Making the Connection: Research and Teaching in Undergraduate Mathematics Education

doi:10.5948/UPO9780883859759

The chapters in this volume convey insights from mathematics education research that have direct implications for anyone interested in improving teaching and learning in undergraduate mathematics. This synthesis of research on learning and teaching mathematics provides relevant information for any mathematics department or any individual faculty member who is working to improve introductory proof courses, the longitudinal coherence of precalculus through differential equations, students' mathematical thinking and problem solving abilities, and students' understanding of fundamental ideas such as variable, and rate of change. Other chapters include information about programs that have been successful in supporting students' continued study of mathematics. The authors provide many examples and ideas to help the reader infuse the knowledge from mathematics education research into mathematics teaching practice.

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Contents

1 - On Developing a Rich Conception of Variable
pp 3-14
- By Maria Trigueros, Instituto Tecnológico Autónomo de México, Sally Jacobs, Scottsdale Community College
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2 - Rethinking Change
pp 15-26
- By Bob Speiser, Brigham Young University, Chuck Walter, Brigham Young University
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3 - Foundational Reasoning Abilities that Promote Coherence in Students' Function Understanding
pp 27-42
- By Michael Oehrtman, Arizona State University, Marilyn Carlson, Arizona State University, Patrick Thompson, Arizona State University
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4 - The Concept of Accumulation in Calculus
pp 43-52
- By Patrick Thompson, Arizona State University, Jason Silverman, Drexel University
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5 - Developing Notions of Infinity
pp 55-64
- By Michael A. McDonald, Occidental College, Anne Brown, Indiana University South Bend
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6 - Layers of Abstraction: Theory and Design for the Instruction of Limit Concepts
pp 65-80
- By Michael Oehrtman, Arizona State University
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7 - Divisibility and Transparency of Number Representations
pp 81-92
- By Rina Zazkis, Simon Fraser University
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8 - Overcoming Students' Difficulties in Learning to Understand and Construct Proofs
pp 95-110
- By Annie Selden, New Mexico State University, John Selden, New Mexico State University
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9 - Mathematical Induction: Cognitive and Instructional Considerations
pp 111-124
- By Guershon Harel, University of California, San Diego, Stacy Brown, Pitzer College
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10 - Proving Starting from Informal Notions of Symmetry and Transformations
pp 125-138
- By Michelle Zandieh, Arizona State University, Sean Larson, Portland State University, Denise Nunley, Arizona State University
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11 - Teaching and Learning Group Theory
pp 139-152
- By Keith Weber, Rutgers University, Sean Larsen, Portland State University
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12 - Teaching for Understanding: A Case of Students' Learning to Use the Uniqueness Theorem as a Tool in Differential Equations
pp 153-164
- By Chris Rasmussen, San Diego State University, Wei Ruan, Purdue University Calumet
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13 - Meeting New Teaching Challenges: Teaching Strategies that Mediate Between All Lecture and All Student Discovery
pp 167-178
- By Karen Marrongelle, Portland State University, Chris Rasmussen, San Diego State University
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14 - Examining Interaction Patterns in College-Level Mathematics Classes: A Case Study
pp 179-190
- By Susan Nickerson, San Diego State University, Janet Bowers, San Diego State University
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15 - Mathematics as a Constructive Activity: Exploiting Dimensions of Possible Variation
pp 191-204
- By John Mason, Open University, Anne Watson, Oxford University
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16 - Supporting High Achievement in Introductory Mathematics Courses: What We Have Learned from 30 Years of the Emerging Scholars Program
pp 205-220
- By Eric Hsu, San Francisco State University, Teri J. Murphy, University of Oklahoma, Uri Treisman, University of Texas at Austin
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17 - The Role of Mathematical Definitions in Mathematics and in Undergraduate Mathematics Courses
pp 223-232
- By Barbara Edwards, Oregon State University, Michael Ward, Western Oregon University
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18 - Computer-Based Technologies and Plausible Reasoning
pp 233-244
- By Natalie Sinclair, Simon Fraser University
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19 - Worked Examples and Concept Example Usage in Understanding Mathematical Concepts and Proofs
pp 245-252
- By Keith Weber, Rutgers University, Mary Porter, Saint Mary's College, David Housman, Goshen College
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Making the Connection

Research and Teaching in Undergraduate Mathematics Education

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