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Making the Connection

Marilyn Carlson and Chris Rasmussen, editors

Ebook Version FREE to MAA Members

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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

  PDF Price   POD Price  
Making the Connection $35.00    
  Price per Chapter   Price per Chapter  
Part I.  Student Thinking        
1a. Foundations for Beginning Calculus        
1.  On Developing a Rich Conception of Variable $7.00 cart $8.50 pod shopping cart
2.  Rethinking Change $7.00 cart $8.50 pod shopping cart
3.  Foundational Reasoning Abilities that Promote Coherence in Students’ Function  Understanding $7.00 cart $9.00 pod shopping cart
4.  The Concept of Accumulation in Calculus $7.00 cart $8.50 pod shopping cart
1b. Infinity, Limit and Divisibility        
5.  Developing Notions of Infinity $7.00 cart $8.50 pod shopping cart
6.  Layers of Abstraction: Theory and Design for the Instruction of Limit Concepts $7.00 cart $9.00 pod shopping cart
7.  Divisibility and Transparency of Number Representations $7.00 cart $8.50 pod shopping cart
1c. Proving Theorems        
8.  Overcoming Students’ Difficulties in Learning to Understand and Construct Proofs $7.00 cart $8.75 pod shopping cart
9.  Mathematical Induction: Cognitive and Instructional Considerations $7.00 cart $8.75 pod shopping cart
10.  Proving Starting from Informal Notions of Symmetry and Transformations $7.00 cart $8.75 pod shopping cart
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 cart $8.75 pod shopping cart
12.  Teaching for Understanding: A Case of Students’ Learning to Use the Uniqueness Theorem as a Tool in Differential Equations $7.00 cart $8.50 pod shopping cart
Part 2. Cross-Cutting Themes        
2a. Interacting with Students        

13.  Meeting New Teaching Challenges: Teaching Strategies That Mediate Between All Lecture and All Student Discovery

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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 cart $9.00 pod shopping cart
2b. Using Definitions, Examples and Technology        

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 cart $8.50 pod shopping cart
19.  Worked Examples and Concept Example Usage in Understanding Mathematical Concepts and Proofs $7.00 cart $9.00 pod shopping cart
2c. Knowledge, Assumptions, and Problem Solving Behaviors for Teaching        
20.  From Concept Images to Pedagogic Structure for a Mathematical Topic $7.00 cart $9.25 pod shopping cart

21.  Promoting Effective Mathematical Practices in Students: Insights from Problem Solving Research

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

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


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