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.

University mathematicians and community college faculty spend much of their time engaged in work to improve their teaching. Frequently, they are left to their own experiences and informal conversations with colleagues to develop new approaches to support student learning and their continuation in mathematics. Over the past 30 years, research in undergraduate mathematics education has produced knowledge about the development of mathematical understandings and models for supporting students' mathematical learning. Currently, very little of this knowledge is affecting teaching practice. We hope that this volume will open a meaningful dialogue between researchers and practitioners toward the goal of realizing improvements in undergraduate mathematics curriculum and instruction.

Electronic ISBN: 9780883859759

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Making the Connection |
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Part I. Student Thinking |
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1a. Foundations for Beginning Calculus |
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1. On Developing a Rich Conception of Variable | $7.00 | $8.50 | http://www.maa.org | |

2. Rethinking Change | $7.00 | $8.50 | ||

3. Foundational Reasoning Abilities that Promote Coherence in Students’ Function Understanding | $7.00 | $9.00 | ||

4. The Concept of Accumulation in Calculus | $7.00 | $8.50 | ||

1b. Infinity, Limit and Divisibility |
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5. Developing Notions of Infinity | $7.00 | $8.50 | ||

6. Layers of Abstraction: Theory and Design for the Instruction of Limit Concepts | $7.00 | $9.00 | ||

7. Divisibility and Transparency of Number Representations | $7.00 | $8.50 | ||

1c. Proving Theorems |
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8. Overcoming Students’ Difficulties in Learning to Understand and Construct Proofs | $7.00 | $8.75 | ||

9. Mathematical Induction: Cognitive and Instructional Considerations | $7.00 | $8.75 | ||

10. Proving Starting from Informal Notions of Symmetry and Transformations | $7.00 | $8.75 | ||

11. Teaching and Learning Group Theory Teaching for Understanding: A Case of Students’ Learning to Use the Uniqueness Theorem as a Tool in Differential Equations | $7.00 | $8.75 | ||

12. Teaching for Understanding: A Case of Students’ Learning to Use the Uniqueness Theorem as a Tool in Differential Equations | $7.00 | $8.50 | ||

Part 2. Cross-Cutting Themes |
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2a. Interacting with Students |
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13. Meeting New Teaching Challenges: Teaching Strategies That Mediate Between All Lecture and All Student Discovery |
$7.00 | $8.50 | ||

14. Examining Interaction Patterns in College-Level Mathematics Classes: A Case Study |
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15. Mathematics as a Constructive Activity: Exploiting Dimensions of Possible Variation |
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16. Supporting High Achievement in Introductory Mathematics Courses: What We Have Learned from 30 Years of the Emerging Scholars Program | $7.00 | $9.00 | ||

2b. Using Definitions, Examples and Technology |
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17. The Role of Mathematical Definitions in Mathematics and in Undergraduate Mathematics Courses |
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18. Computer-Based Technologies and Plausible Reasoning | $7.00 | $8.50 | ||

19. Worked Examples and Concept Example Usage in Understanding Mathematical Concepts and Proofs | $7.00 | $9.00 | ||

2c. Knowledge, Assumptions, and Problem Solving Behaviors for Teaching |
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20. From Concept Images to Pedagogic Structure for a Mathematical Topic | $7.00 | $9.25 | ||

21. Promoting Effective Mathematical Practices in Students: Insights from Problem Solving Research |
$7.00 | $8.75 | ||

22. When Students Don’t Apply the Knowledge You Think They Have, Rethink Your Assumptions about Transfer |
$7.00 | $9.00 | ||

23. How Do Mathematicians Learn To Teach? Implications from Research on Teachers and Teaching for Graduate Student Professional Development | $7.00 | $8.75 |

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