-Panhuizen, Marja; Robitzsch, Alexander
2016-01-01
This study examined the effects of a teacher-delivered intervention with online mathematics mini-games on special education students' multiplicative reasoning ability (multiplication and division). The games involved declarative, procedural, as well as conceptual knowledge of multiplicative relations, and were accompanied with teacher-led lessons…
Towards a Framework for Making Effective Computational Choices: A "Very Big Idea" of Mathematics
ERIC Educational Resources Information Center
Hurst, Chris
2016-01-01
It is important for students to make informed decisions about computation. This article highlights this importance and develops a framework which may assist teachers to help students to make effective computational choices.
NASA Technical Reports Server (NTRS)
Wong, K. W.
1974-01-01
In lunar phototriangulation, there is a complete lack of accurate ground control points. The accuracy analysis of the results of lunar phototriangulation must, therefore, be completely dependent on statistical procedure. It was the objective of this investigation to examine the validity of the commonly used statistical procedures, and to develop both mathematical techniques and computer softwares for evaluating (1) the accuracy of lunar phototriangulation; (2) the contribution of the different types of photo support data on the accuracy of lunar phototriangulation; (3) accuracy of absolute orientation as a function of the accuracy and distribution of both the ground and model points; and (4) the relative slope accuracy between any triangulated pass points.
"Hole-in-the-Wall" Computer Kiosks Foster Mathematics Achievement--A Comparative Study
ERIC Educational Resources Information Center
Inamdar, Parimala; Kulkarni, Arun
2007-01-01
Earlier work at unsupervised playground computer kiosks in rural India, popularly called "hole-in-the-wall", showed that children exposed to these kiosks learn to use computers on their own and that they are able to clear school examinations in computer science, without any classroom teaching for it. Extending this, our recent research…
2006-02-01
International Journal of Computational Methods for...Fluids, in review. "* V. Prabhakar and J. N. Reddy, "Orthogonality of Modal Bases," International Journal of Computational Methods for Fluids...Least-Squares Finite Element Model for Incompressible Navier-Stokes Equations," International Journal of Computational Methods for Fluids, in review.
Summary of research in applied mathematics, numerical analysis, and computer sciences
NASA Technical Reports Server (NTRS)
1986-01-01
The major categories of current ICASE research programs addressed include: numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; control and parameter identification problems, with emphasis on effective numerical methods; computational problems in engineering and physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and computer systems and software, especially vector and parallel computers.
2012-08-20
Leonid V. Kalachev, Ph.D. (University of Montana, not supported on grant) Daniel J. Mollicone, Ph.D. ( Pulsar Informatics, Inc., not supported on grant...project to Pulsar Informatics, Inc., who are providing an implementation suitable for integration with crew rostering to the U.S. Navy (key...individuals involved: Daniel Mollicone, Ph.D. and Mike Stubna, Ph.D. of Pulsar Informatics, Inc.). We transitioned a numerical library for the mathematical
The Fractal Geometry of Nature; Its Mathematical Basis and Application to Computer Graphics
1986-01-01
matematical cotstructr3. It was first popularized by complex renderings of terrain onl a conputer graphic.ý. medium. Fractal geometry has since...geometry has not yet been realized. In the final analysis , we expect that even the skeptical reader will discover the mathematical beauty and...Sinto 10,1] preserves the distribution from the original range ([0,231 - 1]). Analysis of the normalized uniform random numbers S0.0 0.1 = 52 0.1
Not Available
1990-12-01
The issue of global warming and related climatic changes from increasing concentrations of greenhouse gases in the atmosphere has received prominent attention during the past few years. The Computer Hardware, Advanced Mathematics, and Model Physics (CHAMMP) Climate Modeling Program is designed to contribute directly to this rapid improvement. The goal of the CHAMMP Climate Modeling Program is to develop, verify, and apply a new generation of climate models within a coordinated framework that incorporates the best available scientific and numerical approaches to represent physical, biogeochemical, and ecological processes, that fully utilizes the hardware and software capabilities of new computer architectures, that probes the limits of climate predictability, and finally that can be used to address the challenging problem of understanding the greenhouse climate issue through the ability of the models to simulate time-dependent climatic changes over extended times and with regional resolution.
ERIC Educational Resources Information Center
Seo, You-Jin; Woo, Honguk
2010-01-01
Critical user interface design features of computer-assisted instruction programs in mathematics for students with learning disabilities and corresponding implementation guidelines were identified in this study. Based on the identified features and guidelines, a multimedia computer-assisted instruction program, "Math Explorer", which delivers…
ERIC Educational Resources Information Center
Soliman, Mamdouh M.; Hilal, Ahmed J.
2016-01-01
This study evaluates the effectiveness of Computer-Assisted Instruction (CAI) compared with traditional classroom instruction of mathematics of seventh graders in Kuwait's public schools. We aimed to compare students learning outcomes between two groups: the control group, taught traditionally without the use of computers, and the experimental…
Chang, Jiang; Zhang, Jie; Wang, Hou-Yu; Fan, Liu-Yin; Fan, Yin-Ping; Li, Shan; Cao, Cheng-Xi
2013-01-15
In this paper, a mathematical model and computer simulator were developed for offline sample pretreatment of heavy metal ion based on moving precipitate boundary (MPB) electrophoresis. The simulation indicates that (i) the program can easily accomplish numerical computations, such as the velocities of MPB and elution boundary (EB), and enrichment factor (EF) etc; (ii) the simulator can vividly imitate the dynamics of MPB, EB, precipitate zone, and precipitate-elution; and (iii) the software may simply optimized experimental conditions via the influence factors (e.g., voltage, hydroxyl, hydrogen and metal ions) on the EF. As a proof of concept, copper ion and its precipitate with definite blue color were, respectively chosen as mode heavy metal ion and alkaline precipitate for the relevant experiments of MPB-based sample preconcentration of heavy metal ion in large tube. All of the experimental results manifest the validity of developed mathematical model and the relevant simulation results. The model and simulator advanced herein are of clear significance to the optimization of experimental conditions and understanding of offline MPB- based sample condensation of heavy metal ion.
ERIC Educational Resources Information Center
van Herwaarden, Onno A.; Gielen, Joseph L. W.
2002-01-01
Focuses on students showing a lack of conceptual insight while using computer algebra systems (CAS) in the setting of an elementary calculus and linear algebra course for first year university students in social sciences. The use of a computer algebra environment has been incorporated into a more traditional course but with special attention on…
Orchestrating the XO Computer with Digital and Conventional Resources to Teach Mathematics
ERIC Educational Resources Information Center
Díaz, A.; Nussbaum, M.; Varela, I.
2015-01-01
Recent research has suggested that simply providing each child with a computer does not lead to an improvement in learning. Given that dozens of countries across the world are purchasing computers for their students, we ask which elements are necessary to improve learning when introducing digital resources into the classroom. Understood the…
A Dataset from TIMSS to Examine the Relationship between Computer Use and Mathematics Achievement
ERIC Educational Resources Information Center
Kadijevich, Djordje M.
2015-01-01
Because the relationship between computer use and achievement is still puzzling, there is a need to prepare and analyze good quality datasets on computer use and achievement. Such a dataset can be derived from TIMSS data. This paper describes how this dataset can be prepared. It also gives an example of how the dataset may be analyzed. The…
ERIC Educational Resources Information Center
RENO, MARTIN; AND OTHERS
A STUDY WAS UNDERTAKEN TO EXPLORE IN A QUALITATIVE WAY THE POSSIBLE UTILIZATION OF COMPUTER AND DATA PROCESSING METHODS IN HIGH SCHOOL EDUCATION. OBJECTIVES WERE--(1) TO ESTABLISH A WORKING RELATIONSHIP WITH A COMPUTER FACILITY SO THAT ABLE STUDENTS AND THEIR TEACHERS WOULD HAVE ACCESS TO THE FACILITIES, (2) TO DEVELOP A UNIT FOR THE UTILIZATION…
ERIC Educational Resources Information Center
Akkoç, Hatice
2015-01-01
This paper focuses on a specific aspect of formative assessment, namely questioning. Given that computers have gained widespread use in learning and teaching, specific attention should be made when organizing formative assessment in computer learning environments (CLEs). A course including various workshops was designed to develop knowledge and…
Car-Buying. Computer Module for Use in a Mathematics Laboratory Setting.
ERIC Educational Resources Information Center
Hoffman, Irwin; And Others
This is one of a series of computer modules designed for use by secondary students who have access to a computer. The module, designed to help students understand all facets of car-buying, includes a statement of objectives, a time schedule, a list of materials, suggested evaluation procedures, an outline for each section, and several computer…
NASA Astrophysics Data System (ADS)
Tang, Baobao
Different positions of a material used for structures experience different stresses, sometimes at both extremes, when undergoing processing, manufacturing, and serving. Taking the three-point bending as an example, the plate experiences higher stress in the middle span area and lower stress in both sides of the plate. In order to ensure the performance and reduce the cost of the composite, placement of different composite material with different mechanical properties, i.e. selective reinforcement, is proposed. Very few study has been conducted on selective reinforcement. Therefore, basic understanding on the relationship between the selective reinforcing variables and the overall properties of composite material is still unclear and there is still no clear methodology to design composite materials under different types of loads. This study started from the analysis of composite laminate under three point bending test. From the mechanical analysis and simulation result of homogeneously reinforced composite materials, it is found that the stress is not evenly distributed on the plate based on through-thickness direction and longitudinal direction. Based on these results, a map for the stress distribution under three point bending was developed. Next, the composite plate was selectively designed using two types of configurations. Mathematical and finite element analysis (FEA) models were built based on these designs. Experimental data from tests of hybrid composite materials was used to verify the mathematical and FEA models. Analysis of the mathematical model indicates that the increase in stiffness of the material at the top and bottom surfaces and middle-span area is the most effective way to improve the flexural modulus in three point bending test. At the end of this study, a complete methodology to perform the selective design was developed.
Mathematical model and software complex for computer simulation of field emission electron sources
Nikiforov, Konstantin
2015-03-10
The software complex developed in MATLAB allows modelling of function of diode and triode structures based on field emission electron sources with complex sub-micron geometry, their volt-ampere characteristics, calculating distribution of electric field for educational and research needs. The goal of this paper is describing the physical-mathematical model, calculation methods and algorithms the software complex is based on, demonstrating the principles of its function and showing results of its work. For getting to know the complex, a demo version with graphical user interface is presented.
NASA Technical Reports Server (NTRS)
Mosher, R. A.; Palusinski, O. A.; Bier, M.
1982-01-01
A mathematical model has been developed which describes the steady state in an isoelectric focusing (IEF) system with ampholytes or monovalent buffers. The model is based on the fundamental equations describing the component dissociation equilibria, mass transport due to diffusion and electromigration, electroneutrality, and the conservation of charge. The validity and usefulness of the model has been confirmed by using it to formulate buffer systems in actual laboratory experiments. The model has been recently extended to include the evolution of transient states not only in IEF but also in other modes of electrophoresis.
NASA Astrophysics Data System (ADS)
Liang, Feng; Liu, Liren; Wang, Binquan; Wang, Zhijiang
1994-12-01
An alternative to the umbra definition on grey-scale mathematical morphology is proposed in this paper, which uses the top-surface set instead of the umbra to represent grey-scale structuring element. This algorithm greatly decreases the neighborhood connections for the binary morphological operation transformed from a grey-scale morphological operation. An optical incoherent correlator architecture with threshold device is developed to carry out the suggested algorithm, while a spatial digital coding method is used to represent input 3D binary data in a 2D arrangement. Experimental results are demonstrated too.
NASA Technical Reports Server (NTRS)
Johannsen, G.; Rouse, W. B.
1978-01-01
A hierarchy of human activities is derived by analyzing automobile driving in general terms. A structural description leads to a block diagram and a time-sharing computer analogy. The range of applicability of existing mathematical models is considered with respect to the hierarchy of human activities in actual complex tasks. Other mathematical tools so far not often applied to man machine systems are also discussed. The mathematical descriptions at least briefly considered here include utility, estimation, control, queueing, and fuzzy set theory as well as artificial intelligence techniques. Some thoughts are given as to how these methods might be integrated and how further work might be pursued.
2015-02-04
The subjects covered in the past included, but were not limited to, geomaterials, energetic materials, plastic deformation in metals and alloys...understanding plastic deformation Mathematical models Computational techniques currently used Multiscale modeling and multiscale experiments Scale...coupling Role of instabilities • Outline the outstanding challenges in both plasticity and multiscale modeling in general • Promote interactions
ERIC Educational Resources Information Center
Karakis, Hilal; Karamete, Aysen; Okçu, Aydin
2016-01-01
This study examined the effects that computer-assisted instruction had on students' attitudes toward a mathematics lesson and toward learning mathematics with computer-assisted instruction. The computer software we used was based on the ASSURE Instructional Systems Design and the ARCS Model of Motivation, and the software was designed to teach…
2010-10-18
School Cybercampus ChicTech Tech Ambassadors Competition Arduino Project Lead the Way Pico Crickets™ Workshops MIT Media Lab , STEM Rays, UMASS...Computer Science Equity Alliance Way Arduino “Kids Ahead” SMU Caruth August 2010 14 , STEM Rays, UMASS US FIRST Robotics Competition Autonomous
ERIC Educational Resources Information Center
Meagher, Michael
2012-01-01
The research presented here is a group case study of students learning calculus in a Computer Algebra System (CAS) environment which examines the following research questions: What are students' perceptions of the role of technology in their learning? What is the students' relationship to CAS? What is the effect of learning in a CAS environment on…
ERIC Educational Resources Information Center
Holbrook, M. Cay; MacCuspie, P. Ann
2010-01-01
Braille-reading mathematicians, scientists, and computer scientists were asked to examine the usability of the Unified English Braille Code (UEB) for technical materials. They had little knowledge of the code prior to the study. The research included two reading tasks, a short tutorial about UEB, and a focus group. The results indicated that the…
Developing Mathematical Reasoning through Games of Strategy Played against the Computer
ERIC Educational Resources Information Center
Houssart, Jenny; Sams, Claire
2008-01-01
This article examines 9-11 year olds' attempts to beat the computer at a game of strategy and asks how far and under what circumstances they developed a strategic approach to the game. Extracts from videotape transcripts are analysed to reveal the components of children's particular approaches, evident even amongst children who did not develop an…
ERIC Educational Resources Information Center
de Castro, Christopher H.
2011-01-01
This study explored the development of student's conceptual understandings of limit and derivative when utilizing specifically designed computational tools. Fourteen students from a secondary Advanced Placement Calculus AB course learned and explored the limit and derivative concepts from differential calculus using visualization tools in the…
ERIC Educational Resources Information Center
Dershem, Herbert L.
These modules view aspects of computer use in the problem-solving process, and introduce techniques and ideas that are applicable to other modes of problem solving. The first unit looks at algorithms, flowchart language, and problem-solving steps that apply this knowledge. The second unit describes ways in which computer iteration may be used…
NASA Astrophysics Data System (ADS)
Mirgaux, O.; Ablitzer, D.; Waz, E.; Bellot, J. P.
2009-06-01
The removal of inclusions by flotation in mechanically agitated vessels is widely used in liquid aluminum treatments. Originating from different sources (oxide skins, refractory, or recycling wastes), inclusions may have disastrous repercussions such as deterioration of the physical properties of the cast products or difficulties during forging processes. With the aim of both a better understanding of the physical processes acting during flotation and the optimization of the refining process, a mathematical modeling of the behavior of the population of inclusions has been set up. Transport phenomena, agglomeration of inclusions, and flotation are considered here. The model combines population balance with convective transport of the inclusions, in order to calculate the time evolution of the inclusion size distribution. An operator-splitting technique is employed to solve the coupled population balance equation (PBE) and the transport equation. The transport equation is solved using a finite volume technique associated with a total variation diminishing scheme, whereas the PBE resolution relies on the fixed pivot technique developed by Kumar and Ramkrishna. A laboratory-scale flotation vessel is modeled and the results of a two-dimensional (2-D) simulation are presented.
Multi-Strain Deterministic Chaos in Dengue Epidemiology, A Challenge for Computational Mathematics
NASA Astrophysics Data System (ADS)
Aguiar, Maíra; Kooi, Bob W.; Stollenwerk, Nico
2009-09-01
Recently, we have analysed epidemiological models of competing strains of pathogens and hence differences in transmission for first versus secondary infection due to interaction of the strains with previously aquired immunities, as has been described for dengue fever, known as antibody dependent enhancement (ADE). These models show a rich variety of dynamics through bifurcations up to deterministic chaos. Including temporary cross-immunity even enlarges the parameter range of such chaotic attractors, and also gives rise to various coexisting attractors, which are difficult to identify by standard numerical bifurcation programs using continuation methods. A combination of techniques, including classical bifurcation plots and Lyapunov exponent spectra has to be applied in comparison to get further insight into such dynamical structures. Especially, Lyapunov spectra, which quantify the predictability horizon in the epidemiological system, are computationally very demanding. We show ways to speed up computations of such Lyapunov spectra by a factor of more than ten by parallelizing previously used sequential C programs. Such fast computations of Lyapunov spectra will be especially of use in future investigations of seasonally forced versions of the present models, as they are needed for data analysis.
NASA Technical Reports Server (NTRS)
Madnia, C. K.; Frankel, S. H.; Givi, P.
1992-01-01
Closed form analytical expressions are obtained for predicting the limited rate of reactant conversion in a binary reaction of the type F + rO yields (1 + r) Product in unpremixed homogeneous turbulence. These relations are obtained by means of a single point Probability Density Function (PDF) method based on the Amplitude Mapping Closure. It is demonstrated that with this model, the maximum rate of the reactants' decay can be conveniently expressed in terms of definite integrals of the Parabolic Cylinder Functions. For the cases with complete initial segregation, it is shown that the results agree very closely with those predicted by employing a Beta density of the first kind for an appropriately defined Shvab-Zeldovich scalar variable. With this assumption, the final results can also be expressed in terms of closed form analytical expressions which are based on the Incomplete Beta Functions. With both models, the dependence of the results on the stoichiometric coefficient and the equivalence ratio can be expressed in an explicit manner. For a stoichiometric mixture, the analytical results simplify significantly. In the mapping closure, these results are expressed in terms of simple trigonometric functions. For the Beta density model, they are in the form of Gamma Functions. In all the cases considered, the results are shown to agree well with data generated by Direct Numerical Simulations (DNS). Due to the simplicity of these expressions and because of nice mathematical features of the Parabolic Cylinder and the Incomplete Beta Functions, these models are recommended for estimating the limiting rate of reactant conversion in homogeneous reacting flows. These results also provide useful insights in assessing the extent of validity of turbulence closures in the modeling of unpremixed reacting flows. Some discussions are provided on the extension of the model for treating more complicated reacting systems including realistic kinetics schemes and multi-scalar mixing
Stamatakis, Michail; Zygourakis, Kyriacos
2010-01-01
Several approaches have been used in the past to model heterogeneity in bacterial cell populations, with each approach focusing on different source(s) of heterogeneity. However, a holistic approach that integrates all the major sources into a comprehensive framework applicable to cell populations is still lacking. In this work we present the mathematical formulation of a cell population master equation (CPME) that describes cell population dynamics and takes into account the major sources of heterogeneity, namely stochasticity in reaction, DNA-duplication, and division, as well as the random partitioning of species contents into the two daughter cells. The formulation also takes into account cell growth and respects the discrete nature of the molecular contents and cell numbers. We further develop a Monte Carlo algorithm for the simulation of the stochastic processes considered here. To benchmark our new framework, we first use it to quantify the effect of each source of heterogeneity on the intrinsic and the extrinsic phenotypic variability for the well-known two-promoter system used experimentally by Elowitz et al. (2002). We finally apply our framework to a more complicated system and demonstrate how the interplay between noisy gene expression and growth inhibition due to protein accumulation at the single cell level can result in complex behavior at the cell population level. The generality of our framework makes it suitable for studying a vast array of artificial and natural genetic networks. Using our Monte Carlo algorithm, cell population distributions can be predicted for the genetic architecture of interest, thereby quantifying the effect of stochasticity in intracellular reactions or the variability in the rate of physiological processes such as growth and division. Such in silico experiments can give insight into the behavior of cell populations and reveal the major sources contributing to cell population heterogeneity. PMID:20685607
TOPICAL REVIEW: Group theory and biomolecular conformation: I. Mathematical and computational models
NASA Astrophysics Data System (ADS)
Chirikjian, Gregory S.
2010-08-01
Biological macromolecules, and the complexes that they form, can be described in a variety of ways ranging from quantum mechanical and atomic chemical models, to coarser grained models of secondary structure and domains, to continuum models. At each of these levels, group theory can be used to describe both geometric symmetries and conformational motion. In this survey, a detailed account is provided of how group theory has been applied across computational structural biology to analyze the conformational shape and motion of macromolecules and complexes.
ERIC Educational Resources Information Center
Uprichard, A. Edward; Collura, Carolyn
This investigation sought to determine the effect of emphasizing mathematical structure in the acquisition of computational skills by seven- and eight-year-olds. The meaningful development-of-structure approach emphasized closure, commutativity, associativity, and the identity element of addition; the inverse relationship between addition and…
ERIC Educational Resources Information Center
Langer-Osuna, Jennifer
2015-01-01
This paper draws on the constructs of hybridity, figured worlds, and cultural capital to examine how a group of African-American students in a technology-driven, project-based algebra classroom utilized the computer as a resource to coordinate personal and mathematical positional identities during group work. Analyses of several vignettes of small…
ERIC Educational Resources Information Center
Kiss, Gabor
2012-01-01
An analysis of Information Technology knowledge of Hungarian and Romanian students was made with the help of a self developed web based Informatics Test. The goal of this research is an analysis of the Computer Science knowledge level of Hungarian and Romanian students attending a Science course or a Mathematics-Informatics course. Analysed was…
ERIC Educational Resources Information Center
Stein, David; Ostrander, Peter; Lee, G. Maie
2016-01-01
The Magnet Program at Montgomery Blair High School is an application-based magnet program utilizing a curriculum focused on science, mathematics, and computer science catering to interested, talented, and eager to learn students in Montgomery County, Maryland. This article identifies and discusses some of the unique aspects of the Magnet Program…
ERIC Educational Resources Information Center
Allinder, Rose M.; Bolling, Rachelle M.; Oats, Robert G.; Gagnon, Wendy A.
2000-01-01
A study examined the effects of combining curriculum-based measurement in mathematics computation with teachers' self-monitoring of instructional changes on academic progress of 54 elementary students with learning disabilities and mild mental disabilities. The combination of curriculum-based measurement and self-monitoring resulted in…
1985-02-01
Associated with Damage Prediction) Professor John W. Hutchinson Methods for Analyzing the Harvard University Mechanical Properties of Nonlinear Two Phase...ANALYZING THE MECHANICAL PROPERTIES OF NONLINEAR TWO-PHASE COMPOSITE MATERIALS John W. Hutchinson, Harvard University, Cambridge, Massachul•,1: t:!; Thursday...MATHEMATICAL PROPERTIES OF COMPUTATIONAL SETS Charles R. Leake, US Army Concepts Analysis Agency, Bethesda, Maryland S0 NORMAL SOLUTIONS OF LARGE
ERIC Educational Resources Information Center
Joel Popkin and Co., Washington, DC.
Data from the Current Population Surveys of October 1984, October 1989, and January 1991 were used to examine the role of computer and mathematical skills in the U.S. labor market from 1984-91. Particular attention was given to their actual and potential effect on the economic status of women. Data confirmed the overall increase in the education…
ERIC Educational Resources Information Center
Ruthven, Kenneth
2008-01-01
This article examines three important facets of the incorporation of new technologies into educational practice, focusing on emergent usages of the mathematical tools of computer algebra and dynamic geometry. First, it illustrates the interpretative flexibility of these tools, highlighting important differences in ways of conceptualizing and…
ERIC Educational Resources Information Center
Smith, Garth Spencer; Hardman, Joanne
2014-01-01
In this study the impact of computer immersion on performance of school leavers Senior Certificate mathematics scores was investigated across 31 schools in the EMDC East education district of Cape Town, South Africa by comparing performance between two groups: a control and an experimental group. The experimental group (14 high schools) had access…
ERIC Educational Resources Information Center
Lee, Chun-Yi; Chen, Ming-Puu.
2009-01-01
The purpose of this study was to investigate the effects of type of question prompt and level of prior knowledge on non-routine mathematical problem solving. A computer game was blended within the pattern reasoning tasks, along with question prompts, in order to demonstrate and enhance the connections between viable problem-solving strategies and…
Partitioning and packing mathematical simulation models for calculation on parallel computers
NASA Technical Reports Server (NTRS)
Arpasi, D. J.; Milner, E. J.
1986-01-01
The development of multiprocessor simulations from a serial set of ordinary differential equations describing a physical system is described. Degrees of parallelism (i.e., coupling between the equations) and their impact on parallel processing are discussed. The problem of identifying computational parallelism within sets of closely coupled equations that require the exchange of current values of variables is described. A technique is presented for identifying this parallelism and for partitioning the equations for parallel solution on a multiprocessor. An algorithm which packs the equations into a minimum number of processors is also described. The results of the packing algorithm when applied to a turbojet engine model are presented in terms of processor utilization.
ERIC Educational Resources Information Center
Noser, Thomas C.; Tanner, John R.; Shah, Situl
2008-01-01
The purpose of this study was to measure the comprehension of basic mathematical skills of students enrolled in statistics classes at a large regional university, and to determine if the scores earned on a basic math skills test are useful in forecasting student performance in these statistics classes, and to determine if students' basic math…
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…
Mathematical and computational modeling of a ferrofluid deformable mirror for high-contrast imaging
NASA Astrophysics Data System (ADS)
Lemmer, Aaron J.; Griffiths, Ian M.; Groff, Tyler D.; Rousing, Andreas W.; Kasdin, N. Jeremy
2016-07-01
Deformable mirrors (DMs) are an enabling and mission-critical technology in any coronagraphic instrument designed to directly image exoplanets. A new ferro fluid deformable mirror technology for high-contrast imaging is currently under development at Princeton, featuring a flexible optical surface manipulated by the local electromagnetic and global hydraulic actuation of a reservoir of ferro fluid. The ferro fluid DM is designed to prioritize high optical surface quality, high-precision/low-stroke actuation, and excellent low-spatial-frequency performance - capabilities that meet the unique demands of high-contrast coronagraphy in a space-based platform. To this end, the ferro-fluid medium continuously supports the DM face sheet, a configuration that eliminates actuator print-through (or, quilting) by decoupling the nominal surface figure from the geometry of the actuator array. The global pressure control allows independent focus actuation. In this paper we describe an analytical model for the quasi-static deformation response of the DM face sheet to both magnetic and pressure actuation. These modeling efforts serve to identify the key design parameters and quantify their contributions to the DM response, model the relationship between actuation commands and DM surface-profile response, and predict performance metrics such as achievable spatial resolution and stroke precision for specific actuator configurations. Our theoretical approach addresses the complexity of the boundary conditions associated with mechanical mounting of the face sheet, and makes use of asymptotic approximations by leveraging the three distinct length scales in the problem - namely, the low-stroke ( nm) actuation, face sheet thickness ( mm), and mirror diameter (cm). In addition to describing the theoretical treatment, we report the progress of computational multi physics simulations which will be useful in improving the model fidelity and in drawing conclusions to improve the design.
Lee, Stephen R
2010-01-01
Los Alamos National Laboratory will review its Computational Physics and Applied Mathematics (CPAM) capabilities in 2010. The goals of capability reviews are to assess the quality of science, technology, and engineering (STE) performed by the capability, evaluate the integration of this capability across the Laboratory and within the scientific community, examine the relevance of this capability to the Laboratory's programs, and provide advice on the current and future directions of this capability. This is the first such review for CPAM, which has a long and unique history at the laboratory, starting from the inception of the Laboratory in 1943. The CPAM capability covers an extremely broad technical area at Los Alamos, encompassing a wide array of disciplines, research topics, and organizations. A vast array of technical disciplines and activities are included in this capability, from general numerical modeling, to coupled mUlti-physics simulations, to detailed domain science activities in mathematics, methods, and algorithms. The CPAM capability involves over 12 different technical divisions and a majority of our programmatic and scientific activities. To make this large scope tractable, the CPAM capability is broken into the following six technical 'themes.' These themes represent technical slices through the CP AM capability and collect critical core competencies of the Laboratory, each of which contributes to the capability (and each of which is divided into multiple additional elements in the detailed descriptions of the themes in subsequent sections): (1) Computational Fluid Dynamics - This theme speaks to the vast array of scientific capabilities for the simulation of fluids under shocks, low-speed flow, and turbulent conditions - which are key, historical, and fundamental strengths of the laboratory; (2) Partial Differential Equations - The technical scope of this theme is the applied mathematics and numerical solution of partial differential equations
Applied Vocational Mathematics.
ERIC Educational Resources Information Center
South Carolina State Dept. of Education, Columbia. Office of Vocational Education.
Developed for use in teaching a two-semester, one-unit course, this course guide is intended to aid the high school instructor in teaching mathematical problem-solving and computational skills to vocational education students. The state-adopted textbook for general mathematics III, "Applied General Mathematics" serves as the major…
ERIC Educational Resources Information Center
Street, Garrett M.; Laubach, Timothy A.
2013-01-01
We provide a 5E structured-inquiry lesson so that students can learn more of the mathematics behind the logistic model of population biology. By using models and mathematics, students understand how population dynamics can be influenced by relatively simple changes in the environment.
ERIC Educational Resources Information Center
Titus, Freddie
2010-01-01
Fifty percent of college-bound students graduate from high school underprepared for mathematics at the post-secondary level. As a result, thirty-five percent of college students take developmental mathematics courses. What is even more shocking is the high failure rate (ranging from 35 to 42 percent) of students enrolled in developmental…
ERIC Educational Resources Information Center
Berlin, Donna; White, Arthur
1986-01-01
This study investigated the effects of combining interactive microcomputer simulations and concrete activities on the development of abstract thinking in elementary school mathematics. Students in grades 2-4 were assessed on tasks involving designs and patterns. (MNS)
Kirkebøen, G
2000-11-01
There are surprisingly strong connections between the philosophy of mind and the philosophy of mathematics. One particular important example can be seen in the Regulae (1628) of Descartes. In "the noblest example of all," he used his new abstract understanding of numbers to demonstrate how the brain can be considered as a symbol machine and how the intellect's algebraic reasoning can be mirrored as operations on this machine. Even though his attempt failed, it is illuminating to explore it because Descartes launched 2 traditions--mechanistic philosophy of mind and abstract mathematics--that would diverge until A. Turing (1936) approached symbolic reasoning in a similar "symbol machine-existence proof" way. Descrates's and Turing's thought experiments, which mark the beginning of modern psychology and cognitive science, respectively, indicate how important the development of mathematics has been for the constitution of the science of mind.
Shakhawath Hossain, Md; Bergstrom, D J; Chen, X B
2015-12-01
The in vitro chondrocyte cell culture for cartilage tissue regeneration in a perfusion bioreactor is a complex process. Mathematical modeling and computational simulation can provide important insights into the culture process, which would be helpful for selecting culture conditions to improve the quality of the developed tissue constructs. However, simulation of the cell culture process is a challenging task due to the complicated interaction between the cells and local fluid flow and nutrient transport inside the complex porous scaffolds. In this study, a mathematical model and computational framework has been developed to simulate the three-dimensional (3D) cell growth in a porous scaffold placed inside a bi-directional flow perfusion bioreactor. The model was developed by taking into account the two-way coupling between the cell growth and local flow field and associated glucose concentration, and then used to perform a resolved-scale simulation based on the lattice Boltzmann method (LBM). The simulation predicts the local shear stress, glucose concentration, and 3D cell growth inside the porous scaffold for a period of 30 days of cell culture. The predicted cell growth rate was in good overall agreement with the experimental results available in the literature. This study demonstrates that the bi-directional flow perfusion culture system can enhance the homogeneity of the cell growth inside the scaffold. The model and computational framework developed is capable of providing significant insight into the culture process, thus providing a powerful tool for the design and optimization of the cell culture process.
ERIC Educational Resources Information Center
Abdu, Rotem; Schwarz, Baruch; Mavrikis, Manolis
2015-01-01
We investigate teachers' practices in a whole-class context when they scaffold students' learning in situations where students use technologies that facilitate group learning to solve mathematical problems in small groups. We describe teachers' practices in order to evaluate their contribution to "Whole-Class Scaffolding" in the context…
ERIC Educational Resources Information Center
Walkington, Candace; Clinton, Virginia; Ritter, Steven N.; Nathan, Mitchell J.
2015-01-01
Solving mathematics story problems requires text comprehension skills. However, previous studies have found few connections between traditional measures of text readability and performance on story problems. We hypothesized that recently developed measures of readability and topic incidence measured by text-mining tools may illuminate associations…
ERIC Educational Resources Information Center
Piel, John A.; Gretes, John A.
The purpose of this inservice project was to help elementary teachers overcome their reluctance to deviate from commercially prepared materials by becoming aware of and building connections between the understanding of mathematical processes through the use of concrete, representational, and symbolic manipulatives with the four arithmetic…
ERIC Educational Resources Information Center
Becker, Jerry P., Ed.; Miwa, Tatsuro, Ed.
The purpose of a seminar attended by mathematics educators from the United States and Japan was to explore ways that use of technology in teaching problem solving can improve student learning. The following presentations were made: (1) "A Report of U.S.-Japan Cross-cultural Research on Students' Problem-Solving Behavior," (T. Miwa and T.…
ERIC Educational Resources Information Center
Moran, Thomas Patrick
This study provides a critical review of developments in the use of computer extended instruction (CEI), and practical guidelines for implementing a computer system in a school. The study examined special projects, proposals, recommendations, and position papers. Literature reviewed was synthesized under three broad headings: (1) computer hardware…
Advanced Mathematical Thinking in a Technological Workplace.
ERIC Educational Resources Information Center
Magajna, Zlatan; Monaghan, John
2003-01-01
Examines the use of mathematics in a computer-aided design and manufacturing setting, whether this mathematics is related to school mathematics, how technicians understand this mathematics, and the role of technology in the technicians' mathematics-related problem solving activities. Focuses on technician's calculations of the interval volume of…
1982-05-01
authorized documents. The citation of trade name. and names of manLfacturers in this report is not to be construed as official Government indorsement 4 or...ating the light which illuminatis it. For a target and background which are coincident , this is ntot a problem .rid a comparison of r;flectivities can...NBS Applied Mathematics, Series 55, U. S. Government Printing Office, 1046. Allen, G. and B. E. Simonson, 1970: Attenuation of infrared laser radia
NASA Astrophysics Data System (ADS)
Langer-Osuna, Jennifer
2015-03-01
This paper draws on the constructs of hybridity, figured worlds, and cultural capital to examine how a group of African-American students in a technology-driven, project-based algebra classroom utilized the computer as a resource to coordinate personal and mathematical positional identities during group work. Analyses of several vignettes of small group dynamics highlight how hybridity was established as the students engaged in multiple on-task and off-task computer-based activities, each of which drew on different lived experiences and forms of cultural capital. The paper ends with a discussion on how classrooms that make use of student-led collaborative work, and where students are afforded autonomy, have the potential to support the academic engagement of students from historically marginalized communities.
Mathematical techniques: A compilation
NASA Technical Reports Server (NTRS)
1975-01-01
Articles on theoretical and applied mathematics are introduced. The articles cover information that might be of interest to workers in statistics and information theory, computational aids that could be used by scientists and engineers, and mathematical techniques for design and control.
Teaching Mathematical Modelling.
ERIC Educational Resources Information Center
Jones, Mark S.
1997-01-01
Outlines a course at the University of Glamorgan in the United Kingdom in which a computer algebra system (CAS) teaches mathematical modeling. The format is based on continual assessment of group and individual work stating the problem, a feature list, and formulation of the models. No additional mathematical word processing package is necessary.…
Quality Teaching in Mathematics
ERIC Educational Resources Information Center
Ediger, Marlow
2012-01-01
The best teaching possible needs to accrue in the mathematics curriculum. Pupils also need to become proficient in using mathematics in every day situations in life. Individuals buy goods and services. They pay for these in different ways, including cash. Here, persons need to be able to compute the total cost of items purchased and then pay for…
Teaching Mathematics Using Steplets
ERIC Educational Resources Information Center
Bringslid, Odd; Norstein, Anne
2008-01-01
This article evaluates online mathematical content used for teaching mathematics in engineering classes and in distance education for teacher training students. In the EU projects Xmath and dMath online computer algebra modules (Steplets) for undergraduate students assembled in the Xmath eBook have been designed. Two questionnaires, a compulsory…
Betin, A Yu; Bobrinev, V I; Verenikina, N M; Donchenko, S S; Odinokov, S B; Evtikhiev, N N; Zlokazov, E Yu; Starikov, S N; Starikov, R S
2015-08-31
A multiplex method of recording computer-synthesised one-dimensional Fourier holograms intended for holographic memory devices is proposed. The method potentially allows increasing the recording density in the previously proposed holographic memory system based on the computer synthesis and projection recording of data page holograms. (holographic memory)
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…
Teaching Mathematics to Non-Mathematics Majors through Applications
ERIC Educational Resources Information Center
Abramovich, Sergei; Grinshpan, Arcadii Z.
2008-01-01
This article focuses on the important role of applications in teaching mathematics to students with career paths other than mathematics. These include the fields as diverse as education, engineering, business, and life sciences. Particular attention is given to instructional computing as a means for concept development in mathematics education…
Arandjelović, Ognjen
2010-10-01
A large corpus of data obtained by means of empirical study of neuromuscular adaptation is currently of limited use to athletes and their coaches. One of the reasons lies in the unclear direct practical utility of many individual trials. This paper introduces a mathematical model of adaptation to resistance training, which derives its elements from physiological fundamentals on the one side, and empirical findings on the other. The key element of the proposed model is what is here termed the athlete's capability profile. This is a generalization of length and velocity dependent force production characteristics of individual muscles, to an exercise with arbitrary biomechanics. The capability profile, a two-dimensional function over the capability plane, plays the central role in the proposed model of the training-adaptation feedback loop. Together with a dynamic model of resistance the capability profile is used in the model's predictive stage when exercise performance is simulated using a numerical approximation of differential equations of motion. Simulation results are used to infer the adaptational stimulus, which manifests itself through a fed back modification of the capability profile. It is shown how empirical evidence of exercise specificity can be formulated mathematically and integrated in this framework. A detailed description of the proposed model is followed by examples of its application-new insights into the effects of accommodating loading for powerlifting are demonstrated. This is followed by a discussion of the limitations of the proposed model and an overview of avenues for future work.
Using Information Technology in Mathematics Education.
ERIC Educational Resources Information Center
Tooke, D. James, Ed.; Henderson, Norma, Ed.
This collection of essays examines the history and impact of computers in mathematics and mathematics education from the early, computer-assisted instruction efforts through LOGO, the constructivist educational software for K-9 schools developed in the 1980s, to MAPLE, the computer algebra system for mathematical problem solving developed in the…
ERIC Educational Resources Information Center
Smith, David A.; And Others
1986-01-01
APL was invented specifically as a mathematical teaching tool, and is an excellent vehicle for teaching mathematical concepts using computers. This article illustrates the use of APL in teaching many different topics in mathematics, including logic, set theory, functions, statistics, linear algebra, and matrices. (MNS)
Singhal, A.K.; Keeton, L.W.; Spalding, D.B.; Srikantiah, G.S.
1982-10-01
ATHOS (Analysis of the Thermal Hydraulics of Steam Generators) is a computer code developed by CHAM of North America Incorporated, under the contract RP 1066-1 from the Electric Power Research Institute, Palo Alto, California. ATHOS supersedes the earlier code URSULA2. ATHOS is designed for three-dimensional, steady state and transient analyses of PWR steam generators. The current version of the code has been checked out for: three different configurations of the recirculating-type U-tube steam generators; the homogeneous and algebraic-slip flow models; and full and part load operating conditions. The description of ATHOS is divided into four volumes. Volume 1 includes the mathematical and physical models and method of solution.
NASA Astrophysics Data System (ADS)
Starikov, A. I.; Nekrasov, R. Yu; Teploukhov, O. J.; Soloviev, I. V.; Narikov, K. A.
2016-10-01
Manufactures, machinery and equipment improve of constructively as science advances and technology, and requirements are improving of quality and longevity. That is, the requirements for surface quality and precision manufacturing, oil and gas equipment parts are constantly increasing. Production of oil and gas engineering products on modern machine tools with computer numerical control - is a complex synthesis of technical and electrical equipment parts, as well as the processing procedure. Technical machine part wears during operation and in the electrical part are accumulated mathematical errors. Thus, the above-mentioned disadvantages of any of the following parts of metalworking equipment affect the manufacturing process of products in general, and as a result lead to the flaw.
ERIC Educational Resources Information Center
Massey, Tom E.; McCall, Peter T.
A program is described that was developed, implemented, and evaluated at the P.K. Yonge Laboratory School at the University of Florida. It was designed to help middle school students to increase competencies in basic computation. The nine criteria guiding development were: 1) individualized instruction; 2) greater student responsibility for…
ERIC Educational Resources Information Center
Lazakidou, Georgia; Retalis, Symeon
2010-01-01
The main objective of this paper is to investigate the effectiveness of a proposed computer-based instructional method in Primary Education for self-regulated problem solving. The proposed instructional method is based on Sternberg's model of problem solving within an authentic context. It consists of three main phases: observation, collaboration…
ERIC Educational Resources Information Center
Stanford Univ., CA. School Mathematics Study Group.
Topics covered in the first chapter of Unit 8 of this SMSG series include square roots, operations with radicals, operations with real numbers, and the structure of the real number system. The second chapter deals with measurement of area (for rectangular regions, other polygons, and circles), volume and surface area, computation involving…
ERIC Educational Resources Information Center
Bennett, Randy Elliot; Braswell, James; Oranje, Andreas; Sandene, Brent; Kaplan, Bruce; Yan, Fred
2008-01-01
This article describes selected results from the Math Online (MOL) study, one of three field investigations sponsored by the National Center for Education Statistics (NCES) to explore the use of new technology in NAEP. Of particular interest in the MOL study was the comparability of scores from paper- and computer-based tests. A nationally…
ERIC Educational Resources Information Center
Burrows, J. K.
Research on error patterns associated with whole number computation is reviewed. Details of the results of some of the individual studies cited are given in the appendices. In Appendix A, 33 addition errors, 27 subtraction errors, 41 multiplication errors, and 41 division errors are identified, and the frequency of these errors made by 352…
ERIC Educational Resources Information Center
Maltby, Gregory P.; And Others
San Elizario, Texas, is a border community with a high poverty rate, overcrowded school conditions, and a 60% limited English proficiency (LEP) rate among school students. In 1984, the school district began a cooperative university and school system project to improve Hispanic LEP students' achievement through applied computer technology. In…
ERIC Educational Resources Information Center
Moosavi, Seyed A.
2009-01-01
Computer Aided Instruction (CAI) has vast possibilities that are just beginning to emerge as the medium is being utilized by more and more institutions nationwide. The new educational software industries have the potential to meet the educational needs of a large and increasingly diverse student population. The purpose of the present study is…
ERIC Educational Resources Information Center
Reys, Robert; Reys, Rustin
2011-01-01
In their dual roles as mathematics teachers and tennis coaches, the authors have worked with tennis players who have never thought about how a knowledge of mathematics might help them become "better" tennis players. They have also worked with many mathematics students who have never considered how much mathematics is associated with tennis. This…
NASA Technical Reports Server (NTRS)
Aggarwal, Arun K.
1993-01-01
Spherical roller bearings have typically been used in applications with speeds limited to about 5000 rpm and loads limited for operation at less than about 0.25 million DN. However, spherical roller bearings are now being designed for high load and high speed applications including aerospace applications. A computer program, SASHBEAN, was developed to provide an analytical tool to design, analyze, and predict the performance of high speed, single row, angular contact (including zero contact angle), spherical roller bearings. The material presented is the mathematical formulation and analytical methods used to develop computer program SASHBEAN. For a given set of operating conditions, the program calculates the bearings ring deflections (axial and radial), roller deflections, contact areas stresses, depth and magnitude of maximum shear stresses, axial thrust, rolling element and cage rotational speeds, lubrication parameters, fatigue lives, and rates of heat generation. Centrifugal forces and gyroscopic moments are fully considered. The program is also capable of performing steady-state and time-transient thermal analyses of the bearing system.
Educating in Place: Mathematics and Technology
ERIC Educational Resources Information Center
Klein, Robert
2007-01-01
Mathematics education discourse routinely promotes the idea that mathematics is everywhere. That mathematics is everywhere seems a reasonable implication of "We all use math everyday." Modern technology, mostly in the form of computational devices and control systems, is often cited as evidence of the omnipresence of mathematics.…
Winning Moves and Illuminating Mathematical Patterns
ERIC Educational Resources Information Center
Ginat, David
2006-01-01
In this paper, the author aims to offer an elaboration of simple, yet powerful, mathematical patterns through mathematical games. Mathematical games may serve as colorful instructional tools for teachers and textbooks, and may raise students' motivation and intuition. Patterns are fundamental in mathematics and computer science. In the case of…
ERIC Educational Resources Information Center
Reglin, Gary L.; Butler, Don
This study examined the effectiveness of computer assisted instruction (CAI) in improving the mathematics achievement and academic self-confidence of black students in an Education Entrance Examination (EEE) seminar at a predominantly black college in South Carolina. Subjects were 49 students participating in the seminar, 43% black males and 47%…
ERIC Educational Resources Information Center
Mahaffey, Michael L.; McKillip, William D.
This manual is designed for teachers using the Career Oriented Mathematics units on owning an automobile and driving as a career, retail sales, measurement, and area-perimeter. The volume begins with a discussion of the philosophy and scheduling of the program which is designed to improve students' attitudes and ability in computation by…
Rector, D.R.; Wheeler, C.L.; Lombardo, N.J.
1986-11-01
COBRA-SFS (Spent Fuel Storage) is a general thermal-hydraulic analysis computer code used to predict temperatures and velocities in a wide variety of systems. The code was refined and specialized for spent fuel storage system analyses for the US Department of Energy's Commercial Spent Fuel Management Program. The finite-volume equations governing mass, momentum, and energy conservation are written for an incompressible, single-phase fluid. The flow equations model a wide range of conditions including natural circulation. The energy equations include the effects of solid and fluid conduction, natural convection, and thermal radiation. The COBRA-SFS code is structured to perform both steady-state and transient calculations: however, the transient capability has not yet been validated. This volume describes the finite-volume equations and the method used to solve these equations. It is directed toward the user who is interested in gaining a more complete understanding of these methods.
Landauer, C.; Bellman, K.L.
1996-12-31
In this paper, we study foundational issues that we believe will help us develop a theoretically sound approach to constructing complex systems. The two theoretical approaches that have helped us understand and develop computational systems in the past are mathematics and linguistics. We describe some differences and strengths of the approaches, and propose a research program to combine the richness of linguistic reasoning with the precision of mathematics.
NASA Astrophysics Data System (ADS)
Ligomenides, Panos A.
2009-05-01
The power of mathematics is discussed as a way of expressing reasoning, aesthetics and insight in symbolic non-verbal communication. The human culture of discovering mathematical ways of thinking in the enterprise of exploring the understanding of the nature and the evolution of our world through hypotheses, theories and experimental affirmation of the scientific notion of algorithmic and non-algorithmic [`]computation', is examined and commended upon.
The Greatest Mathematical Discovery?
Bailey, David H.; Borwein, Jonathan M.
2010-05-12
What mathematical discovery more than 1500 years ago: (1) Is one of the greatest, if not the greatest, single discovery in the field of mathematics? (2) Involved three subtle ideas that eluded the greatest minds of antiquity, even geniuses such as Archimedes? (3) Was fiercely resisted in Europe for hundreds of years after its discovery? (4) Even today, in historical treatments of mathematics, is often dismissed with scant mention, or else is ascribed to the wrong source? Answer: Our modern system of positional decimal notation with zero, together with the basic arithmetic computational schemes, which were discovered in India about 500 CE.
Mathematical Concepts and Maple Animations
NASA Astrophysics Data System (ADS)
Siddique, Mohammad; Mitchell, Kristy
2010-09-01
Maple is a mathematics software package, which contains graphic, computation, and programming tools. Maple animation is a powerful tool that can help in comprehending many fundamental concepts in mathematics and other sciences. This paper deals with the use of maple animation to demonstrate many fundamental concepts in mathematics that are difficult to explain verbally or through static figures. We show Maple animations effectively convey different concepts. We present problems taken from the literature to exemplify and explain Maple animation procedures. Using Maple in teaching mathematics facilitates the students with a tool to experiment and visualize complicated mathematical concepts and thus, strengthen their grasp of the subject.
NASA Astrophysics Data System (ADS)
Minárová, Mária; Sumec, Jozef
2016-01-01
The paper deals with the biomechanical investigation on the human lumbar intervertebral disc under the static load. The disc is regarded as a two - phased ambient consisting of a fibrous outer part called annulus fibrosis and a liquid inner part nucleus pulposus. Due to the fibrous structure, the annulus fibrosis can be treated by using a special case of anisotropy - transversal isotropy. In the paper the corresponding tensor of material constants is derived. The tensor consequently incomes to the constitutive equations determining the stress - strain relation in the material. In order to study the mechanical behaviour the disc is observed within the motion segment, the basic unit for motion tracing. The motion segment involves two neighbouring vertebrae and the intervertebral disc between them that connect them both. When constitutive equations are accomplished, they can be incorporated in the finite element analysis. The illustrative example of the intervertebral disc L2/L3, the disc between the second and the third lumbar vertebrae the lumbar part of spine, with its computer implementation is performed. Finally the comparison of the results of using anisotropic and homogenized approach is provided. The comparison illustrates the eligibility of such a kind of approach.
ERIC Educational Resources Information Center
Hanh, Vu Duc, Ed.
This document gives a listing of mathematical terminology in both the English and Vietnamese languages. Vocabulary used in algebra and geometry is included along with a translation of mathematical symbols. (DT)
ERIC Educational Resources Information Center
Jones, Thomas A.
1983-01-01
Mathematical techniques used to solve geological problems are briefly discussed (including comments on use of geostatistics). Highlights of conferences/meetings and conference papers in mathematical geology are also provided. (JN)
... this page: //medlineplus.gov/ency/article/001534.htm Mathematics disorder To use the sharing features on this page, please enable JavaScript. Mathematics disorder is a condition in which a child's ...
ERIC Educational Resources Information Center
Kilpatrick, Jeremy
2014-01-01
This paper addresses the contested way that ethnomathematics has sometimes been received by mathematicians and others and what that disagreement might suggest about issues in mathematics education; namely, (a) the relation of ethnomathematics to academic mathematics; (b) recent efforts to reform secondary school mathematics so that it prepares…
Mathematical Machines in Science (Matematicheskie Mashiny i Nauka),
The report gives an interview with Sergey L’vovich Sobolev, the famous Soviet mathematician, on general relationships between computers and mathematics, mathematical modeling and the use of mathematical machines in information science . (Author)
Keeton, L.W.; Singhal, A.K.; Srikantiah, G.S.
1986-07-01
The mathematical and physical models as well as the method of solution are presented for ATHOS3. ATHOS3 is a computer code for three-dimensional, steady-state and transient analyses of PWR steam generators. It has been developed by upgrading an earlier code, ATHOS (Analysis of the Thermal Hydraulics of Steam Generators). Both ATHOS and ATHOS3 have been developed by CHAM of North America, Inc., under the contract RP1066-1 from the Electric Power Research Institute. ATHOS3 supercedes ATHOS and all other intermediate versions of the code. ATHOS3 has several additional capabilities, including a much improved and generalized geometry pre-processor module, and has been developed in a fully upwards-compatible manner from the predecessor ATHOS code. For the convenience of new users, the ATHOS3 code is documented in four self-contained volumes, i.e. no reference to the earlier ATHOS volumes is necessary. Furthermore, for the benefit of old (i.e. ATHOS code) users, it may be stated that the new (ATHOS3) documentation has been produced by updating and modifying the earlier documentation.
NASA Astrophysics Data System (ADS)
Latypov, A. F.
2009-03-01
The fuel economy was estimated at boost trajectory of aerospace plane during energy supply to the free stream. Initial and final velocities of the flight were given. A model of planning flight above cold air in infinite isobaric thermal wake was used. The comparison of fuel consumption was done at optimal trajectories. The calculations were done using a combined power plant consisting of ramjet and liquid-propellant engine. An exergy model was constructed in the first part of the paper for estimating the ramjet thrust and specific impulse. To estimate the aerodynamic drag of aircraft a quadratic dependence on aerodynamic lift is used. The energy for flow heating is obtained at the sacrifice of an equivalent decrease of exergy of combustion products. The dependencies are obtained for increasing the range coefficient of cruise flight at different Mach numbers. In the second part of the paper, a mathematical model is presented for the boost part of the flight trajectory of the flying vehicle and computational results for reducing the fuel expenses at the boost trajectory at a given value of the energy supplied in front of the aircraft.
1991-07-26
the career education component which was designed to provide participants an opportunity to see "mathematics at work" in every day life 2 through films ...and a film , and discussed career opportunities in mathematics-based fields. The students viewed the video tapes: "The Challenge of the Unknown... film "Donald in Mathemagic Land" which shows how mathematics grows from simple ideas. 0 This component also includes a career awareness forum which is a
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…
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.
The Mathematics of Global Change
ERIC Educational Resources Information Center
Kreith, Kurt
2011-01-01
This paper is a descriptive and preliminary report on recent efforts to address two questions: 1) Can school mathematics be used to enhance our students' ability to understand their changing world? and 2) What role might computer technology play in this regard? After recounting some of the mathematical tools that led to a better understanding of…
Explorations in Elementary Mathematical Modeling
ERIC Educational Resources Information Center
Shahin, Mazen
2010-01-01
In this paper we will present the methodology and pedagogy of Elementary Mathematical Modeling as a one-semester course in the liberal arts core. We will focus on the elementary models in finance and business. The main mathematical tools in this course are the difference equations and matrix algebra. We also integrate computer technology and…
Student Produced Advanced Mathematical Software.
ERIC Educational Resources Information Center
Hogben, Leslie
The intent of this project was to develop a course for mathematics graduate students at Iowa State University. They would design and write computer programs for use by undergraduate mathematics students, and then offer the course and actually produce the software. Phase plane graphics for ordinary differential equations was selected as the topic.…
Discrete Mathematics and Its Applications
ERIC Educational Resources Information Center
Oxley, Alan
2010-01-01
The article gives ideas that lecturers of undergraduate Discrete Mathematics courses can use in order to make the subject more interesting for students and encourage them to undertake further studies in the subject. It is possible to teach Discrete Mathematics with little or no reference to computing. However, students are more likely to be…
The Mathematical Sciences in 2025
ERIC Educational Resources Information Center
National Academies Press, 2013
2013-01-01
The mathematical sciences are part of nearly all aspects of everyday life--the discipline has underpinned such beneficial modern capabilities as Internet search, medical imaging, computer animation, numerical weather predictions, and all types of digital communications. "The Mathematical Sciences in 2025" examines the current state of the…
Determining Learning Disabilities in Mathematics.
ERIC Educational Resources Information Center
Dunlap, William P.; And Others
1979-01-01
To determine the generalizability of reading expectancy formulas in ascertaining mathematics expectancy levels, correlation coefficients were computed between the scores of 150 Ss (7 to 12 years old) with learning problems on standardized mathematics and reading tests and expectancy scores. Formulas correlated higher with Ss' actual mathematics…
ERIC Educational Resources Information Center
Bogdany, Melvin
The curriculum guide offers a course of training in the fundamentals of mathematics as applied to baking. Problems specifically related to the baking trade are included to maintain a practical orientation. The course is designed to help the student develop proficiency in the basic computation of whole numbers, fractions, decimals, percentage,…
Verbalizing Mathematics Using APL.
ERIC Educational Resources Information Center
Matthews, George E.
The nature of "A Programing Language" (APL) is viewed as unambiguous, consistent, and powerful. It is based on the notion of functions as imperative verbs, and is used by a small but growing number of mathematicians and computer programers. Three areas of mathematical activity are addressed: calculation of arithmetic expressions,…
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,…
García-Peñarrubia, Pilar; Gálvez, Juan J; Gálvez, Jesús
2014-09-01
Cell signalling processes involve receptor trafficking through highly connected networks of interacting components. The binding of surface receptors to their specific ligands is a key factor for the control and triggering of signalling pathways. But the binding process still presents many enigmas and, by analogy with surface catalytic reactions, two different mechanisms can be conceived: the first mechanism is related to the Eley-Rideal (ER) mechanism, i.e. the bulk-dissolved ligand interacts directly by pure three-dimensional (3D) diffusion with the specific surface receptor; the second mechanism is similar to the Langmuir-Hinshelwood (LH) process, i.e. 3D diffusion of the ligand to the cell surface followed by reversible ligand adsorption and subsequent two-dimensional (2D) surface diffusion to the receptor. A situation where both mechanisms simultaneously contribute to the signalling process could also occur. The aim of this paper is to perform a computational study of the behavior of the signalling response when these different mechanisms for ligand-receptor interactions are integrated into a model for signal transduction and ligand transport. To this end, partial differential equations have been used to develop spatio-temporal models that show trafficking dynamics of ligands, cell surface components, and intracellular signalling molecules through the different domains of the system. The mathematical modeling developed for these mechanisms has been applied to the study of two situations frequently found in cell systems: (a) dependence of the signal response on cell density; and (b) enhancement of the signalling response in a synaptic environment.
ERIC Educational Resources Information Center
Steen, Lynn Arthur
1981-01-01
The development of symbolic computer algebra designed to manipulate abstract mathematical expressions is discussed. The ability of this software to mimic the standard patterns of human problem solving represents a major advance toward "true" artificial intelligence. (MP)
Mathematical Aspects of Scattering Amplitudes
NASA Astrophysics Data System (ADS)
Duhr, Claude
In these lectures we discuss some of the mathematical structures that appear when computing multi-loop Feynman integrals. We focus on a specific class of special functions, the so-called multiple polylogarithms, and introduce their Hopf algebra structure. We show how these mathematical concepts are useful in physics by illustrating on several examples how these algebraic structures are useful to perform analytic computations of loop integrals, in particular to derive functional equations among polylogarithms.
Mathematical Modeling of Diverse Phenomena
NASA Technical Reports Server (NTRS)
Howard, J. C.
1979-01-01
Tensor calculus is applied to the formulation of mathematical models of diverse phenomena. Aeronautics, fluid dynamics, and cosmology are among the areas of application. The feasibility of combining tensor methods and computer capability to formulate problems is demonstrated. The techniques described are an attempt to simplify the formulation of mathematical models by reducing the modeling process to a series of routine operations, which can be performed either manually or by computer.
ERIC Educational Resources Information Center
Prochazka, Helen
2004-01-01
One section of this "scrapbook" section describes Pythagoras' belief in the connections between music and mathematics -- that everything in the universe was a series of harmonies and regulated by music. Another section explains why Phythagoras felt it important for women to be encouraged to learn mathematics. At least 28 women were involved in his…
ERIC Educational Resources Information Center
Langbort, Carol, Ed.; Curtis, Deborah, Ed.
2000-01-01
The focus of this special issue is mathematics education. All articles were written by graduates of the new masters Degree program in which students earn a Master of Arts degree in Education with a concentration in Mathematics Education at San Francisco State University. Articles include: (1) "Developing Teacher-Leaders in a Masters Degree Program…
ERIC Educational Resources Information Center
Flannery, Carol A.
This manuscript provides information and problems for teaching mathematics to vocational education students. Problems reflect applications of mathematical concepts to specific technical areas. The materials are organized into six chapters. Chapter 1 covers basic arithmetic, including fractions, decimals, ratio and proportions, percentages, and…
ERIC Educational Resources Information Center
McClellan, Kathryn T.
Why mathematics should be learned is discussed. Its role as an important active force in the development of our civilization, and as the most useful subject taught in our schools, next to English, is noted. The primary objective of all mathematics work is to help man study nature, and some practical achievements of this connection are noted.…
ERIC Educational Resources Information Center
Martin, Hope
2007-01-01
"Mathematical literacy" implies that a person is able to reason, analyze, formulate, and solve problems in a real-world setting. Mathematically literate individuals are informed citizens and intelligent consumers. They have the ability to interpret and analyze the vast amount of information they are inundated with daily in newspapers, on…
1990-07-27
designed to provide participants an opportunity to experience "mathematics at work" in every day life through films , videos, etc., and to visit the...Trips The instructional phase of the program will be supplemented by field trips, films and a forum scheduled on Friday afternoons. The field trips and... films will allow students an opportunity to see the use of mathematics in the working world of the scientist, and the forum will present a situation
College Preparatory Mathematics: Change from Within.
ERIC Educational Resources Information Center
Kysh, Judith M.
1995-01-01
The College Preparatory Mathematics: Change from Within Project (CPM) was created to develop a rich, integrated mathematics curriculum, based on the best current wisdom of how people learn and the mathematics needed in an era of computers, and involving teachers in materials development. (MKR)
Babylonian Mathematical Astronomy
NASA Astrophysics Data System (ADS)
Ossendrijver, Mathieu
The earliest known form of mathematical astronomy of the ancient world was developed in Babylonia in the 5th century BCE. It was used for predicting a wide range of phenomena of the Moon, the Sun, and the planets. After a brief discussion of the material evidence and historical context of Babylonian mathematical astronomy, its main concepts and methods are illustrated on the basis of a tablet with computed data for Jupiter. Finally, the past, present, and future directions of research are briefly addressed.
Mathematical Astronomy in India
NASA Astrophysics Data System (ADS)
Plofker, Kim
Astronomy in South Asia's Sanskrit tradition, apparently originating in simple calendric computations regulating the timing of ancient ritual practices, expanded over the course of two or three millennia to include detailed spherical models, an endless variety of astrological systems, and academic mathematics in general. Assimilating various technical models, methods, and genres from the astronomy of neighboring cultures, Indian astronomers created new forms that were in turn borrowed by their foreign counterparts. Always recognizably related to the main themes of Eurasian geocentric mathematical astronomy, Indian astral science nonetheless maintained its culturally distinct character until Keplerian heliocentrism and Newtonian mechanics replaced it in colonial South Asia's academic mainstream.
ERIC Educational Resources Information Center
Bossé, Michael J.; Adu-Gyamfi, Kwaku; Chandler, Kayla; Lynch-Davis, Kathleen
2016-01-01
Dynamic mathematical environments allow users to reify mathematical concepts through multiple representations, transform mathematical relations and organically explore mathematical properties, investigate integrated mathematics, and develop conceptual understanding. Herein, we integrate Boolean algebra, the functionalities of a dynamic…
Mathematical wit and mathematical cognition.
Aberdein, Andrew
2013-04-01
The published works of scientists often conceal the cognitive processes that led to their results. Scholars of mathematical practice must therefore seek out less obvious sources. This article analyzes a widely circulated mathematical joke, comprising a list of spurious proof types. An account is proposed in terms of argumentation schemes: stereotypical patterns of reasoning, which may be accompanied by critical questions itemizing possible lines of defeat. It is argued that humor is associated with risky forms of inference, which are essential to creative mathematics. The components of the joke are explicated by argumentation schemes devised for application to topic-neutral reasoning. These in turn are classified under seven headings: retroduction, citation, intuition, meta-argument, closure, generalization, and definition. Finally, the wider significance of this account for the cognitive science of mathematics is discussed.
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 geometry 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.
ERIC Educational Resources Information Center
Jarvis, John J.; Papaconstadopoulos, Chris
Developed and demonstrated here is the design of interface systems for cost-effective communication of the user with the computerized operations research procedures. The concentration is in the area of interfacing methods for implementing the optimization techniques of mathematical programing. Emphasis is given to flexibility of accessing the…
ERIC Educational Resources Information Center
Burns, Matthew K.
2005-01-01
Previous research suggested that Incremental Rehearsal (IR; Tucker, 1989) led to better retention than other drill practices models. However, little research exists in the literature regarding drill models for mathematics and no studies were found that used IR to practice multiplication facts. Therefore, the current study used IR as an…
ERIC Educational Resources Information Center
Grimaldi, Ralph P.
This material was developed to provide an application of matrix mathematics in chemistry, and to show the concepts of linear independence and dependence in vector spaces of dimensions greater than three in a concrete setting. The techniques presented are not intended to be considered as replacements for such chemical methods as oxidation-reduction…
ERIC Educational Resources Information Center
Alqallaf, Nadeyah
2016-01-01
The purpose of this study was to examine Kuwaiti mathematical elementary teachers' perceptions about their ability to integrate M-learning (mobile learning) into their current teaching practices and the major barriers hindering teachers' ability to create an M-learning environment. Furthermore, this study sought to understand teachers' perceptions…
ERIC Educational Resources Information Center
Aly, Geillan Dahab
2016-01-01
Community colleges are tasked with helping all students regardless of their academic background to receive a degree, certificate, or other form of education. Many of these students need support in learning the mathematical content necessary to take college-level courses. Since a large proportion of students in these developmental classes are…
ERIC Educational Resources Information Center
Fey, James T., Ed.; And Others
The papers in this report represent the imagination, analysis, and experiences of many people involved in recent curricular studies in secondary school mathematics. It differs from reports that seek broad agreement on conservative, traditional curricula, representing instead the point of view of those working with emerging electronic technology…
Some unsolved problems in discrete mathematics and mathematical cybernetics
NASA Astrophysics Data System (ADS)
Korshunov, Aleksei D.
2009-10-01
There are many unsolved problems in discrete mathematics and mathematical cybernetics. Writing a comprehensive survey of such problems involves great difficulties. First, such problems are rather numerous and varied. Second, they greatly differ from each other in degree of completeness of their solution. Therefore, even a comprehensive survey should not attempt to cover the whole variety of such problems; only the most important and significant problems should be reviewed. An impersonal choice of problems to include is quite hard. This paper includes 13 unsolved problems related to combinatorial mathematics and computational complexity theory. The problems selected give an indication of the author's studies for 50 years; for this reason, the choice of the problems reviewed here is, to some extent, subjective. At the same time, these problems are very difficult and quite important for discrete mathematics and mathematical cybernetics. Bibliography: 74 items.
NASA Technical Reports Server (NTRS)
Miller, Richard H.
1987-01-01
Astronomy is an area of applied physics in which unusually beautiful objects challenge the imagination to explain observed phenomena in terms of known laws of physics. It is a field that has stimulated the development of physical laws and of mathematical and computational methods. Current computational applications are discussed in terms of stellar and galactic evolution, galactic dynamics, and particle motions.
ERIC Educational Resources Information Center
Dewdney, A. K.
1989-01-01
Discussed are three examples of computer graphics including biomorphs, Truchet tilings, and fractal popcorn. The graphics are shown and the basic algorithm using multiple iteration of a particular function or mathematical operation is described. An illustration of a snail shell created by computer graphics is presented. (YP)
Richardson, mathematical modeller
NASA Astrophysics Data System (ADS)
Vreugdenhil, C. B.
1994-03-01
On the occasion of the 70th anniversary of Richardson's book Weather Prediction by Numerical Process (Cambridge University Press, Cambridge), a review is given of Richardson's scientific work. He made lasting contributions to very diverse fields of interest, such as finite-difference methods and related numerical methods, weather forecasting by computer, turbulence, international relations, and fractals. Although he was an original experimenter, the main present-day interest is in his mathematical modelling work.
Pre Service Teachers' Usage of Dynamic Mathematics Software
ERIC Educational Resources Information Center
Bulut, Mehmet; Bulut, Neslihan
2011-01-01
Aim of this study is about mathematics education and dynamic mathematics software. Dynamic mathematics software provides new opportunities for using both computer algebra system and dynamic geometry software. GeoGebra selected as dynamic mathematics software in this research. In this study, it is investigated that what is the usage of pre service…
ERIC Educational Resources Information Center
de Mestre, Neville
2004-01-01
Computers were invented to help mathematicians perform long and complicated calculations more efficiently. By the time that a computing area became a familiar space in primary and secondary schools, the initial motivation for computer use had been submerged in the many other functions that modern computers now accomplish. Not only the mathematics…
The Effects of Pedagogical Agents on Mathematics Anxiety and Mathematics Learning
ERIC Educational Resources Information Center
Wei, Quan
2010-01-01
The purpose of this study was to investigate the impact of the mathematics anxiety treatment messages in a computer-based environment on ninth-grade students' mathematics anxiety and mathematics learning. The study also examined whether the impact of the treatment messages would be differentiated by learner's gender and by learner's prior…
Longitudinal associations between reading and mathematics achievement.
Grimm, Kevin J
2008-01-01
The association between early reading skills and changes in mathematics was examined in a large, low-income sample to determine whether students who have a greater level of reading skills in early elementary school exhibit more rapid gains in tests of mathematics. The longitudinal associations between third grade reading comprehension and changes in three components of mathematics achievement (Problem Solving and Data Interpretation, Mathematical Concepts and Estimation, Mathematical Computation) from third through eighth grade were examined. Latent growth models were fit to the repeated assessments of each mathematics component and the students' third grade reading and global mathematics scores were included as predictors of the intercept and slope. Gender, poverty status, and ethnicity were included in the models as control variables. The results showed males and African-American students tended to have shallower rates of change than females and non-African-American/non-Hispanic students. In terms of the effect of reading on changes in mathematics, third grade reading comprehension was found to be a positive significant predictor of change for each component of mathematics, suggesting students with a greater level of reading achievement in early elementary school change more rapidly in mathematics skills controlling for prior mathematics skills and student characteristics. The largest effects were shown for the Problem Solving and Data Interpretation test, a test focused on the applications of mathematics knowledge, and the Mathematical Concepts and Estimation test. Negligible effects were found for changes in Mathematical Computation. Thus, early reading comprehension was shown to be related to a conceptual understanding of mathematics and the application of mathematics knowledge. These findings lend support for the notion that early reading skills are important for success in mathematics.
Quotable Quotes in Mathematics
ERIC Educational Resources Information Center
Lo, Bruce W. N.
1983-01-01
As a way to dispel negative feelings toward mathematics, a variety of quotations are given. They are categorized by: what mathematics is, mathematicians, mathematics and other disciplines, different areas of mathematics, mathematics and humor, applications of mathematics, and pure versus applied mathematics. (MNS)
Sound Blending of Techniques in Mathematics and Physics (abstract)
NASA Astrophysics Data System (ADS)
Malmini, Ranasinghe
2009-04-01
This paper discusses methods that can be used to inspire physics students to learn advanced differential equations. Numerous problems in physics are described by this type of equation. There has been rapid advancement in computer technology and development of computational mathematics-a branch of mathematics using computers to generate solutions to advanced differential equations. Arguably, this branch of mathematics is becoming more important to physicists than traditional analytical mathematics. Computer Algebra Software (CAS) packages have also emerged as a means to perform elaborate and complicated analytical mathematics much faster than possible by humans.
ERIC Educational Resources Information Center
Hadlock, Charles R
2013-01-01
The movement of groundwater in underground aquifers is an ideal physical example of many important themes in mathematical modeling, ranging from general principles (like Occam's Razor) to specific techniques (such as geometry, linear equations, and the calculus). This article gives a self-contained introduction to groundwater modeling with…
ERIC Educational Resources Information Center
Kennard, Jackie
2007-01-01
One of the most interesting developments in teaching has been the growing importance of the outdoor environment. Whether it be playground, garden or field, the outdoors offers a range of challenging experiences, especially in the delivery of early mathematics. Oral feedback to parents, together with photographic displays, can show them that…
ERIC Educational Resources Information Center
Lao, Andrew Chan-Chio; Cheng, Hercy N. H.; Huang, Mark C. L.; Ku, Oskar; Chan, Tak-Wai
2017-01-01
One-to-one technology, which allows every student to receive equal access to learning tasks through a personal computing device, has shown increasing potential for self-directed learning in elementary schools. With computer-supported self-directed learning (CS-SDL), students may set their own learning goals through the suggestions of the system…
ERIC Educational Resources Information Center
Mohd Syah, Nor Elleeiana; Hamzaid, Nur Azah; Murphy, Belinda Pingguan; Lim, Einly
2016-01-01
This study describes the development of a basic computer-based play pedagogy intervention using a dyscalculia-remedy-oriented approach such as repetition and number orientation manipulation, and the investigation of its effect on children displaying dyscalculia characteristics. This computer play was evaluated in a group of 50 seven-year-old…
ERIC Educational Resources Information Center
Robitaille, David F.
Boys' and girls' achievement in arithmetic computation was compared with their feelings of self-confidence in performing computations. A total of 2654 girls and 2786 boys from grades 5 through 8 in one school system participated. Each student was given a test to assess the degree of self-confidence in methods of performing the four basic…
ERIC Educational Resources Information Center
Maltby, Gregory P.; And Others
This report is the fifth year and last evaluation of the Title VII Bilingual Computer Literacy Project for San Elizario Independent School District, Texas. Several points in the fourth year evaluation focused on the need for the computer assisted instruction (CAI) project to obtain and maintain community and parent involvement and to secure and…
Mathematics Curriculum Guide. Mathematics IV.
ERIC Educational Resources Information Center
Gary City Public School System, IN.
GRADES OR AGES: Grade 12. SUBJECT MATTER: Mathematics. ORGANIZATION AND PHYSICAL APPEARANCE: The subject matter is presented in four columns: major areas, significant outcomes, observations and suggestions, and films and references. The topics include: sets-relations-functions, circular functions, graphs of circular functions, inverses of circular…
What Is the Point of Group Discussion in Mathematics?
ERIC Educational Resources Information Center
Hoyles, Celia
1985-01-01
Implications of using pupil-to-pupil discussion with mathematics classrooms are discussed, with different ways in which such discussion might promote mathematical understanding. A framework for instruction includes the learning of the computer language Logo. (MNS)
NASA Technical Reports Server (NTRS)
1947-01-01
Langley's human computers at work in 1947. The female presence at Langley, who performed mathematical computations for male staff. Photograph published in Winds of Change, 75th Anniversary NASA publication (page 48), by James Schultz.
The emerging field of computational toxicology applies mathematical and computer models and molecular biological and chemical approaches to explore both qualitative and quantitative relationships between sources of environmental pollutant exposure and adverse health outcomes. Th...
Materials inspired by mathematics.
Kotani, Motoko; Ikeda, Susumu
2016-01-01
Our world is transforming into an interacting system of the physical world and the digital world. What will be the materials science in the new era? With the rising expectations of the rapid development of computers, information science and mathematical science including statistics and probability theory, 'data-driven materials design' has become a common term. There is knowledge and experience gained in the physical world in the form of know-how and recipes for the creation of material. An important key is how we establish vocabulary and grammar to translate them into the language of the digital world. In this article, we outline how materials science develops when it encounters mathematics, showing some emerging directions.
Materials inspired by mathematics
Kotani, Motoko; Ikeda, Susumu
2016-01-01
Abstract Our world is transforming into an interacting system of the physical world and the digital world. What will be the materials science in the new era? With the rising expectations of the rapid development of computers, information science and mathematical science including statistics and probability theory, ‘data-driven materials design’ has become a common term. There is knowledge and experience gained in the physical world in the form of know-how and recipes for the creation of material. An important key is how we establish vocabulary and grammar to translate them into the language of the digital world. In this article, we outline how materials science develops when it encounters mathematics, showing some emerging directions. PMID:27877877
Logic via Computer Programming.
ERIC Educational Resources Information Center
Wieschenberg, Agnes A.
This paper proposed the question "How do we teach logical thinking and sophisticated mathematics to unsophisticated college students?" One answer among many is through the writing of computer programs. The writing of computer algorithms is mathematical problem solving and logic in disguise and it may attract students who would otherwise stop…
Sajjadi, Baharak; Raman, Abdul Aziz Abdul; Ibrahim, Shaliza
2015-05-01
This paper aims at investigating the influence of ultrasound power amplitude on liquid behaviour in a low-frequency (24 kHz) sono-reactor. Three types of analysis were employed: (i) mechanical analysis of micro-bubbles formation and their activities/characteristics using mathematical modelling. (ii) Numerical analysis of acoustic streaming, fluid flow pattern, volume fraction of micro-bubbles and turbulence using 3D CFD simulation. (iii) Practical analysis of fluid flow pattern and acoustic streaming under ultrasound irradiation using Particle Image Velocimetry (PIV). In mathematical modelling, a lone micro bubble generated under power ultrasound irradiation was mechanistically analysed. Its characteristics were illustrated as a function of bubble radius, internal temperature and pressure (hot spot conditions) and oscillation (pulsation) velocity. The results showed that ultrasound power significantly affected the conditions of hotspots and bubbles oscillation velocity. From the CFD results, it was observed that the total volume of the micro-bubbles increased by about 4.95% with each 100 W-increase in power amplitude. Furthermore, velocity of acoustic streaming increased from 29 to 119 cm/s as power increased, which was in good agreement with the PIV analysis.
Dilemma in Teaching Mathematics
ERIC Educational Resources Information Center
Md Kamaruddin, Nafisah Kamariah; Md Amin, Zulkarnain
2012-01-01
The challenge in mathematics education is finding the best way to teach mathematics. When students learn the reasoning and proving in mathematics, they will be proficient in mathematics. Students must know mathematics before they can apply it. Symbolism and logic is the key to both the learning of mathematics and its effective application to…
Making the Learning of Mathematics More Meaningful
NASA Technical Reports Server (NTRS)
Ward, Robin A.
1998-01-01
In the early 1980's, the National Commission on Excellence in Education responded to the call for reform in the teaching and learning of mathematics. In particular, the Commission developed a document addressing the consensus that all students need to learn more, and often different, mathematics and that instruction in mathematics must be significantly revised. In a response to these calls for mathematics education reform, the National Council of Teachers of Mathematics (NCTM) developed its Curriculum and Evaluation Standards (1989) with a two-fold purpose: 1) to create a coherent vision of what it means to be mathematically literate in a world that relies on calculators and computers, and 2) to create a set of standards to guide the revisions of school mathematics curriculum.
Mathematical models in medicine: Diseases and epidemics
Witten, M.
1987-01-01
This volume presents the numerous applications of mathematics in the life sciences and medicine, and demonstrates how mathematics and computers have taken root in these fields. The work covers a variety of techniques and applications including mathematical and modelling methodology, modelling/simulation technology, and philosophical issues in model formulation, leading to speciality medical modelling, artificial intelligence, psychiatric models, medical decision making, and molecular modelling.
Mathematical modeling in soil science
NASA Astrophysics Data System (ADS)
Tarquis, Ana M.; Gasco, Gabriel; Saa-Requejo, Antonio; Méndez, Ana; Andina, Diego; Sánchez, M. Elena; Moratiel, Rubén; Antón, Jose Manuel
2015-04-01
Teaching in context can be defined as teaching a mathematical idea or process by using a problem, situation, or data to enhance the teaching and learning process. The same problem or situation may be used many times, at different mathematical levels to teach different objectives. A common misconception exists that assigning/teaching applications is teaching in context. While both use problems, the difference is in timing, in purpose, and in student outcome. In this work, one problem situation is explored thoroughly at different levels of understanding and other ideas are suggested for classroom explorations. Some teachers, aware of the difficulties some students have with mathematical concepts, try to teach quantitative sciences without using mathematical tools. Such attempts are not usually successful. The answer is not in discarding the mathematics, but in finding ways to teach mathematically-based concepts to students who need them but who find them difficult. The computer is an ideal tool for this purpose. To this end, teachers of the Soil Science and Mathematics Departments of the UPM designed a common practice to teach to the students the role of soil on the carbon sequestration. The objective of this work is to explain the followed steps to the design of the practice. Acknowledgement Universidad Politécnica de Madrid (UPM) for the Projects in Education Innovation IE12_13-02009 and IE12_13-02012 is gratefully acknowledge.
Mathematics Worth Teaching, Mathematics Worth Understanding.
ERIC Educational Resources Information Center
Romberg, Thomas A.; Kaput, James J.
This chapter examines the scope of the mathematical content educators expect students to understand after they have participated in mathematics courses. It is organized under four headings: (1) Traditional School Mathematics, to clarify what the shift is away from; (2) Mathematics as Human Activity, to portray the direction the shift is toward;…
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…
Scheiner, Stefan; Komlev, Vladimir S.; Gurin, Alexey N.; Hellmich, Christian
2016-01-01
We here explore for the very first time how an advanced multiscale mathematical modeling approach may support the design of a provenly successful tissue engineering concept for mandibular bone. The latter employs double-porous, potentially cracked, single millimeter-sized granules packed into an overall conglomerate-type scaffold material, which is then gradually penetrated and partially replaced by newly grown bone tissue. During this process, the newly developing scaffold-bone compound needs to attain the stiffness of mandibular bone under normal physiological conditions. In this context, the question arises how the compound stiffness is driven by the key design parameters of the tissue engineering system: macroporosity, crack density, as well as scaffold resorption/bone formation rates. We here tackle this question by combining the latest state-of-the-art mathematical modeling techniques in the field of multiscale micromechanics, into an unprecedented suite of highly efficient, semi-analytically defined computation steps resolving several levels of hierarchical organization, from the millimeter- down to the nanometer-scale. This includes several types of homogenization schemes, namely such for porous polycrystals with elongated solid elements, for cracked matrix-inclusion composites, as well as for assemblies of coated spherical compounds. Together with the experimentally known stiffnesses of hydroxyapatite crystals and mandibular bone tissue, the new mathematical model suggests that early stiffness recovery (i.e., within several weeks) requires total avoidance of microcracks in the hydroxyapatite scaffolds, while mid-term stiffness recovery (i.e., within several months) is additionally promoted by provision of small granule sizes, in combination with high bone formation and low scaffold resorption rates. PMID:27708584
Free Mathematics Software Resources--Which Word Caught Your Eye?
ERIC Educational Resources Information Center
Reeves, Howard
2007-01-01
Computers have been in schools and indeed some mathematics classrooms for more than 35 years. Some schools have chosen to centralise their computers in laboratories, while others have a mix of configurations and networks. Whatever the case, how extensive has been the classroom use of computers for teaching and learning in mathematics? What has…
BASIC Simulation Programs; Volumes III and IV. Mathematics, Physics.
ERIC Educational Resources Information Center
Digital Equipment Corp., Maynard, MA.
The computer programs presented here were developed as a part of the Huntington Computer Project. They were tested on a Digital Equipment Corporation TSS-8 time-shared computer and run in a version of BASIC. Mathematics and physics programs are presented in this volume. The 20 mathematics programs include ones which review multiplication skills;…
The Mathematics Laboratory in Engineering Studies.
ERIC Educational Resources Information Center
Quesada, Jose Fco. Carballido
1986-01-01
Discusses the need for mathematics laboratories to supplement classroom instruction in mathematics for engineering students. Provides a description of such a laboratory, including a listing of equipment and materials that are recommended. Describes the uses for personal computers and suggests various problems that could be explored in the…
Sequences, Series, and Spreadsheets: A Mathematical Excursion.
ERIC Educational Resources Information Center
Rochowicz, John A., Jr.
The use of technology allows students to look at mathematical concepts in many different ways. With a variety of perspectives, studying ideas that were at one time difficult to understand are possible. Mathematics learning focuses more on concepts and less on computations. Various sequences including arithmetic, geometric, and partial sum can be…
Characterizing Interaction with Visual Mathematical Representations
ERIC Educational Resources Information Center
Sedig, Kamran; Sumner, Mark
2006-01-01
This paper presents a characterization of computer-based interactions by which learners can explore and investigate visual mathematical representations (VMRs). VMRs (e.g., geometric structures, graphs, and diagrams) refer to graphical representations that visually encode properties and relationships of mathematical structures and concepts.…
CAS-Induced Difficulties in Learning Mathematics?
ERIC Educational Resources Information Center
Jankvist, Uffe Thomas; Misfeldt, Morten
2015-01-01
In recent years computer algebra systems (CAS) have become an integrated part of the upper secondary school mathematics program. Despite the many positive possibilities of CAS, there also seems to be a flip side of the coin in relation to actual difficulties in learning mathematics, not least because a strong dependence on CAS for mathematical…
Modelling and Optimizing Mathematics Learning in Children
ERIC Educational Resources Information Center
Käser, Tanja; Busetto, Alberto Giovanni; Solenthaler, Barbara; Baschera, Gian-Marco; Kohn, Juliane; Kucian, Karin; von Aster, Michael; Gross, Markus
2013-01-01
This study introduces a student model and control algorithm, optimizing mathematics learning in children. The adaptive system is integrated into a computer-based training system for enhancing numerical cognition aimed at children with developmental dyscalculia or difficulties in learning mathematics. The student model consists of a dynamic…
Developing the Young Gifted Child's Mathematical Mind
ERIC Educational Resources Information Center
Fisher, Carol
2016-01-01
Schools seem firmly rooted in the emphasis on computational mastery, and seldom seem to have time to develop other areas of mathematical thinking, such as real-world problem solving and the application of mathematical concepts. All too often, children seem to do well in math in the early grades because they easily memorize the facts and the…
A Cryptological Way of Teaching Mathematics
ERIC Educational Resources Information Center
Caballero-Gil, Pino; Bruno-Castaneda, Carlos
2007-01-01
This work addresses the subject of mathematics education at secondary schools from a current and stimulating point of view intimately related to computational science. Cryptology is a captivating way of introducing into the classroom different mathematical subjects such as functions, matrices, modular arithmetic, combinatorics, equations,…
Mathematical analysis of deception.
Rogers, Deanna Tamae Koike; Durgin, Nancy Ann
2003-10-01
This report describes the results of a three year research project about the use of deception in information protection. The work involved a collaboration between Sandia employees and students in the Center for Cyber Defenders (CCD) and at the University of California at Davis. This report includes a review of the history of deception, a discussion of some cognitive issues, an overview of previous work in deception, the results of experiments on the effects of deception on an attacker, and a mathematical model of error types associated with deception in computer systems.
Technology, Mathematics, and the Young Child.
ERIC Educational Resources Information Center
Clements, Douglas H.
2000-01-01
Examines two types of computer environments suggested by the new Standards, one of which is the computer manipulative and the other a navigational environment such as the computer turtle. Discusses the contribution that these environments can make to young children's mathematics learning. (Contains 12 references.) (ASK)
Mathematical Discovery Prolog-Style.
ERIC Educational Resources Information Center
Lopez, Antonio M., Jr.
1991-01-01
The programing language PROLOG is compared to LOGO in terms of its ability to handle mathematical ideas. This is demonstrated by using PROLOG in solving a geometric theorem and two lemmas. The listings of the computer programs used to solve the problems are included. (KR)
ERIC Educational Resources Information Center
Yamaguchi, Shinobu; Sukhbaatar, Javzan; Takada, Jun-ichi; Dayan-Ochir, Khishigbuyan
2014-01-01
In 2008, Mongolia took part in One Laptop per Child (OLPC) project. Since that time, over 10,000 students in grades 2-5 in 43 primary education schools are using XO computers. This paper presents the findings of a study conducted in 2012 to evaluate the impact of the OLPC initiatives on students' literacy and math skills. This study covered 14…
ERIC Educational Resources Information Center
Lee, Chun-Yi; Chen, Ming-Jang; Chang, Wen-Long
2014-01-01
The aim of this study is to investigate the effects of solution methods and question prompts on generalization and justification of non-routine problem solving for Grade 9 students. The learning activities are based on the context of the frog jumping game. In addition, related computer tools were used to support generalization and justification of…
A Seminar in Mathematical Model-Building.
ERIC Educational Resources Information Center
Smith, David A.
1979-01-01
A course in mathematical model-building is described. Suggested modeling projects include: urban problems, biology and ecology, economics, psychology, games and gaming, cosmology, medicine, history, computer science, energy, and music. (MK)
Authenticity of Mathematical Modeling
ERIC Educational Resources Information Center
Tran, Dung; Dougherty, Barbara J.
2014-01-01
Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…
Lu, Shufang; Jin, Xiaogang; Jaffer, Aubrey; Gao, Fei; Mao, Xiaoyang
2016-05-25
Years of research have been devoted to computer-generated two-dimensional marbling. However, three-dimensional marbling has yet to be explored. In this paper, we present mathematical marbling of three-dimensional solids which supports a compact random-access vector representation. Our solid marbling textures are created by composing closed-form 3D pattern tool functions. These tool functions are an injection function and five deformation functions. The injection function is used to generate basic patterns, and the deformation functions are responsible for transforming the basic pattern into complex marbling effects. The resulting representation is feature preserving and resolution-independent. Our approach can render high-quality images preserving both the sharp features and the smooth color variations of a solid texture. When implemented on the GPU, our representation enables efficient color evaluation during the real-time solid marbling texture mapping. The color of a point in the volume space is computed by the 3D pattern tool functions from its coordinates. Our method consumes very little memory because only the mathematical functions and their corresponding parameters are stored. In addition, we develop an intuitive user interface and a genetic algorithm to facilitate the solid marbling texture authoring process. We demonstrate the effectiveness of our approach through various solid marbling textures and 3D objects carved from them.
Using Dynamic Software in Mathematics: The Case of Reflection Symmetry
ERIC Educational Resources Information Center
Tatar, Enver; Akkaya, Adnan; Kagizmanli, Türkan Berrin
2014-01-01
This study was carried out to examine the effects of computer-assisted instruction (CAI) using dynamic software on the achievement of students in mathematics in the topic of reflection symmetry. The study also aimed to ascertain the pre-service mathematics teachers' opinions on the use of CAI in mathematics lessons. In the study, a mixed research…
The Role of Mathematics Learning Centres in Engineering Education.
ERIC Educational Resources Information Center
Fuller, Milton
2002-01-01
Points out the diminishing demand for mathematics undergraduate programs and the strong trend in engineering education to make greater use of computer coursework such as Mathcad, Matlab, and other software systems for the mathematical and statistical components of engineering programs. Describes the changing role of mathematics learning centers…
Equity and Access: All Students Are Mathematical Problem Solvers
ERIC Educational Resources Information Center
Franz, Dana Pompkyl; Ivy, Jessica; McKissick, Bethany R.
2016-01-01
Often mathematical instruction for students with disabilities, especially those with learning disabilities, includes an overabundance of instruction on mathematical computation and does not include high-quality instruction on mathematical reasoning and problem solving. In fact, it is a common misconception that students with learning disabilities…
Using CAS to Solve a Mathematics Task: A Deconstruction
ERIC Educational Resources Information Center
Berger, Margot
2010-01-01
I investigate how and whether a heterogeneous group of first-year university mathematics students in South Africa harness the potential power of a computer algebra system (CAS) when doing a specific mathematics task. In order to do this, I develop a framework for deconstructing a mathematics task requiring the use of CAS, into its primary…
Mathematics and My Career. A Collection of Essays.
ERIC Educational Resources Information Center
Turner, Nura Dorothea Rains, Ed.
The essays in this booklet have been written by persons who had ranked in the top one percent of the 1958-60 Upstate New York Mathematical Association of America Contests. Personal accounts are given of the role of mathematics in the authors' education and career. The careers described include applied mathematics, computer research and programing,…
Modern Perspectives in Applied Mathematics: Theory and Numerics of PDEs
2015-04-13
SECURITY CLASSIFICATION OF: The International Conference on “Modern Perspectives in Applied Mathematics : Theory and Numerics of PDEs” took place April... mathematics , focusing on theoretical, computational and applied aspects of partial differential equations. The meeting brought together researchers from...Release; Distribution Unlimited Final Report: Modern Perspectives in Applied Mathematics : Theory and Numerics of PDEs The views, opinions and/or
1993-09-01
conformity of roller and raceway spherical crowns, while lending the bearing its self- aligning and high load capacity, also results in relative sliding...thus in the negative direction. A positive axial load, acting along the X-axis is also shown in Figure 1. Due to the self- aligning ability of a...Hadden, G.B., Kleckner, R.J., Ragen, M.A., and Sheynin, L., "Research’ Report and User’s Manual for Computer Program SHABERTH", SKF Report No. AT8YO0003
NASA Technical Reports Server (NTRS)
Zolotukhin, V. G.; Kolosov, B. I.; Usikov, D. A.; Borisenko, V. I.; Mosin, S. T.; Gorokhov, V. N.
1980-01-01
A description of a batch of programs for the YeS-1040 computer combined into an automated system for processing photo (and video) images of the Earth's surface, taken from spacecraft, is presented. Individual programs with the detailed discussion of the algorithmic and programmatic facilities needed by the user are presented. The basic principles for assembling the system, and the control programs are included. The exchange format within whose framework the cataloging of any programs recommended for the system of processing will be activated in the future is displayed.
Chinese Calendar and Mathematical Astronomy
NASA Astrophysics Data System (ADS)
Sun, Xiaochun
The Chinese calendar (li 历) was a system of mathematical astronomy that included mathematical techniques for the computation of celestial movements. It was the basis for producing astronomical ephemerides and annual almanacs. Calendar making started early in China. Since the Great Inception calendar reform in 104 BC, China has produced about 100 calendars (astronomical systems). The focus of calendar making was the prediction of solar, lunar, and planetary motions. As astronomy developed, new observational discoveries were incorporated into the calendar to make the system more precise. The history of astronomy in ancient China was largely a history of calendar making.
Mathematical Modelling Approach in Mathematics Education
ERIC Educational Resources Information Center
Arseven, Ayla
2015-01-01
The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…
Mathematical Story: A Metaphor for Mathematics Curriculum
ERIC Educational Resources Information Center
Dietiker, Leslie
2015-01-01
This paper proposes a theoretical framework for interpreting the content found in mathematics curriculum in order to offer teachers and other mathematics educators comprehensive conceptual tools with which to make curricular decisions. More specifically, it describes a metaphor of "mathematics curriculum as story" and defines and…
Discrete Mathematics and the Secondary Mathematics Curriculum.
ERIC Educational Resources Information Center
Dossey, John
Discrete mathematics, the mathematics of decision making for finite settings, is a topic of great interest in mathematics education at all levels. Attention is being focused on resolving the diversity of opinion concerning the exact nature of the subject, what content the curriculum should contain, who should study that material, and how that…
A Multifaceted Mathematical Approach for Complex Systems
Alexander, F.; Anitescu, M.; Bell, J.; Brown, D.; Ferris, M.; Luskin, M.; Mehrotra, S.; Moser, B.; Pinar, A.; Tartakovsky, A.; Willcox, K.; Wright, S.; Zavala, V.
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 significant 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.
A Study of Visualization for Mathematics Education
NASA Technical Reports Server (NTRS)
Daugherty, Sarah C.
2008-01-01
Graphical representations such as figures, illustrations, and diagrams play a critical role in mathematics and they are equally important in mathematics education. However, graphical representations in mathematics textbooks are static, Le. they are used to illustrate only a specific example or a limited set. of examples. By using computer software to visualize mathematical principles, virtually there is no limit to the number of specific cases and examples that can be demonstrated. However, we have not seen widespread adoption of visualization software in mathematics education. There are currently a number of software packages that provide visualization of mathematics for research and also software packages specifically developed for mathematics education. We conducted a survey of mathematics visualization software packages, summarized their features and user bases, and analyzed their limitations. In this survey, we focused on evaluating the software packages for their use with mathematical subjects adopted by institutions of secondary education in the United States (middle schools and high schools), including algebra, geometry, trigonometry, and calculus. We found that cost, complexity, and lack of flexibility are the major factors that hinder the widespread use of mathematics visualization software in education.
ERIC Educational Resources Information Center
Rheinboldt, Werner C.
This material contains two units which view applications of computer science. The first of these examines Horner's scheme; and is designed to instruct the user on how to apply both this scheme and related algorithms. The second unit aims for student understanding of standard bisection, secant, and Newton methods of root finding and appreciation of…
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…
ERIC Educational Resources Information Center
Lo, Jane-Jane; And Others
Calls for increased student involvement in mathematics classroom learning situations are due primarily to the recognition that a traditional lecture/demonstration format within school mathematics instruction is not effective in fostering and promoting students' problem-solving abilities, mathematical reasoning power, and mathematical communication…
ERIC Educational Resources Information Center
Ricks, Thomas E.
2010-01-01
Mathematics is motivating; at least, it should be. I argue that mathematical activity is an inherently attractive enterprise for human beings because as intellectual organisms, we are naturally enticed by the intellectual stimulation of mathematizing, and, as social beings, we are drawn to the socializing aspects of mathematical activity. These…
Students as Mathematics Consultants
ERIC Educational Resources Information Center
Jensen, Jennifer L.
2013-01-01
If students are going to develop reasoning and thinking skills, use their mathematical knowledge, and recognize the relevance of mathematics in their lives, they need to experience mathematics in meaningful ways. Only then will their mathematical skills be transferrable to all other parts of their lives. To promote such flexible mathematical…
NASA Astrophysics Data System (ADS)
Tegmark, Max
2014-02-01
The world can be described using mathematical equations and numbers, but why does maths do it so well? In his new book Our Mathematical Universe, a section of which is abridged and edited here, Max Tegmark makes the radical proposal that our reality isn't just described by mathematics - it is mathematics.
Mathematics Lessons without ...
ERIC Educational Resources Information Center
Cross, Kath; Hibbs, John
2006-01-01
In the Association of Teachers of Mathematics (ATM) Easter conference, 2006, the authors presented a list of important aspects of mathematics lessons, recommended for students to have a positive attitude to mathematics and for teachers to acquire effective teaching. The following are discussed in detail: (1) Mathematics lessons without good…
ERIC Educational Resources Information Center
Cain, David
2007-01-01
This article presents the first part of the closing address given by the author to the 2007 Association of Teachers of Mathematics (ATM) Easter conference at Loughborough. In his closing address, the author focuses on functioning mathematically as opposed to functional mathematics. His view of functional mathematics is that the focus is on someone…
Transforming Primary Mathematics
ERIC Educational Resources Information Center
Askew, Mike
2011-01-01
What is good mathematics teaching? What is mathematics teaching good for? Who is mathematics teaching for? These are just some of the questions addressed in "Transforming Primary Mathematics", a highly timely new resource for teachers which accessibly sets out the key theories and latest research in primary maths today. Under-pinned by findings…
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.
ERIC Educational Resources Information Center
Nwabueze, Kenneth K.
2004-01-01
The current emphasis on flexible modes of mathematics delivery involving new information and communication technology (ICT) at the university level is perhaps a reaction to the recent change in the objectives of education. Abstract algebra seems to be one area of mathematics virtually crying out for computer instructional support because of the…
Assessing Effects of Technology Usage on Mathematics Learning
ERIC Educational Resources Information Center
Lynch, Julianne
2006-01-01
Computer-based technologies are now commonplace in classrooms, and the integration of these media into the teaching and learning of mathematics is supported by government policy in most developed countries. However, many questions about the impact of computer-based technologies on classroom mathematics learning remain unanswered, and debates about…
On the Integration of Digital Technologies into Mathematics Classrooms
ERIC Educational Resources Information Center
Hoyles, Celia; Noss, Richard; Kent, Phillip
2004-01-01
Trouche's [Third Computer Algebra in Mathematics Education Symposiums, Reims, France, June 2003] presentation at the Third Computer Algebra in Mathematics Education Symposium focused on the notions of instrumental genesis and of orchestration: the former concerning the mutual transformation of learner and artefact in the course of constructing…
Willenbring, James M.; Bartlett, Roscoe Ainsworth; Heroux, Michael Allen
2012-01-01
Software lifecycles are becoming an increasingly important issue for computational science and engineering (CSE) software. The process by which a piece of CSE software begins life as a set of research requirements and then matures into a trusted high-quality capability is both commonplace and extremely challenging. Although an implicit lifecycle is obviously being used in any effort, the challenges of this process - respecting the competing needs of research vs. production - cannot be overstated. Here we describe a proposal for a well-defined software lifecycle process based on modern Lean/Agile software engineering principles. What we propose is appropriate for many CSE software projects that are initially heavily focused on research but also are expected to eventually produce usable high-quality capabilities. The model is related to TriBITS, a build, integration and testing system, which serves as a strong foundation for this lifecycle model, and aspects of this lifecycle model are ingrained in the TriBITS system. Here, we advocate three to four phases or maturity levels that address the appropriate handling of many issues associated with the transition from research to production software. The goals of this lifecycle model are to better communicate maturity levels with customers and to help to identify and promote Software Engineering (SE) practices that will help to improve productivity and produce better software. An important collection of software in this domain is Trilinos, which is used as the motivation and the initial target for this lifecycle model. However, many other related and similar CSE (and non-CSE) software projects can also make good use of this lifecycle model, especially those that use the TriBITS system. Indeed this lifecycle process, if followed, will enable large-scale sustainable integration of many complex CSE software efforts across several institutions.
Taking the Guesswork out of Computational Estimation
ERIC Educational Resources Information Center
Cochran, Jill; Dugger, Megan Hartmann
2013-01-01
Computational estimation is an important skill necessary for students' mathematical development. Students who can estimate well for computations rely on an understanding of many mathematical topics, including a strong number sense, which facilitates understanding the mathematical operations and contextual evidence within a problem. In turn, good…