- 巻冊次
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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
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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.
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