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Learn from the Masters

Learn From the Masters

Frank Swetz, John Fauvel, Otto Bekken, Bengt Johansson, and Victor Katz, Editors

Print ISBN: 978-0-88385-703-8
312 pp., Paperbound, 1995
List Price: $40.00
Member Price: $30.00
Series: Classroom Resource Materials

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This book is for college and secondary school 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 the 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 secondary school mathematics, and the second on its use in university mathematics. So, teachers planning a discussion of logarithms, will find here the historical background of that idea along with suggestions for incorporating that history in the development of the idea in class. Teachers of abstract algebra will benefit by reading the three articles in the book dealing with aspects of that subject and considering their ideas for presenting groups, rings, and fields.

Table of Contents

1. History of Mathematics Can Help Improve Instruction and Learning
2. The Role in the History of Mathematics of Algorithms and Analogies
3. Using Problems from the History of Mathematics in Classroom Instruction
4. Revisiting the History of Logarithms
5. Napier’s Logarithms Adapted for Today’s Classroom
6. Trigonometry Comes Out of the Shadows
7. Alluvial Deposits, Conic Sections, and Improper Glasses
8. An Historical Example of Mathematical Modelig: The Trajectory of a Cannonball
9. Concept of Function—Its History and Teaching
10. My Favorite Ways of Using History in Teaching Calculus
11. Improved Teaching of the Calculus Through the Use of Historical Materials
12. Euler and Heuristic Reasoning
13. Converging Concepts of Series: Learning from History
14. Historical Thoughts on Infinite Numbers
15. Historical Ideas in Teaching Linear Algebra
16. Wessel on Vectors
17. Who Needs Vectors
18. The Teaching of Abstract Algebra: An Historical Perspective
19. Toward the Definition of an Abstract Ring
20. In Hilbert’s Shadow: Notes Toward a Redefinition of Introductory Group Theory
21. An Episode in the History of Celestial Mechanics and Its Utility in the Teaching of Applied Mathematics
22. Mathematical Thinking and History of Mathematics
23. A Topics Course in Mathematics
Niels Henrik Abel (1802-1829) A Tribute
About the Authors

About the Editors

Frank Swetz is Professor of Mathematics and Education at the Pennsylvania State University at Harrisburg. His research concerns societal impact on the learning and teaching of mathematics. These interests have led him into studies on the history of mathematics and ethnomathematics. His findings are incorporated into teaching strategies which humanize mathematics teaching. His most recent books are: The Sea Island Mathematical Manual: Surveying and Mathematics in Ancient China (1992) and From Five Fingers to Infinity: A Journey through the History of Mathematics (1993).

Otto Bekken is Professor of Mathematics at Adger College, Kristiansand, Norway. His major research interests focus on the life and work of Niels Henrik Abel. He is particularly active in the incorporation of the history of mathematics into teacher training programs. He has written materials for this purpose for use in Scandinavia and Peru. He served as the chief organizer and director of the Kristiansand Conference.

John Fauvel is Lecturer in Mathematics at the Open University, England, and chaired the Open University course, “Topics in the History of Mathematics.” He has been an editor of several books, including Darwin to Einstein: Historical Studies on Science and Belief (1980), Conceptions of Inquiry (1981), The History of Mathematics: A Reader (1987) and Let Newton Be! (1988). He is the chair of the International Study Group on the Relations between History and Pedagogy of Mathematics.

Victor Katz is Professor of Mathematics at the University of the District of Columbia in Washington, D.C. He has been interested in the history of mathematics for many years, and in particular, in ways in which it can be used in the mathematics classroom. He has published several papers on both history and on its use in teaching. His textbook A History of Mathematics (Harper Collins, 1993) contains many suggestions as to how the material can be used in teaching on both the secondary and the undergraduate levels.