Using History to Teach Mathematics: An International Perspective (Anneli Lax New Mathematical Library, Series Number 51)

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. Cover Title page Preface Part I: General Ideas on the Use of History in Teaching The ABCD of Using History of Mathematics in the (Undergraduate) Classroom, Siu Man-Keung Mathematical Pedagogy: An Historical Perspective, Frank Swetz On the Benefits of Introducing Undergraduates to the History of Mathematics: A French Perspecûve, Anne Michel-Pajus Part II: Historical Ideas and their Relationship to Pedagogy The History of Mathematics and Its Influence on Pedagogical Problems, Lucia Grugnetti Euclid versus Liu Hui: A Pedagogical Reflection, Wann-Sheng Horng The Long Tradition of History in Mathematics Teaching: An Old Italian Case, Fulvia Furinghetti Problem Solving from the History of Mathematics, Frank Swetz Part III: Teaching a Particular Subject Using History Second Degree Equations in the Classroom: A Babylonian Approach, Luis Radford and George Gutrette Anomalies and the Development of Mathematical Understanding, Janet Heine Barnett The Historicity of the Notion of What is Obvious in Geometry, Evelyne Barbin Use of History in a Research Work on the Teaching of Linear Algebra, Jean-Luc Dorier Presenting the Relation Between Mathematics and Physics on the Basis of Their History: A Genetic Approach, 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, Jan Isaacs, V. Mohan Ram, and Ann Richards The Analysis of Regula Falsi as an Instance for Professional Development of Elementary School Teachers, Greisy Winicki Mathematics and its History: An Educational Partnersbip, Maxim Bruckheimer and Abrahmn Areavi Part V: The History of Mathematics Mesopotamian Mathematics: Some Historical Background, Eleanor Robson An Excursion in Ancient Chinese Mathematics, Siu Man-Keung The Value of Mathematics: A Medieval Islamic View, George W. Heine III Mathematics, Humanism, and Urban Planning in Renaissance Italy, Uwe Gellert An Epistemological History of Number and Variation, Luis E. Moreno-Armella and Guillermina Waldegg Combinatorics: A Historical and Pedagogical Approach, Robin Wilson The History of Non-Euclidean Geometry, Torkil Heiede Scientific Research and Teaching Problems in Beltrami's Letters to Hoüel. Livia Giacardi A Window on the World of Mathematics, 1870, Gavin Hitchcock Some Notes on the History of Mathematics in Portugal, Antônio Leal Duarte, Jaime Carvalho e Silva, and Joao Filipe Queirô Mathematics in South and Central America: An Overview, Ubiratan D'Ambrosio Notes on Contributors This book is a collection of articles by international specialists in the history of mathematics and its use in teaching, based on presentations given at an international conference in 1996. Although the articles vary in technical or educational level and in the level of generality, they show how and why an understanding of the history of mathematics is necessary for informed teaching of various subjects in the mathematics curriculum, both at secondary and at university levels. Many of the articles can serve teachers directly as the basis of classroom lessons, while others will give teachers plenty to think about in designing courses or entire curricula. For example, there are articles dealing with the teaching of geometry and quadratic equations to high school students, the teaching of linear algebra, combinatorics, and geometry to university students, and the notion of pi at various levels. But there is also an article showing how to use historical problems in various courses and one dealing with mathematical anomalies and their classroom use.

Although the primary focus of the book is the teaching of mathematics through its history, some of the articles deal more directly with topics in the history of mathematics not usually found in textbooks. These articles will give teachers valuable background.

Mathematics is a human endeavour which has spanned over four thousand years; it is part of our cultural heritage; it is a very useful, beautiful and prosperous subject.