Research in Collegiate Mathematics Education. III

Research in Collegiate Mathematics Education. III

by Alan H. Schoenfeld
     
 

ISBN-10: 0821808826

ISBN-13: 9780821808825

Pub. Date: 08/01/1998

Publisher: American Mathematical Society

Volume III of Research in Collegiate Mathematics Education (RCME) presents state-of-the-art research on understanding, teaching, and learning mathematics at the post-secondary level. This volume contains information on methodology and research concentrating on these areas of student learning: Problem solving. Included here are three different articles analyzing

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Overview

Volume III of Research in Collegiate Mathematics Education (RCME) presents state-of-the-art research on understanding, teaching, and learning mathematics at the post-secondary level. This volume contains information on methodology and research concentrating on these areas of student learning: 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.

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Product Details

ISBN-13:
9780821808825
Publisher:
American Mathematical Society
Publication date:
08/01/1998
Series:
Cbms Issues in Mathematics Education Series, #7
Pages:
316
Product dimensions:
7.09(w) x 9.84(h) x (d)

Table of Contents

Preface
Teaching Mathematical Problem Solving: An Analysis of an Emergent Classroom Community1
An Overview of the Problem Solving Course5
Presenting and Doing Mathematics: An Introduction to Heuristics16
Making the Case for Heuristics: Authority and Direction in the Inscribed Square26
Practicing Mathematical Communication: Using Heuristics with the Magic Square42
On the Implementation of Mathematical Problem Solving Instruction: Qualities of Some Learning Activities71
Reflections on a Course in Mathematical Problem Solving81
A Cross-Sectional Investigation of the Development of the Function Concept114
Honors Students' Calculus Understandings: Comparing Calculus & Mathematica and Traditional Calculus Students163
Supplementary Methods for Assessing Student Performance on a Standardized Test in Elementary Algebra216
Students' Proof Schemes: Results from Exploratory Studies234
Students' Use of Diagrams to Develop Proofs in an Introductory Analysis Course284
Questions Regarding the Teaching and Learning of Undergraduate Mathematics (and Research Thereon)308

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