This portfolio contains the papers produced by school teachers and graduate students during a one semester workshop at New Mexico State University during the Spring of 1995, and a resulting graduate course in subsequent years. The workshop occurred in the form of the course MATH 495/501, Workshop for Teachers: Using Historical Sources in Teaching Mathematics, and evolved into the regular graduate course MATH 561, The Role of History in Teaching Mathematics.
The papers in this volume have been prepared as teaching resources, mostly built around original historical source material in mathematics. Each is a self-contained supplement ready for use with students, most comprising an original source, mathematical and historical annotation for teacher and students, a discussion of the context of the mathematics, guidance for the teacher on how and where to use the supplement, exercises, and suggestions for further reading. The papers are intended for all levels ranging from middle school to graduate-level mathematics. Also included in the portfolio is a set of assessment guidelines prepared by the participants and ourselves, with guidance from Bonnie Votaw, for assessing the effectiveness of these teaching materials with students.
Our desire to work with present and future teachers grew out of our use of original historical sources in the undergraduate curriculum. We have found that exposing students directly to historical sources in mathematics contributes greatly to motivation and understanding, and brings mathematics alive as an ongoing process of discovery. Our philosophy and experiences are expressed in the article ``Recovering Motivation in Mathematics: Teaching with Original Sources'', included in this portfolio.
The papers in this volume are outstanding examples of what can be achieved through enthusiasm and commitment by dedicated educators. We hope they represent the beginning of an ongoing enterprise to produce a rich collection of teaching resources based on historical texts.
The original workshop was made possible by funding from the NMSU Department of Mathematical Sciences and Dean of the College of Arts and Sciences, the Las Cruces Public Schools, and the New Mexico Center for Teaching Excellence. We owe special thanks to Bonnie Votaw, Amalya Nattiv, and Doug Kurtz, for recognizing the promise of this endeavor.
Reinhard Laubenbacher and David Pengelley
Department of Mathematical Sciences
New Mexico State University
Las Cruces, NM 88003
Tel. 505--646--3901; FAX 505--646--1064
e-mail reinhard@nmsu.edu davidp@nmsu.edu
May 3, 1995 (with later additions)
1. An Ancient Construction Yields Solutions to Cubic Equations (Ali
Ahmad, NMSU)
Algebra, Euclid and Omar Khayyam
2. Graphs and More Graphs (Daniel Fish, NMSU)
Statistics, Florence Nightingale
3. Stem and Leaf Diagrams (Daniel Fish, NMSU)
Statistics, John Tukey
4. Box Plots (Daniel Fish, NMSU)
Statistics, John Tukey
5. Restoring the Square - The Methods of Al-jabr (Mike Goar,
Mayfield
High School)
Algebra and Geometry, al-Khowarizmi
6. Getting to the Root of the Problem: A Hint from René
Descartes
(Mike Goar, Mayfield High School)
Algebra, René Descartes
7. Linear Programming and the Simplex Algorithm (Jeff Holland, NMSU)
Linear Algebra, George Dantzig
8. Lobachevskian Geometry (Jeff Holland, NMSU)
Geometry, Lobachevsky
9. The Bernoulli Numbers (Tuesday Johnson, NMSU)
Number theory, Jacob Bernoulli
10. Every Integer is a Sum of Four Squares (Tuesday Johnson, NMSU)
Number Theory, Leonhard Euler
11. Ptolemy's ``Table of Straight Lines in a Circle'' (Mary Joy,
Mayfield
High School)
Trigonometry, Claudius Ptolemy
12. Developing the Quadratic Formula (Glendel DeVon Love, Las Cruces
High School)
Algebra, al-Khowarizmi
13. The Euclidean Algorithm (Glendel DeVon Love, Las Cruces High
School)
Number Theory and Geometry, Euclid
14. Egyptian Mathematics (Cynthia Oszman, White Sands Middle School)
Arithmetic, The Rhind Papyrus
15. Mathematics Using Sumerian Economic Texts (Cynthia Oszman, White
Sands Middle School)
Arithmetic, Texts from the Drehem archive
16. Fibonacci's Rabbit Problem, and Consecutive Odd Numbers (Carmen
Pareo, Gadsden High School)
Number Theory, Leonardo Fibonacci
17. Operation Tangent (Michael Quintana, NMSU)
Tangent Lines to Curves, Rene Descartes and Pierre de Fermat
18. Diophantine Equations (Gina Rivera, Vista Middle School)
Algebra and Number Theory, Diophantus
19. Goldbach's Conjecture (Chatt Williamson, NMSU)
Number theory, Christian Goldbach
20. Euler's Formula (Chatt Williamson, NMSU)
Analysis of the Infinite, Leonhard Euler
21. The Cayley-Hamilton Theorem (Eric York, NMSU)
Linear Algebra, Arthur Cayley and William Rowan Hamilton
Additions from May, 1997 (NMSU students)
22. Cramer's Rule and the Determinant (Rebecca Brown)
Linear Algebra, Gabriel Cramer
23. Olivier and Abel on Series Convergence: An Episode from Early
19th
Century Analysis (Michael Goar)
Calculus and Real Analysis, Niels Abel
24. Historical Sources in Elementary and Intermediate Algebra (Karen
Trujillo)
Algebra, Ancient Chinese, Mayan, Greek sources, and Descartes
Additions from May, 1998 (NMSU students)
25. Arthur Cayley and the Origins of Group Theory: An Introduction
to
Abstract Algebra (Daniele Richardson)
Abstract Algebra, Arthur Cayley
26. Appendix to ``Restoring the Square: The Methods of Al-Jabr''
(Daniele
Richardson)
Algebra and Geometry, al-Khowarizmi
27. Using Diophantus of Alexandria to Teach Algebra (Shelly Hangen)
Algebra, Diophantus
28. Using Stigler's ``Diet Problem'' to Teach Linear Programming
(Rumiya
Masagutova)
Linear Programming, George Stigler
Additions from May, 2000 (NMSU students)
29. Logic Through the Looking Glass: Learning the Basics of Symbolic
Logic Through the Works of Lewis Carroll (Gloria Johnson)
Symbolic Logic, Lewis Carroll
30. Navigation and Map Making (Karen Ondo)
Geometry, Trigonometry, and Calculus, Gerardus Mercator and Edward
Wright
31. Mayan Arithmetic (Elaine Cohen)
Arithmetic, Mayan numeration
32. Cantor's Set Theory (Murat Basaran)
Set Theory, Georg Cantor
33. Napierian Logarithms: Who, When and How (Mary Williams)
Logarithms, John Napier
34. Introducing Characteristics of Functions to Elementary School
Students
(Elaine Cohen)
Functions Concepts
35. The Theory of Galois: A Historical Approach (Rebecca Pablo)
Galois Theory, Solutions of Equations, Evariste Galois
Additions from Spring, 2002 (NMSU students)
36. Fundamental Thoerem of Calculus (Hideo Nagahashi)Additions from Spring, 2004 (NMSU students)
45. Solving Linear Equations in the Footsteps of Ancient Egyptians (Elizabeth (Lisa) Sullivan)Appendices
Recovering Motivation in Mathematics: Teaching with Original Sources
Assessment Guidelines