Vita Mathematica: Historical Research and Integration with Teaching

(Mathematical Association of America Notes and Reports, No. 40)

Ronald Calinger (Editor)


Mathematical Association of America (MAA) | 1996 | 364 páginas | DjVu (10 mb)

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Vita Mathematica will enable teachers to learn the relevant history of various topics in the undergraduate curriculum and help them incorporate this history in their teaching. It contains articles dealing not only with calculus, but also with algebra, combinatorics, graph theory, and geometry, as well as more general articles on teaching courses for prospective teachers, and describes courses taught entirely using original sources. Judith Grabiner shows us how two important eighteenth century mathematicians, Colin Maclaurin and Joseph-Louis Lagrange, understood the calculus from these different standpoints and how their legacy is still important in teaching calculus today. We learn from Hans Nils Jahnke why Lagrange's algebraic approach dominated teaching in Germany in the nineteenth century. Wilbur Knorr traces the ancient history of one of the possible foundations, the concept of indivisibles. This volume demonstrates that the history of mathematics is no longer tangential to the mathematics curriculum, but in fact deserves a central role.

 Contents
Foreword VB
I. Historiography and Sources
New Trends and Old Images in The History of Mathematics, David E. Rowe 3
The Role of Problems in the History and Teaching of Mathematics, Evelyne Barbin 17
Dramatizing the Birth and Adventures of Mathematical Concepts:
Two Dialogues, Gavin Hitchcock 27
II. Historical Studies:
From Antiquity to the Scientific Revolution
The Four Sides and The Area: Oblique Light on the Prehistory of Algebra, Jens HrjJyrup 45
The Method of Indivisibles in Ancient Geometry, Wilbur Knorr 67
Enigmas of Chinese Mathematics, Frank Swetz 87
Combinatorics and Induction in Medieval Hebrew and Islamic Mathematics, Victor Katz 99
The Earliest Correct Algebraic Solutions of Cubic Equations, Barnabus Hughes 107
From the Scientific Revolution to the Present
The Early Geometrical Works of Marin Getaldic, Zarko Dadic 115
Empowerment through Modelling: the Abolition of the Slave Trade, John Fauvel 125
The Calculus as Algebra, the Calculus as Geometry: Lagrange, Maclaurin, and their Legacy, Judith Grabiner 131
The Development of Algebraic Analysis from Euler to Klein and Its Impact on School Mathematics in the Nineteenth Century, Hans Niels Jahnke 145
The Mathematics Seminar at the University of Berlin: Origins, Founding, and the Kummer-Weierstrass Years, Ronald Calinger 153
S. V. Kovalevskaya's Mathematical Legacy: The Rotation of a Rigid Body, Roger Cooke 177
Aspects and Problems of the Development of Mathematical Education at Technical Colleges in Germany during the Nineteenth Century, Susann Hensel 191
American Mathematics Viewed Objectively: The Case of Geometric Models, Peggy Kidwell 197
The Social and Intellectual Shaping of a New Mathematical Discipline:
The Role of the National Science Foundation in the Rise of Theoretical Computer
Science and Engineering, William Aspray, Andrew Goldstein, and Bernard Williams 209
III. Integration of History with Mathematics Teaching:
Fundamentals and Selected Cases
History of Mathematics and the Teacher, Torkil Heiede 231
Ethnomathematics: An Explanation, Ubiratan D'Ambrosio 245
The Necessity of History in Teaching Mathematics, \.t:' Frederick Rickey 251
Mathematical Masterpieces: Teaching with Original Sources, Reinhard C. Laubenbacher and David J. Pengelley 257
A History-of-Mathematics Course For Teachers, Based on Great Quotations, Israel Kleiner 261
Measuring an Arc of Meridian, Marie Franroise Jozeau and Michele Gregoire 269
From Egypt to Benjamin Banneker: African Origins of False Position Solutions, Beatrice Lumpkin 279
Mary Everest Boole (1832-1916):
An Erstwhile Pedagogist for Contemporary Times, Karen Dee Michalowicz 291
Origins and Teaching of Calculus
Pupils' Perception of the Continuum, Peter Bero 303
Historical Motivation for a Calculus Course: Barrow's Theorem, Martin Flashman 309
The History of the Concept of Function and Some Implications for Classroom Teaching,
Manfred Kronfellner 317
Integration in Finite Terms: From Liouville's Work to the Calculus Classroom of Today, SIU Man-Keung 321
How Many People Ever Lived? James Tattersall 331
Notes on Contributors 339
Index 345