Research in Collegiate Mathematics Education. III

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Brand new. We distribute directly for the publisher. 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. Read more Show Less

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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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Editorial Reviews

Booknews
Thirteen contributions address three main topics: methods for examining student thinking; the ways in which students think about, and try to deal with, the idea of proof in mathematics; and a particular undergraduate course in mathematical problem solving. Topics include the development of the function concept, honors students' understanding of calculus, and the use of heuristics in the course. No index. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

Table of Contents

Preface
Teaching Mathematical Problem Solving: An Analysis of an Emergent Classroom Community 1
An Overview of the Problem Solving Course 5
Presenting and Doing Mathematics: An Introduction to Heuristics 16
Making the Case for Heuristics: Authority and Direction in the Inscribed Square 26
Practicing Mathematical Communication: Using Heuristics with the Magic Square 42
On the Implementation of Mathematical Problem Solving Instruction: Qualities of Some Learning Activities 71
Reflections on a Course in Mathematical Problem Solving 81
A Cross-Sectional Investigation of the Development of the Function Concept 114
Honors Students' Calculus Understandings: Comparing Calculus & Mathematica and Traditional Calculus Students 163
Supplementary Methods for Assessing Student Performance on a Standardized Test in Elementary Algebra 216
Students' Proof Schemes: Results from Exploratory Studies 234
Students' Use of Diagrams to Develop Proofs in an Introductory Analysis Course 284
Questions Regarding the Teaching and Learning of Undergraduate Mathematics (and Research Thereon) 308
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