NCTM’s 84th Annual Meeting will take place in St. Louis April 26-29, 2006. Among the hundreds of presentations are many dealing with the history of mathematics and its use in teaching. These include the following, numbered as in the Program Book. If a handout is available electronically, you can click on the link. These handouts are provided as a service to both the presenter and the audience, but the editors of Convergence take no responsibility for their content.
213: Hidden African and Asian Roots of School Mathematics, 12:00-1:30pm Beatrice Lumpkin, Malcolm X College (retired), Chicago, Illinois and Patricia Flagg Poole, Illinois State Board of Education (retired), Chicago, Illinois (America's Center, 223/224)
This presentation is dedicated in memory of Claudia Zaslavsky, who died January 13, 2006. Zaslavsky played a key role in uncovering some of the hidden mathematics of Africa, especially south of the Sahara. She was a founder of ethnomathematics and pioneered in the study of symmetry patterns, mathematical games and magic squares. She was a strong advocate of equity in mathematics education in particular and peace and justice in general.
A brief outline of the debt that school mathematics owes to the people of Africa and Asia includes number systems and basic algebra, also less well-known topics such as infinite series and the beginnings of calculus in medieval India, the right triangle theorem in Babylonia 1300 years before Pythagoras, early proofs of the theorem in China and the advanced trigonometry and combinatorics of medieval Islamic and Hebrew mathematicians. From ancient Egypt alone, we have the slope of a line, solution of first and some second degree equations, direct and inverse proportions in problem solving, formulas for the sum of arithmetic and geometric series, formulas for areas of rectangles, triangles, trapezoids, circles, surface area of hemispheres, and volumes of cylinders and truncated pyramids. Egyptian love of debate and litigation is mentioned as a precursor of deductive proofs. In addition to this outline, evidence for the ancient Egyptian concept of zero and the Egyptian use of rectangular coordinates to sketch a curve will be presented. The question of pre-Columbian American contributions is also raised as well as the question of how and why some of these contributions were hidden. A partial list of early African and Asian mathematical contributions, now labeled with later European names, will be provided. A brief report on classroom experiences will conclude with questions and discussion. Handouts will include copies of the presentation, a bibliography and some classroom-ready materials.
237: Newton and Lovelace Can Help You Use History in Any Mathematics Class, 12:30-1:30pm Art Johnson, Boston University, Boston, Massachusetts firstname.lastname@example.org (America's Center, 241)
Mathematical history humanizes mathematics. The real-life experiences of past mathematicians can enliven mathematics for all students. This session will suggest how to include history into an existing mathematics curriculum by using historical projects, problems from the past, and engaging events of the mathematicians from the past.
288.1: Doing It the Old Way: Conceptual Activities from the History of Mathematics, 1:00-2:30pm Mary Ann Matras, East Stroudsburg University, East Stroudsburg, Pennsylvania email@example.com (Adam's Mark Hotel, St. Louis H)
Sometimes not allowing such modern inventions as the quadratic formula or logarithms during classroom activities can result in conceptual understanding relevant to twenty-first-century mathematics learning.
524: The Mathematics of Da Vinci and Dan Brown's Novels, 9:30-10:30am Scott D. Oliver, Adlai Stevenson High School, Lincolnshire, Illinois firstname.lastname@example.org (Renaissance Grand Hotel, Majestic D)
Explore the mathematical topics mentioned in Dan Brown's novels and the mathematics of Leonardo Da Vinci and his peers. We will look at Fibonacci numbers, the golden ratio, the mathematics of beauty, spirals and other curves, the mathematics of Da Vinci's inventions, the geometry of perspective drawing, the mathematics of codes, and more.
569: A Historical Geometric Journey with GSP: Assessing Students' Understanding, 10:30am-12:00n Armando M. Martinez-Cruz, California State University-Fullerton, Fullerton, California, David Booze, Troy High School, Fullerton, California, Fernando Rodriquez, Buena Park High School, Buena Park, California email@example.com (America's Center, 262)
A teacher will present his work on Pythagorean tripels. We use Geometer's Sketchpad (GSP) in a college geometry class to demonstrate and extend historical geometry problems (e.g., quadrature, Pythagorean theorem). We will engage participants in GSP explorations to revisit and extend these historical problems. Scritps and handouts provided. No familiarity with GSP required.
636: Carl Friedrich Gauss: Prince of Mathematicians, 12:30-1:30pm Margaret W. Tent, Altamont School, Birmingham, Alabama firstname.lastname@example.org (America's Center, 220)
Carl Friedrich Gauss (1777-1855) was a gifted mathematician who astonished everyone with his mathematical insights and accomplishments from his early childhood to old age. The presentation includes anecdotes from his life and descriptions of many of his accomplishments.
649: Historical Topics in Math: Chinese Remainder Theorem and Divisibility, 12:30-1:30pm Jim Fulmer, University of Arkansas-Little Rock, Little Rock, Arkansas email@example.com (Renaissance Grand Hotel, Hawthorne/Lucas/Flora)
Participants will investigate historical problems modeling as divisibility problems with integer solutions. Chinese mathematicans of the 3rd century A.D. posed divisiblity problems of this kind. Questioning will engage participants in solving historical divisibility problems using the Chinese remainder theorem: Coconut Problem, Scouts and Cookies, Basket of Eggs, Coconuts and Sailors, Farmers and Rice, Labor Gangs and Workdays, and problems from Regiomontanus and Euler.
960: History of Mathematics: What Is Hindu Mathematics? 11:00am-12:00n, Jeganathan Sriskandarajah, Madison Area Technical College, Madison, Wisconsin (America's Center, 142)
The speaker will share his knowledge on the Hindu-Arabic number system and Hindu mathematics. The latter has some elegant techniques applied to basic fractions through differential calculus. Hindu mathematics will enhance the understanding of some of the topics that will be discussed in this talk.
Although the following talk is not historical, it will be of interest to all readers of Convergence, particularly since the speaker has recently been awarded the 2005 Felix Klein Prize of the International Commission on Mathematical Instruction. (See the link below for the citation.)
575: Mathematics as Crucial and Timely for Shaping a New Civilization, Friday, April 28, 11:00am-12:00n Ubiratan D'Ambrosio, Pontificia Universidade Católica de São Paulo (Emeritus), São Paulo, Brazil
Mathematics is regarded as the dorsal spine of modern civilization. It is the basis on which science, technology, and human behavior rely. In this talk, the speaker will address the possibilities of mathematics becoming the dorsal spine of a new civilization, which will be characterized by dignity for all.
Ubiratan D'Ambrosio has served as chief of the Unit of Curriculum of the Organization of American States; director of the Institute of Mathematics, Statistics, and Computer Science at the State University of Campinas, Brazil; and as graduate chairman at the State University of New York at Buffalo, in addition to teaching mathematics at both universities and at the Pontificia Universidade Católica de São Paulo. In 1983, he was elected a Fellow of the American Association for the Advancement of Science, with the citation "for imaginative and effective leadership in Latin American mathematics education and in efforts toward international cooperation."
One other activity which will be of interest to readers is the annual meeting of the North American Study Group on Ethnomathematics (NASGEm), which will be held Thursday, April 27, from 7:00-9:00pm in Majestic C at the Renaissance Grand Hotel. Among the activities will be a memorial tribute to Claudia Zaslavsky, the author of Africa Counts, among many other books. Claudia died in January of 2006.