Sample records for mathematical computing

  1. Mathematics, the Computer, and the Impact on Mathematics Education.

    ERIC Educational Resources Information Center

    Tooke, D. James

    2001-01-01

    Discusses the connection between mathematics and the computer; mathematics curriculum; mathematics instruction, including teachers learning to use computers; and the impact of the computer on learning mathematics. (LRW)

  2. The challenge of computer mathematics.

    PubMed

    Barendregt, Henk; Wiedijk, Freek

    2005-10-15

    Progress in the foundations of mathematics has made it possible to formulate all thinkable mathematical concepts, algorithms and proofs in one language and in an impeccable way. This is not in spite of, but partially based on the famous results of Gödel and Turing. In this way statements are about mathematical objects and algorithms, proofs show the correctness of statements and computations, and computations are dealing with objects and proofs. Interactive computer systems for a full integration of defining, computing and proving are based on this. The human defines concepts, constructs algorithms and provides proofs, while the machine checks that the definitions are well formed and the proofs and computations are correct. Results formalized so far demonstrate the feasibility of this 'computer mathematics'. Also there are very good applications. The challenge is to make the systems more mathematician-friendly, by building libraries and tools. The eventual goal is to help humans to learn, develop, communicate, referee and apply mathematics.

  3. 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…

  4. Mathematical Modeling and Computational Thinking

    ERIC Educational Resources Information Center

    Sanford, John F.; Naidu, Jaideep T.

    2017-01-01

    The paper argues that mathematical modeling is the essence of computational thinking. Learning a computer language is a valuable assistance in learning logical thinking but of less assistance when learning problem-solving skills. The paper is third in a series and presents some examples of mathematical modeling using spreadsheets at an advanced…

  5. 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.

  6. Will the digital computer transform classical mathematics?

    PubMed

    Rotman, Brian

    2003-08-15

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

  7. Experimental Mathematics and Computational Statistics

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

    Bailey, David H.; Borwein, Jonathan M.

    2009-04-30

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

  8. 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.

  9. The Mathematics of Computer Error.

    ERIC Educational Resources Information Center

    Wood, Eric

    1988-01-01

    Why a computer error occurred is considered by analyzing the binary system and decimal fractions. How the computer stores numbers is then described. Knowledge of the mathematics behind computer operation is important if one wishes to understand and have confidence in the results of computer calculations. (MNS)

  10. 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…

  11. Computer programming in the UK undergraduate mathematics curriculum

    NASA Astrophysics Data System (ADS)

    Sangwin, Christopher J.; O'Toole, Claire

    2017-11-01

    This paper reports a study which investigated the extent to which undergraduate mathematics students in the United Kingdom are currently taught to programme a computer as a core part of their mathematics degree programme. We undertook an online survey, with significant follow-up correspondence, to gather data on current curricula and received replies from 46 (63%) of the departments who teach a BSc mathematics degree. We found that 78% of BSc degree courses in mathematics included computer programming in a compulsory module but 11% of mathematics degree programmes do not teach programming to all their undergraduate mathematics students. In 2016, programming is most commonly taught to undergraduate mathematics students through imperative languages, notably MATLAB, using numerical analysis as the underlying (or parallel) mathematical subject matter. Statistics is a very popular choice in optional courses, using the package R. Computer algebra systems appear to be significantly less popular for compulsory first-year courses than a decade ago, and there was no mention of logic programming, functional programming or automatic theorem proving software. The modal form of assessment of computing modules is entirely by coursework (i.e. no examination).

  12. 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…

  13. Research on Computers in Mathematics Education, IV. The Use of Computers in Mathematics Education Resource Series.

    ERIC Educational Resources Information Center

    Kieren, Thomas E.

    This last paper in a set of four reviews research on a wide variety of computer applications in the mathematics classroom. It covers computer-based instruction, especially drill-and-practice and tutorial modes; computer-managed instruction; and computer-augmented problem-solving. Analytical comments on the findings and status of the research are…

  14. CDM: Teaching Discrete Mathematics to Computer Science Majors

    ERIC Educational Resources Information Center

    Sutner, Klaus

    2005-01-01

    CDM, for computational discrete mathematics, is a course that attempts to teach a number of topics in discrete mathematics to computer science majors. The course abandons the classical definition-theorem-proof model, and instead relies heavily on computation as a source of motivation and also for experimentation and illustration. The emphasis on…

  15. Mathematical challenges from theoretical/computational chemistry

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

    NONE

    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 assembledmore » 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.« less

  16. Computational and mathematical methods in brain atlasing.

    PubMed

    Nowinski, Wieslaw L

    2017-12-01

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

  17. 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…

  18. 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…

  19. 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…

  20. 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…

  1. Equity and Computers for Mathematics Learning: Access and Attitudes

    ERIC Educational Resources Information Center

    Forgasz, Helen J.

    2004-01-01

    Equity and computer use for secondary mathematics learning was the focus of a three year study. In 2003, a survey was administered to a large sample of grade 7-10 students. Some of the survey items were aimed at determining home access to and ownership of computers, and students' attitudes to mathematics, computers, and computer use for…

  2. 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…

  3. 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…

  4. The 6th International Conference on Computer Science and Computational Mathematics (ICCSCM 2017)

    NASA Astrophysics Data System (ADS)

    2017-09-01

    The ICCSCM 2017 (The 6th International Conference on Computer Science and Computational Mathematics) has aimed to provide a platform to discuss computer science and mathematics related issues including Algebraic Geometry, Algebraic Topology, Approximation Theory, Calculus of Variations, Category Theory; Homological Algebra, Coding Theory, Combinatorics, Control Theory, Cryptology, Geometry, Difference and Functional Equations, Discrete Mathematics, Dynamical Systems and Ergodic Theory, Field Theory and Polynomials, Fluid Mechanics and Solid Mechanics, Fourier Analysis, Functional Analysis, Functions of a Complex Variable, Fuzzy Mathematics, Game Theory, General Algebraic Systems, Graph Theory, Group Theory and Generalizations, Image Processing, Signal Processing and Tomography, Information Fusion, Integral Equations, Lattices, Algebraic Structures, Linear and Multilinear Algebra; Matrix Theory, Mathematical Biology and Other Natural Sciences, Mathematical Economics and Financial Mathematics, Mathematical Physics, Measure Theory and Integration, Neutrosophic Mathematics, Number Theory, Numerical Analysis, Operations Research, Optimization, Operator Theory, Ordinary and Partial Differential Equations, Potential Theory, Real Functions, Rings and Algebras, Statistical Mechanics, Structure Of Matter, Topological Groups, Wavelets and Wavelet Transforms, 3G/4G Network Evolutions, Ad-Hoc, Mobile, Wireless Networks and Mobile Computing, Agent Computing & Multi-Agents Systems, All topics related Image/Signal Processing, Any topics related Computer Networks, Any topics related ISO SC-27 and SC- 17 standards, Any topics related PKI(Public Key Intrastructures), Artifial Intelligences(A.I.) & Pattern/Image Recognitions, Authentication/Authorization Issues, Biometric authentication and algorithms, CDMA/GSM Communication Protocols, Combinatorics, Graph Theory, and Analysis of Algorithms, Cryptography and Foundation of Computer Security, Data Base(D.B.) Management & Information

  5. 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,…

  6. New computer system simplifies programming of mathematical equations

    NASA Technical Reports Server (NTRS)

    Reinfelds, J.; Seitz, R. N.; Wood, L. H.

    1966-01-01

    Automatic Mathematical Translator /AMSTRAN/ permits scientists or engineers to enter mathematical equations in their natural mathematical format and to obtain an immediate graphical display of the solution. This automatic-programming, on-line, multiterminal computer system allows experienced programmers to solve nonroutine problems.

  7. 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…

  8. 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…

  9. The Use of Computers in Mathematics Education: A Paradigm Shift from "Computer Assisted Instruction" towards "Student Programming"

    ERIC Educational Resources Information Center

    Aydin, Emin

    2005-01-01

    The purpose of this study is to review the changes that computers have on mathematics itself and on mathematics curriculum. The study aims at investigating different applications of computers in education in general, and mathematics education in particular and their applications on mathematics curriculum and on teaching and learning of…

  10. Creating Printed Materials for Mathematics with a Macintosh Computer.

    ERIC Educational Resources Information Center

    Mahler, Philip

    This document gives instructions on how to use a Macintosh computer to create printed materials for mathematics. A Macintosh computer, Microsoft Word, and objected-oriented (Draw-type) art program, and a function-graphing program are capable of producing high quality printed instructional materials for mathematics. Word 5.1 has an equation editor…

  11. Secondary School Mathematics Teachers' and Students' Views on Computer Assisted Mathematics Instruction in Turkey: Mathematica Example

    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…

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

    ERIC Educational Resources Information Center

    Karatas, Ilhan

    2014-01-01

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

  13. 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…

  14. Mathematics and Computer Science: Exploring a Symbiotic Relationship

    ERIC Educational Resources Information Center

    Bravaco, Ralph; Simonson, Shai

    2004-01-01

    This paper describes a "learning community" designed for sophomore computer science majors who are simultaneously studying discrete mathematics. The learning community consists of three courses: Discrete Mathematics, Data Structures and an Integrative Seminar/Lab. The seminar functions as a link that integrates the two disciplines. Participation…

  15. 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,…

  16. Computational Literacy and "The Big Picture" Concerning Computers in Mathematics Education

    ERIC Educational Resources Information Center

    diSessa, Andrea A.

    2018-01-01

    This article develops some ideas concerning the "big picture" of how using computers might fundamentally change learning, with an emphasis on mathematics (and, more generally, STEM education). I develop the big-picture model of "computation as a new literacy" in some detail and with concrete examples of sixth grade students…

  17. 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…

  18. The Relationship between Computational Fluency and Student Success in General Studies Mathematics

    ERIC Educational Resources Information Center

    Hegeman, Jennifer; Waters, Gavin

    2012-01-01

    Many developmental mathematics programs emphasize computational fluency with the assumption that this is a necessary contributor to student success in general studies mathematics. In an effort to determine which skills are most essential, scores on a computational fluency test were correlated with student success in general studies mathematics at…

  19. Teachers, Equity, and Computers for Secondary Mathematics Learning

    ERIC Educational Resources Information Center

    Forgasz, Helen

    2006-01-01

    The findings presented in this article were derived from a 3-year study aimed at examining issues associated with the use of computers for secondary mathematics learning in Victorian (Australia) schools. Gender and other equity factors were of particular interest. In this article, the focus is on the participating mathematics teachers. Data on…

  20. Computer Programming in the UK Undergraduate Mathematics Curriculum

    ERIC Educational Resources Information Center

    Sangwin, Christopher J.; O'Toole, Claire

    2017-01-01

    This paper reports a study which investigated the extent to which undergraduate mathematics students in the United Kingdom are currently taught to programme a computer as a core part of their mathematics degree programme. We undertook an online survey, with significant follow-up correspondence, to gather data on current curricula and received…

  1. The Effects of Computer Games on the Achievement of Basic Mathematical Skills

    ERIC Educational Resources Information Center

    Sayan, Hamiyet

    2015-01-01

    This study aims to analyze the relationship between playing computer games and learning basic mathematics skills. It shows the role computer games play in the learning and achievement of basic mathematical skills by students. Nowadays it is clear that individuals, especially young persons are very fond of computer and computer games. Since…

  2. Attitudes towards Computer and Computer Self-Efficacy as Predictors of Preservice Mathematics Teachers' Computer Anxiety

    ERIC Educational Resources Information Center

    Awofala, Adeneye O. A.; Akinoso, Sabainah O.; Fatade, Alfred O.

    2017-01-01

    The study investigated attitudes towards computer and computer self-efficacy as predictors of computer anxiety among 310 preservice mathematics teachers from five higher institutions of learning in Lagos and Ogun States of Nigeria using the quantitative research method within the blueprint of the descriptive survey design. Data collected were…

  3. Computer-Assisted Problem Solving in School Mathematics

    ERIC Educational Resources Information Center

    Hatfield, Larry L.; Kieren, Thomas E.

    1972-01-01

    A test of the hypothesis that writing and using computer programs related to selected mathematical content positively affects performance on those topics. Results particularly support the hypothesis. (MM)

  4. Explicating mathematical thinking in differential equations using a computer algebra system

    NASA Astrophysics Data System (ADS)

    Zeynivandnezhad, Fereshteh; Bates, Rachel

    2018-07-01

    The importance of developing students' mathematical thinking is frequently highlighted in literature regarding the teaching and learning of mathematics. Despite this importance, most curricula and instructional activities for undergraduate mathematics fail to bring the learner beyond the mathematics. The purpose of this study was to enhance students' mathematical thinking by implementing a computer algebra system and active learning pedagogical approaches. students' mathematical thinking processes were analyzed while completing specific differential equations tasks based on posed prompts and questions and Instrumental Genesis. Data were collected from 37 engineering students in a public Malaysian university. This study used the descriptive and interpretive qualitative research design to investigate the students' perspectives of emerging mathematical understanding and approaches to learning mathematics in an undergraduate differential equations course. Results of this study concluded that students used a variety of mathematical thinking processes in a non-sequential manner. Additionally, the outcomes provide justification for continued use of technologies such as computer algebra systems in undergraduate mathematics courses and the need for further studies to uncover the various processes students utilize to complete specific mathematical tasks.

  5. Teaching Mathematics: Computers in the Classroom.

    ERIC Educational Resources Information Center

    Borba, Marcelo C.

    1995-01-01

    Discusses some major changes that computers, calculators, and graphing calculators have brought to the mathematics classroom, including quasi-empirical studies in the classroom, use of multiple representations, emphasis on visualization, emphasis on tables, an altered classroom "ecology," and increasing complexity for students. (SR)

  6. The Mathematics and Computer Science Learning Center (MLC).

    ERIC Educational Resources Information Center

    Abraham, Solomon T.

    The Mathematics and Computer Science Learning Center (MLC) was established in the Department of Mathematics at North Carolina Central University during the fall semester of the 1982-83 academic year. The initial operations of the MLC were supported by grants to the University from the Burroughs-Wellcome Company and the Kenan Charitable Trust Fund.…

  7. 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.

  8. Computation Error Analysis: Students with Mathematics Difficulty Compared to Typically Achieving Students

    ERIC Educational Resources Information Center

    Nelson, Gena; Powell, Sarah R.

    2018-01-01

    Though proficiency with computation is highly emphasized in national mathematics standards, students with mathematics difficulty (MD) continue to struggle with computation. To learn more about the differences in computation error patterns between typically achieving students and students with MD, we assessed 478 third-grade students on a measure…

  9. Can Computers Be Used Successfully for Teaching College Mathematics?

    ERIC Educational Resources Information Center

    Hatfield, Steven H.

    1976-01-01

    Author states that the use of computers in mathematics courses tends to generate interest in course subject matter and make learning a less passive experience. Computers also introduce students to computer science as a field of study, and provide basic knowledge of computers as an important aspect of today's technology. (Author/RW)

  10. 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.

  11. 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…

  12. Applications of Massive Mathematical Computations

    DTIC Science & Technology

    1990-04-01

    particles from the first principles of QCD . This problem is under intensive numerical study 11-6 using special purpose parallel supercomputers in...several places around the world. The method used here is the Monte Carlo integration for a fixed 3-D plus time lattices . Reliable results are still years...mathematical and theoretical physics, but its most promising applications are in the numerical realization of QCD computations. Our programs for the solution

  13. 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…

  14. Assessing Mathematics Automatically Using Computer Algebra and the Internet

    ERIC Educational Resources Information Center

    Sangwin, Chris

    2004-01-01

    This paper reports some recent developments in mathematical computer-aided assessment which employs computer algebra to evaluate students' work using the Internet. Technical and educational issues raised by this use of computer algebra are addressed. Working examples from core calculus and algebra which have been used with first year university…

  15. The Computer Student Worksheet Based Mathematical Literacy for Statistics

    NASA Astrophysics Data System (ADS)

    Manoy, J. T.; Indarasati, N. A.

    2018-01-01

    The student worksheet is one of media teaching which is able to improve teaching an activity in the classroom. Indicators in mathematical literacy were included in a student worksheet is able to help the students for applying the concept in daily life. Then, the use of computers in learning can create learning with environment-friendly. This research used developmental research which was Thiagarajan (Four-D) development design. There are 4 stages in the Four-D, define, design, develop, and disseminate. However, this research was finish until the third stage, develop stage. The computer student worksheet based mathematical literacy for statistics executed good quality. This student worksheet is achieving the criteria if able to achieve three aspects, validity, practicality, and effectiveness. The subject in this research was the students at The 1st State Senior High School of Driyorejo, Gresik, grade eleven of The 5th Mathematics and Natural Sciences. The computer student worksheet products based mathematical literacy for statistics executed good quality, while it achieved the aspects for validity, practical, and effectiveness. This student worksheet achieved the validity aspects with an average of 3.79 (94.72%), and practical aspects with an average of 2.85 (71.43%). Besides, it achieved the effectiveness aspects with a percentage of the classical complete students of 94.74% and a percentage of the student positive response of 75%.

  16. 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…

  17. 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…

  18. Does Computer Use Matter? The Influence of Computer Usage on Eighth-Grade Students' Mathematics Reasoning

    ERIC Educational Resources Information Center

    Ayieko, Rachel A.; Gokbel, Elif N.; Nelson, Bryan

    2017-01-01

    This study uses the 2011 Trends in International Mathematics and Science Study to investigate the relationships among students' and teachers' computer use, and eighth-grade students' mathematical reasoning in three high-achieving nations: Finland, Chinese Taipei, and Singapore. The study found a significant negative relationship in all three…

  19. [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.

  20. 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…

  1. 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.

  2. Methodological Potential of Computer Experiment in Teaching Mathematics at University

    ERIC Educational Resources Information Center

    Lin, Kequan; Sokolova, Anna Nikolaevna; Vlasova, Vera K.

    2017-01-01

    The study is relevant due to the opportunity of increasing efficiency of teaching mathematics at university through integration of students of computer experiment conducted with the use of IT in this process. The problem of there search is defined by a contradiction between great potential opportunities of mathematics experiment for motivating and…

  3. The presence of mathematics and computer anxiety in nursing students and their effects on medication dosage calculations.

    PubMed

    Glaister, Karen

    2007-05-01

    To determine if the presence of mathematical and computer anxiety in nursing students affects learning of dosage calculations. The quasi-experimental study compared learning outcomes at differing levels of mathematical and computer anxiety when integrative and computer based learning approaches were used. Participants involved a cohort of second year nursing students (n=97). Mathematical anxiety exists in 20% (n=19) of the student nurse population, and 14% (n=13) experienced mathematical testing anxiety. Those students more anxious about mathematics and the testing of mathematics benefited from integrative learning to develop conditional knowledge (F(4,66)=2.52 at p<.05). Computer anxiety was present in 12% (n=11) of participants, with those reporting medium and high levels of computer anxiety performing less well than those with low levels (F(1,81)=3.98 at p<.05). Instructional strategies need to account for the presence of mathematical and computer anxiety when planning an educational program to develop competency in dosage calculations.

  4. Mathematical and Computational Modeling in Complex Biological Systems

    PubMed Central

    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

  5. Mathematical and Computational Modeling in Complex Biological Systems.

    PubMed

    Ji, Zhiwei; Yan, Ke; Li, Wenyang; Hu, Haigen; 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.

  6. Artificial Intelligence, Computational Thinking, and Mathematics Education

    ERIC Educational Resources Information Center

    Gadanidis, George

    2017-01-01

    Purpose: The purpose of this paper is to examine the intersection of artificial intelligence (AI), computational thinking (CT), and mathematics education (ME) for young students (K-8). Specifically, it focuses on three key elements that are common to AI, CT and ME: agency, modeling of phenomena and abstracting concepts beyond specific instances.…

  7. 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…

  8. War of Ontology Worlds: Mathematics, Computer Code, or Esperanto?

    PubMed Central

    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

  9. War of ontology worlds: mathematics, computer code, or Esperanto?

    PubMed

    Rzhetsky, Andrey; Evans, James A

    2011-09-01

    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.

  10. 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.

  11. Research in progress in applied mathematics, numerical analysis, fluid mechanics, and computer science

    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.

  12. Factors That Encourage or Inhibit Computer Use for Secondary Mathematics Teaching

    ERIC Educational Resources Information Center

    Forgasz, Helen

    2006-01-01

    Included in contemporary mathematics curricula is the expectation that mathematics teachers will use technology--computers and calculators--in their classrooms. It is widely believed in Australian educational circles and in society at large that students' learning will be enhanced by engaging with these technologies. For children to use computers…

  13. Increasing Mathematical Computation Skills for Students with Physical and Health Disabilities

    ERIC Educational Resources Information Center

    Webb, Paula

    2017-01-01

    Students with physical and health disabilities struggle with basic mathematical concepts. The purpose of this research study was to increase the students' mathematical computation skills through implementing new strategies and/or methods. The strategies implemented with the students was utilizing the ten-frame tiles and technology with the purpose…

  14. Computers in mathematics: teacher-inservice training at a distance

    NASA Astrophysics Data System (ADS)

    Friedman, Edward A.; Jurkat, M. P.

    1993-01-01

    While research and experience show many advantages for incorporation of computer technology into secondary school mathematics instruction, less than 5 percent of the nation's teachers are actively using computers in their classrooms. This is the case even though mathematics teachers in grades 7 - 12 are often familiar with computer technology and have computers available to them in their schools. The implementation bottleneck is in-service teacher training and there are few models of effective implementation available for teachers to emulate. Stevens Institute of Technology has been active since 1988 in research and development efforts to incorporate computers into classroom use. We have found that teachers need to see examples of classroom experience with hardware and software and they need to have assistance as they experiment with applications of software and the development of lesson plans. High-band width technology can greatly facilitate teacher training in this area through transmission of video documentaries, software discussions, teleconferencing, peer interactions, classroom observations, etc. We discuss the experience that Stevens has had with face-to-face teacher training as well as with satellite-based teleconferencing using one-way video and two- way audio. Included are reviews of analyses of this project by researchers from Educational Testing Service, Princeton University, and Bank Street School of Education.

  15. The mathematical and computer modeling of the worm tool shaping

    NASA Astrophysics Data System (ADS)

    Panchuk, K. L.; Lyashkov, A. A.; Ayusheev, T. V.

    2017-06-01

    Traditionally mathematical profiling of the worm tool is carried out on the first T. Olivier method, known in the theory of gear gearings, with receiving an intermediate surface of the making lath. It complicates process of profiling and its realization by means of computer 3D-modeling. The purpose of the work is the improvement of mathematical model of profiling and its realization based on the methods of 3D-modeling. Research problems are: receiving of the mathematical model of profiling which excludes the presence of the making lath in it; realization of the received model by means of frame and superficial modeling; development and approbation of technology of solid-state modeling for the solution of the problem of profiling. As the basic, the kinematic method of research of the mutually envelope surfaces is accepted. Computer research is executed by means of CAD based on the methods of 3D-modeling. We have developed mathematical model of profiling of the worm tool; frame, superficial and solid-state models of shaping of the mutually enveloping surfaces of the detail and the tool are received. The offered mathematical models and the technologies of 3D-modeling of shaping represent tools for theoretical and experimental profiling of the worm tool. The results of researches can be used at design of metal-cutting tools.

  16. 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'…

  17. 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.

  18. Equity and Beliefs about the Efficacy of Computers for Mathematics Learning

    ERIC Educational Resources Information Center

    Forgasz, Helen J.

    2003-01-01

    Members of society appear to have great faith in the educational value of computers. It is widely believed that computer use will promote learning. Unsupported by research evidence, many contemporary mathematics curriculum documents include statements advocating computer use and the benefits to be derived. As part of a larger study in which equity…

  19. Structural Equation Model to Validate: Mathematics-Computer Interaction, Computer Confidence, Mathematics Commitment, Mathematics Motivation and Mathematics Confidence

    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…

  20. Effectiveness of Computer-Assisted Mathematics Education (CAME) over Academic Achievement: A Meta-Analysis Study

    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…

  1. 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.

  2. 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…

  3. Improving science and mathematics education with computational modelling in interactive engagement environments

    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.

  4. 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…

  5. Problem Solving and Computational Skill: Are They Shared or Distinct Aspects of Mathematical Cognition?

    PubMed Central

    Fuchs, Lynn S.; Fuchs, Douglas; Hamlett, Carol L.; Lambert, Warren; Stuebing, Karla; Fletcher, Jack M.

    2009-01-01

    The purpose of this study was to explore patterns of difficulty in 2 domains of mathematical cognition: computation and problem solving. Third graders (n = 924; 47.3% male) were representatively sampled from 89 classrooms; assessed on computation and problem solving; classified as having difficulty with computation, problem solving, both domains, or neither domain; and measured on 9 cognitive dimensions. Difficulty occurred across domains with the same prevalence as difficulty with a single domain; specific difficulty was distributed similarly across domains. Multivariate profile analysis on cognitive dimensions and chi-square tests on demographics showed that specific computational difficulty was associated with strength in language and weaknesses in attentive behavior and processing speed; problem-solving difficulty was associated with deficient language as well as race and poverty. Implications for understanding mathematics competence and for the identification and treatment of mathematics difficulties are discussed. PMID:20057912

  6. Topics in Computer Literacy as Elements of Two Introductory College Mathematics Courses.

    ERIC Educational Resources Information Center

    Spresser, Diane M.

    1986-01-01

    Explains the integrated approach implemented by James Madison University, Virginia, in enhancing computer literacy. Reviews the changes in the mathematics courses and provides topical listings and outlines of the courses that emphasize computer applications. (ML)

  7. Variables that Affect Math Teacher Candidates' Intentions to Integrate Computer-Assisted Mathematics Education (CAME)

    ERIC Educational Resources Information Center

    Erdogan, Ahmet

    2010-01-01

    Based on Social Cognitive Carier Theory (SCCT) (Lent, Brown, & Hackett, 1994, 2002), this study tested the effects of mathematics teacher candidates' self-efficacy in, outcome expectations from, and interest in CAME on their intentions to integrate Computer-Assisted Mathematics Education (CAME). While mathematics teacher candidates' outcome…

  8. Understanding Mathematics and Logic Using BASIC Computer Games.

    ERIC Educational Resources Information Center

    Ahl, David H.

    This combination teacher's guide and student workbook serves as a companion volume to 101 BASIC Computer Games (EM 011 681). It presents ideas, exercises and supplemental projects which will aid the teaching and learning of a wide variety of academic subjects in grades 7 through 12, although the emphasis is upon mathematics and logic. In addition,…

  9. Computational Fluency Performance Profile of High School Students with Mathematics Disabilities

    ERIC Educational Resources Information Center

    Calhoon, Mary Beth; Emerson, Robert Wall; Flores, Margaret; Houchins, David E.

    2007-01-01

    The purpose of this descriptive study was to develop a computational fluency performance profile of 224 high school (Grades 9-12) students with mathematics disabilities (MD). Computational fluency performance was examined by grade-level expectancy (Grades 2-6) and skill area (whole numbers: addition, subtraction, multiplication, division;…

  10. Computer-Assisted Mathematics Instruction for Students with Specific Learning Disability: A Review of the Literature

    ERIC Educational Resources Information Center

    Stultz, Sherry L.

    2017-01-01

    This review was conducted to evaluate the current body of scholarly research regarding the use of computer-assisted instruction (CAI) to teach mathematics to students with specific learning disability (SLD). For many years, computers are utilized for educational purposes. However, the effectiveness of CAI for teaching mathematics to this specific…

  11. The transformation of aerodynamic stability derivatives by symbolic mathematical computation

    NASA Technical Reports Server (NTRS)

    Howard, J. C.

    1975-01-01

    The formulation of mathematical models of aeronautical systems for simulation or other purposes, involves the transformation of aerodynamic stability derivatives. It is shown that these derivatives transform like the components of a second order tensor having one index of covariance and one index of contravariance. Moreover, due to the equivalence of covariant and contravariant transformations in orthogonal Cartesian systems of coordinates, the transformations can be treated as doubly covariant or doubly contravariant, if this simplifies the formulation. It is shown that the tensor properties of these derivatives can be used to facilitate their transformation by symbolic mathematical computation, and the use of digital computers equipped with formula manipulation compilers. When the tensor transformations are mechanised in the manner described, man-hours are saved and the errors to which human operators are prone can be avoided.

  12. Cultivating Computational Thinking Practices and Mathematical Habits of Mind in Lattice Land

    ERIC Educational Resources Information Center

    Pei, Christina; Weintrop, David; Wilensky, Uri

    2018-01-01

    There is a great deal of overlap between the set of practices collected under the term "computational thinking" and the mathematical habits of mind that are the focus of much mathematics instruction. Despite this overlap, the links between these two desirable educational outcomes are rarely made explicit, either in classrooms or in the…

  13. 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…

  14. Secondary School Students' Attitudes towards Mathematics Computer--Assisted Instruction Environment in Kenya

    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…

  15. 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…

  16. 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.…

  17. 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…

  18. 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…

  19. 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.

  20. Development of an Intelligent Instruction System for Mathematical Computation

    ERIC Educational Resources Information Center

    Kim, Du Gyu; Lee, Jaemu

    2013-01-01

    In this paper, we propose the development of a web-based, intelligent instruction system to help elementary school students for mathematical computation. We concentrate on the intelligence facilities which support diagnosis and advice. The existing web-based instruction systems merely give information on whether the learners' replies are…

  1. 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…

  2. The Computer as a Teaching Aid for Eleventh Grade Mathematics: A Comparison Study.

    ERIC Educational Resources Information Center

    Kieren, Thomas Ervin

    To determine the effect of learning computer programming and the use of a computer on mathematical achievement of eleventh grade students, for each of two years, average and above average students were randomly assigned to an experimental and control group. The experimental group wrote computer programs and used the output from the computer in…

  3. Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis and computer science

    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.

  4. Learning Mathematics by Designing, Programming, and Investigating with Interactive, Dynamic Computer-Based Objects

    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…

  5. 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.

  6. Tensor Arithmetic, Geometric and Mathematic Principles of Fluid Mechanics in Implementation of Direct Computational Experiments

    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.

  7. Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis and computer science

    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.

  8. Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis and computer science

    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.

  9. Massive Symbolic Mathematical Computations and Their Applications

    DTIC Science & Technology

    1988-08-16

    NUMBER ORGANIZATION (if appi cable) AFOSR I A_ /__ I F49620-87- C -0113 Bc. ADDRESS (City, Stare, and ZIP Code) %. SOURCE OF FUNDING NUMBERS PROGRAM PROJECT...TASK WORK UNIT - < ’/I/ "//ELEMENT NO. NO. NO. ACCESSION NO. /,, AF,; c 9r ;- 6 (4/tL’ " ’ ’! /K’, 11 TITLE (Incoue Secuirty Classification) Massive...DARPA R & D Status Report AFOSR.m. 8 8-1 12Contract No. F49620-87- C -0113 MASSIVE SYMBOLIC MATHEMATICAL COMPUTATIONS AND THEIR APPLICATIONS Quarterly

  10. A Computer Based Education (CBE) Program for Middle School Mathematics Intervention

    ERIC Educational Resources Information Center

    Gulley, Bill

    2009-01-01

    A Computer Based Education (CBE) program for intervention mathematics was developed, used, and modified over a period of three years in a computer lab at an Arizona Title I middle school. The program is described along with a rationale for the need, design, and use of such a program. Data was collected in the third year and results of the program…

  11. Computing Linear Mathematical Models Of Aircraft

    NASA Technical Reports Server (NTRS)

    Duke, Eugene L.; Antoniewicz, Robert F.; Krambeer, Keith D.

    1991-01-01

    Derivation and Definition of Linear Aircraft Model (LINEAR) computer program provides user with powerful, and flexible, standard, documented, and verified software tool for linearization of mathematical models of aerodynamics of aircraft. Intended for use in software tool to drive linear analysis of stability and design of control laws for aircraft. Capable of both extracting such linearized engine effects as net thrust, torque, and gyroscopic effects, and including these effects in linear model of system. Designed to provide easy selection of state, control, and observation variables used in particular model. Also provides flexibility of allowing alternate formulations of both state and observation equations. Written in FORTRAN.

  12. [AERA. Dream machines and computing practices at the Mathematical Center].

    PubMed

    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

  13. Using Mental Imagery Processes for Teaching and Research in Mathematics and Computer Science

    ERIC Educational Resources Information Center

    Arnoux, Pierre; Finkel, Alain

    2010-01-01

    The role of mental representations in mathematics and computer science (for teaching or research) is often downplayed or even completely ignored. Using an ongoing work on the subject, we argue for a more systematic study and use of mental representations, to get an intuition of mathematical concepts, and also to understand and build proofs. We…

  14. A mathematical model for computer image tracking.

    PubMed

    Legters, G R; Young, T Y

    1982-06-01

    A mathematical model using an operator formulation for a moving object in a sequence of images is presented. Time-varying translation and rotation operators are derived to describe the motion. A variational estimation algorithm is developed to track the dynamic parameters of the operators. The occlusion problem is alleviated by using a predictive Kalman filter to keep the tracking on course during severe occlusion. The tracking algorithm (variational estimation in conjunction with Kalman filter) is implemented to track moving objects with occasional occlusion in computer-simulated binary images.

  15. The effects of computer-assisted instruction on the mathematics performance and classroom behavior of children with ADHD.

    PubMed

    Mautone, Jennifer A; DuPaul, George J; Jitendra, Asha K

    2005-08-01

    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' mathematics achievement improve and their on-task behavior increase during the CAI sessions relative to independent seatwork conditions. In addition, students and teachers consider CAI to be an acceptable intervention for some students with ADHD who are having difficulty with mathematics. Implications of these results for practice and research are discussed.

  16. Summary of research in applied mathematics, numerical analysis and computer science at the Institute for Computer Applications in Science and Engineering

    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.

  17. The Impact of Specialist School Status: A Case Study of Two Contrasting Mathematics and Computing Colleges

    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…

  18. 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…

  19. Mathematics for the Technical Student: The Use of the Computer in the Systems Approach to Instruction.

    ERIC Educational Resources Information Center

    Capps, Joan P.

    An instructional method using flow-chart symbols to make mathematical abstractions more concrete was implemented for a year in a technical mathematics course. Students received instruction in computer applications and programming in the BASIC language in order to increase motivation and firm the mathematical skills and problem-solving approaches…

  20. 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…

  1. 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…

  2. 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…

  3. Traditional vs. Innovative Uses of Computers among Mathematics Pre-Service Teachers in Serbia

    ERIC Educational Resources Information Center

    Teo, Timothy; Milutinovic, Verica; Zhou, Mingming; Bankovic, Dragic

    2017-01-01

    This study examined pre-service teachers' intentions to use computers in traditional and innovative teaching practices in primary mathematics classrooms. It extended the technology acceptance model (TAM) by adding as external variables pre-service teachers' experience with computers and their technological pedagogical content knowledge (TPCK).…

  4. Clinical and mathematical introduction to computer processing of scintigraphic images

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

    Goris, M.L.; Briandet, P.A.

    The authors state in their preface:''...we believe that there is no book yet available in which computing in nuclear medicine has been approached in a reasonable manner. This book is our attempt to correct the situation.'' The book is divided into four sections: (1) Clinical Applications of Quantitative Scintigraphic Analysis; (2) Mathematical Derivations; (3) Processing Methods of Scintigraphic Images; and (4) The (Computer) System. Section 1 has chapters on quantitative approaches to congenital and acquired heart diseases, nephrology and urology, and pulmonary medicine.

  5. Instrumentation for Scientific Computing in Neural Networks, Information Science, Artificial Intelligence, and Applied Mathematics.

    DTIC Science & Technology

    1987-10-01

    include Security Classification) Instrumentation for scientific computing in neural networks, information science, artificial intelligence, and...instrumentation grant to purchase equipment for support of research in neural networks, information science, artificail intellignece , and applied mathematics...in Neural Networks, Information Science, Artificial Intelligence, and Applied Mathematics Contract AFOSR 86-0282 Principal Investigator: Stephen

  6. Formative questioning in computer learning environments: a course for pre-service mathematics teachers

    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.

  7. 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…

  8. Personalized Computer-Assisted Mathematics Problem-Solving Program and Its Impact on Taiwanese Students

    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.…

  9. Summary of research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis and computer science

    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.

  10. Five Affordances of Computational Thinking to Support Elementary Mathematics Education

    ERIC Educational Resources Information Center

    Gadanidis, George

    2017-01-01

    With the increased focus on computational thinking (CT) in education, it is important to investigate the affordances that CT may offer to support teaching and learning. This paper outlines five affordances of CT that may support elementary mathematics education, whose conceptualization was refined in a year-long study involving eight Grades 3-4…

  11. Computer Conferencing in Mathematics Classrooms: Distance Education--The Long and the Short of It.

    ERIC Educational Resources Information Center

    Lamb, Charles E.; Klemm, William R.

    One of the major goals of mathematics education reform efforts is for students to become more confident in their abilities. This paper suggests that computer conferencing provides a way to change classroom practice so that students can work together in a self-paced manner that builds self-esteem and confidence in mathematics. A pedagogical…

  12. Mathematics Word Problem Solving: An Investigation into Schema-Based Instruction in a Computer-Mediated Setting and a Teacher-Mediated Setting with Mathematically Low-Performing Students

    ERIC Educational Resources Information Center

    Leh, Jayne

    2011-01-01

    Substantial evidence indicates that teacher-delivered schema-based instruction (SBI) facilitates significant increases in mathematics word problem solving (WPS) skills for diverse students; however research is unclear whether technology affordances facilitate superior gains in computer-mediated (CM) instruction in mathematics WPS when compared to…

  13. 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…

  14. Effective Teacher Qualities from International Mathematics, Science, and Computer Teachers' Perspectives

    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…

  15. 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)

  16. The Influence of Computers and Informatics on Mathematics and Its Teaching. Science and Technology Education Series, 44.

    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…

  17. The Effectiveness of Computer-Assisted Instruction for Teaching Mathematics to Students with Specific Learning Disability

    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…

  18. 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…

  19. 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.

  20. 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…

  1. A Computer Based Program to Improve Reading and Mathematics Scores for High School Students.

    ERIC Educational Resources Information Center

    Bond, Carole L.; And Others

    A study examined the effect on reading achievement, mathematics achievement, and ACT scores when computer based instruction (CBI) was compressed into a 6-week period of time. In addition, the effects of learning style and receptive language deficits on these scores were studied. Computer based instruction is a primary source of instruction that…

  2. Neural Mechanisms Underlying the Computation of Hierarchical Tree Structures in Mathematics

    PubMed Central

    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. PMID:25379713

  3. Influence of Computer-Aided Assessment on Ways of Working with Mathematics

    ERIC Educational Resources Information Center

    Rønning, Frode

    2017-01-01

    This paper is based on an on-going project for modernizing the basic education in mathematics for engineers at the Norwegian University of Science and Technology. One of the components in the project is using a computer-aided assessment system (Maple T.A.) for handling students' weekly hand-ins. Successful completion of a certain number of problem…

  4. Effects of Computer Algebra System (CAS) with Metacognitive Training on Mathematical Reasoning.

    ERIC Educational Resources Information Center

    Kramarski, Bracha; Hirsch, Chaya

    2003-01-01

    Describes a study that investigated the differential effects of Computer Algebra Systems (CAS) and metacognitive training (META) on mathematical reasoning. Participants were 83 Israeli eighth-grade students. Results showed that CAS embedded within META significantly outperformed the META and CAS alone conditions, which in turn significantly…

  5. Experimental Mathematics and Mathematical Physics

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

    Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David

    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.

  6. Adding It Up: Is Computer Use Associated with Higher Achievement in Public Elementary Mathematics Classrooms?

    ERIC Educational Resources Information Center

    Kao, Linda Lee

    2009-01-01

    Despite support for technology in schools, there is little evidence indicating whether using computers in public elementary mathematics classrooms is associated with improved outcomes for students. This exploratory study examined data from the Early Childhood Longitudinal Study, investigating whether students' frequency of computer use was related…

  7. Mathematical modeling and computational prediction of cancer drug resistance.

    PubMed

    Sun, Xiaoqiang; Hu, Bin

    2017-06-23

    Diverse forms of resistance to anticancer drugs can lead to the failure of chemotherapy. Drug resistance is one of the most intractable issues for successfully treating cancer in current clinical practice. Effective clinical approaches that could counter drug resistance by restoring the sensitivity of tumors to the targeted agents are urgently needed. As numerous experimental results on resistance mechanisms have been obtained and a mass of high-throughput data has been accumulated, mathematical modeling and computational predictions using systematic and quantitative approaches have become increasingly important, as they can potentially provide deeper insights into resistance mechanisms, generate novel hypotheses or suggest promising treatment strategies for future testing. In this review, we first briefly summarize the current progress of experimentally revealed resistance mechanisms of targeted therapy, including genetic mechanisms, epigenetic mechanisms, posttranslational mechanisms, cellular mechanisms, microenvironmental mechanisms and pharmacokinetic mechanisms. Subsequently, we list several currently available databases and Web-based tools related to drug sensitivity and resistance. Then, we focus primarily on introducing some state-of-the-art computational methods used in drug resistance studies, including mechanism-based mathematical modeling approaches (e.g. molecular dynamics simulation, kinetic model of molecular networks, ordinary differential equation model of cellular dynamics, stochastic model, partial differential equation model, agent-based model, pharmacokinetic-pharmacodynamic model, etc.) and data-driven prediction methods (e.g. omics data-based conventional screening approach for node biomarkers, static network approach for edge biomarkers and module biomarkers, dynamic network approach for dynamic network biomarkers and dynamic module network biomarkers, etc.). Finally, we discuss several further questions and future directions for the use of

  8. Interpolation Environment of Tensor Mathematics at the Corpuscular Stage of Computational Experiments in Hydromechanics

    NASA Astrophysics Data System (ADS)

    Bogdanov, Alexander; Degtyarev, Alexander; Khramushin, Vasily; Shichkina, Yulia

    2018-02-01

    Stages of direct computational experiments in hydromechanics based on tensor mathematics tools are represented by conditionally independent mathematical models for calculations separation in accordance with physical processes. Continual stage of numerical modeling is constructed on a small time interval in a stationary grid space. Here coordination of continuity conditions and energy conservation is carried out. Then, at the subsequent corpuscular stage of the computational experiment, kinematic parameters of mass centers and surface stresses at the boundaries of the grid cells are used in modeling of free unsteady motions of volume cells that are considered as independent particles. These particles can be subject to vortex and discontinuous interactions, when restructuring of free boundaries and internal rheological states has place. Transition from one stage to another is provided by interpolation operations of tensor mathematics. Such interpolation environment formalizes the use of physical laws for mechanics of continuous media modeling, provides control of rheological state and conditions for existence of discontinuous solutions: rigid and free boundaries, vortex layers, their turbulent or empirical generalizations.

  9. Teacher's Guide to Secondary Mathematics.

    ERIC Educational Resources Information Center

    Duval County Schools, Jacksonville, FL.

    This is a teacher's guide to secondary school mathematics. Developed for use in the Duval County Public Schools, Jacksonville, Florida. Areas of mathematics covered are algebra, analysis, calculus, computer literacy, computer science, geometry, analytic geometry, general mathematics, consumer mathematics, pre-algebra, probability and statistics,…

  10. 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…

  11. Mathematical Language Development and Talk Types in Computer Supported Collaborative Learning Environments

    ERIC Educational Resources Information Center

    Symons, Duncan; Pierce, Robyn

    2015-01-01

    In this study we examine the use of cumulative and exploratory talk types in a year 5 computer supported collaborative learning environment. The focus for students in this environment was to participate in mathematical problem solving, with the intention of developing the proficiencies of problem solving and reasoning. Findings suggest that…

  12. Development process of in-service training intended for teachers to perform teaching of mathematics with computer algebra systems

    NASA Astrophysics Data System (ADS)

    Ardıç, Mehmet Alper; Işleyen, Tevfik

    2018-01-01

    In this study, we deal with the development process of in-service training activities designed in order for mathematics teachers of secondary education to realize teaching of mathematics, utilizing computer algebra systems. In addition, the results obtained from the researches carried out during and after the in-service training were summarized. Last section focuses on suggestions any teacher can use to carry out activities aimed at using computer algebra systems in teaching environments.

  13. Mathematical and computational modelling of skin biophysics: a review

    PubMed Central

    2017-01-01

    The objective of this paper is to provide a review on some aspects of the mathematical and computational modelling of skin biophysics, with special focus on constitutive theories based on nonlinear continuum mechanics from elasticity, through anelasticity, including growth, to thermoelasticity. Microstructural and phenomenological approaches combining imaging techniques are also discussed. Finally, recent research applications on skin wrinkles will be presented to highlight the potential of physics-based modelling of skin in tackling global challenges such as ageing of the population and the associated skin degradation, diseases and traumas. PMID:28804267

  14. Mathematical and computational modelling of skin biophysics: a review

    NASA Astrophysics Data System (ADS)

    Limbert, Georges

    2017-07-01

    The objective of this paper is to provide a review on some aspects of the mathematical and computational modelling of skin biophysics, with special focus on constitutive theories based on nonlinear continuum mechanics from elasticity, through anelasticity, including growth, to thermoelasticity. Microstructural and phenomenological approaches combining imaging techniques are also discussed. Finally, recent research applications on skin wrinkles will be presented to highlight the potential of physics-based modelling of skin in tackling global challenges such as ageing of the population and the associated skin degradation, diseases and traumas.

  15. What Is the Predict Level of Which Computer Using Skills Measured in PISA for Achievement in Mathematics

    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…

  16. Mathematical and computational aspects of nonuniform frictional slip modeling

    NASA Astrophysics Data System (ADS)

    Gorbatikh, Larissa

    2004-07-01

    A mechanics-based model of non-uniform frictional sliding is studied from the mathematical/computational analysis point of view. This problem is of a key importance for a number of applications (particularly geomechanical ones), where materials interfaces undergo partial frictional sliding under compression and shear. We show that the problem is reduced to Dirichlet's problem for monotonic loading and to Riemman's problem for cyclic loading. The problem may look like a traditional crack interaction problem, however, it is confounded by the fact that locations of n sliding intervals are not known. They are to be determined from the condition for the stress intensity factors: KII=0 at the ends of the sliding zones. Computationally, it reduces to solving a system of 2n coupled non-linear algebraic equations involving singular integrals with unknown limits of integration.

  17. 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…

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

    NASA Astrophysics Data System (ADS)

    Jogesh Babu, G.

    2017-01-01

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

  19. Mathematical modeling and computer simulation of isoelectric focusing with electrochemically defined ampholytes

    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.

  20. Incorporating Partial Credit in Computer-Aided Assessment of Mathematics in Secondary Education

    ERIC Educational Resources Information Center

    Ashton, Helen S.; Beevers, Cliff E.; Korabinski, Athol A.; Youngson, Martin A.

    2006-01-01

    In a mathematical examination on paper, partial credit is normally awarded for an answer that is not correct, but, nevertheless, contains some of the correct working. Assessment on computer normally marks an incorrect answer wrong and awards no marks. This can lead to discrepancies between marks awarded for the same examination given in the two…

  1. Learner Perceptions of the Introduction of Computer-Assisted Learning in Mathematics at a Peri-Urban School in South Africa

    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…

  2. Derivation and computation of discrete-delay and continuous-delay SDEs in mathematical biology.

    PubMed

    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.

  3. Gender Differences in Preschool Children's Recall of Competitive and Noncompetitive Computer Mathematics Games

    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…

  4. The Effects of Computer-Assisted Instruction on the Achievement, Attitudes and Retention of Fourth Grade Mathematics Students in North Cyprus

    ERIC Educational Resources Information Center

    Pilli, Olga; Aksu, Meral

    2013-01-01

    The purpose of this study was to examine the effects of the educational software "Frizbi Mathematics 4" on 4th grade student's mathematics achievement, retention, attitudes toward mathematics and attitude toward computer assisted learning. Two groups (experimental and control) of students from the state primary school in Gazimagusa,…

  5. REVIEWS OF TOPICAL PROBLEMS: Analytic calculations on digital computers for applications in physics and mathematics

    NASA Astrophysics Data System (ADS)

    Gerdt, V. P.; Tarasov, O. V.; Shirkov, Dmitrii V.

    1980-01-01

    The present state of analytic calculations on computers is reviewed. Several programming systems which are used for analytic calculations are discussed: SCHOONSCHIP, CLAM, REDUCE-2, SYMBAL, CAMAL, AVTO-ANALITIK, MACSYMA, etc. It is shown that these systems can be used to solve a wide range of problems in physics and mathematics. Some physical applications are discussed in celestial mechanics, the general theory of relativity, quantum field theory, plasma physics, hydrodynamics, atomic and molecular physics, and quantum chemistry. Some mathematical applications which are discussed are evaluating indefinite integrals, solving differential equations, and analyzing mathematical expressions. This review is addressed to physicists and mathematicians working in a wide range of fields.

  6. Investigation of the computer experiences and attitudes of pre-service mathematics teachers: new evidence from Turkey.

    PubMed

    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.

  7. Design and Development Computer-Based E-Learning Teaching Material for Improving Mathematical Understanding Ability and Spatial Sense of Junior High School Students

    NASA Astrophysics Data System (ADS)

    Nurjanah; Dahlan, J. A.; Wibisono, Y.

    2017-02-01

    This paper aims to make a design and development computer-based e-learning teaching material for improving mathematical understanding ability and spatial sense of junior high school students. Furthermore, the particular aims are (1) getting teaching material design, evaluation model, and intrument to measure mathematical understanding ability and spatial sense of junior high school students; (2) conducting trials computer-based e-learning teaching material model, asessment, and instrument to develop mathematical understanding ability and spatial sense of junior high school students; (3) completing teaching material models of computer-based e-learning, assessment, and develop mathematical understanding ability and spatial sense of junior high school students; (4) resulting research product is teaching materials of computer-based e-learning. Furthermore, the product is an interactive learning disc. The research method is used of this study is developmental research which is conducted by thought experiment and instruction experiment. The result showed that teaching materials could be used very well. This is based on the validation of computer-based e-learning teaching materials, which is validated by 5 multimedia experts. The judgement result of face and content validity of 5 validator shows that the same judgement result to the face and content validity of each item test of mathematical understanding ability and spatial sense. The reliability test of mathematical understanding ability and spatial sense are 0,929 and 0,939. This reliability test is very high. While the validity of both tests have a high and very high criteria.

  8. Modeling Students' Problem Solving Performance in the Computer-Based Mathematics Learning Environment

    ERIC Educational Resources Information Center

    Lee, Young-Jin

    2017-01-01

    Purpose: The purpose of this paper is to develop a quantitative model of problem solving performance of students in the computer-based mathematics learning environment. Design/methodology/approach: Regularized logistic regression was used to create a quantitative model of problem solving performance of students that predicts whether students can…

  9. Mathematical and Computational Foundations of Recurrence Quantifications

    NASA Astrophysics Data System (ADS)

    Marwan, Norbert; Webber, Charles L.

    Real-world systems possess deterministic trajectories, phase singularities and noise. Dynamic trajectories have been studied in temporal and frequency domains, but these are linear approaches. Basic to the field of nonlinear dynamics is the representation of trajectories in phase space. A variety of nonlinear tools such as the Lyapunov exponent, Kolmogorov-Sinai entropy, correlation dimension, etc. have successfully characterized trajectories in phase space, provided the systems studied were stationary in time. Ubiquitous in nature, however, are systems that are nonlinear and nonstationary, existing in noisy environments all of which are assumption breaking to otherwise powerful linear tools. What has been unfolding over the last quarter of a century, however, is the timely discovery and practical demonstration that the recurrences of system trajectories in phase space can provide important clues to the system designs from which they derive. In this chapter we will introduce the basics of recurrence plots (RP) and their quantification analysis (RQA). We will begin by summarizing the concept of phase space reconstructions. Then we will provide the mathematical underpinnings of recurrence plots followed by the details of recurrence quantifications. Finally, we will discuss computational approaches that have been implemented to make recurrence strategies feasible and useful. As computers become faster and computer languages advance, younger generations of researchers will be stimulated and encouraged to capture nonlinear recurrence patterns and quantification in even better formats. This particular branch of nonlinear dynamics remains wide open for the definition of new recurrence variables and new applications untouched to date.

  10. 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…

  11. Sets, Probability and Statistics: The Mathematics of Life Insurance. [Computer Program.] Second Edition.

    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…

  12. A New Start for Mathematics Curriculum.

    ERIC Educational Resources Information Center

    Tucker, Alan

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

  13. Comparison of the Effects of Computer-Based Practice and Conceptual Understanding Interventions on Mathematics Fact Retention and Generalization

    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…

  14. Engineering physics and mathematics division

    NASA Astrophysics Data System (ADS)

    Sincovec, R. F.

    1995-07-01

    This report provides a record of the research activities of the Engineering Physics and Mathematics Division for the period 1 Jan. 1993 - 31 Dec. 1994. This report is the final archival record of the EPM Division. On 1 Oct. 1994, ORELA was transferred to Physics Division and on 1 Jan. 1995, the Engineering Physics and Mathematics Division and the Computer Applications Division reorganized to form the Computer Science and Mathematics Division and the Computational Physics and Engineering Division. Earlier reports in this series are identified on the previous pages, along with the progress reports describing ORNL's research in the mathematical sciences prior to 1984 when those activities moved into the Engineering Physics and Mathematics Division.

  15. A Computer-Based Game That Promotes Mathematics Learning More than a Conventional Approach

    ERIC Educational Resources Information Center

    McLaren, Bruce M.; Adams, Deanne M.; Mayer, Richard E.; Forlizzi, Jodi

    2017-01-01

    Excitement about learning from computer-based games has been papable in recent years and has led to the development of many educational games. However, there are relatively few sound empirical studies in the scientific literature that have shown the benefits of learning mathematics from games as opposed to more traditional approaches. The…

  16. Multiple-Choice versus Constructed-Response Tests in the Assessment of Mathematics Computation Skills.

    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…

  17. 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…

  18. Approach to Computer Implementation of Mathematical Model of 3-Phase Induction Motor

    NASA Astrophysics Data System (ADS)

    Pustovetov, M. Yu

    2018-03-01

    This article discusses the development of the computer model of an induction motor based on the mathematical model in a three-phase stator reference frame. It uses an approach that allows combining during preparation of the computer model dual methods: means of visual programming circuitry (in the form of electrical schematics) and logical one (in the form of block diagrams). The approach enables easy integration of the model of an induction motor as part of more complex models of electrical complexes and systems. The developed computer model gives the user access to the beginning and the end of a winding of each of the three phases of the stator and rotor. This property is particularly important when considering the asymmetric modes of operation or when powered by the special circuitry of semiconductor converters.

  19. Current problems in applied mathematics and mathematical physics

    NASA Astrophysics Data System (ADS)

    Samarskii, A. A.

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

  20. An Interdisciplinary Collaboration between Computer Engineering and Mathematics/Bilingual Education to Develop a Curriculum for Underrepresented Middle School Students

    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…

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

    NASA Astrophysics Data System (ADS)

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

    2013-06-01

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

  2. Evaluation of the Effectiveness of a Tablet Computer Application (App) in Helping Students with Visual Impairments Solve Mathematics Problems

    ERIC Educational Resources Information Center

    Beal, Carole R.; Rosenblum, L. Penny

    2018-01-01

    Introduction: The authors examined a tablet computer application (iPad app) for its effectiveness in helping students studying prealgebra to solve mathematical word problems. Methods: Forty-three visually impaired students (that is, those who are blind or have low vision) completed eight alternating mathematics units presented using their…

  3. Using the TouchMath Program to Teach Mathematical Computation to At-Risk Students and Students with Disabilities

    ERIC Educational Resources Information Center

    Ellingsen, Ryleigh; Clinton, Elias

    2017-01-01

    This manuscript reviews the empirical literature of the TouchMath© instructional program. The TouchMath© program is a commercial mathematics series that uses a dot notation system to provide multisensory instruction of computation skills. Using the program, students are taught to solve computational tasks in a multisensory manner that does not…

  4. Higher Mathematics Education at a Distance: The Use of Computers at the Open University of the Netherlands.

    ERIC Educational Resources Information Center

    Hummel, Hans G. K.; Smit, Herjan

    1996-01-01

    Describes mathematics courses developed for guided self-study at a distance. The courses incorporate new educational media and special didactic techniques. Provides details about how a computer can be used in such a setting, and focuses on a computer practical examination used for an advanced course in Fourier transforms. (27 references) (DDR)

  5. The Impact of Computer-Assisted Instruction on Mathematics Achievement of Underachieving Fifth-Grade Students

    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…

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

    NASA Astrophysics Data System (ADS)

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

    2013-12-01

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

  7. 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…

  8. A Meta-Analysis of the Effects of Computer Technology on School Students' Mathematics Learning

    ERIC Educational Resources Information Center

    Li, Qing; Ma, Xin

    2010-01-01

    This study examines the impact of computer technology (CT) on mathematics education in K-12 classrooms through a systematic review of existing literature. A meta-analysis of 85 independent effect sizes extracted from 46 primary studies involving a total of 36,793 learners indicated statistically significant positive effects of CT on mathematics…

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

    ERIC Educational Resources Information Center

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

    2016-01-01

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

  10. Improving the Fraction Word Problem Solving of Students with Mathematics Learning Disabilities: Interactive Computer Application

    ERIC Educational Resources Information Center

    Shin, Mikyung; Bryant, Diane P.

    2017-01-01

    Students with mathematics learning disabilities (MLD) have a weak understanding of fraction concepts and skills, which are foundations of algebra. Such students might benefit from computer-assisted instruction that utilizes evidence-based instructional components (cognitive strategies, feedback, virtual manipulatives). As a pilot study using a…

  11. Connecting Expectations and Values: Students' Perceptions of Developmental Mathematics in a Computer-Based Learning Environment

    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…

  12. Current research activities: Applied and numerical mathematics, fluid mechanics, experiments in transition and turbulence and aerodynamics, and computer science

    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.

  13. Uncertainty and variability in computational and mathematical models of cardiac physiology.

    PubMed

    Mirams, Gary R; Pathmanathan, Pras; Gray, Richard A; Challenor, Peter; Clayton, Richard H

    2016-12-01

    Mathematical and computational models of cardiac physiology have been an integral component of cardiac electrophysiology since its inception, and are collectively known as the Cardiac Physiome. We identify and classify the numerous sources of variability and uncertainty in model formulation, parameters and other inputs that arise from both natural variation in experimental data and lack of knowledge. The impact of uncertainty on the outputs of Cardiac Physiome models is not well understood, and this limits their utility as clinical tools. We argue that incorporating variability and uncertainty should be a high priority for the future of the Cardiac Physiome. We suggest investigating the adoption of approaches developed in other areas of science and engineering while recognising unique challenges for the Cardiac Physiome; it is likely that novel methods will be necessary that require engagement with the mathematics and statistics community. The Cardiac Physiome effort is one of the most mature and successful applications of mathematical and computational modelling for describing and advancing the understanding of physiology. After five decades of development, physiological cardiac models are poised to realise the promise of translational research via clinical applications such as drug development and patient-specific approaches as well as ablation, cardiac resynchronisation and contractility modulation therapies. For models to be included as a vital component of the decision process in safety-critical applications, rigorous assessment of model credibility will be required. This White Paper describes one aspect of this process by identifying and classifying sources of variability and uncertainty in models as well as their implications for the application and development of cardiac models. We stress the need to understand and quantify the sources of variability and uncertainty in model inputs, and the impact of model structure and complexity and their consequences for

  14. What Is Measured in Mathematics Tests? Construct Validity of Curriculum-Based Mathematics Measures.

    ERIC Educational Resources Information Center

    Thurber, Robin Schul; Shinn, Mark R.; Smolkowski, Keith

    2002-01-01

    Mathematics curriculum-based measurement (M-CBM) is one tool that has been developed for formative evaluation in mathematics. This study examines what constructs M-CBM actually measures in the context of a range of other mathematics measures. Results indicated that a two-factor model of mathematics where Computation and Applications were distinct…

  15. Pedagogical Factors Affecting Integration of Computers in Mathematics Instruction in Secondary Schools in Kenya

    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…

  16. 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

  17. Computer Mathematics Games and Conditions for Enhancing Young Children's Learning of Number Sense

    ERIC Educational Resources Information Center

    Kermani, Hengameh

    2017-01-01

    Purpose: The present study was designed to examine whether mathematics computer games improved young children's learning of number sense under three different conditions: when used individually, with a peer, and with teacher facilitation. Methodology: This study utilized a mixed methodology, collecting both quantitative and qualitative data. A…

  18. Inquiry Based-Computational Experiment, Acquisition of Threshold Concepts and Argumentation in Science and Mathematics Education

    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…

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

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

    NONE

    2013-07-01

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

  20. Investigating the Effects of Computer-Assisted Instruction on Achievement and Attitudes towards Mathematics among Seventh-Grade Students in Kuwait

    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…

  1. 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)

  2. Internationalizing the Mathematical Finance Course

    ERIC Educational Resources Information Center

    Okonkwo, Zephyrinus C.

    2017-01-01

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

  3. The Effect of Advisement and Competition on Transfer, Advisor Use, and Attitude toward Mathematics Using a Computer-Based Simulation Game.

    ERIC Educational Resources Information Center

    Van Eck, Richard

    This study looks at the roles that competition and context of advisement play in transfer, advisor use, attitude toward mathematics, and attitude toward instruction in a computer-based simulation game that required the use of mathematics skills. It is concluded that for transfer training, non-competitive simulation games might be the best choice,…

  4. Careers in Applied Mathematics and Computational Sciences.

    ERIC Educational Resources Information Center

    Society for Industrial and Applied Mathematics, Philadelphia, PA.

    This booklet provides some answers to questions on how mathematics is used in the world of work, what kinds of problems it solves, and why it is the key to so many careers, particularly to the jobs of the 21st century. Part of that preparation is mathematical knowledge, tools such as derivatives, probability, and matrices as well as central themes…

  5. Transitioning the GED[R] Mathematics Test to Computer with and without Accommodations: A Pilot Project

    ERIC Educational Resources Information Center

    Patterson, Margaret Becker; Higgins, Jennifer; Bozman, Martha; Katz, Michael

    2011-01-01

    We conducted a pilot study to see how the GED Mathematics Test could be administered on computer with embedded accessibility tools. We examined test scores and test-taker experience. Nineteen GED test centers across five states and 216 randomly assigned GED Tests candidates participated in the project. GED candidates completed two GED mathematics…

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

    USGS Publications Warehouse

    Iverson, Richard M.; LeVeque, Randall J.

    2009-01-01

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

  7. Mathematical and Computational Modeling for Tumor Virotherapy with Mediated Immunity.

    PubMed

    Timalsina, Asim; Tian, Jianjun Paul; Wang, Jin

    2017-08-01

    We propose a new mathematical modeling framework based on partial differential equations to study tumor virotherapy with mediated immunity. The model incorporates both innate and adaptive immune responses and represents the complex interaction among tumor cells, oncolytic viruses, and immune systems on a domain with a moving boundary. Using carefully designed computational methods, we conduct extensive numerical simulation to the model. The results allow us to examine tumor development under a wide range of settings and provide insight into several important aspects of the virotherapy, including the dependence of the efficacy on a few key parameters and the delay in the adaptive immunity. Our findings also suggest possible ways to improve the virotherapy for tumor treatment.

  8. An Analysis of Mathematics Interventions: Increased Time-on-Task Compared with Computer-Assisted Mathematics Instruction

    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…

  9. Mathematics and engineering in real life through mathematical competitions

    NASA Astrophysics Data System (ADS)

    More, M.

    2018-02-01

    We bring out an experience of organizing mathematical competitions that can be used as a medium to motivate the student and teacher minds in new directions of thinking. This can contribute to fostering research, innovation and provide a hands-on experience of mathematical concepts with the real world. Mathematical competitions can be used to build curiosity and give an understanding of mathematical applications in real life. Participation in the competition has been classified under four broad categories. Student can showcase their findings in various forms of expression like model, poster, soft presentation, animation, live performance, art and poetry. The basic focus of the competition is on using open source computation tools and modern technology, to emphasize the relationship of mathematical concepts with engineering applications in real life.

  10. Beyond Cognitive Increase: Investigating the Influence of Computer Programming on Perception and Application of Mathematical Skills

    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…

  11. The Talent Development Middle School. An Elective Replacement Approach to Providing Extra Help in Math--The CATAMA Program (Computer- and Team-Assisted Mathematics Acceleration). Report No. 21.

    ERIC Educational Resources Information Center

    Mac Iver, Douglas J.; Balfanz, Robert; Plank, Stephen B.

    In Talent Development Middle Schools, students needing extra help in mathematics participate in the Computer- and Team-Assisted Mathematics Acceleration (CATAMA) course. CATAMA is an innovative combination of computer-assisted instruction and structured cooperative learning that students receive in addition to their regular math course for about…

  12. The semantic system is involved in mathematical problem solving.

    PubMed

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

    2018-02-01

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

  13. 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…

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

    PubMed

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

    2005-05-01

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

  15. Cognitive Play and Mathematical Learning in Computer Microworlds.

    ERIC Educational Resources Information Center

    Steffe, Leslie P.; Wiegel, Heide G.

    1994-01-01

    Uses the constructivist principle of active learning to explore the possibly essential elements in transforming a cognitive play activity into mathematical activity. Suggests that for such transformation to occur, cognitive play activity must involve operations of intelligence that, yield situations of mathematical schemes. Illustrates the…

  16. 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.…

  17. Status Report: Mathematics Curriculum-Development Projects Today

    ERIC Educational Resources Information Center

    Arithmetic Teacher, 1972

    1972-01-01

    Brief reports on the Cambridge Conference on School Mathematics, Comprehensive School Mathematics Program, Computer-Assisted Instruction Projects at Stanford, Individually Prescribed Instruction Project, The Madison Project, Mathematics/Science Learning System, MINNEMAST, and School Mathematics Study Group. (MM)

  18. 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.

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

    NASA Astrophysics Data System (ADS)

    Mead, J.; Wright, G. B.

    2013-12-01

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

  20. Does the Computer-Assisted Remedial Mathematics Program at Kearny High School Lead to Improved Scores on the N.J. Early Warning Test?

    ERIC Educational Resources Information Center

    Schalago-Schirm, Cynthia

    Eighth-grade students in New Jersey take the Early Warning Test (EWT), which involves reading, writing, and mathematics. Students with EWT scores below the state level of competency take a remedial mathematics course that provides students with computer-assisted instruction (2 days per week) as well as regular classroom instruction (3 days per…

  1. 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.

  2. Introducing Laptops to Children: An Examination of Ubiquitous Computing in Grade 3 Reading, Language, and Mathematics

    ERIC Educational Resources Information Center

    Bernard, Robert M.; Bethel, Edward Clement; Abrami, Philip C.; Wade, C. Anne

    2007-01-01

    This study examines the achievement outcomes accompanying the implementation of a Grade 3 laptop or so-­called "ubiquitous computing" program in a Quebec school district. CAT­3 reading, language, and mathematics batteries were administered at the end of Grade 2 and again at the end of Grade 3, after the first year of computer…

  3. The mathematics of a quantum Hamiltonian computing half adder Boolean logic gate.

    PubMed

    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.

  4. 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.

  5. 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.

  6. High-Productivity Computing in Computational Physics Education

    NASA Astrophysics Data System (ADS)

    Tel-Zur, Guy

    2011-03-01

    We describe the development of a new course in Computational Physics at the Ben-Gurion University. This elective course for 3rd year undergraduates and MSc. students is being taught during one semester. Computational Physics is by now well accepted as the Third Pillar of Science. This paper's claim is that modern Computational Physics education should deal also with High-Productivity Computing. The traditional approach of teaching Computational Physics emphasizes ``Correctness'' and then ``Accuracy'' and we add also ``Performance.'' Along with topics in Mathematical Methods and case studies in Physics the course deals a significant amount of time with ``Mini-Courses'' in topics such as: High-Throughput Computing - Condor, Parallel Programming - MPI and OpenMP, How to build a Beowulf, Visualization and Grid and Cloud Computing. The course does not intend to teach neither new physics nor new mathematics but it is focused on an integrated approach for solving problems starting from the physics problem, the corresponding mathematical solution, the numerical scheme, writing an efficient computer code and finally analysis and visualization.

  7. Mathematical model for steady state, simple ampholyte isoelectric focusing: Development, computer simulation and implementation

    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.

  8. 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)

  9. Promoting Transfer of Mathematics Skills through the Use of a Computer-Based Instructional Simulation Game and Advisement.

    ERIC Educational Resources Information Center

    Van Eck, Richard

    This study looked at the effect of contextual advisement and competition on transfer of mathematics skills in a computer-based instructional simulation game and simulation in which game participants helped their "aunt and uncle" fix up a house. Competition referred to whether or not the participant was playing against a computer…

  10. Primary Trainee Teachers' Attitudes to and Use of Computer and Technology in Mathematics: The Case of Turkey

    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…

  11. Mathematical and computational model for the analysis of micro hybrid rocket motor

    NASA Astrophysics Data System (ADS)

    Stoia-Djeska, Marius; Mingireanu, Florin

    2012-11-01

    The hybrid rockets use a two-phase propellant system. In the present work we first develop a simplified model of the coupling of the hybrid combustion process with the complete unsteady flow, starting from the combustion port and ending with the nozzle. The physical and mathematical model are adapted to the simulations of micro hybrid rocket motors. The flow model is based on the one-dimensional Euler equations with source terms. The flow equations and the fuel regression rate law are solved in a coupled manner. The platform of the numerical simulations is an implicit fourth-order Runge-Kutta second order cell-centred finite volume method. The numerical results obtained with this model show a good agreement with published experimental and numerical results. The computational model developed in this work is simple, computationally efficient and offers the advantage of taking into account a large number of functional and constructive parameters that are used by the engineers.

  12. Revisiting Mathematics Manipulative Materials

    ERIC Educational Resources Information Center

    Swan, Paul; Marshall, Linda

    2010-01-01

    It is over 12 years since "APMC" published Bob Perry and Peter Howard's research on the use of mathematics manipulative materials in primary mathematics classrooms. Since then the availability of virtual manipulatives and associated access to computers and interactive whiteboards have caused educators to rethink the use of mathematics…

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

    NASA Astrophysics Data System (ADS)

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

    2009-05-01

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

  14. Explicating Mathematical Thinking in Differential Equations Using a Computer Algebra System

    ERIC Educational Resources Information Center

    Zeynivandnezhad, Fereshteh; Bates, Rachel

    2018-01-01

    The importance of developing students' mathematical thinking is frequently highlighted in literature regarding the teaching and learning of mathematics. Despite this importance, most curricula and instructional activities for undergraduate mathematics fail to bring the learner beyond the mathematics. The purpose of this study was to enhance…

  15. Discrete Mathematics Course Supported by CAS MATHEMATICA

    ERIC Educational Resources Information Center

    Ivanov, O. A.; Ivanova, V. V.; Saltan, A. A.

    2017-01-01

    In this paper, we discuss examples of assignments for a course in discrete mathematics for undergraduate students majoring in business informatics. We consider several problems with computer-based solutions and discuss general strategies for using computers in teaching mathematics and its applications. In order to evaluate the effectiveness of our…

  16. Orthogonal Reflections on Computer Microworlds, Constructivism, Play and Mathematical Understanding.

    ERIC Educational Resources Information Center

    Kieren, Thomas E.

    1994-01-01

    Comments on the Fractions Project presented in this same issue. Discusses two major ideas: the construction of mathematics of children and its basis and playful actions as a basis for mathematical actions. Highlights the understanding of children's mathematical concepts and schemes as they grow and are organized in the context of computer…

  17. What is the Role of Mathematics Education in the Computer Age?

    ERIC Educational Resources Information Center

    Popp, Jerome A.

    1986-01-01

    Proposes that the role of mathematics education be re-examined in terms of an increased emphasis on mathematical knowledge rather than attainment of calculational speed. Offers perspectives on the reform movement in mathematics education and advocates the teaching of the history, logic, and method of mathematical thinking. (ML)

  18. 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…

  19. Business Mathematics Curriculum Guide.

    ERIC Educational Resources Information Center

    Ebersole, Benjamin P., Comp.; And Others

    This revised course in business mathematics emphasizes computations needed for problem solving, but greater attention is focused on mathematical principles that were developed in previous grades. In addition, the course aims to develop further an understanding of business principles and practices which can be used in gainful employment and in the…

  20. The Development of an Individualized Instructional Program in Beginning College Mathematics Utilizing Computer Based Resource Units. Final Report.

    ERIC Educational Resources Information Center

    Rockhill, Theron D.

    Reported is an attempt to develop and evaluate an individualized instructional program in pre-calculus college mathematics. Four computer based resource units were developed in the areas of set theory, relations and function, algebra, trigonometry, and analytic geometry. Objectives were determined by experienced calculus teachers, and…

  1. a Discrete Mathematical Model to Simulate Malware Spreading

    NASA Astrophysics Data System (ADS)

    Del Rey, A. Martin; Sánchez, G. Rodriguez

    2012-10-01

    With the advent and worldwide development of Internet, the study and control of malware spreading has become very important. In this sense, some mathematical models to simulate malware propagation have been proposed in the scientific literature, and usually they are based on differential equations exploiting the similarities with mathematical epidemiology. The great majority of these models study the behavior of a particular type of malware called computer worms; indeed, to the best of our knowledge, no model has been proposed to simulate the spreading of a computer virus (the traditional type of malware which differs from computer worms in several aspects). In this sense, the purpose of this work is to introduce a new mathematical model not based on continuous mathematics tools but on discrete ones, to analyze and study the epidemic behavior of computer virus. Specifically, cellular automata are used in order to design such model.

  2. BIBLIOGRAPHIES, HIGH SCHOOL MATHEMATICS.

    ERIC Educational Resources Information Center

    WOODS, PAUL E.

    THIS ANNOTATED BIBLIOGRAPHY IS A COMPILATION OF A NUMBER OF HIGHLY REGARDED BOOK LISTS CONSISTING OF LIBRARY BOOKS AND TEXTBOOKS FOR GRADES 7-12. THE BOOKS IN THIS LIST ARE CURRENTLY IN PRINT AND THE CONTENT IS REPRESENTATIVE OF THE FOLLOWING AREAS OF MATHEMATICS--MATHEMATICAL RECREATION, COMPUTERS, ARITHMETIC, ALGEBRA, EUCLIDEAN GEOMETRY,…

  3. The Identification, Implementation, and Evaluation of Critical User Interface Design Features of Computer-Assisted Instruction Programs in Mathematics for Students with Learning Disabilities

    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…

  4. Effectiveness of Computer Animation and Geometrical Instructional Model on Mathematics Achievement and Retention among Junior Secondary School Students

    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…

  5. 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…

  6. Prospects of a mathematical theory of human behavior in complex man-machine systems tasks. [time sharing computer analogy of automobile driving

    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.

  7. An Exploratory Case Study of Computer Use in a Primary School Mathematics Classroom: New Technology, New Pedagogy? Research: Information and Communication Technologies

    ERIC Educational Resources Information Center

    Hardman, Joanne

    2005-01-01

    Because computers potentially transform pedagogy, much has been made of their ability to impact positively on student performance, particularly in subjects such as mathematics and science. However, there is currently a dearth of research regarding exactly how the computer acts as a transformative tool in disadvantaged schools. Drawing on a…

  8. Transactions of the Army Conference on Applied Mathematics and Computing (6th) Held in Boulder, Colorado on 31 May - 3 June 1988

    DTIC Science & Technology

    1989-02-01

    North American algebraists, in academic mathematics departments, appear to have computer anxiety or computation anxiety . Conferences and...the Heaviside function of S[4,51. H(S)[(p+ Vov] =0 (1) D H(S)[ HRv + Vp = 0 (2) Dt where D 8 a -- = +3- (3) We nondimensionalize the equations by using

  9. The Effects of a Computer-Assisted Teaching Material, Designed According to the ASSURE Instructional Design and the ARCS Model of Motivation, on Students' Achievement Levels in a Mathematics Lesson and Their Resulting Attitudes

    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…

  10. Winning the Popularity Contest: Researcher Preference When Selecting Resources for Civil Engineering, Computer Science, Mathematics and Physics Dissertations

    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…

  11. Application of Mathematical and Three-Dimensional Computer Modeling Tools in the Planning of Processes of Fuel and Energy Complexes

    NASA Astrophysics Data System (ADS)

    Aksenova, Olesya; Nikolaeva, Evgenia; Cehlár, Michal

    2017-11-01

    This work aims to investigate the effectiveness of mathematical and three-dimensional computer modeling tools in the planning of processes of fuel and energy complexes at the planning and design phase of a thermal power plant (TPP). A solution for purification of gas emissions at the design development phase of waste treatment systems is proposed employing mathematical and three-dimensional computer modeling - using the E-nets apparatus and the development of a 3D model of the future gas emission purification system. Which allows to visualize the designed result, to select and scientifically prove economically feasible technology, as well as to ensure the high environmental and social effect of the developed waste treatment system. The authors present results of a treatment of planned technological processes and the system for purifying gas emissions in terms of E-nets. using mathematical modeling in the Simulink application. What allowed to create a model of a device from the library of standard blocks and to perform calculations. A three-dimensional model of a system for purifying gas emissions has been constructed. It allows to visualize technological processes and compare them with the theoretical calculations at the design phase of a TPP and. if necessary, make adjustments.

  12. 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…

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

    ERIC Educational Resources Information Center

    Coddington, Lorelei R.

    2014-01-01

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

  14. 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…

  15. A Functional Analytic Approach To Computer-Interactive Mathematics

    PubMed Central

    2005-01-01

    Following a pretest, 11 participants who were naive with regard to various algebraic and trigonometric transformations received an introductory lecture regarding the fundamentals of the rectangular coordinate system. Following the lecture, they took part in a computer-interactive matching-to-sample procedure in which they received training on particular formula-to-formula and formula-to-graph relations as these formulas pertain to reflections and vertical and horizontal shifts. In training A-B, standard formulas served as samples and factored formulas served as comparisons. In training B-C, factored formulas served as samples and graphs served as comparisons. Subsequently, the program assessed for mutually entailed B-A and C-B relations as well as combinatorially entailed C-A and A-C relations. After all participants demonstrated mutual entailment and combinatorial entailment, we employed a test of novel relations to assess 40 different and complex variations of the original training formulas and their respective graphs. Six of 10 participants who completed training demonstrated perfect or near-perfect performance in identifying novel formula-to-graph relations. Three of the 4 participants who made more than three incorrect responses during the assessment of novel relations showed some commonality among their error patterns. Derived transfer of stimulus control using mathematical relations is discussed. PMID:15898471

  16. A functional analytic approach to computer-interactive mathematics.

    PubMed

    Ninness, Chris; Rumph, Robin; McCuller, Glen; Harrison, Carol; Ford, Angela M; Ninness, Sharon K

    2005-01-01

    Following a pretest, 11 participants who were naive with regard to various algebraic and trigonometric transformations received an introductory lecture regarding the fundamentals of the rectangular coordinate system. Following the lecture, they took part in a computer-interactive matching-to-sample procedure in which they received training on particular formula-to-formula and formula-to-graph relations as these formulas pertain to reflections and vertical and horizontal shifts. In training A-B, standard formulas served as samples and factored formulas served as comparisons. In training B-C, factored formulas served as samples and graphs served as comparisons. Subsequently, the program assessed for mutually entailed B-A and C-B relations as well as combinatorially entailed C-A and A-C relations. After all participants demonstrated mutual entailment and combinatorial entailment, we employed a test of novel relations to assess 40 different and complex variations of the original training formulas and their respective graphs. Six of 10 participants who completed training demonstrated perfect or near-perfect performance in identifying novel formula-to-graph relations. Three of the 4 participants who made more than three incorrect responses during the assessment of novel relations showed some commonality among their error patterns. Derived transfer of stimulus control using mathematical relations is discussed.

  17. Longitudinal associations between reading and mathematics achievement.

    PubMed

    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.

  18. The Language Factor in Elementary Mathematics Assessments: Computational Skills and Applied Problem Solving in a Multidimensional IRT Framework

    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…

  19. 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…

  20. 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.

  1. An Evaluation into the Views of Candidate Mathematics Teachers over "Tablet Computers" to be Applied in Secondary Schools

    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…

  2. The Effect of Using Computer Games in Teaching Mathematics on Developing the Number Sense of Fourth Grade Students

    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…

  3. Turbine Engine Mathematical Model Validation

    DTIC Science & Technology

    1976-12-01

    AEDC-TR-76-90 ~Ec i ? Z985 TURBINE ENGINE MATHEMATICAL MODEL VALIDATION ENGINE TEST FACILITY ARNOLD ENGINEERING DEVELOPMENT CENTER AIR FORCE...i f n e c e s e a ~ ~ d i den t i f y by b l ock number) YJI01-GE-100 engine turbine engines mathematical models computations mathematical...report presents and discusses the results of an investigation to develop a rationale and technique for the validation of turbine engine steady-state

  4. Implementing an Effective Mathematics Fact Fluency Practice Activity

    ERIC Educational Resources Information Center

    Riccomini, Paul J.; Stocker, James D., Jr.; Morano, Stephanie

    2017-01-01

    Proficiency in mathematics involves the seamless synchronization of conceptual understanding, procedural knowledge, computational fluency, and problem solving (NMAP, 2008). Clearly, fluency with mathematics facts is one element embedded within mathematical proficiency and important for students with disabilities to develop. As more and more…

  5. Introducing Seismic Tomography with Computational Modeling

    NASA Astrophysics Data System (ADS)

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

    2011-12-01

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

  6. Discrete Mathematics in the Schools. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Volume 36.

    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…

  7. Secondary Schools Curriculum Guide, Mathematics, Grades 10-12. Revised.

    ERIC Educational Resources Information Center

    Cranston School Dept., RI.

    Behavioral objectives for grades 10 through 12 are specified for plane geometry, algebra, general mathematics, computer mathematics, slide rule mathematics, basic college mathematics, trigonometry, analytic geometry, calculus and probability. Most sections present material in terms of portions of a school year. At least one major objective is…

  8. The reality 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.

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

    ERIC Educational Resources Information Center

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

    2017-01-01

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

  10. Mathematics reflecting sensorimotor organization.

    PubMed

    McCollum, Gin

    2003-02-01

    This review combines short presentations of several mathematical approaches that conceptualize issues in sensorimotor neuroscience from different perspectives and levels of analysis. The intricate organization of neural structures and sensorimotor performance calls for characterization using a variety of mathematical approaches. This review points out the prospects for mathematical neuroscience: in addition to computational approaches, there is a wide variety of mathematical approaches that provide insight into the organization of neural systems. By starting from the perspective that provides the greatest clarity, a mathematical approach avoids specificity that is inaccurate in characterizing the inherent biological organization. Approaches presented include the mathematics of ordered structures, motion-phase space, subject-coincident coordinates, equivalence classes, topological biodynamics, rhythm space metric, and conditional dynamics. Issues considered in this paper include unification of levels of analysis, response equivalence, convergence, relationship of physics to motor control, support of rhythms, state transitions, and focussing on low-dimensional subspaces of a high-dimensional sensorimotor space.

  11. Differences in the Mathematics-Vocabulary Knowledge of Fifth-Grade Students with and without Learning Difficulties

    ERIC Educational Resources Information Center

    Forsyth, Suzanne R.; Powell, Sarah R.

    2017-01-01

    The purpose of this pilot study was to explore the impact of mathematics and reading learning difficulties on the mathematics-vocabulary understanding of fifth-grade students. Students (n = 114) completed three measures: mathematics computation, general vocabulary, and mathematics vocabulary. Based on performance on the mathematics computation and…

  12. 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…

  13. 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…

  14. Learning to Calculate and Learning Mathematics.

    ERIC Educational Resources Information Center

    Fearnley-Sander, Desmond

    1980-01-01

    A calculator solution of a simple computational problem is discussed with emphasis on its ramifications for the understanding of some fundamental theorems of pure mathematics and techniques of computing. (Author/MK)

  15. 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.…

  16. The Effects of Computer Programming on High School Students' Reasoning Skills and Mathematical Self-Efficacy and Problem Solving

    ERIC Educational Resources Information Center

    Psycharis, Sarantos; Kallia, Maria

    2017-01-01

    In this paper we investigate whether computer programming has an impact on high school student's reasoning skills, problem solving and self-efficacy in Mathematics. The quasi-experimental design was adopted to implement the study. The sample of the research comprised 66 high school students separated into two groups, the experimental and the…

  17. Effects of Using a Computer Algebra System (CAS) on Junior College Students' Attitudes towards CAS and Achievement in Mathematics

    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…

  18. A preoperative mathematic model for computed tomographic guided microwave ablation treatment of hepatic dome tumors.

    PubMed

    Gao, Fei; Wang, Guo-Bao; Xiang, Zhan-Wang; Yang, Bin; Xue, Jing-Bing; Mo, Zhi-Qiang; Zhong, Zhi-Hui; Zhang, Tao; Zhang, Fu-Jun; Fan, Wei-Jun

    2016-05-03

    This study sought to prospectively evaluate the feasibility and safety of a preoperative mathematic model for computed tomographic(CT) guided microwave(MW) ablation treatment of hepatic dome tumors. This mathematic model was a regular cylinder quantifying appropriate puncture routes from the bottom up. A total of 103 patients with hepatic dome tumors were enrolled and randomly divided into 2 groups based on whether this model was used or not: Group A (using the model; n = 43) versus Group B (not using the model; n = 60). All tumors were treated by CT-guided MW ablation and follow-up contrast CT were reviewed. The average number of times for successful puncture, average ablation time, and incidence of right shoulder pain were less in Group A than Group B (1.4 vs. 2.5, P = 0.001; 8.8 vs. 11.1 minutes, P = 0.003; and 4.7% vs. 20%, P = 0.039). The technical success rate was higher in Group A than Group B (97.7% vs. 85.0%, P = 0.032). There were no significant differences between the two groups in primary and secondary technique efficacy rates (97.7% vs. 88.3%, P = 0.081; 90.0% vs. 72.7%, P = 0.314). No major complications occurred in both groups. The mathematic model of regular cylinder is feasible and safe for CT-guided MW ablation in treating hepatic dome tumors.

  19. Integrating First-Year Technology and Finite Mathematics Courses

    ERIC Educational Resources Information Center

    Shafii-Mousavi, Morteza; Kochanowski, Paul

    2006-01-01

    This paper describes an interdisciplinary project-based mathematics course linked to a computer technology course. The linkage encourages an appreciation of mathematics and technology as students see an immediate use for these skills in completing actual real-world projects. Linking mathematics and technology integrates subjects taught in…

  20. Symbolic-Graphical Calculators: Teaching Tools for Mathematics.

    ERIC Educational Resources Information Center

    Dick, Thomas P.

    1992-01-01

    Explores the role that symbolic-graphical calculators can play in the current calls for reform in the mathematics curriculum. Discusses symbolic calculators and graphing calculators in relation to problem solving, computational skills, and mathematics instruction. (MDH)

  1. Competence with Fractions Predicts Gains in Mathematics Achievement

    PubMed Central

    Bailey, Drew H.; Hoard, Mary K.; Nugent, Lara; Geary, David C.

    2012-01-01

    Competence with fractions predicts later mathematics achievement, but the co-developmental pattern between fractions knowledge and mathematics achievement is not well understood. We assessed this co-development through examination of the cross-lagged relation between a measure of conceptual knowledge of fractions and mathematics achievement in sixth and seventh grade (n = 212). The cross-lagged effects indicated that performance on the sixth grade fractions concepts measure predicted one year gains in mathematics achievement (β = .14, p<.01), controlling for the central executive component of working memory and intelligence, but sixth grade mathematics achievement did not predict gains on the fractions concepts measure (β = .03, p>.50). In a follow-up assessment, we demonstrated that measures of fluency with computational fractions significantly predicted seventh grade mathematics achievement above and beyond the influence of fluency in computational whole number arithmetic, performance on number fluency and number line tasks, and central executive span and intelligence. Results provide empirical support for the hypothesis that competence with fractions underlies, in part, subsequent gains in mathematics achievement. PMID:22832199

  2. Competence with fractions predicts gains in mathematics achievement.

    PubMed

    Bailey, Drew H; Hoard, Mary K; Nugent, Lara; Geary, David C

    2012-11-01

    Competence with fractions predicts later mathematics achievement, but the codevelopmental pattern between fractions knowledge and mathematics achievement is not well understood. We assessed this codevelopment through examination of the cross-lagged relation between a measure of conceptual knowledge of fractions and mathematics achievement in sixth and seventh grades (N=212). The cross-lagged effects indicated that performance on the sixth grade fractions concepts measure predicted 1-year gains in mathematics achievement (ß=.14, p<.01), controlling for the central executive component of working memory and intelligence, but sixth grade mathematics achievement did not predict gains on the fractions concepts measure (ß=.03, p>.50). In a follow-up assessment, we demonstrated that measures of fluency with computational fractions significantly predicted seventh grade mathematics achievement above and beyond the influence of fluency in computational whole number arithmetic, performance on number fluency and number line tasks, central executive span, and intelligence. Results provide empirical support for the hypothesis that competence with fractions underlies, in part, subsequent gains in mathematics achievement. Copyright © 2012 Elsevier Inc. All rights reserved.

  3. 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…

  4. 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.

  5. 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,…

  6. Cross-Age Peer Tutoring and Fluency-Based Instruction to Achieve Fluency with Mathematics Computation Skills: A Randomized Controlled Trial

    ERIC Educational Resources Information Center

    Greene, Irene; Mc Tiernan, Aoife; Holloway, Jennifer

    2018-01-01

    The current study employed a randomized controlled trial to evaluate the use of peer tutoring and fluency-based instruction to increase mathematics fluency with addition and subtraction computation skills. Forty-one elementary school students between the ages of eight and 12 years participated in the 8-week study using cross-age peer tutoring, Say…

  7. Current problems in applied mathematics and mathematical modeling

    NASA Astrophysics Data System (ADS)

    Alekseev, A. S.

    Papers are presented on mathematical modeling noting applications to such fields as geophysics, chemistry, atmospheric optics, and immunology. Attention is also given to models of ocean current fluxes, atmospheric and marine interactions, and atmospheric pollution. The articles include studies of catalytic reactors, models of global climate phenomena, and computer-assisted atmospheric models.

  8. Using Two Languages when Learning Mathematics

    ERIC Educational Resources Information Center

    Moschkovich, Judit

    2007-01-01

    This article reviews two sets of research studies from outside of mathematics education to consider how they may be relevant to the study of bilingual mathematics learners using two languages. The first set of studies is psycholinguistics experiments comparing monolinguals and bilinguals using two languages during arithmetic computation (language…

  9. Discrete mathematics course supported by CAS MATHEMATICA

    NASA Astrophysics Data System (ADS)

    Ivanov, O. A.; Ivanova, V. V.; Saltan, A. A.

    2017-08-01

    In this paper, we discuss examples of assignments for a course in discrete mathematics for undergraduate students majoring in business informatics. We consider several problems with computer-based solutions and discuss general strategies for using computers in teaching mathematics and its applications. In order to evaluate the effectiveness of our approach, we conducted an anonymous survey. The results of the survey provide evidence that our approach contributes to high outcomes and aligns with the course aims and objectives.

  10. The Greatest Mathematical Discovery?

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

    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 aboutmore » 500 CE.« less

  11. 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…

  12. 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…

  13. Understanding Teachers' Attitudes to Change in a LogoMathematics Environment.

    ERIC Educational Resources Information Center

    Moreira, Candida; Noss, Richard

    1995-01-01

    Describes and analyzes attitudes of two Portuguese elementary teachers toward mathematics, mathematics teaching, and use of computers in instruction. Semistructured interviews and questionnaires, before and after an inservice LOGO computer course, showed that both teachers changed their attitude, but only one implemented her ideas in teaching. (20…

  14. A preoperative mathematic model for computed tomographic guided microwave ablation treatment of hepatic dome tumors

    PubMed Central

    Yang, Bin; Xue, Jing-Bing; Mo, Zhi-Qiang; Zhong, Zhi-Hui; Zhang, Tao; Zhang, Fu-Jun; Fan, Wei-Jun

    2016-01-01

    Purpose This study sought to prospectively evaluate the feasibility and safety of a preoperative mathematic model for computed tomographic(CT) guided microwave(MW) ablation treatment of hepatic dome tumors. Methods This mathematic model was a regular cylinder quantifying appropriate puncture routes from the bottom up. A total of 103 patients with hepatic dome tumors were enrolled and randomly divided into 2 groups based on whether this model was used or not: Group A (using the model; n = 43) versus Group B (not using the model; n = 60). All tumors were treated by CT-guided MW ablation and follow-up contrast CT were reviewed. Results The average number of times for successful puncture, average ablation time, and incidence of right shoulder pain were less in Group A than Group B (1.4 vs. 2.5, P = 0.001; 8.8 vs. 11.1 minutes, P = 0.003; and 4.7% vs. 20%, P = 0.039). The technical success rate was higher in Group A than Group B (97.7% vs. 85.0%, P = 0.032). There were no significant differences between the two groups in primary and secondary technique efficacy rates (97.7% vs. 88.3%, P = 0.081; 90.0% vs. 72.7%, P = 0.314). No major complications occurred in both groups. Conclusion The mathematic model of regular cylinder is feasible and safe for CT-guided MW ablation in treating hepatic dome tumors. PMID:27028994

  15. 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.

  16. 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)

  17. Mathematical Visualization

    ERIC Educational Resources Information Center

    Rogness, Jonathan

    2011-01-01

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

  18. 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.

  19. The justification of mathematical statements.

    PubMed

    Swinnerton-Dyer, Peter

    2005-10-15

    The uncompromising ethos of pure mathematics in the early post-war period was that any theorem should be provided with a proof which the reader could and should check. Two things have made this no longer realistic: (i) the appearance of increasingly long and complicated proofs and (ii) the involvement of computers. This paper discusses what compromises the mathematical community needs to make as a result.

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

    PubMed

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

    2010-01-01

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

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

    PubMed Central

    Davies, Robin; Hodge, Terrell; Enyedi, Alexander

    2010-01-01

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

  2. Algorithms in Modern Mathematics and Computer Science.

    DTIC Science & Technology

    1980-01-01

    importance, since we will go on doing what we are doing no matter what it is called; after all, other disciplines like Mathematics and Chemistry are no...longer related very strongly to the etymology of their names. However, if I had a chance to vote for the name of my own discipline, I would choose to call

  3. 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,…

  4. Computer simulation of the mathematical modeling involved in constitutive equation development: Via symbolic computations

    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.

  5. 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…

  6. Mathematical form models of tree trunks

    Treesearch

    Rudolfs Ozolins

    2000-01-01

    Assortment structure analysis of tree trunks is a characteristic and proper problem that can be solved by using mathematical modeling and standard computer programs. Mathematical form model of tree trunks consists of tapering curve equations and their parameters. Parameters for nine species were obtained by processing measurements of 2,794 model trees and studying the...

  7. 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…

  8. Computing the stability of steady-state solutions of mathematical models of the electrical activity in the heart.

    PubMed

    Tveito, Aslak; Skavhaug, Ola; Lines, Glenn T; Artebrant, Robert

    2011-08-01

    Instabilities in the electro-chemical resting state of the heart can generate ectopic waves that in turn can initiate arrhythmias. We derive methods for computing the resting state for mathematical models of the electro-chemical process underpinning a heartbeat, and we estimate the stability of the resting state by invoking the largest real part of the eigenvalues of a linearized model. The implementation of the methods is described and a number of numerical experiments illustrate the feasibility of the methods. In particular, we test the methods for problems where we can compare the solutions with analytical results, and problems where we have solutions computed by independent software. The software is also tested for a fairly realistic 3D model. Copyright © 2011 Elsevier Ltd. All rights reserved.

  9. 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…

  10. 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…

  11. Environmental Studies: Mathematical, Computational and Statistical Analyses

    DTIC Science & Technology

    1993-03-03

    mathematical analysis addresses the seasonally and longitudinally averaged circulation which is under the influence of a steady forcing located asymmetrically...employed, as has been suggested for some situations. A general discussion of how interfacial phenomena influence both the original contamination process...describing the large-scale advective and dispersive behaviour of contaminants transported by groundwater and the uncertainty associated with field-scale

  12. Modellus: Learning Physics with Mathematical Modelling

    NASA Astrophysics Data System (ADS)

    Teodoro, Vitor

    Computers are now a major tool in research and development in almost all scientific and technological fields. Despite recent developments, this is far from true for learning environments in schools and most undergraduate studies. This thesis proposes a framework for designing curricula where computers, and computer modelling in particular, are a major tool for learning. The framework, based on research on learning science and mathematics and on computer user interface, assumes that: 1) learning is an active process of creating meaning from representations; 2) learning takes place in a community of practice where students learn both from their own effort and from external guidance; 3) learning is a process of becoming familiar with concepts, with links between concepts, and with representations; 4) direct manipulation user interfaces allow students to explore concrete-abstract objects such as those of physics and can be used by students with minimal computer knowledge. Physics is the science of constructing models and explanations about the physical world. And mathematical models are an important type of models that are difficult for many students. These difficulties can be rooted in the fact that most students do not have an environment where they can explore functions, differential equations and iterations as primary objects that model physical phenomena--as objects-to-think-with, reifying the formal objects of physics. The framework proposes that students should be introduced to modelling in a very early stage of learning physics and mathematics, two scientific areas that must be taught in very closely related way, as they were developed since Galileo and Newton until the beginning of our century, before the rise of overspecialisation in science. At an early stage, functions are the main type of objects used to model real phenomena, such as motions. At a later stage, rates of change and equations with rates of change play an important role. This type of equations

  13. The effects of home computer access and social capital on mathematics and science achievement among Asian-American high school students in the NELS:88 data set

    NASA Astrophysics Data System (ADS)

    Quigley, Mark Declan

    The purpose of this researcher was to examine specific environmental, educational, and demographic factors and their influence on mathematics and science achievement. In particular, the researcher ascertained the interconnections of home computer access and social capital, with Asian American students and the effect on mathematics and science achievement. Coleman's theory on social capital and parental influence was used as a basis for the analysis of data. Subjects for this study were the base year students from the National Education Longitudinal Study of 1988 (NELS:88) and the subsequent follow-up survey data in 1990, 1992, and 1994. The approximate sample size for this study is 640 ethnic Asians from the NELS:88 database. The analysis was a longitudinal study based on the Student and Parent Base Year responses and the Second Follow-up survey of 1992, when the subjects were in 12th grade. Achievement test results from the NELS:88 data were used to measure achievement in mathematics and science. The NELS:88 test battery was developed to measure both individual status and a student's growth in a number of achievement areas. The subject's responses were analyzed by principal components factor analysis, weights, effect sizes, hierarchial regression analysis, and PLSPath Analysis. The results of this study were that prior ability in mathematics and science is a major influence in the student's educational achievement. Findings from the study support the view that home computer access has a negative direct effect on mathematics and science achievement for both Asian American males and females. None of the social capital factors in the study had either a negative or positive direct effect on mathematics and science achievement although some indirect effects were found. Suggestions were made toward increasing parental involvement in their children's academic endeavors. Computer access in the home should be considered related to television viewing and should be closely

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

    ERIC Educational Resources Information Center

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

    2016-01-01

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

  15. Computer Simulations: Inelegant Mathematics and Worse Social Science?

    ERIC Educational Resources Information Center

    Alker, Hayward R., Jr.

    1974-01-01

    Achievements, limitations, and difficulties of social science simulation efforts are discussed with particular reference to three examples. The pedagogical use of complementary developmental, philosophical, mathematical, and scientific approaches is advocated to minimize potential abuses of social simulation research. (LS)

  16. Improving Pupils' Mathematical Communication Abilities through Computer-Supported Reciprocal Peer Tutoring

    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…

  17. Performance on Monitoring Basic Skills Progress--Computation Probes in First, Second, and Third Grade: Is It a Predictor of Pennsylvania System of School Assessment Mathematics Achievement in Third Grade?

    ERIC Educational Resources Information Center

    Campbell, Adelle C.

    2017-01-01

    This study examined the predictive relationship of a brief computation measure administered in the fall, winter, and spring of first, second, and third grade with the mathematic portion of a state-mandated academic achievement test administered in the spring of third grade. The relationship between mathematical achievement and resource…

  18. A Mathematical Theory of System Information Flow

    DTIC Science & Technology

    2016-06-27

    AFRL-AFOSR-VA-TR-2016-0232 A Mathematical Theory of System Information Flow Michael Mislove ADMINISTRATORS OF THE TULANE EDUCATIONAL FUND THE 6823...MM-YYYY) 17-06-2016 2. REPORT TYPE Final 3. DATES COVERED (From - To) 27MAR2013 - 31MAR2016 4. TITLE AND SUBTITLE A Mathematical Theory of System...systems using techniques from information theory , domain theory and other areas of mathematics and computer science. Over time, the focus shifted

  19. Mathematics of Computed Tomography

    NASA Astrophysics Data System (ADS)

    Hawkins, William Grant

    A review of the applications of the Radon transform is presented, with emphasis on emission computed tomography and transmission computed tomography. The theory of the 2D and 3D Radon transforms, and the effects of attenuation for emission computed tomography are presented. The algebraic iterative methods, their importance and limitations are reviewed. Analytic solutions of the 2D problem the convolution and frequency filtering methods based on linear shift invariant theory, and the solution of the circular harmonic decomposition by integral transform theory--are reviewed. The relation between the invisible kernels, the inverse circular harmonic transform, and the consistency conditions are demonstrated. The discussion and review are extended to the 3D problem-convolution, frequency filtering, spherical harmonic transform solutions, and consistency conditions. The Cormack algorithm based on reconstruction with Zernike polynomials is reviewed. An analogous algorithm and set of reconstruction polynomials is developed for the spherical harmonic transform. The relations between the consistency conditions, boundary conditions and orthogonal basis functions for the 2D projection harmonics are delineated and extended to the 3D case. The equivalence of the inverse circular harmonic transform, the inverse Radon transform, and the inverse Cormack transform is presented. The use of the number of nodes of a projection harmonic as a filter is discussed. Numerical methods for the efficient implementation of angular harmonic algorithms based on orthogonal functions and stable recursion are presented. The derivation of a lower bound for the signal-to-noise ratio of the Cormack algorithm is derived.

  20. Automatic mathematical modeling for space application

    NASA Technical Reports Server (NTRS)

    Wang, Caroline K.

    1987-01-01

    A methodology for automatic mathematical modeling is described. The major objective is to create a very friendly environment for engineers to design, maintain and verify their model and also automatically convert the mathematical model into FORTRAN code for conventional computation. A demonstration program was designed for modeling the Space Shuttle Main Engine simulation mathematical model called Propulsion System Automatic Modeling (PSAM). PSAM provides a very friendly and well organized environment for engineers to build a knowledge base for base equations and general information. PSAM contains an initial set of component process elements for the Space Shuttle Main Engine simulation and a questionnaire that allows the engineer to answer a set of questions to specify a particular model. PSAM is then able to automatically generate the model and the FORTRAN code. A future goal is to download the FORTRAN code to the VAX/VMS system for conventional computation.

  1. 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…

  2. Facilitating mathematics learning for students with upper extremity disabilities using touch-input system.

    PubMed

    Choi, Kup-Sze; Chan, Tak-Yin

    2015-03-01

    To investigate the feasibility of using tablet device as user interface for students with upper extremity disabilities to input mathematics efficiently into computer. A touch-input system using tablet device as user interface was proposed to assist these students to write mathematics. User-switchable and context-specific keyboard layouts were designed to streamline the input process. The system could be integrated with conventional computer systems only with minor software setup. A two-week pre-post test study involving five participants was conducted to evaluate the performance of the system and collect user feedback. The mathematics input efficiency of the participants was found to improve during the experiment sessions. In particular, their performance in entering trigonometric expressions by using the touch-input system was significantly better than that by using conventional mathematics editing software with keyboard and mouse. The participants rated the touch-input system positively and were confident that they could operate at ease with more practice. The proposed touch-input system provides a convenient way for the students with hand impairment to write mathematics and has the potential to facilitate their mathematics learning. Implications for Rehabilitation Students with upper extremity disabilities often face barriers to learning mathematics which is largely based on handwriting. Conventional computer user interfaces are inefficient for them to input mathematics into computer. A touch-input system with context-specific and user-switchable keyboard layouts was designed to improve the efficiency of mathematics input. Experimental results and user feedback suggested that the system has the potential to facilitate mathematics learning for the students.

  3. Multiplayer Activities That Develop Mathematical Coordination.

    ERIC Educational Resources Information Center

    Bricker, Lauren J.; Tanimoto, Steven L.; Rothenberg, Alex I.; Hutama, Danny C.; Wong, Tina H.

    Four computer applications are presented that encourage students to develop "mathematical coordination"--the ability to manipulate numerical variables in cooperation with other students so as to achieve a definite goal. The programs enable a form of computer-supported cooperative learning (CSCL). This paper describes the rationale and…

  4. An Investigation into the Perceptions of Mathematics and Information Literacy Self-Efficacy Levels of Pre-Service Primary Mathematics Teachers

    ERIC Educational Resources Information Center

    Dinçer, Bahar; Yilmaz, Süha

    2016-01-01

    The purpose of this study is to examine the relationship between perceptions of the self-efficacy levels for both mathematics literacy and information literacy in pre-service primary mathematics teachers and the factors on which the relationship depends (variables include gender, class level, hours spent reading books and computer-access…

  5. Integrating Mathematics into the Introductory Biology Laboratory Course

    ERIC Educational Resources Information Center

    White, James D.; Carpenter, Jenna P.

    2008-01-01

    Louisiana Tech University has an integrated science curriculum for its mathematics, chemistry, physics, computer science, biology-research track and secondary mathematics and science education majors. The curriculum focuses on the calculus sequence and introductory labs in biology, physics, and chemistry. In the introductory biology laboratory…

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

    ERIC Educational Resources Information Center

    Liang, Jiajuan; Pan, William S. Y.

    2009-01-01

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

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

    ERIC Educational Resources Information Center

    Afamasaga-Fuata'i, Karoline; Sooaemalelagi, Lumaava

    2014-01-01

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

  8. Using Google Apps to Develop the Mathematical Practices

    ERIC Educational Resources Information Center

    Layton, Rebecca D.; Cady, Jo Ann; Layton, Christopher A.

    2017-01-01

    Recent recommendations for the teaching of mathematics place an emphasis on the Common Core's Standards for Mathematical Practice (SMP) (CCSSI 2010). The SMPs emphasize constructing viable arguments, critiquing the ideas of others, reasoning abstractly and quantitatively, and using computational procedures. These skills, including the use of…

  9. Computational physics and applied mathematics capability review June 8-10, 2010

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

    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. Themore » 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

  10. 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…

  11. Interactivity of Visual Mathematical Representations: Factors Affecting Learning and Cognitive Processes

    ERIC Educational Resources Information Center

    Sedig, Kamran; Liang, Hai-Ning

    2006-01-01

    Computer-based mathematical cognitive tools (MCTs) are a category of external aids intended to support and enhance learning and cognitive processes of learners. MCTs often contain interactive visual mathematical representations (VMRs), where VMRs are graphical representations that encode properties and relationships of mathematical concepts. In…

  12. Student Science Training Program in Mathematics, Physics and Computer Science. Final Report to the National Science Foundation. Artificial Intelligence Memo No. 393.

    ERIC Educational Resources Information Center

    Abelson, Harold; diSessa, Andy

    During the summer of 1976, the MIT Artificial Intelligence Laboratory sponsored a Student Science Training Program in Mathematics, Physics, and Computer Science for high ability secondary school students. This report describes, in some detail, the style of the program, the curriculum and the projects the students under-took. It is hoped that this…

  13. Case Study of an Epistemic Mathematics Computer Game

    ERIC Educational Resources Information Center

    Buteau, Chantal; Muller, Eric

    2018-01-01

    E-Brock Bugs is a serious educational game (SEG) about probability which was created based on Devlin's design principles for games whose players adopt identities of mathematically able persons. This kind of games in which "players think and act like real world professionals" has been called epistemic. This article presents an empirical…

  14. 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.

  15. The Effect of a Math Emporium Course Redesign in Developmental and Introductory Mathematics Courses on Student Achievement and Students' Attitudes toward Mathematics at a Two-Year College

    ERIC Educational Resources Information Center

    Bishop, Amy Renee

    2010-01-01

    The purpose of this research was to determine the effect of computer-based instruction on student mathematics achievement and students' attitudes toward mathematics in developmental and introductory mathematics courses, namely Elementary Algebra, Intermediate Algebra, and College Algebra, at a community college. The researcher also examined the…

  16. School Mathematics Study Group, Unit Number Two. Chapter 3 - Informal Algorithms and Flow Charts. Chapter 4 - Applications and Mathematics Models.

    ERIC Educational Resources Information Center

    Stanford Univ., CA. School Mathematics Study Group.

    This is the second unit of a 15-unit School Mathematics Study Group (SMSG) mathematics text for high school students. Topics presented in the first chapter (Informal Algorithms and Flow Charts) include: changing a flat tire; algorithms, flow charts, and computers; assignment and variables; input and output; using a variable as a counter; decisions…

  17. 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…

  18. 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…

  19. FOREWORD: Third Nordic Symposium on Computer Simulation in Physics, Chemistry, Biology and Mathematics

    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

  20. Strategy Instruction in Mathematics.

    ERIC Educational Resources Information Center

    Goldman, Susan R.

    1989-01-01

    Experiments in strategy instruction for mathematics have been conducted using three models (direct instruction, self-instruction, and guided learning) applied to the tasks of computation and word problem solving. Results have implications for effective strategy instruction for learning disabled students. It is recommended that strategy instruction…

  1. Mathematics Programming on the Apple II and IBM PC.

    ERIC Educational Resources Information Center

    Myers, Roy E.; Schneider, David I.

    1987-01-01

    Details the features of BASIC used in mathematics programming and provides the information needed to translate between the Apple II and IBM PC computers. Discusses inputing a user-defined function, setting scroll windows, displaying subscripts and exponents, variable names, mathematical characters and special symbols. (TW)

  2. Addressing current challenges in cancer immunotherapy with mathematical and computational modelling.

    PubMed

    Konstorum, Anna; Vella, Anthony T; Adler, Adam J; Laubenbacher, Reinhard C

    2017-06-01

    The goal of cancer immunotherapy is to boost a patient's immune response to a tumour. Yet, the design of an effective immunotherapy is complicated by various factors, including a potentially immunosuppressive tumour microenvironment, immune-modulating effects of conventional treatments and therapy-related toxicities. These complexities can be incorporated into mathematical and computational models of cancer immunotherapy that can then be used to aid in rational therapy design. In this review, we survey modelling approaches under the umbrella of the major challenges facing immunotherapy development, which encompass tumour classification, optimal treatment scheduling and combination therapy design. Although overlapping, each challenge has presented unique opportunities for modellers to make contributions using analytical and numerical analysis of model outcomes, as well as optimization algorithms. We discuss several examples of models that have grown in complexity as more biological information has become available, showcasing how model development is a dynamic process interlinked with the rapid advances in tumour-immune biology. We conclude the review with recommendations for modellers both with respect to methodology and biological direction that might help keep modellers at the forefront of cancer immunotherapy development. © 2017 The Author(s).

  3. Cognitive correlates of performance in advanced mathematics.

    PubMed

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

    2012-03-01

    Much research has been devoted to understanding cognitive correlates of elementary mathematics performance, but little such research has been done for advanced mathematics (e.g., modern algebra, statistics, and mathematical logic). To promote mathematical knowledge among college students, it is necessary to understand what factors (including cognitive factors) are important for acquiring advanced mathematics. We recruited 80 undergraduates from four universities in Beijing. The current study investigated the associations between students' performance on a test of advanced mathematics and a battery of 17 cognitive tasks on basic numerical processing, complex numerical processing, spatial abilities, language abilities, and general cognitive processing. The results showed that spatial abilities were significantly correlated with performance in advanced mathematics after controlling for other factors. In addition, certain language abilities (i.e., comprehension of words and sentences) also made unique contributions. In contrast, basic numerical processing and computation were generally not correlated with performance in advanced mathematics. Results suggest that spatial abilities and language comprehension, but not basic numerical processing, may play an important role in advanced mathematics. These results are discussed in terms of their theoretical significance and practical implications. ©2011 The British Psychological Society.

  4. 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,…

  5. 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)

  6. Handbook of applied mathematics for engineers and scientists

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

    Kurtz, M.

    1991-12-31

    This book is intended to be reference for applications of mathematics in a wide range of topics of interest to engineers and scientists. An unusual feature of this book is that it covers a large number of topics from elementary algebra, trigonometry, and calculus to computer graphics and cybernetics. The level of mathematics covers high school through about the junior level of an engineering curriculum in a major univeristy. Throughout, the emphasis is on applications of mathematics rather than on rigorous proofs.

  7. Enhancing Undergraduate Mathematics Curriculum via Coding Theory and Cryptography

    ERIC Educational Resources Information Center

    Aydin, Nuh

    2009-01-01

    The theory of error-correcting codes and cryptography are two relatively recent applications of mathematics to information and communication systems. The mathematical tools used in these fields generally come from algebra, elementary number theory, and combinatorics, including concepts from computational complexity. It is possible to introduce the…

  8. An "Elective Replacement" Approach to Providing Extra Help in Math: The Talent Development Middle Schools' Computer- and Team-Assisted Mathematics Acceleration (CATAMA) Program.

    ERIC Educational Resources Information Center

    Mac Iver, Douglas J.; Balfanz, Robert; Plank, Stephan B.

    1999-01-01

    Two studies evaluated the Computer- and Team-Assisted Mathematics Acceleration course (CATAMA) in Talent Development Middle Schools. The first study compared growth in math achievement for 96 seventh-graders (48 of whom participated in CATAMA and 48 of whom did not); the second study gathered data from interviews with, and observations of, CATAMA…

  9. Computational Toxicology (S)

    EPA Science Inventory

    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...

  10. 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.

  11. Mathematical and computational studies of the stability of axisymmetric annular capillary free surfaces

    NASA Technical Reports Server (NTRS)

    Albright, N.; Concus, P.; Karasalo, I.

    1977-01-01

    Of principal interest is the stability of a perfectly wetting liquid in an inverted, vertical, right circular-cylindrical container having a concave spheroidal bottom. The mathematical conditions that the contained liquid be in stable static equilibrium are derived, including those for the limiting case of zero contact angle. Based on these results, a computational investigation is carried out for a particular container that is used for the storage of liquid fuels in NASA Centaur space vehicles, for which the axial ratio of the container bottom is 0.724. It is found that for perfectly wetting liquids the qualitative nature of the onset of instability changes at a critical liquid volume, which for the Centaur fuel tank corresponds to a mean fill level of approximately 0.503 times the tank's radius. Small-amplitude periodic sloshing modes for this tank were calculated; oscillation frequencies or growth rates are given for several Bond numbers and liquid volumes, for normal modes having up to six angular nodes.

  12. 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.

  13. Mathematical Education of Engineers.

    ERIC Educational Resources Information Center

    Organisation for Economic Cooperation and Development, Paris (France).

    The seminar reported in this document examined the university mathematics courses which should be available to future engineers, and was especially concerned with the introduction of computer science education. There are four major sections. The first reports a survey of electrical engineers in the United Kingdom which investigated how often they…

  14. Evaluation of Mathematical Self-Explanations with LSA in a Counterintuitive Problem of Probabilities

    ERIC Educational Resources Information Center

    Guiu, Jordi Maja

    2012-01-01

    In this paper different type of mathematical explanations are presented in relation to the mathematical problem of probabilities Monty Hall (card version) and the computational tool Latent Semantic Analyses (LSA) is used. At the moment the results in the literature about this computational tool to study texts show that this technique is…

  15. Measuring Computer Science Knowledge Level of Hungarian Students Specialized in Informatics with Romanian Students Attending a Science Course or a Mathematics-Informatics Course

    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…

  16. 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.

  17. Mathematical modeling of fluxgate magnetic gradiometers

    NASA Astrophysics Data System (ADS)

    Milovzorov, D. G.; Yasoveev, V. Kh.

    2017-07-01

    Issues of designing fluxgate magnetic gradiometers are considered. The areas of application of fluxgate magnetic gradiometers are determined. The structure and layout of a two-component fluxgate magnetic gradiometer are presented. It is assumed that the fluxgates are strictly coaxial in the gradiometer body. Elements of the classical approach to the mathematical modeling of the spatial arrangement of solids are considered. The bases of the gradiometer body and their transformations during spatial displacement of the gradiometer are given. The problems of mathematical modeling of gradiometers are formulated, basic mathematical models of a two-component fluxgate gradiometer are developed, and the mathematical models are analyzed. A computer experiment was performed. Difference signals from the gradiometer fluxgates for the vertical and horizontal position of the gradiometer body are shown graphically as functions of the magnitude and direction of the geomagnetic field strength vector.

  18. The mathematical theory of signal processing and compression-designs

    NASA Astrophysics Data System (ADS)

    Feria, Erlan H.

    2006-05-01

    The mathematical theory of signal processing, named processor coding, will be shown to inherently arise as the computational time dual of Shannon's mathematical theory of communication which is also known as source coding. Source coding is concerned with signal source memory space compression while processor coding deals with signal processor computational time compression. Their combination is named compression-designs and referred as Conde in short. A compelling and pedagogically appealing diagram will be discussed highlighting Conde's remarkable successful application to real-world knowledge-aided (KA) airborne moving target indicator (AMTI) radar.

  19. Computer Recreations.

    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)

  20. From Greeks to Today: Cipher Trees and Computer Cryptography.

    ERIC Educational Resources Information Center

    Grady, M. Tim; Brumbaugh, Doug

    1988-01-01

    Explores the use of computers for teaching mathematical models of transposition ciphers. Illustrates the ideas, includes activities and extensions, provides a mathematical model and includes computer programs to implement these topics. (MVL)

  1. Could Elementary Mathematics Textbooks Help Give Attention to Reasons in the Classroom?

    ERIC Educational Resources Information Center

    Newton, Douglas P.; Newton, Lynn D.

    2007-01-01

    Trainee teachers, new and non-specialist teachers of elementary mathematics have a tendency to avoid thought about reasons in mathematics. Instead, they tend to favour the development of computational skill through the rote application of procedures, routines and algorithms. Could elementary mathematics textbooks serve as models of practice and…

  2. Mathematical and computational modeling simulation of solar drying Systems

    USDA-ARS?s Scientific Manuscript database

    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...

  3. Mathematics for the Baker.

    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,…

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

    ERIC Educational Resources Information Center

    Mumcu, Hayal Yavuz

    2016-01-01

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

  5. High-precision arithmetic in mathematical physics

    DOE PAGES

    Bailey, David H.; Borwein, Jonathan M.

    2015-05-12

    For many scientific calculations, particularly those involving empirical data, IEEE 32-bit floating-point arithmetic produces results of sufficient accuracy, while for other applications IEEE 64-bit floating-point is more appropriate. But for some very demanding applications, even higher levels of precision are often required. Furthermore, this article discusses the challenge of high-precision computation, in the context of mathematical physics, and highlights what facilities are required to support future computation, in light of emerging developments in computer architecture.

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

    NASA Astrophysics Data System (ADS)

    Moldovanu, Simona; Moraru, Luminita; Bibicu, Dorin

    2012-11-01

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

  7. How Computer Graphics Work.

    ERIC Educational Resources Information Center

    Prosise, Jeff

    This document presents the principles behind modern computer graphics without straying into the arcane languages of mathematics and computer science. Illustrations accompany the clear, step-by-step explanations that describe how computers draw pictures. The 22 chapters of the book are organized into 5 sections. "Part 1: Computer Graphics in…

  8. A Multifaceted Mathematical Approach for Complex Systems

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

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

    2012-03-07

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

  9. The Effect of Contextual Pedagogical Advisement and Competition on Middle-School Students' Attitude toward Mathematics and Mathematics Instruction Using a Computer-Based Simulation Game

    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…

  10. The Impact of Computer and Mathematics Software Usage on Performance of School Leavers in the Western Cape Province of South Africa: A Comparative Analysis

    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…

  11. How students process equations in solving quantitative synthesis problems? Role of mathematical complexity in students' mathematical performance

    NASA Astrophysics Data System (ADS)

    Ibrahim, Bashirah; Ding, Lin; Heckler, Andrew F.; White, Daniel R.; Badeau, Ryan

    2017-12-01

    We examine students' mathematical performance on quantitative "synthesis problems" with varying mathematical complexity. Synthesis problems are tasks comprising multiple concepts typically taught in different chapters. Mathematical performance refers to the formulation, combination, and simplification of equations. Generally speaking, formulation and combination of equations require conceptual reasoning; simplification of equations requires manipulation of equations as computational tools. Mathematical complexity is operationally defined by the number and the type of equations to be manipulated concurrently due to the number of unknowns in each equation. We use two types of synthesis problems, namely, sequential and simultaneous tasks. Sequential synthesis tasks require a chronological application of pertinent concepts, and simultaneous synthesis tasks require a concurrent application of the pertinent concepts. A total of 179 physics major students from a second year mechanics course participated in the study. Data were collected from written tasks and individual interviews. Results show that mathematical complexity negatively influences the students' mathematical performance on both types of synthesis problems. However, for the sequential synthesis tasks, it interferes only with the students' simplification of equations. For the simultaneous synthesis tasks, mathematical complexity additionally impedes the students' formulation and combination of equations. Several reasons may explain this difference, including the students' different approaches to the two types of synthesis problems, cognitive load, and the variation of mathematical complexity within each synthesis type.

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

    NASA Astrophysics Data System (ADS)

    Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

    2011-04-01

    of computer-based science simulations. Although there are several exceptional computer-based science simulations designed for mathematics classes (see, e.g. Kinetic Book (http://www.kineticbooks.com/) or Gizmos (http://www.explorelearning.com/)), we concentrate mainly on the PhET Interactive Simulations developed at the University of Colorado at Boulder (http://phet.colorado.edu/) in generating our argument that computer simulations more accurately represent the contextual characteristics of scientific phenomena than their textual descriptions.

  13. Computer Language For Optimization Of Design

    NASA Technical Reports Server (NTRS)

    Scotti, Stephen J.; Lucas, Stephen H.

    1991-01-01

    SOL is computer language geared to solution of design problems. Includes mathematical modeling and logical capabilities of computer language like FORTRAN; also includes additional power of nonlinear mathematical programming methods at language level. SOL compiler takes SOL-language statements and generates equivalent FORTRAN code and system calls. Provides syntactic and semantic checking for recovery from errors and provides detailed reports containing cross-references to show where each variable used. Implemented on VAX/VMS computer systems. Requires VAX FORTRAN compiler to produce executable program.

  14. Computers and Hot Potatoes: Starch for Teacher Preparation Diets.

    ERIC Educational Resources Information Center

    Johnson, Jerry

    1984-01-01

    Computers present a problem for mathematics teachers that may be solved through teacher education programs. Classroom teachers should be competent in programing languages, exploring software, and understanding the emphasis of computers in the mathematics curriculum. (DF)

  15. Categories of Computer Use and Their Relationships with Attitudes toward Computers.

    ERIC Educational Resources Information Center

    Mitra, Anandra

    1998-01-01

    Analysis of attitude and use questionnaires completed by undergraduates (n1,444) at Wake Forest University determined that computers were used most frequently for word processing. Other uses were e-mail for task and non-task activities and mathematical and statistical computation. Results suggest that the level of computer use was related to…

  16. The Relations among Mathematics Anxiety, Gender, and Standardized Test Performance

    ERIC Educational Resources Information Center

    Anis, Yasmeen; Krause, Jeremy A.; Blum, Emily N.

    2016-01-01

    Mathematics anxiety typically involves apprehension toward activities that require computation, which can lead to complications in every-day-life activities (Ashcraft, 2002). Mathematics anxiety also has become accepted as an issue associated with academic success for both children and adults (Ashcraft, 2002; Ashcraft & Moore, 2009; Beilock,…

  17. Investigating Student Use of Electronic Support Tools and Mathematical Reasoning

    ERIC Educational Resources Information Center

    Higgins, Kristina N.; Crawford, Lindy; Huscroft-D'Angelo, Jacqueline; Horney, Mark

    2016-01-01

    Mathematical reasoning involves comprehending mathematical information and concepts in a logical way and forming conclusions and generalizations based on this comprehension. Computer-based learning has been incorporated into classrooms across the country, and specific aspects of technology need to be studied to determine how programs are…

  18. Student-Made Games to Learn the History of Mathematics

    ERIC Educational Resources Information Center

    Huntley, Mary Ann; Flores, Alfinio

    2011-01-01

    In this article, the authors describe how prospective secondary mathematics teachers designed their own adaptations of popular board and computer games to learn the history of mathematics. They begin the article by describing some of the games students designed and used, and follow this with a discussion of factors for successful use of games in…

  19. The Teaching of Polar Coordinates with Dynamic Mathematics Software

    ERIC Educational Resources Information Center

    Zengin, Yilmaz; Tatar, Enver

    2015-01-01

    The purpose of this study was to determine the effects of dynamic mathematics software on the achievement of pre-service mathematics teachers in the topic of polar coordinates and to solicit their opinions about computer-assisted instruction. The study was conducted for 11 weeks with 33 pre-service teachers in the Department of Mathematics…

  20. LASER APPLICATIONS AND OTHER TOPICS IN QUANTUM ELECTRONICS: Methods of computational physics in the problem of mathematical interpretation of laser investigations

    NASA Astrophysics Data System (ADS)

    Brodyn, M. S.; Starkov, V. N.

    2007-07-01

    It is shown that in laser experiments performed by using an 'imperfect' setup when instrumental distortions are considerable, sufficiently accurate results can be obtained by the modern methods of computational physics. It is found for the first time that a new instrumental function — the 'cap' function — a 'sister' of a Gaussian curve proved to be demanded namely in laser experiments. A new mathematical model of a measurement path and carefully performed computational experiment show that a light beam transmitted through a mesoporous film has actually a narrower intensity distribution than the detected beam, and the amplitude of the real intensity distribution is twice as large as that for measured intensity distributions.

  1. A Flexible, Extensible Online Testing System for Mathematics

    ERIC Educational Resources Information Center

    Passmore, Tim; Brookshaw, Leigh; Butler, Harry

    2011-01-01

    An online testing system developed for entry-skills testing of first-year university students in algebra and calculus is described. The system combines the open-source computer algebra system "Maxima" with computer scripts to parse student answers, which are entered using standard mathematical notation and conventions. The answers can…

  2. Introducing Computational Thinking to Young Learners: Practicing Computational Perspectives through Embodiment in Mathematics Education

    ERIC Educational Resources Information Center

    Sung, Woonhee; Ahn, Junghyun; Black, John B.

    2017-01-01

    A science, technology, engineering, and mathematics-influenced classroom requires learning activities that provide hands-on experiences with technological tools to encourage problem-solving skills (Brophy et al. in "J Eng Educ" 97(3):369-387, 2008; Mataric et al. in "AAAI spring symposium on robots and robot venues: resources for AI…

  3. Materials inspired by mathematics.

    PubMed

    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.

  4. Materials inspired by mathematics

    PubMed Central

    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

  5. Space Mathematics: A Resource for Secondary School Teachers

    NASA Technical Reports Server (NTRS)

    Kastner, Bernice

    1985-01-01

    A collection of mathematical problems related to NASA space science projects is presented. In developing the examples and problems, attention was given to preserving the authenticity and significance of the original setting while keeping the level of mathematics within the secondary school curriculum. Computation and measurement, algebra, geometry, probability and statistics, exponential and logarithmic functions, trigonometry, matrix algebra, conic sections, and calculus are among the areas addressed.

  6. The Relationship between Computer-Assisted Instruction and Alternative Programs to Enhance Fifth-Grade Mathematics Success on the Annual Texas Assessment of Knowledge and Skills

    ERIC Educational Resources Information Center

    Tucker, Tommy Howard

    2009-01-01

    The purpose of this study was to determine the relationship between using computer-assisted instruction (CAI) size and success on the Texas Assessment of Knowledge and Skills (TAKS) mathematics exam with fifth-grade students in Texas compared to the effect of alternative improvement approaches used by a control group. Research explored the use of…

  7. The Eye of a Mathematical Physicist

    NASA Astrophysics Data System (ADS)

    Hepp, Klaus

    2009-03-01

    In this essay we are searching for neural correlates of `doing mathematical physics'. We introduce a toy model of a mathematical physicist, a brain connected with the outside world only by vision and saccadic eye movements and interacting with a computer screen. First, we describe the neuroanatomy of the visuo-saccadic system and Listing's law, which binds saccades and the optics of the eye. Then we explain space-time transformations in the superior colliculus, the performance of a canonical cortical circuit in the frontal eye field and finally the recurrent interaction of both areas, which leads to a coherent percept of space in spite of saccades. This sets the stage in the brain for doing mathematical physics, which is analyzed in simple examples.

  8. The Effect of Emphasizing Mathematical Structure in the Acquisition of Whole Number Computation Skills (Addition and Subtraction) By Seven- and Eight-Year Olds: A Clinical Investigation.

    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…

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

    NASA Technical Reports Server (NTRS)

    Wang, Caroline; Purinton, Steve

    1989-01-01

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

  10. What Is the Relationship between Technology and Mathematics Teaching Anxiety?

    ERIC Educational Resources Information Center

    Tatar, Enver; Zengin, Yilmaz; Kagizmanli, Türkan Berrin

    2015-01-01

    The aim of this study is to determine the relationship between pre-service teachers' perceptions regarding technology use in mathematics teaching and their computer literacy levels as well as their mathematics teaching anxiety. The nonexperimental correlational research, which is included in the quantitative research approach, was used in the…

  11. Mathematical models of cell motility.

    PubMed

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

    2007-01-01

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

  12. Mathematical and computational approaches can complement experimental studies of host-pathogen interactions.

    PubMed

    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.

  13. Students' Use of Electronic Support Tools in Mathematics

    ERIC Educational Resources Information Center

    Crawford, Lindy; Higgins, Kristina N.; Huscroft-D'Angelo, Jacqueline N.; Hall, Lindsay

    2016-01-01

    This study investigated students' use of electronic support tools within a computer-based mathematics program. Electronic support tools are tools, such as hyperlinks or calculators, available within many computer-based instructional programs. A convenience sample of 73 students in grades 4-6 was selected to participate in the study. Students…

  14. Information Communication Technology Pedagogical Integration in Mathematics Instruction among Teachers in Secondary Schools in Kenya

    ERIC Educational Resources Information Center

    Wanjala, Martin

    2016-01-01

    This paper reports finding of the study that sought to ascertain the extent of ICT-pedagogical integration in mathematics instruction among secondary school teachers in Kenya. Information was sought on professional development experiences and needs in computer technology use in mathematics instruction, the type of computer software used in…

  15. Mathematical Model for Dengue Epidemics with Differential Susceptibility and Asymptomatic Patients Using Computer Algebra

    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.

  16. Coordinating Formal and Informal Aspects of Mathematics in a Computer Based Learning Environment

    ERIC Educational Resources Information Center

    Skouras, A. S.

    2006-01-01

    The introduction of educational technology to school classes promises--through the students' active engagement with mathematical concepts--the creation of teaching and learning opportunities in mathematics. However, the way technological tools are used in the teaching practice as a means of human thought and action remains an unsettled matter as…

  17. Measuring Technological and Content Knowledge of Undergraduate Primary Teachers in Mathematics

    NASA Astrophysics Data System (ADS)

    Doukakis, Spyros; Chionidou-Moskofoglou, Maria; Mangina-Phelan, Eleni; Roussos, Petros

    Twenty-five final-year undergraduate students of primary education who were attending a course on mathematics education participated in a research project during the 2009 spring semester. A repeated measures experimental design was used. Quantitative data on students' computer attitudes, self-efficacy in ICT, attitudes toward educational software, and self-efficacy in maths were collected. Data analysis showed a statistically non-significant improvement on participants' computer attitudes and self-efficacy in ICT and ES, but a significant improvement of self-efficacy in mathematics.

  18. Mathematics anxiety and mathematics achievement

    NASA Astrophysics Data System (ADS)

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

    2003-09-01

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

  19. Computational oncology.

    PubMed

    Lefor, Alan T

    2011-08-01

    Oncology research has traditionally been conducted using techniques from the biological sciences. The new field of computational oncology has forged a new relationship between the physical sciences and oncology to further advance research. By applying physics and mathematics to oncologic problems, new insights will emerge into the pathogenesis and treatment of malignancies. One major area of investigation in computational oncology centers around the acquisition and analysis of data, using improved computing hardware and software. Large databases of cellular pathways are being analyzed to understand the interrelationship among complex biological processes. Computer-aided detection is being applied to the analysis of routine imaging data including mammography and chest imaging to improve the accuracy and detection rate for population screening. The second major area of investigation uses computers to construct sophisticated mathematical models of individual cancer cells as well as larger systems using partial differential equations. These models are further refined with clinically available information to more accurately reflect living systems. One of the major obstacles in the partnership between physical scientists and the oncology community is communications. Standard ways to convey information must be developed. Future progress in computational oncology will depend on close collaboration between clinicians and investigators to further the understanding of cancer using these new approaches.

  20. Tensor methodology and computational geometry in direct computational experiments in fluid mechanics

    NASA Astrophysics Data System (ADS)

    Degtyarev, Alexander; Khramushin, Vasily; Shichkina, Julia

    2017-07-01

    The paper considers a generalized functional and algorithmic construction of direct computational experiments in fluid dynamics. Notation of tensor mathematics is naturally embedded in the finite - element operation in the construction of numerical schemes. Large fluid particle, which have a finite size, its own weight, internal displacement and deformation is considered as an elementary computing object. Tensor representation of computational objects becomes strait linear and uniquely approximation of elementary volumes and fluid particles inside them. The proposed approach allows the use of explicit numerical scheme, which is an important condition for increasing the efficiency of the algorithms developed by numerical procedures with natural parallelism. It is shown that advantages of the proposed approach are achieved among them by considering representation of large particles of a continuous medium motion in dual coordinate systems and computing operations in the projections of these two coordinate systems with direct and inverse transformations. So new method for mathematical representation and synthesis of computational experiment based on large particle method is proposed.

  1. Satellite orbit computation methods

    NASA Technical Reports Server (NTRS)

    1977-01-01

    Mathematical and algorithmical techniques for solution of problems in satellite dynamics were developed, along with solutions to satellite orbit motion. Dynamical analysis of shuttle on-orbit operations were conducted. Computer software routines for use in shuttle mission planning were developed and analyzed, while mathematical models of atmospheric density were formulated.

  2. Development of Ideas in a GeoGebra-Aided Mathematics Instruction

    ERIC Educational Resources Information Center

    Ljajko, Eugen; Ibro, Vait

    2013-01-01

    With GeoGebra introduced into mathematics instruction the teaching/learning process is not improved in terms of speed and quality only. Mathematical concepts, rules and procedures must be adjusted to the new environment. On the other hand, characteristics of the computer and the educational software in use must be thoroughly examined and a…

  3. Mathematics Objectives and Measurement Specifications 1986-1990. Exit Level. Texas Educational Assessment of Minimum Skills (TEAMS).

    ERIC Educational Resources Information Center

    Texas Education Agency, Austin. Div. of Educational Assessment.

    This document lists the objectives for the Texas educational assessment program in mathematics. Eighteen objectives for exit level mathematics are listed, by category: number concepts (4); computation (3); applied computation (5); statistical concepts (3); geometric concepts (2); and algebraic concepts (1). Then general specifications are listed…

  4. A preliminary study of achievement, attitudes toward success in mathematics, and mathematics anxiety with technology-based instruction in brief calculus.

    PubMed

    Alkhateeb, Haitham M

    2002-02-01

    This study was designed to compare achievement, attitudes toward success in mathematics, and mathematics anxiety of college students taught brief calculus using a graphic calculator, with the achievement and attitudes and anxiety of students taught using the computer algebra system Maple, using a technology based text book. 50 men and 50 women, students in three classes at a large public university in the southwestern United States, participated. Students' achievement in brief calculus was measured by performance on a teacher-made achievement test given at the end of the study. Analysis of variance showed no significant difference in achievement between the groups. To measure change in attitudes and anxiety, responses to paper-and-pencil inventories indicated significant differences in favor of students using the computer.

  5. MATHEMATICAL METHODS IN MEDICAL IMAGE PROCESSING

    PubMed Central

    ANGENENT, SIGURD; PICHON, ERIC; TANNENBAUM, ALLEN

    2013-01-01

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

  6. Implementing a Game for Supporting Learning in Mathematics

    ERIC Educational Resources Information Center

    Katmada, Aikaterini; Mavridis, Apostolos; Tsiatsos, Thrasyvoulos

    2014-01-01

    This paper focuses on the design, implementation and evaluation of an online game for elementary and middle school mathematics. Its aim is twofold: (a) the development of the prototype of a flexible and adaptable computer game, and (b) the evaluation of this prototype, as to its usability and technical aspects. The particular computer game was…

  7. Computer Attitude, Use, Experience, Software Familiarity and Perceived Pedagogical Usefulness: The Case of Mathematics Professors

    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.…

  8. Preservice Teachers' Perceptions about Computer Use for Tutoring.

    ERIC Educational Resources Information Center

    Willner, Elizabeth; Willner, Jonathan

    Preservice teachers had the opportunity to make use of computers while tutoring elementary and middle school children in reading, mathematics, and integrated reading and mathematics. These tutors (n=128) responded to a survey that was designed to elicit responses about the value of computer use for tutoring and the motivational and learning…

  9. Can Computers be Social?

    NASA Astrophysics Data System (ADS)

    Ekdahl, Bertil

    2002-09-01

    Of main concern in agent based computing is the conception that software agents can attain socially responsible behavior. This idea has its origin in the need for agents to interact with one another in a cooperating manner. Such interplay between several agents can be seen as a combinatorial play where the rules are fixed and the actors are supposed to closely analyze the play in order to behave rational. This kind of rationality has successfully being mathematically described. When the social behavior is extended beyond rational behavior, mere mathematical analysis falls short. For such behavior language is decisive for transferring concepts and language is a holistic entity that cannot be analyzed and defined mathematically. Accordingly, computers cannot be furnished with a language in the sense that meaning can be conveyed and consequently they lack all the necessary properties to be made social. The attempts to postulate mental properties to computer programs are a misconception that is blamed the lack of true understanding of language and especially the relation between formal system and its semantics.

  10. Using Instructional Activities Game to Promote Mathematics: Teachers' Innovative Instruction

    ERIC Educational Resources Information Center

    Matsuda, Toshiki

    2008-01-01

    NIER (National Institute of Educational Research, 2004) survey revealed that the most common attitude of Japanese high school students to mathematics is that "it is not useful in daily life but must be learnt for entrance examinations". It was also clarified that only 3.2 percent of mathematics teachers use computers in their classes.…

  11. Visual Modeling as a Motivation for Studying Mathematics and Art

    ERIC Educational Resources Information Center

    Sendova, Evgenia; Grkovska, Slavica

    2005-01-01

    The paper deals with the possibility of enriching the curriculum in mathematics, informatics and art by means of visual modeling of abstract paintings. The authors share their belief that in building a computer model of a construct, one gains deeper insight into the construct, and is motivated to elaborate one's knowledge in mathematics and…

  12. Computers and Creativity.

    ERIC Educational Resources Information Center

    Ten Dyke, Richard P.

    1982-01-01

    A traditional question is whether or not computers shall ever think like humans. This question is redirected to a discussion of whether computers shall ever be truly creative. Creativity is defined and a program is described that is designed to complete creatively a series problem in mathematics. (MP)

  13. A Spreadsheet in the Mathematics Classroom.

    ERIC Educational Resources Information Center

    Watkins, Will; Taylor, Monty

    1989-01-01

    Demonstrates how spreadsheets can be used to implement linear system solving algorithms in college mathematics classes. Lotus 1-2-3 is described, a linear system of equations is illustrated using spreadsheets, and the interplay between applications, computations, and theory is discussed. (four references) (LRW)

  14. Computer Courseware Evaluations. A Series of Reports Compiled by the Clearinghouse Computer Technology Project.

    ERIC Educational Resources Information Center

    Alberta Dept. of Education, Edmonton.

    This report reviews Apple computer courseware in business education, library skills, mathematics, science, special education, and word processing based on the curricular requirements of Alberta, Canada. It provides detailed evaluations of 23 authorized titles in business education (2), mathematics (20), and science (1); 3 of the math titles are…

  15. Review and verification of CARE 3 mathematical model and code

    NASA Technical Reports Server (NTRS)

    Rose, D. M.; Altschul, R. E.; Manke, J. W.; Nelson, D. L.

    1983-01-01

    The CARE-III mathematical model and code verification performed by Boeing Computer Services were documented. The mathematical model was verified for permanent and intermittent faults. The transient fault model was not addressed. The code verification was performed on CARE-III, Version 3. A CARE III Version 4, which corrects deficiencies identified in Version 3, is being developed.

  16. Mathematical methods in medicine: neuroscience, cardiology and pathology

    PubMed Central

    Amigó, José M.

    2017-01-01

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

  17. Mathematical methods in medicine: neuroscience, cardiology and pathology.

    PubMed

    Amigó, José M; Small, Michael

    2017-06-28

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

  18. DURIP: High Performance Computing in Biomathematics Applications

    DTIC Science & Technology

    2017-05-10

    Mathematics and Statistics (AMS) at the University of California, Santa Cruz (UCSC) to conduct research and research-related education in areas of...Computing in Biomathematics Applications Report Title The goal of this award was to enhance the capabilities of the Department of Applied Mathematics and...DURIP: High Performance Computing in Biomathematics Applications The goal of this award was to enhance the capabilities of the Department of Applied

  19. Quantum Analog Computing

    NASA Technical Reports Server (NTRS)

    Zak, M.

    1998-01-01

    Quantum analog computing is based upon similarity between mathematical formalism of quantum mechanics and phenomena to be computed. It exploits a dynamical convergence of several competing phenomena to an attractor which can represent an externum of a function, an image, a solution to a system of ODE, or a stochastic process.

  20. Mathematical manipulative models: in defense of "beanbag biology".

    PubMed

    Jungck, John R; Gaff, Holly; Weisstein, Anton E

    2010-01-01

    Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process-1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets-we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project (http://bioquest.org/esteem) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education.

  1. Terrestrial implications of mathematical modeling developed for space biomedical research

    NASA Technical Reports Server (NTRS)

    Lujan, Barbara F.; White, Ronald J.; Leonard, Joel I.; Srinivasan, R. Srini

    1988-01-01

    This paper summarizes several related research projects supported by NASA which seek to apply computer models to space medicine and physiology. These efforts span a wide range of activities, including mathematical models used for computer simulations of physiological control systems; power spectral analysis of physiological signals; pattern recognition models for detection of disease processes; and computer-aided diagnosis programs.

  2. Using Student-Made Games to Learn Mathematics

    ERIC Educational Resources Information Center

    Gallegos, Irene; Flores, Alfinio

    2010-01-01

    First-year university students design and play their own games, including board, computer, and other kinds of games, to learn mathematical concepts and practice procedures for their pre-calculus and calculus courses. (Contains 2 tables and 8 figures.)

  3. Technology and Mathematics Education: A Survey of Recent Developments and Important Problems.

    ERIC Educational Resources Information Center

    Fey, James T.

    1989-01-01

    Provided is an overview and analysis of recent progress in applying electronic information technology to creation of new environments for intellectual work in mathematics. Describes the impact of numerical computation, graphic computation, symbolic computation, multiple representation of information, programing and information, and artificial…

  4. Using Computation Curriculum-Based Measurement Probes for Error Pattern Analysis

    ERIC Educational Resources Information Center

    Dennis, Minyi Shih; Calhoon, Mary Beth; Olson, Christopher L.; Williams, Cara

    2014-01-01

    This article describes how "curriculum-based measurement--computation" (CBM-C) mathematics probes can be used in combination with "error pattern analysis" (EPA) to pinpoint difficulties in basic computation skills for students who struggle with learning mathematics. Both assessment procedures provide ongoing assessment data…

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

    ERIC Educational Resources Information Center

    Cosler, Norma, Ed.

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

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

    ERIC Educational Resources Information Center

    Cosler, Norma, Ed.

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

  7. Applied Mathematics for agronomical engineers in Spain at UPM

    NASA Astrophysics Data System (ADS)

    Anton, J. M.; Grau, J. B.; Tarquis, A. M.; Fabregat, J.; Sanchez, M. E.

    2009-04-01

    variables are an example, maybe since Leibnitz, of the difficulty of balance rigor and usefulness in limited hours of teaching. In part engineers use of mathematics with manuals and now with computers that use packages, general (MAPLE, MATLAB, may be MATHCAD, et. C. ) or specific, such as for Statistics, Topography, Structural design, Hydraulics, specific Machines,…, and mostly the details of the algorithms are hidden, but the engineer must have in mind the basic mathematical schemas justifying what he is constructing with these tools, the PC being also used for organisation and drawing. The engineers must adapt to the evolution of these packages and computers that get much changed and improved in five or ten years, quicker than the specific engineering environment, and a clear idea of the much more stable mathematical structures behind gives a solid mental ground for that. An initiation to using computers also with a mathematical structure behind is necessary, to be followed in professional life. A specific actualisation of mathematical knowledge is often necessary for some new applications.

  8. Computer-Generated Feedback on Student Writing

    ERIC Educational Resources Information Center

    Ware, Paige

    2011-01-01

    A distinction must be made between "computer-generated scoring" and "computer-generated feedback". Computer-generated scoring refers to the provision of automated scores derived from mathematical models built on organizational, syntactic, and mechanical aspects of writing. In contrast, computer-generated feedback, the focus of this article, refers…

  9. Computational Fluid Dynamics at ICMA (Institute for Computational Mathematics and Applications)

    DTIC Science & Technology

    1988-10-18

    PERSONAL. AUTHOR(S) Charles A. Hall and Thomas A. Porsching 13a. TYPE OF REPORT 13b. TIME COVERED 114. DATE OF REPORT (YearMOth, De ) 1. PAGE COUNT...of ten ICtA (Institute for Computational Mathe- matics and Applications) personnel, relating to the general area of computational fluid mechanics...questions raised in the previous subsection. Our previous work in this area concentrated on a study of the differential geometric aspects of the prob- lem

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

    PubMed

    Walsh, Kathleen A

    2008-01-01

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

  11. Using e-Learning Platforms for Mastery Learning in Developmental Mathematics Courses

    ERIC Educational Resources Information Center

    Boggs, Stacey; Shore, Mark; Shore, JoAnna

    2004-01-01

    Many colleges and universities have adopted e-learning platforms to utilize computers as an instructional tool in developmental (i.e., beginning and intermediate algebra) mathematics courses. An e-learning platform is a computer program used to enhance course instruction via computers and the Internet. Allegany College of Maryland is currently…

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

    PubMed

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

    2016-01-01

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

  13. An Investigation into Pre-Service Special Education Teachers' Mathematical Skills, Self-Efficacy, and Teaching Methodology

    ERIC Educational Resources Information Center

    Hinton, Vanessa; Flores, Margaret; Burton, Megan; Curtis, Rebecca

    2015-01-01

    The purpose of this mixed method study was to investigate future special education teachers' preparation for effectively teaching mathematics. During the last semester of their program, pre-service special education teachers completed elementary level mathematics computation and problem solving assessments, a mathematics efficacy beliefs survey,…

  14. Mathematical formula recognition using graph grammar

    NASA Astrophysics Data System (ADS)

    Lavirotte, Stephane; Pottier, Loic

    1998-04-01

    This paper describes current results of Ofr, a system for extracting and understanding mathematical expressions in documents. Such a tool could be really useful to be able to re-use knowledge in scientific books which are not available in electronic form. We currently also study use of this system for direct input of formulas with a graphical tablet for computer algebra system softwares. Existing solutions for mathematical recognition have problems to analyze 2D expressions like vectors and matrices. This is because they often try to use extended classical grammar to analyze formulas, relatively to baseline. But a lot of mathematical notations do not respect rules for such a parsing and that is the reason why they fail to extend text parsing technic. We investigate graph grammar and graph rewriting as a solution to recognize 2D mathematical notations. Graph grammar provide a powerful formalism to describe structural manipulations of multi-dimensional data. The main two problems to solve are ambiguities between rules of grammar and construction of graph.

  15. Demographic Computer Library.

    ERIC Educational Resources Information Center

    Shaw, David C.; Johnson, Dorothy M.

    The complete comprehension of this paper requires a firm grasp of both mathematical demography and FORTRAN programming. The paper aims at the establishment of a language with which complex demographic manipulations can be briefly expressed in a form intelligible both to demographic analysts and to computers. The Demographic Computer Library (DCL)…

  16. Mathematics, Grade 5, Part 2.

    ERIC Educational Resources Information Center

    New York City Board of Education, Brooklyn, NY.

    This curriculum bulletin is designed to help teachers meet the diverse needs in mathematics of the children in fifth grade classes. In addition to the emphasis that is placed on arithmetic computational skills, the bulletin shows how to include other areas considered important, such as concepts, skills, and ideas from algebra and geometry. The 80…

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

    ERIC Educational Resources Information Center

    Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent

    2017-01-01

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

  18. Teaching Mathematical Modelling for Earth Sciences via Case Studies

    NASA Astrophysics Data System (ADS)

    Yang, Xin-She

    2010-05-01

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

  19. Constructing Contracts: Making Discrete Mathematics Relevant to Beginning Programmers

    ERIC Educational Resources Information Center

    Gegg-Harrison, Timothy S.

    2005-01-01

    Although computer scientists understand the importance of discrete mathematics to the foundations of their field, computer science (CS) students do not always see the relevance. Thus, it is important to find a way to show students its relevance. The concept of program correctness is generally taught as an activity independent of the programming…

  20. High Level Technology in a Low Level Mathematics Course.

    ERIC Educational Resources Information Center

    Schultz, James E.; Noguera, Norma

    2000-01-01

    Describes a teaching experiment in which spreadsheets and computer algebra systems were used to teach a low-level college consumer mathematics course. Students were successful in using different types of functions to solve a variety of problems drawn from real-world situations. Provides an existence proof that computer algebra systems can assist…

  1. Teaching mathematics in the PC lab - the students' viewpoints

    NASA Astrophysics Data System (ADS)

    Schmidt, Karsten; Köhler, Anke

    2013-04-01

    The Matrix Algebra portion of the intermediate mathematics course at the Schmalkalden University Faculty of Business and Economics has been moved from a traditional classroom setting to a technology-based setting in the PC lab. A Computer Algebra System license was acquired that also allows its use on the students' own PCs. A survey was carried out to analyse the students' attitudes towards the use of technology in mathematics teaching.

  2. The Mathematics of the Global Positioning System.

    ERIC Educational Resources Information Center

    Nord, Gail D.; Jabon, David; Nord, John

    1997-01-01

    Presents an activity that illustrates the application of mathematics to modern navigation and utilizes the Global Positioning System (GPS). GPS is a constellation of 24 satellites that enables receivers to compute their position anywhere on the earth with great accuracy. (DDR)

  3. 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…

  4. Engineering Mathematics Assessment Using "MapleTA"

    ERIC Educational Resources Information Center

    Jones, Ian S.

    2008-01-01

    The assessment of degree level engineering mathematics students using the computer-aided assessment package MapleTA is discussed. Experience of academic and practical issues for both online coursework and examination assessments is presented, hopefully benefiting other academics in this novel area of activity. (Contains 6 figures and 1 table.)

  5. Treatment of control data in lunar phototriangulation. [application of statistical procedures and development of mathematical and computer techniques

    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.

  6. Imagination, Intuition, and Computing in School Algebra.

    ERIC Educational Resources Information Center

    Kieren, Thomas E.; Olson, Alton T.

    1989-01-01

    Two incidents involving novice teachers with classes in grades 7 and 10 are presented. Then considered are the nature of intuitive mathematics and contributions computers can make to such intuitive mathematics, particularly in Algebra. (MNS)

  7. The Psychology of Mathematics Learning: Past and Present.

    ERIC Educational Resources Information Center

    Education and Urban Society, 1985

    1985-01-01

    Reviews trends in applying psychology to mathematics learning. Discusses the influence of behaviorism and other functionalist theories, Gestalt theory, Piagetian theory, and the "new functionalism" evident in computer-oriented theories of information processing. (GC)

  8. 4th Annual Conference for African-American Researchers in the Mathematical Sciences (CAARMS4). Preliminary Program

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

    Tapia, Richard

    1998-06-01

    In June, The Center for Research on Parallel Computation (CRPC), an NSF-funded Science and Technology Center, hosted the 4th Annual Conference for African-American Reserachers in the Mathematical Sciences (CAARMS4) at Rice University. The main goal of this conference was to highlight current work by African-American researchers and graduate students in mathematics. This conference strengthened the mathematical sciences by encouraging the increased participation of African-American and underrepresented groups into the field, facilitating working relationships between them and helping to cultivate their careers. In addition to the talks there was a graduate student poster session and tutorials on topics in mathematics andmore » computer science. These talks, presentations, and discussions brought a broader perspective to the critical issues involving minority participation in mathematics.« less

  9. Research and the Personal Computer.

    ERIC Educational Resources Information Center

    Blackburn, D. A.

    1989-01-01

    Discussed is the history and elements of the personal computer. Its uses as a laboratory assistant and generic toolkit for mathematical analysis and modeling are included. The future of the personal computer in research is addressed. (KR)

  10. The Effect of Mathematics Research on Mathematics Majors' Mathematical Beliefs

    ERIC Educational Resources Information Center

    Goodson, Joshua E.

    2012-01-01

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

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

    ERIC Educational Resources Information Center

    Cosler, Norma, Ed.

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

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

    ERIC Educational Resources Information Center

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

    2010-01-01

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

  13. WOW! Mathematics Convention: A Community Connection

    ERIC Educational Resources Information Center

    Cavazos, Rebecca R.

    2014-01-01

    This article details how certain mathematical "discoveries" that Cavazos' fourth graders made were recorded throughout the year. Cavazos invited a math professor, a biologist, a literacy professor, a chemist, a statistician, and an engineering student, as well as their school principal and computer lab technician, both of whom are…

  14. Computer Synthesis Approaches of Hyperboloid Gear Drives with Linear Contact

    NASA Astrophysics Data System (ADS)

    Abadjiev, Valentin; Kawasaki, Haruhisa

    2014-09-01

    The computer design has improved forming different type software for scientific researches in the field of gearing theory as well as performing an adequate scientific support of the gear drives manufacture. Here are attached computer programs that are based on mathematical models as a result of scientific researches. The modern gear transmissions require the construction of new mathematical approaches to their geometric, technological and strength analysis. The process of optimization, synthesis and design is based on adequate iteration procedures to find out an optimal solution by varying definite parameters. The study is dedicated to accepted methodology in the creation of soft- ware for the synthesis of a class high reduction hyperboloid gears - Spiroid and Helicon ones (Spiroid and Helicon are trademarks registered by the Illinois Tool Works, Chicago, Ill). The developed basic computer products belong to software, based on original mathematical models. They are based on the two mathematical models for the synthesis: "upon a pitch contact point" and "upon a mesh region". Computer programs are worked out on the basis of the described mathematical models, and the relations between them are shown. The application of the shown approaches to the synthesis of commented gear drives is illustrated.

  15. Teachers' Mathematics as Mathematics-at-Work

    ERIC Educational Resources Information Center

    Bednarz, Nadine; Proulx, Jérôme

    2017-01-01

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

  16. Computers in Undergraduate Science Education. Conference Proceedings.

    ERIC Educational Resources Information Center

    Blum, Ronald, Ed.

    Six areas of computer use in undergraduate education, particularly in the fields of mathematics and physics, are discussed in these proceedings. The areas included are: the computational mode; computer graphics; the simulation mode; analog computing; computer-assisted instruction; and the current politics and management of college level computer…

  17. The Computational Estimation and Instructional Perspectives of Elementary School Teachers

    ERIC Educational Resources Information Center

    Tsao, Yea-Ling; Pan, Ting-Rung

    2013-01-01

    The purpose of this study is to investigate teachers' understanding and knowledge of computational estimation, and teaching practice toward to computational estimation. There are six fifth-grade elementary teachers who participated in this study; three teachers with mathematics/ science major and three teachers with non-mathematics/science major.…

  18. Computational ecology as an emerging science

    PubMed Central

    Petrovskii, Sergei; Petrovskaya, Natalia

    2012-01-01

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

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

    ERIC Educational Resources Information Center

    Natour, Denise M.

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

  20. 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…

  1. A Caribbean Pre-Service Mathematics Teacher's Impetus to Integrate Computer Technology in His Practice

    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…

  2. Empowering K-12 Students with Disabilities to Learn Computational Thinking and Computer Programming

    ERIC Educational Resources Information Center

    Israel, Maya; Wherfel, Quentin M.; Pearson, Jamie; Shehab, Saadeddine; Tapia, Tanya

    2015-01-01

    This article's focus is on including computing and computational thinking in K-12 instruction within science, technology, engineering, and mathematics (STEM) education, and to provide that instruction in ways that promote access for students traditionally underrepresented in the STEM fields, such as students with disabilities. Providing computing…

  3. Guidelines to Mathematics, K-8.

    ERIC Educational Resources Information Center

    Chambers, Donald L., Ed.

    This document is a revised edition of the 1967 Guidelines to Mathematics, K-6, and is thought to reveal few changes in detail and no changes of substance. The guidelines are seen as firmly rooted in the successful curriculums of the past while encouraging changes appropriate to the needs of students who will be adults in the computer age. Major…

  4. Toward integration of in vivo molecular computing devices: successes and challenges

    PubMed Central

    Hayat, Sikander; Hinze, Thomas

    2008-01-01

    The computing power unleashed by biomolecule based massively parallel computational units has been the focus of many interdisciplinary studies that couple state of the art ideas from mathematical logic, theoretical computer science, bioengineering, and nanotechnology to fulfill some computational task. The output can influence, for instance, release of a drug at a specific target, gene expression, cell population, or be a purely mathematical entity. Analysis of the results of several studies has led to the emergence of a general set of rules concerning the implementation and optimization of in vivo computational units. Taking two recent studies on in vivo computing as examples, we discuss the impact of mathematical modeling and simulation in the field of synthetic biology and on in vivo computing. The impact of the emergence of gene regulatory networks and the potential of proteins acting as “circuit wires” on the problem of interconnecting molecular computing device subunits is also highlighted. PMID:19404433

  5. Career Oriented Mathematics, Teacher's Manual. [Includes Mastering Computational Skill: A Use-Based Program; Owning an Automobile and Driving as a Career; Retail Sales; Measurement; and Area-Perimeter.

    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…

  6. Applicability of mathematical modeling to problems of environmental physiology

    NASA Technical Reports Server (NTRS)

    White, Ronald J.; Lujan, Barbara F.; Leonard, Joel I.; Srinivasan, R. Srini

    1988-01-01

    The paper traces the evolution of mathematical modeling and systems analysis from terrestrial research to research related to space biomedicine and back again to terrestrial research. Topics covered include: power spectral analysis of physiological signals; pattern recognition models for detection of disease processes; and, computer-aided diagnosis programs used in conjunction with a special on-line biomedical computer library.

  7. Optimization of computations

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

    Mikhalevich, V.S.; Sergienko, I.V.; Zadiraka, V.K.

    1994-11-01

    This article examines some topics of optimization of computations, which have been discussed at 25 seminar-schools and symposia organized by the V.M. Glushkov Institute of Cybernetics of the Ukrainian Academy of Sciences since 1969. We describe the main directions in the development of computational mathematics and present some of our own results that reflect a certain design conception of speed-optimal and accuracy-optimal (or nearly optimal) algorithms for various classes of problems, as well as a certain approach to optimization of computer computations.

  8. Khan Academy as Supplemental Instruction: A Controlled Study of a Computer-Based Mathematics Intervention

    ERIC Educational Resources Information Center

    Kelly, Daniel P.; Rutherford, Teomara

    2017-01-01

    Khan Academy is a large and popular open educational resource (OER) with little empirical study into its impact on student achievement in mathematics when used in schools. In this study, we examined the use of Khan Academy as a mathematics intervention among seventh grade students over a 4-week period versus a control group. We also compared…

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

    ERIC Educational Resources Information Center

    Hebert, Michael A.; Powell, Sarah R.

    2016-01-01

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

  10. Software For Computing Reliability Of Other Software

    NASA Technical Reports Server (NTRS)

    Nikora, Allen; Antczak, Thomas M.; Lyu, Michael

    1995-01-01

    Computer Aided Software Reliability Estimation (CASRE) computer program developed for use in measuring reliability of other software. Easier for non-specialists in reliability to use than many other currently available programs developed for same purpose. CASRE incorporates mathematical modeling capabilities of public-domain Statistical Modeling and Estimation of Reliability Functions for Software (SMERFS) computer program and runs in Windows software environment. Provides menu-driven command interface; enabling and disabling of menu options guides user through (1) selection of set of failure data, (2) execution of mathematical model, and (3) analysis of results from model. Written in C language.

  11. Programming Languages, Natural Languages, and Mathematics

    ERIC Educational Resources Information Center

    Naur, Peter

    1975-01-01

    Analogies are drawn between the social aspects of programming and similar aspects of mathematics and natural languages. By analogy with the history of auxiliary languages it is suggested that Fortran and Cobol will remain dominant. (Available from the Association of Computing Machinery, 1133 Avenue of the Americas, New York, NY 10036.) (Author/TL)

  12. Mathematics. Exceptional Child Education Curriculum K-12.

    ERIC Educational Resources Information Center

    Jordon, Thelma; And Others

    The mathematics curriculum provides a framework of instruction for exceptional child education in grades K-12. Content areas include: numeration, whole numbers, rational numbers, real/complex numbers, calculator literacy, measurement, geometry, statistics, functions/relations, computer literacy, and pre-algebra. The guide is organized by content…

  13. Spatial Skill Profile of Mathematics Pre-Service Teachers

    NASA Astrophysics Data System (ADS)

    Putri, R. O. E.

    2018-01-01

    This study is aimed to investigate the spatial intelligence of mathematics pre-service teachers and find the best instructional strategy that facilitates this aspect. Data were collected from 35 mathematics pre-service teachers. The Purdue Spatial Visualization Test (PSVT) was used to identify the spatial skill of mathematics pre-service teachers. Statistical analysis indicate that more than 50% of the participants possessed spatial skill in intermediate level, whereas the other were in high and low level of spatial skill. The result also shows that there is a positive correlation between spatial skill and mathematics ability, especially in geometrical problem solving. High spatial skill students tend to have better mathematical performance compare to those in two other levels. Furthermore, qualitative analysis reveals that most students have difficulty in manipulating geometrical objects mentally. This problem mostly appears in intermediate and low-level spatial skill students. The observation revealed that 3-D geometrical figures is the best method that can overcome the mentally manipulation problem and develop the spatial visualization. Computer application can also be used to improve students’ spatial skill.

  14. 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…

  15. Mathematical Manipulative Models: In Defense of “Beanbag Biology”

    PubMed Central

    Gaff, Holly; Weisstein, Anton E.

    2010-01-01

    Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process—1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets—we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project (http://bioquest.org/esteem) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education. PMID:20810952

  16. A Mathematical Model for the Middle Ear Ventilation

    NASA Astrophysics Data System (ADS)

    Molnárka, G.; Miletics, E. M.; Fücsek, M.

    2008-09-01

    The otitis media is one of the mostly existing illness for the children, therefore investigation of the human middle ear ventilation is an actual problem. In earlier investigations both experimental and theoretical approach one can find in ([l]-[3]). Here we give a new mathematical and computer model to simulate this ventilation process. This model able to describe the diffusion and flow processes simultaneously, therefore it gives more precise results than earlier models did. The article contains the mathematical model and some results of the simulation.

  17. Mathematical modeling of swirled flows in industrial applications

    NASA Astrophysics Data System (ADS)

    Dekterev, A. A.; Gavrilov, A. A.; Sentyabov, A. V.

    2018-03-01

    Swirled flows are widely used in technological devices. Swirling flows are characterized by a wide range of flow regimes. 3D mathematical modeling of flows is widely used in research and design. For correct mathematical modeling of such a flow, it is necessary to use turbulence models, which take into account important features of the flow. Based on the experience of computational modeling of a wide class of problems with swirling flows, recommendations on the use of turbulence models for calculating the applied problems are proposed.

  18. Teaching CAD on the Apple Computer.

    ERIC Educational Resources Information Center

    Norton, Robert L.

    1984-01-01

    Describes a course designed to teach engineers how to accomplish computer graphics techniques on a limited scale with the Apple computer. The same mathematics and program code will also function for larger and more complex computers. Course content, instructional strategies, student evaluation, and recommendations are considered. (JN)

  19. 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…

  20. A study of rural preschool practitioners' views on young children's mathematical thinking

    NASA Astrophysics Data System (ADS)

    Hunting, Robert P.; Mousley, Judith A.; Perry, Bob

    2012-03-01

    The project Mathematical Thinking of Preschool Children in Rural and Regional Australia: Research and Practice aimed to investigate views of preschool practitioners about young children's mathematical thinking and development. Structured individual interviews were conducted with 64 preschool practitioners from rural areas of three Australian states. The questions focused on five broad themes: children's mathematics learning, support for mathematics teaching, technology and computers, attitudes and feelings, and assessment and record keeping. We review results from the interview data for each of these themes, discuss their importance, and outline recommendations related to teacher education as well as resource development and research.

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

    ERIC Educational Resources Information Center

    Cosler, Norma, Ed.

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

  2. Interpreting Mathematics Scores on the New Jersey College Basic Skills Placement Test.

    ERIC Educational Resources Information Center

    Dass, Jane; Pine, Charles

    The New Jersey College Basic Skills Placement Test (NJCBSPT) is designed to measure certain basic language and mathematics skills of students entering New Jersey colleges. The primary purpose of the two mathematics sections is to determine whether students are prepared to begin certain college-level work without a handicap in computation or…

  3. On the Computational Capabilities of Physical Systems. Part 1; The Impossibility of Infallible Computation

    NASA Technical Reports Server (NTRS)

    Wolpert, David H.; Koga, Dennis (Technical Monitor)

    2000-01-01

    In this first of two papers, strong limits on the accuracy of physical computation are established. First it is proven that there cannot be a physical computer C to which one can pose any and all computational tasks concerning the physical universe. Next it is proven that no physical computer C can correctly carry out any computational task in the subset of such tasks that can be posed to C. This result holds whether the computational tasks concern a system that is physically isolated from C, or instead concern a system that is coupled to C. As a particular example, this result means that there cannot be a physical computer that can, for any physical system external to that computer, take the specification of that external system's state as input and then correctly predict its future state before that future state actually occurs; one cannot build a physical computer that can be assured of correctly 'processing information faster than the universe does'. The results also mean that there cannot exist an infallible, general-purpose observation apparatus, and that there cannot be an infallible, general-purpose control apparatus. These results do not rely on systems that are infinite, and/or non-classical, and/or obey chaotic dynamics. They also hold even if one uses an infinitely fast, infinitely dense computer, with computational powers greater than that of a Turing Machine. This generality is a direct consequence of the fact that a novel definition of computation - a definition of 'physical computation' - is needed to address the issues considered in these papers. While this definition does not fit into the traditional Chomsky hierarchy, the mathematical structure and impossibility results associated with it have parallels in the mathematics of the Chomsky hierarchy. The second in this pair of papers presents a preliminary exploration of some of this mathematical structure, including in particular that of prediction complexity, which is a 'physical computation

  4. Linking Preservice Teachers' Mathematics Self-Efficacy and Mathematics Teaching Efficacy to Their Mathematical Performance

    ERIC Educational Resources Information Center

    Bates, Alan B.; Latham, Nancy; Kim, Jin-ah

    2011-01-01

    This study examined preservice teachers' mathematics self-efficacy and mathematics teaching efficacy and compared them to their mathematical performance. Participants included 89 early childhood preservice teachers at a Midwestern university. Instruments included the Mathematics Self-Efficacy Scale (MSES), Mathematics Teaching Efficacy Beliefs…

  5. Visual short term memory related brain activity predicts mathematical abilities.

    PubMed

    Boulet-Craig, Aubrée; Robaey, Philippe; Lacourse, Karine; Jerbi, Karim; Oswald, Victor; Krajinovic, Maja; Laverdière, Caroline; Sinnett, Daniel; Jolicoeur, Pierre; Lippé, Sarah

    2017-07-01

    Previous research suggests visual short-term memory (VSTM) capacity and mathematical abilities are significantly related. Moreover, both processes activate similar brain regions within the parietal cortex, in particular, the intraparietal sulcus; however, it is still unclear whether the neuronal underpinnings of VSTM directly correlate with mathematical operation and reasoning abilities. The main objective was to investigate the association between parieto-occipital brain activity during the retention period of a VSTM task and performance in mathematics. The authors measured mathematical abilities and VSTM capacity as well as brain activity during memory maintenance using magnetoencephalography (MEG) in 19 healthy adult participants. Event-related magnetic fields (ERFs) were computed on the MEG data. Linear regressions were used to estimate the strength of the relation between VSTM related brain activity and mathematical abilities. The amplitude of parieto-occipital cerebral activity during the retention of visual information was related to performance in 2 standardized mathematical tasks: mathematical reasoning and calculation fluency. The findings show that brain activity during retention period of a VSTM task is associated with mathematical abilities. Contributions of VSTM processes to numerical cognition should be considered in cognitive interventions. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

  6. CAS as Environments for Implementing Mathematical Microworlds.

    ERIC Educational Resources Information Center

    Alpers, Burkhard

    2002-01-01

    Investigates whether computer algebra systems (CAS) are suitable environments for implementing mathematical microworlds. Recalls what constitutes a microworld and explores how CAS can be used for implementation, stating potentials as well as limitations. Provides as an example the microworld "Formula 1", implemented in Maple Software. (Author/KHR)

  7. Cryptanalysis in World War II--and Mathematics Education.

    ERIC Educational Resources Information Center

    Hilton, Peter

    1984-01-01

    Hilton describes the team of cryptanalysts who tried to decipher German and Japanese codes during the Second World War. The work of Turing, essentially developing the computer, is reported, as well as inferences about pure and applied mathematics. (MNS)

  8. Case Study Projects for College Mathematics Courses Based on a Particular Function of Two Variables

    ERIC Educational Resources Information Center

    Shi, Y.

    2007-01-01

    Based on a sequence of number pairs, a recent paper (Mauch, E. and Shi, Y., 2005, Using a sequence of number pairs as an example in teaching mathematics, "Mathematics and Computer Education," 39(3), 198-205) presented some interesting examples that can be used in teaching high school and college mathematics classes such as algebra, geometry,…

  9. Computational Evaluation of the Traceback Method

    ERIC Educational Resources Information Center

    Kol, Sheli; Nir, Bracha; Wintner, Shuly

    2014-01-01

    Several models of language acquisition have emerged in recent years that rely on computational algorithms for simulation and evaluation. Computational models are formal and precise, and can thus provide mathematically well-motivated insights into the process of language acquisition. Such models are amenable to robust computational evaluation,…

  10. Contrasts in Mathematical Challenges in A-Level Mathematics and Further Mathematics, and Undergraduate Mathematics Examinations

    ERIC Educational Resources Information Center

    Darlington, Ellie

    2014-01-01

    This article describes part of a study which investigated the role of questions in students' approaches to learning mathematics at the secondary-tertiary interface, focussing on the enculturation of students at the University of Oxford. Use of the Mathematical Assessment Task Hierarchy taxonomy revealed A-level Mathematics and Further Mathematics…

  11. An overview of the mathematical and statistical analysis component of RICIS

    NASA Technical Reports Server (NTRS)

    Hallum, Cecil R.

    1987-01-01

    Mathematical and statistical analysis components of RICIS (Research Institute for Computing and Information Systems) can be used in the following problem areas: (1) quantification and measurement of software reliability; (2) assessment of changes in software reliability over time (reliability growth); (3) analysis of software-failure data; and (4) decision logic for whether to continue or stop testing software. Other areas of interest to NASA/JSC where mathematical and statistical analysis can be successfully employed include: math modeling of physical systems, simulation, statistical data reduction, evaluation methods, optimization, algorithm development, and mathematical methods in signal processing.

  12. Invasion emerges from cancer cell adaptation to competitive microenvironments: Quantitative predictions from multiscale mathematical models

    PubMed Central

    Rejniak, Katarzyna A.; Gerlee, Philip

    2013-01-01

    Summary In this review we summarize our recent efforts using mathematical modeling and computation to simulate cancer invasion, with a special emphasis on the tumor microenvironment. We consider cancer progression as a complex multiscale process and approach it with three single-cell based mathematical models that examine the interactions between tumor microenvironment and cancer cells at several scales. The models exploit distinct mathematical and computational techniques, yet they share core elements and can be compared and/or related to each other. The overall aim of using mathematical models is to uncover the fundamental mechanisms that lend cancer progression its direction towards invasion and metastasis. The models effectively simulate various modes of cancer cell adaptation to the microenvironment in a growing tumor. All three point to a general mechanism underlying cancer invasion: competition for adaptation between distinct cancer cell phenotypes, driven by a tumor microenvironment with scarce resources. These theoretical predictions pose an intriguing experimental challenge: test the hypothesis that invasion is an emergent property of cancer cell populations adapting to selective microenvironment pressure, rather than culmination of cancer progression producing cells with the “invasive phenotype”. In broader terms, we propose that fundamental insights into cancer can be achieved by experimentation interacting with theoretical frameworks provided by computational and mathematical modeling. PMID:18524624

  13. Mathematical modeling in realistic mathematics education

    NASA Astrophysics Data System (ADS)

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

    2017-12-01

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

  14. Mathematics for the Workplace. Applications from Medical Laboratory Technology. A Teacher's Guide.

    ERIC Educational Resources Information Center

    Wallace, Johnny M.; Jones, Dallas

    This module presents a real-world context in which mathematics skills are used as part of a daily routine. The context is the medical laboratory technology field, and the module aims to help students develop the ability to use mathematics computations while performing tasks similar to those performed by a medical technologist. Materials in the…

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

    ERIC Educational Resources Information Center

    Lewis, Jerome

    2005-01-01

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

  16. Multiscale Mathematics for Biomass Conversion to Renewable Hydrogen

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

    Plechac, Petr

    2016-03-01

    The overall objective of this project was to develop multiscale models for understanding and eventually designing complex processes for renewables. To the best of our knowledge, our work is the first attempt at modeling complex reacting systems, whose performance relies on underlying multiscale mathematics and developing rigorous mathematical techniques and computational algorithms to study such models. Our specific application lies at the heart of biofuels initiatives of DOE and entails modeling of catalytic systems, to enable economic, environmentally benign, and efficient conversion of biomass into either hydrogen or valuable chemicals.

  17. Computer Training Helps Appalachians Compete.

    ERIC Educational Resources Information Center

    Newman, Anne

    1984-01-01

    Describes two computer literacy programs funded by the Appalachian Regional Commission, one using microcomputers to introduce computers to mathematics, science, and vocational education teachers in Mississippi, and the other using a statewide microcomputer network to train West Virginia vocational education students in word processing, spread…

  18. Computational Thinking in Mathematics Teacher Education

    ERIC Educational Resources Information Center

    Gadanidis, George; Cendros, Rosa; Floyd, Lisa; Namukasa, Immaculate

    2017-01-01

    As computational thinking (CT) is increasing in focus in K-12 education, it is important to consider how teacher education programs may better prepare teacher candidates (TCs). Previous studies have found that TCs do not always have a firm understanding of what CT involves, and they might not have clear ideas about how to develop CT in their…

  19. High School Mathematics Curricula, University Mathematics Placement Recommendations, and Student University Mathematics Performance

    ERIC Educational Resources Information Center

    Norman, Ke Wu; Medhanie, Amanuel G.; Harwell, Michael R.; Anderson, Edwin; Post, Thomas R.

    2011-01-01

    Recent "math wars" have drawn attention to how well various high school mathematics curricula prepare students for college-level mathematics. The purpose of this study was to investigate the relationship between the high school mathematics curricula and students' post-secondary mathematics placement recommendation, specifically how…

  20. Using Mathematics Literature with Prospective Secondary Mathematics Teachers

    ERIC Educational Resources Information Center

    Jett, Christopher C.

    2014-01-01

    Literature in mathematics has been found to foster positive improvements in mathematics learning. This manuscript reports on a mathematics teacher educator's use of literature via literature circles with 11 prospective secondary mathematics teachers in a mathematics content course. Using survey and reflection data, the author found that…

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