Mathematics as a Constructive Activity: Learners Generating Examples

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ISBN: 9780805843439 | 0805843434
Cover: Hardcover
Copyright: 5/17/2005

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Explains & demonstrates the role of examples in the teaching & learning of mathematics, & their place in mathematics generally at all levels.Includes a combination of exercises for the reader, practical applications for teaching,&solid scholarly groundin

Preface	p. ix
Introduction to Exemplification in Mathematics	p. 1
What Is an Example?	p. 3
On Whose Shoulders Are We Standing?	p. 6
Summary	p. 9
Learner-Generated Examples in Classrooms	p. 10
Teacher-Initiated, Learner-Generated Examples	p. 12
Learners Using Examples, Counterexamples, and Extreme Examples	p. 25
Initial Theorizing: Shifting Responsibility	p. 30
Summary	p. 32
From Examples to Example Spaces	p. 33
A Difference of 2	p. 34
Inter-Rootal Distances	p. 39
How Do These Themes Relate to Our Work With Other Groups?	p. 51
Summary	p. 57
The Development of Learners' Example Spaces	p. 59
Reminder: What Is an Example Space?	p. 59
Metaphors	p. 60
Central Examples	p. 62
Nonexamples and Counterexamples	p. 65
Promoting Development	p. 70
Summary	p. 90
Pedagogical Tools for Developing Example Spaces	p. 92
Kinds of Examples	p. 92
Encountering Important Examples	p. 103
Constructing New Objects for Oneself	p. 110
Being Asked to Give Examples: The Larder Metaphor	p. 130
Summary	p. 132
Strategies for Prompting and Using Learner-Generated Examples	p. 133
Case Studies	p. 133
Summary of Strategies	p. 150
Focus on Action	p. 157
Practice and Fluency	p. 158
Summary	p. 159
Mathematics as a Constructive Activity	p. 160
Constructive Constraints	p. 161
Building Confidence	p. 168
Learning as Construction	p. 176
Gathering Threads	p. 183
Constructed Outcomes	p. 191
Epilogue: Constructing Tasks	p. 195
Some Historical Remarks on Teaching by Examples	p. 197
Early Practices and Implicit Theories	p. 198
Explicit Theories and Implicit Practices	p. 200
The Inductive Method	p. 204
Toward the More Active Learner	p. 206
Summary	p. 208
Suggestions About Some of the Tasks	p. 210
References	p. 213
Author Index	p. 223
Subject Index	p. 227
Table of Contents provided by Ingram. All Rights Reserved.

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Mathematics as a Constructive Activity: Learners Generating Examples

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Table of Contents

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