The Companion Guide to the Mathematical Experience Study Edition
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1995
Birkhiuser Boston • Basel • Berlin
Philip 1. Davis Division of Applied Mathematics Brown University Providence, RI 02912 Elena Anne Marchisotto Department of Mathematics California State University, Northridge Northridge, CA 91330-8313
Reuben Hersh Department of Mathematics and Statistics University of New Mexico Albuquerque, NM 87131
Printed on acid-free paper
«> 1995 Birkhliuser
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e-ISBN-13: 978-1-4612-4280-2
Text for The Companion Guide to the Mathematical Experience Study Edition was typeset by Martin Stock, Cambridge, MA
987654321
Contents I. Introduction to this Companion Guide
A Note to Instructors Special Features In the Text Topics to Explore, Essay Assignments, Problems, Computer Problems, Suggested Readings In the Companion Guide Expository Research Papers, Topics for Classroom Discussion, Projects, Tutorials
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5
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II. Chapter Guidelines
1. The Mathematical Landscape 2. Varieties of Mathematical Experience 3. Outer Issues 4. Inner Issues 5. Selected Topics in Mathematics 6. Teaching and Learning 7. From Certainty to Fallibility 8. Mathematical Reality
11 12 32 37 54 59 64 67
III. Sample Syllabus
First Day Handout Syllabus
75 76
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Contents IV. Sample Group Activities The Mathematical Experience The Mathematical Landscape Varieties of Mathematical Experience Outer Issues: Utility Inner Issues The Pythagorean Theorem Pythagorean Triples Pascal's Triangle Connections: The Golden Ratio and Fibonacci Numbers From Certainty to Fallibility Mathematical Reality
89 90 91
92 93 94
95 96
97 98 99
V. Sample Examinations Sample Take-Home Examination Sample Examination Sample Midterm Examination Sample Final Examination VI. Topics for Expository Research Papers Topics for Expository Research Papers Suggestions for Grading Essays and Research Papers
vi
103 105 107 108 113 119
The COlDpanion Guide to
The Mathematical Experience Study Edition
Part I Introduction to this Companion Guide
A Note to Instructors The first Mathematical Experience appeared in 1981. At that time, only a few years ago, it was commonly believed that it was impossible to make contemporary mathematics meaningful to the intelligent non-mathematician. Since then, dozens of popular
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