Learn from the Masters (Classroom Resource Materials)

✍ Scribed by Frank Swetz, John Fauvel, Bengt Johansson, Victor Katz, Otto Bekken

• Publisher: The Mathematical Association of America
• Year: 1997
• Tongue: English
• Leaves: 311
• Category: Library

✦ Synopsis

This book is for high school and college teachers who want to know how they can use the history of mathematics as a pedagogical tool to help their students construct their own knowledge of mathematics. Often, a historical development of a particular topic is the best way to present a mathematical topic, but teachers may not have the time to do the research needed to present the material. This book provides its readers with historical ideas and insights which can be immediately applied in the classroom. The book is divided into two sections: the first on the use of history in high school mathematics, and the second on its use in university mathematics. The articles are diverse, covering fields such as trigonometry, mathematical modeling, calculus, linear algebra, vector analysis, and celestial mechanics. Also included are articles of a somewhat philosophical nature, which give general ideas on why history should be used in teaching and how it can be used in various special kinds of courses. Each article contains a bibliography to guide the reader to further reading on the subject.

✦ Table of Contents

Cover......Page 1
Title page......Page 2
Preface......Page 6
Contents......Page 8
Part I: History in School Mathematics......Page 10
1. History of Mathematics Can Help Improve Instruction and Learning by Shmuel Avital......Page 12
2. The Role in the History of Mathematics of Algorithms and Analogies by Phi11ip S. Jones......Page 22
3. Using Problems from the History of Mathematics in Classroom Instruction by Frank. J. Swetz......Page 34
4. Revisiting the History of Logarithms by John Fauvel......Page 48
5. Napier's Logarithms Adapted for Today's Classroom by Victor J. Katt......Page 58
6. Trigonometry Comes Out of the Shadows by Frank J. Swetz......Page 66
7. Alluvial Deposits, Conic Sections and Improper Glasses, or History of Mathematics Applied in the Classroom by Jan A. van Maanen......Page 82
8. An Historical Example of Mathematical Modeling:The Trajectory of a Cannonball by Frank J. Swetz......Page 102
Part II: History in Higher Mathematics......Page 112
9. Concept of Function-Its History and Teaching by Man-Keung Siu......Page 114
10. My Favorite Ways of Using History in Teaching Calculus by V. Frederick Rickey......Page 132
11. Improved Teaching of the Calculus Through the Use of Historical Materials by Michel Helfgott......Page 144
12. Euler and Heuristic Reasoning by Man-Keung Siu......Page 154
13. Converging Concepts of Series: Learning from History by Joel P. Lehmann......Page 170
14. Historical Thoughts on Infinite Numbers by Lars Mejbo......Page 190
15. Historical Ideas in Teaching Linear Algebra by Victor J. Katz......Page 198
16. Wessel on Vectors by Otto B. Bekken......Page 216
17. Who Needs Vectors? by Karen Reich......Page 224
18. The Teaching of Abstract Algebra: An Historical Perspective by Israel Kleiner......Page 234
19. Toward the Definition of an Abstract Ring by David M. Burton and Donovan H. Van Osdol......Page 250
20. In Hilbert's Shadow: Notes Toward a Redefinition of Introductory Group Theory by Anthony D.Gardiner......Page 262
21. An Episode in the History of Celestial Mechanics and Its Utility in the Teaching of Applied Mathematics by Eric J. Aiton......Page 276
22. Mathematical Thinking and History of Mathematics by Man-Keung Siu......Page 288
23. A Topics Course in Mathematics by Abe Shenitzer......Page 292
Niels Henrik Abel (I 802-1 829): A Tribute......Page 306
About the Authors:......Page 310