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

Preface

Part I: History in School Mathematics

1. History of Mathematics can Help Improve Instruction and Learning by Shmuel Avital

2. The Role in the History of Mathematics of Algorithms and Analogies by Phillip S. Jones

3. Using Problems from the History of Mathematics in Classroom Instructions by Frank J. Swetz

4. Revisiting the History of Logarithms by John Fauvel

5. Napeir's Logarithms Adapted for Today's Classroom by Victor J. Katz

6. Trigonometry Comes Out of the Shadows by Frank J. Swetz

7. Alluvial Deposits, Conic Sections, and Improper Glasses, or History of Mathematics Applied in the Classroom by Jan A. can Maanen

8. An Historical Example of Mathematical Modeling: The Trajectory of a Cannonball by Frank J. Swift

Part II: History in Higher Mathematics

9. Concept of Function-Its History and Teaching by Man-Keung Siu

10. My Favorite Ways of Using History in Teaching Calculus by V. Fredrick Rickey

11. Improved Teaching of the Calculus Through the Use of Historical Materials by Michel Helfgott

12. Euler and Heuristic Reasoning by Man-Keung Siu

13. Converging Concepts of Series: Learning from History by Joel P. Lehmann

14. Historical Thoughts on Infinite Numbers by Lars Mejibo

15. Historical Ideas in Teaching Linear Algebra by Victor J. Katz

16. Wessel on Vectors by Otto B. Bekken

17. Who Needs Vectors? By Karen Reich

18. The Teaching of Abstract Algebra: An Historical Perspective by Israel Kleiner

19. Toward the Definition of an Abstract Ring by David M. Burton and Donovan H. Can Osdol

20. In Hilbert's Shadow: Notes Toward a Redefinition of Introductory Group Theory by Anthony D. Gardiner

21. An Episode in the History of Celestial Mechanics and Its Utility in the Teaching of Applied Mathematics by Eric J. Aiton

22. Mathematical Thinking and History of Mathematics by Man-Keung Siu

23. A Topics Course in Mathematics by Abe Shenitzer