Research in collegiate mathematics education

著者

• Dubinsky, Ed
• Schoenfeld, Alan H.
• Kaput, Jim
• Conference Board of the Mathematical Sciences
• Selden, Annie
• Hitt, Fernando
• Harel, Guershon
• Holton, Derek
• Thompson, Patrick W.

書誌事項

Research in collegiate mathematics education

Ed Dubinsky, Alan H. Schoenfeld, Jim Kaput, editors

（Issues in mathematics education, v. 4,6-8,12-13,16）

American Mathematical Society in cooperation with Mathematical Association of America, c1994-

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タイトル別名

CBMS : Conference Board of the Mathematical Sciences

注記

5: Annie Selden ... [et al.]

6: Fernando Hitt, Guershon Harel, Annie Selden, editors. Shandy Hauk, production editor

Includes bibliographical references

7: Fernando Hitt, Derek Holton, Patrick W. Thompson, editors

内容説明・目次

巻冊次

2 ISBN 9780821803820

内容説明

The field of research in collegiate mathematics education has grown rapidly over the past twenty-five years. Many people are convinced that improvement in mathematics education can only come with a greater understanding of what is involved when a student tries to learn mathematics and how pedagogy can be more directly related to the learning process. Today there is a substantial body of work and a growing group of researchers addressing both basic and applied issues of mathematics education at the collegiate level.This second volume in ""Research in Collegiate Mathematics Education"" begins with a paper that attends to methodology and closes with a list of questions. The lead-off paper describes a distinctive approach to research on key concepts in the undergraduate mathematics curriculum. This approach is distinguished from others in several ways, especially its integration of research and instruction. The papers in this volume exhibit a large diversity in methods and purposes, ranging from historical studies, to theoretical examinations of the role of gender in mathematics education, to practical evaluations of particular practices and circumstances. As in RCME I, this volume poses a list of questions to the reader related to undergraduate mathematics education. The eighteen questions were raised at the first Oberwolfach Conference in Undergraduate Mathematics Education, which was held in the fall of 1995, and are related to both research and curriculum.

目次

A framework for research and curriculum development in undergraduate mathematics education by M. Asiala, A. Brown, D. J. DeVries, E. Dubinsky, D. Mathews, and K. Thomas The creation of continuous exponents: A study of the methods and epistemology of John Wallis by D. Dennis and J. Confrey Dihedral groups: A tale of two interpretations by R. Zazkis and E. Dubinsky To major or not major in mathematics? Affective factors in the choice-of-major decision by A. R. Leitze Success in mathematics: Increasing talent and gender diversity among college majors by M. C. Linn and C. Kessel Analysis of effectiveness of supplemental instruction (SI) sessions for college algebra, calculus, and statistics by S. L. Burmeister, P. A. Kenney, and D. L. Nice A comparative study of a computer-based and a standard college first-year calculus course by K. Park and K. J. Travers Differential patterns of guessing and omitting in mathematics placement testing by A. Baranchik and B. Cherkas A perspective on mathematical problem-solving expertise based on the performances of male Ph.D. mathematicians by T. C. DeFranco Questions on new trends in the teaching and learning of mathematics: The Oberwolfach Conference, 27 November-1 December, 1995.

巻冊次

3 ISBN 9780821808825

内容説明

Volume III of Research in Collegiate Mathematics Education (RCME) presents state-of-the-art research on understanding, teaching, and learning mathematics at the post-secondary level. This volume contains information on methodology and research concentrating on these areas of student learning: Problem solving - included here are three different articles analyzing aspects of Schoenfeld's undergraduate problem-solving instruction. The articles provide new detail and insight on a well-known and widely discussed course taught by Schoenfeld for many years. Understanding concepts - these articles feature a variety of methods used to examine students' understanding of the concept of a function and selected concepts from calculus. The conclusions presented offer unique and interesting perspectives on how students learn concepts.Understanding proofs - this section provides insight from a distinctly psychological framework. Researchers examine how existing practices can foster certain weaknesses. They offer ways to recognize and interpret students' proof behaviors and suggest alternative practices and curricula to build more powerful schemes. The section concludes with a focused look at using diagrams in the course of proving a statement.

目次

Teaching mathematical problem solving: An analysis of an emergent classroom community by A. Arcavi, L. Meira, J. P. Smith III, and C. Kessel On the implementation of mathematical problem solving instruction: Qualities of some learning activities by M. Santos-Trigo Reflections on a course in mathematical problem solving by A. H. Schoenfeld A cross-sectional investigation of the development of the function concept by M. P. Carlson Honors students' calculus understandings: Comparing calculus&mathematica and traditional calculus students by D. E. Meel Supplementary methods for assessing student performance on a standardized test in elementary algebra by A. Baranchik and B. Cherkas Students' proof schemes: Results from exploratory studies by G. Harel and L. Sowder Students' use of diagrams to develop proofs in an introductory analysis course by D. Gibson Questions regarding the teaching and learning of undergraduate mathematics (and research thereon) by A. Selden and J. Selden.

巻冊次

4 ISBN 9780821820285

内容説明

This fourth volume of ""Research in Collegiate Mathematics Education"" (""RCME IV"") reflects the themes of student learning and calculus. Included are overviews of calculus reform in France and in the U.S. and large-scale and small-scale longitudinal comparisons of students enrolled in first-year reform courses and in traditional courses. The work continues with detailed studies relating students' understanding of calculus and associated topics. Direct focus is then placed on instruction and student comprehension of courses other than calculus, namely abstract algebra and number theory. The volume concludes with a study of a concept that overlaps the areas of focus, quantifiers. The book clearly reflects the trend towards a growing community of researchers who systematically gather and distill data regarding collegiate mathematics' teaching and learning.

目次

Teaching and learning calculus: What can be learned from education research and curricular changes in France? by M. Artigue Evaluating calculus reform: A review and a longitudinal study by B. Darken, R. Wynegar, and S. Kuhn The need for evaluation in the calculus reform movement. A comparison of two calculus teaching methods by S. L. Ganter and M. R. Jiroutek A longitudinal study of the C$^4$L calculus reform program: Comparisons of C$^4$L and traditional students by K. E. Schwingendorf, G. P. McCabe, and J. Kuhn Understanding sequences: A tale of two objects by M. A. McDonald, D. M. Mathews, and K. H. Strobel A theoretical framework for analyzing student understanding of the concept of derivative by M. J. Zandieh Why can't calculus students access their knowledge to solve non-routine problems? by A. Selden, J. Selden, S. Hauk, and A. Mason Lasting effects of the integrated use of graphing technologies in precalculus mathematics by W. O. Martin Visual confusion in permutation representations by J. Hannah Factors, divisors, and multiples: Exploring the web of students' connections by R. Zazkis On student understanding of AE and EA quantification by E. Dubinsky and O. Yiparaki.

巻冊次

5 ISBN 9780821833025

内容説明

This fifth volume of ""Research in Collegiate Mathematics Education"" (RCME) presents state-of-the-art research on understanding, teaching, and learning mathematics at the post-secondary level. The articles in RCME are peer-reviewed for two major features: advancing our understanding of collegiate mathematics education, and readability by a wide audience of practicing mathematicians interested in issues affecting their own students. This is not a collection of scholarly arcana, but a compilation of useful and informative research regarding the ways our students think about and learn mathematics.The volume begins with a study from Mexico of the cross-cutting concept of variable followed by two studies dealing with aspects of calculus reform. The next study frames its discussion of students' conceptions of infinite sets using the psychological work of Efraim Fischbein on (mathematical) intuition. This is followed by two papers concerned with APOS theory and other frameworks regarding mathematical understanding. The final study provides some preliminary results on student learning using technology when lessons are delivered via the Internet. Whether specialists in education or mathematicians interested in finding out about the field, readers will obtain new insights about teaching and learning and will take away ideas they can use.

目次

First-year undergraduates' difficulties in working with different uses of variable by M. Trigueros and S. Ursini Cooperative learning in calculus reform: What have we learned? by A. Herzig and D. T. Kung Calculus reform and traditional students' use of calculus in an engineering mechanics course by C. Roddick Primary intuitions and instruction: The case of actual infinity by P. Tsamir Student performance and attitudes in courses based on APOS theory and the ACE teaching cycle by K. Weller, J. M. Clark, E. Dubinsky, S. Loch, M. A. McDonald, and R. R. Merkovsky Models and theories of mathematical understanding: Comparing Pirie and Kieren's model of the growth of mathematical understanding and APOS theory by D. E. Meel The nature of learning in interactive technological environments: A proposal for a research agenda based on grounded theory by J. Bookman and D. Malone.

巻冊次

1 ISBN 9780821835043

内容説明

The field of research in collegiate mathematics education has grown rapidly over the past twenty-five years. Many people are convinced that improvement in mathematics education can only come with a greater understanding of what is involved when a student tries to learn mathematics and how pedagogy can be more directly related to the learning process. Today there is a substantial body of work and a growing group of researchers addressing both basic and applied issues of mathematics education at the collegiate level.This volume is testimony to the growth of the field. The intention is to publish volumes on this topic annually, doing more or less as the level of growth dictates. The introductory articles, survey papers, and current research that appear in this first issue convey some aspects of the state of the art. The book is aimed at researchers in collegiate mathematics education and teachers of college-level mathematics courses who may find ideas and results that are useful to them in their practice of teaching, as well as the wider community of scholars interested in the intellectual issues raised by the problem of learning mathematics.

目次

Some notes on the enterprise (research in collegiate mathematics education, that is) by A. H. Schoenfeld Students, functions, and the undergraduate curriculum by P. W. Thompson On understanding how students learn to visualize function transformations by T. Eisenberg and T. Dreyfus Three approaches to undergraduate calculus instruction: Their nature and potential impact on students' language use and sources of conviction by S. Frid A comparison of the problem solving performance of students in lab based and traditional calculus by J. Bookman and C. P. Friedman An efficacy study of the calculus workshop model by M. V. Bonsangue The case of Dan: Student construction of a functional situation through visual attributes by S. Monk and R. Nemirovsky The effect of the graphing calculator on female students' spatial visualization skills and level-of-understanding in elementary graphing and algebra concepts by M. M. Shoaf-Grubbs To the right of the "decimal" point: Preservice teachers' concepts of place value and multidigit structures by R. Zazkis and H. Khoury Twenty questions about research on undergraduate mathematics education by L. A. Steen.

巻冊次

6 ISBN 9780821842430

内容説明

The sixth volume of Research in Collegiate Mathematics Education presents state-of-the-art research on understanding, teaching, and learning mathematics at the postsecondary level. The articles advance our understanding of collegiate mathematics education while being readable by a wide audience of mathematicians interested in issues affecting their own students. This is a collection of useful and informative research regarding the ways our students think about and learn mathematics. The volume opens with studies on students' experiences with calculus reform and on the effects of concept-based calculus instruction. The next study uses technology and the van Hiele framework to help students construct concept images of sequential convergence. The volume continues with studies on developing and assessing specific competencies in real analysis, on introductory complex analysis, and on using geometry in teaching and learning linear algebra. It closes with a study on the processes used in proof construction and another on the transition to graduate studies in mathematics. Whether they are specialists in education or mathematicians interested in finding out about the field, readers will obtain new insights about teaching and learning and will take away ideas that they can use. Information for our distributors: This series is published in cooperation with the Mathematical Association of America.

目次

An image of calculus reform: Students' experiences of Harvard calculus by J. R. Star and J. P. Smith III Effects of concept-based instruction on calculus students' acquisition of conceptual understanding and procedural skill by K. K. Chappell Constructing a concept image of convergence of sequences in the van Hiele framework by M. A. Navarro and P. P. Carreras Developing and assessing specific competencies in a first course on real analysis by N. Gronbaek and C. Winslow Introductory complex analysis at two British Columbia universities: The first week-complex numbers by P. Danenhower Using geometry to teach and learn linear algebra by G. Gueudet-Chartier Investigating and teaching the processes used to construct proofs by K. Weber The transition to independent graduate studies in mathematics by J. Duffin and A. Simpson.

巻冊次

7 ISBN 9780821849965

内容説明

The present volume of Research in Collegiate Mathematics Education, like previous volumes in this series, reflects the importance of research in mathematics education at the collegiate level. The editors in this series encourage communication between mathematicians and mathematics educators, and as pointed out by the International Commission of Mathematics Instruction (ICMI), much more work is needed in concert with these two groups. Indeed, editors of RCME are aware of this need and the articles published in this series are in line with that goal. Nine papers constitute this volume. The first two examine problems students experience when converting a representation from one particular system of representations to another. The next three papers investigate students learning about proofs. In the next two papers, the focus is instructor knowledge for teaching calculus. The final two papers in the volume address the nature of "conception" in mathematics. Whether they are specialists in education or mathematicians interested in finding out about the field, readers will obtain new insights about teaching and learning and will take away ideas that they can use. This series is published in cooperation with the Mathematical Association of America.

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詳細情報

• NII書誌ID(NCID): BA23474267
• ISBN:
  • 0821835041
  • 0821803824
  • 0821808826
  • 0821820281
  • 0821833022
  • 0821842439
  • 9780821849965
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Providence, R.I.
• ページ数/冊数: v.
• 大きさ: 26 cm
• 分類:
  • NDC8 : 410.7
• 親書誌ID:
  • BA1072604X