Using History to Teach Mathematics

by Katz, Victor J.

• ISBN13: 9780883851630
• ISBN10: 0883851636
• Format: Paperback
• Copyright: 2000-07-01
• Publisher: Mathematical Assn of Amer

Summary

There is a long tradition of relating the history of mathematics to its teaching, and increasingly this has extended throughout mathematical education. This volume brings together articles from well known figures in this area, and provides many insights, both in particular cases and in generality, into how the history of mathematics can find application in the teaching of mathematics itself. Educators at all levels, and mathematicians interested in the history of their subject, will find much of interest in this book.

Table of Contents

Preface	vii
Part I: General Ideas on the Use of History in Teaching
The ABCD of Using History of Mathematics in the (Undergraduate) Classroom	3	(8)
Siu Man-Keung
Mathematical Pedagogy: An Historical Perspective	11	(6)
Frank Swetz
On the Benefits of Introducing Undergraduates to the History of Mathematics: A French Perspective	17	(12)
Anne Michel-Pajus
Part II: Historical Ideas and their Relationship to Pedagogy
The History of Mathematics and Its Influence on Pedagogical Problems	29	(8)
Lucia Grugnetti
Euclid versus Liu Hui: A Pedagogical Reflection	37	(12)
Wann-Sheng Horng
The Long Tradition of History in Mathematics Teaching: An Old Italian Case	49	(10)
Fulvia Furinghetti
Problem Solving from the History of Mathematics	59	(10)
Frank Swetz
Part III: Teaching a Particular Subject Using History
Second Degree Equations in the Classroom: A Babylonian Approach	69	(8)
Luis Radford
George Guerette
Anomalies and the Development of Mathematical Understanding	77	(12)
Janet Heine Barnett
The Historicity of the Notion of What is Obvious in Geometry	89	(10)
Evelyne Barbin
Use of History in a Research Work on the Teaching of Linear Algebra	99	(12)
Jean-Luc Dorier
Presenting the Relation Between Mathematics and Physics on the Basis of Their History: A Genetic Approach	111	(12)
Constantinos Tzanakis
Part IV: The Use of History in Teacher Training
A Historical Approach to Developing the Cultural Significance of Mathematics Among First Year Preservice Primary School Teachers	123	(6)
Ian Isaacs
V. Mohan Ram
Ann Richards
The Analysis of Regula Falsi as an Instance for Professional Development of Elementary School Teachers	129	(6)
Greisy Winicki
Mathematics and its History: An Educational Partnership	135	(14)
Maxim Bruckheimer
Abraham Arcavi
Part V: The History of Mathematics
Mesopotamian Mathematics: Some Historical Background	149	(10)
Eleanor Robson
An Excursion in Ancient Chinese Mathematics	159	(8)
Siu Man-Keung
The Value of Mathematics: A Medieval Islamic View	167	(10)
George W. Heine, III
Mathematics, Humanism, and Urban Planning in Renaissance Italy	177	(6)
Uwe Gellert
An Epistemological History of Number and Variation	183	(8)
Luis E. Moreno-Armella
Guillermina Waldegg
Combinatorics: A Historical and Pedagogical Approach	191	(10)
Robin Wilson
The History of Non-Euclidean Geometry	201	(12)
Torkil Heiede
Scientific Research and Teaching Problems in Beltrami's Letters to Houel	213	(12)
Livia Giacardi
A Window on the World of Mathematics, 1870	225	(6)
Gavin Hitchcock
Some Notes on the History of Mathematics in Portugal	231	(14)
Antonio Leal Duarte
Jaime Carvalho e Silva
Joao Filipe Queiro
Mathematics in South and Central America: An Overview	245	(12)
Ubiratan D'Ambrosio
Notes on Contributors	257