# Research in Collegiate Mathematics Education. III

Share this page *Edited by *
*Alan H. Schoenfeld; Jim Kaput; Ed Dubinsky; Thomas Dick*

A co-publication of the AMS and CBMS

Volume III of

- 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.

This series is published in cooperation with the Mathematical Association of America.

#### Readership

Graduate students, research mathematicians and general mathematical readers interested in mathematics education.

#### Table of Contents

# Table of Contents

## Research in Collegiate Mathematics Education. III

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents v6 free
- Preface vii8 free
- Teaching Mathematical Problem Solving: An Analysis of an Emergent Classroom Community 114 free
- An Overview of the Problem Solving Course 518
- Presenting and Doing Mathematics: An Introduction to Heuristics 1629
- Making the Case for Heuristics: Authority and Direction in the Inscribed Square 2639
- Practicing Mathematical Communication: Using Heuristics with the Magic Square 4255
- On the Implementation of Mathematical Problem Solving Instruction: Qualities of Some Learning Activities 7184
- Reflections on a Course in Mathematical Problem Solving 8194
- A Cross-Sectional Investigation of the Development of the Function Concept 114127
- Honors Students' Calculus Understandings: Comparing Calculus&Mathematica and Traditional Calculus Students 163176
- Supplementary Methods for Assessing Student Performance on a Standardized Test in Elementary Algebra 216229
- Students' Proof Schemes: Results from Exploratory Studies 234247
- Students' Use of Diagrams to Develop Proofs in an Introductory Analysis Course 284297
- Questions Regarding the Teaching and Learning of Undergraduate Mathematics (and Research Thereon) 308321
- Back Cover Back Cover1330