NCTM’s 82^{nd} Annual Meeting took place in Philadelphia April 21-24, 2004. Among the hundreds of presentations were 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.

**April 22**

22: 8:00-9:00 am Linda Shuey, lshuey@pen.k12.va.us, Western Albemarle High School, Charlottesville, Virginia **Historical Activities for Algebra and Geometry Classes**

Activities from ancient sources will be demonstrated to show teachers how they can add interest to their algebra and geometry classes. Problems will be selected from the Rhind papyrus, Babylonian tablets, Chinese Shang numerals, Al-Khwarizmi’s book on algebra, Euler’s signed-number patterns, President Garfield’s proof of the Pythagorean theorem, and more as time permits.

110: 9:30-10:30am Karen Michalowicz, karendm@aol.com, Langley School, McLean, Virginia **Celebrating the Contributions of Benjamin Banneker, 200 Years Later**

The presentation is intended to address the outstanding contributions of Banneker in order to dispel any myths about his activities. A small collection of Banneker artifacts will be shared. Some problems from Banneker’s journal will be introduced.

185: 11:00am-12:00n William Berlinghoff, Colby College, Waterville, Maine **What History Can Tell Us about Teaching Algebra**

How are symbols related to algebraic concepts? Are algorithms important? How did geometry influence the development of algebra? The history of the algebra we teach today can help us focus on what is truly fundamental and see why some students’ difficulties may be more reasonable than we might think.

278: 1:30-2:00pm Kathie Noonan & Carolyn Harney, knoonan@delmar.k12.de.us, Delmar High School, Delmar, Delaware, **History of Mathematicians: A Multicultural Approach**

This presentation is designed to provide middle and high school mathematics teachers with methods of incorporating the history of mathematicians into their daily lessons. By studying these great individuals from varying cultures and backgrounds, students can easily find at least one example with which they can identify.

300.1: 2:00-3:00pm Michael Lanstrum, lanstrum@yahoo.com, Cuyahoga Community College-Western Campus, Parma, Ohio, **Historical Women in Mathematics**

This session will present a nontechnical talk on the patterns found in the lives of women who have made significant contributions to what Gauss called “the queen of the sciences.” The women considered range from Hypatia to Grace Hopper. Particular attention will be given to the life and mathematics of Hypatia. Handout available.

333: 3:00-4:30pm Bernadette A. Berken, bonnie.berken@snc.edu, Saint Norbert College, De Pere, Wisconsin, **Ethnomathematics: Unlocking the Wonders of Mathematical Ideas**

Engage, challenge, and delight yourself and your students in learning mathematical ideas through activities that integrate history, culture, mathematics, and art into highly interactive, interdisciplinary classroom lessons that draw from 10,000 years of human experiences. Learn to use museums, art centers, nature, and the community to experience and do mathematics. Handout available.

**April 23**

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**498: 9:30-10:30am Ron B. Eglash, eglash@rpi.edu, Rensselaer Polytechnic Institute, Troy, New York,

The geometric patterns in African American cornrow hairstyles are just one of the many mathematical traditions of Africa. The author of

African Fractalswill lead teachers through the use of free, online software for integrating this ethnomathematics into the standards-based curriculum. Handout available.

573: 11:00am-12:00n Jim Fulmer, jrfulmer@ualr.edu, University of Arkansas at Little Rock, Little Rock, Arkansas, **Historical topics in Mathematics: Patterns on Pascal's Triangle**

Pascal’s triangle was known by the Chinese 500 years before Pascal ever lived. Patterns continue to be discovered. Patterns include rows, columns, diagonals, powers of 11 and 2, binomial expansions with positive and negative integer exponents, probability, hexagons, cubic and triangular numbers, multiples of two and three, and Fibonacci numbers.

615: 12:30-1:30pm Anthony Piccolino, piccolinoa@mail.montclair.edu, Montclair State University, Upper Montclair, New Jersey, **Integrating Historical and Multicultural
Activities in Mathematics Classes**

Specific activities and problems from the history of mathematics will be demonstrated for inclusion in the secondary school mathematics curriculum. Activities will focus on promoting multiculturalism in mathematics classrooms. A resource guide will be provided.

648: 1:00-2:30pm Alyson Tramaglini, alytram219@aol.com, Herbert Hoover Middle School, Edison, New Jersey, **The Great Men and Women of Mathematics**

Mathematics and history–perfect together. Create a historical quilt that focuses the valuable contributions of mathematicians throughout history. This activity will actively engage your students in computer research, mathematical writing, and artistic expression.

668. 1:00-2:30pm Lawrence H. Shirley, lslhirley@towson.edu, Towson University, Towson, Maryland, Luis Ortiz-Franco, Chapman University, Orange, California, Dawn Leigh Anderson, California State University Fullerton, Fullerton, California, **Using Ethnomathematics from Around the World in Your Classroom**

Find examples of ethnomathematics that you can use in your classroom as we take a world tour – the Americas, Europe, Africa, South Asia, and East Asia.

742: 3:00-4:30pm Richard D. Faloon, rfaloon@ross.org, Ross School, East Hampton, New York, **Leonardo da Vinci’s Notebook: An Integrated Mathematics, Science, and Art Unit**

This poster session will demonstrate a highly successful and integrated unit with four math projects (two science and four art) that can be incorporated into any curriculum. Leonardo’s engineering, geometry, mathematics, sculpture, sketches, painting, and more will be discussed. Lesson plans, students’ work, and all resources necessary will be presented to participants. Handout available.

753: 3:30-4:00pm Elizabeth Mauch, emauch@bloomu.edu , Bloomsburg University, Bloomsburg, Pennsylvania & James Mauch, Pennsylvania State University, University Park, Pennsylvania, **Integrating Mathematics and History for the Benefit of Reluctant Learners**

A husband (social studies) and wife (mathematics) combine their experience in a series of articles designed to explore how mathematics was used in nineteenth-century America. Ideas for teachers on developing integrated strategies and how to engage reluctant learners by illustrating how adept some ordinary Americans were at “ciphering.” Handout available.

**April 24**

841: 8:00-9:30am Robert McGee, bmcgee@cabrini.edu, Cabrini College, Radnor, Pennsylvania, **Using Historical Problems in the Middle School: Variations on a Theme**

Historical problems provide challenging alternatives for middle school instruction. Students from the Armenian Sister’s Academy worked on a number of historical problems, especially those from nineteenth-century American arithmetic texts. They then translated and solved similar problems from Armenian texts of the same period. They will demonstrate their work.

892: 9:30-10:30am Suzanne R. Harper, harpersr@muohio.edu, Miami University, Oxford, Ohio & Shannon Driskell, University of Dayton, Dayton, Ohio, **Using Dynamic Geometry Software to Explore Topics in Mathematics History**

Participants will explore historical mathematics activities suited for middle and secondary school students. The main focus of this session will be making connections to specific NCTM Standards in algebra, geometry, and precalculus. Historical topics will include the Quadratrix of Hippias, Pythagorean theorem, Witch of Agnesi, and others, as time permits. Handout available.

966: 11:00am-12:00n William Dunham, wdunham@muhlenberg.edu, Muhlenberg College, Allentown, Pennsylvania, **A Sampler of Euler's Calculus**

This talk examines a few of Euler’s contributions to differential and integral calculus, as well as his analytic approximation of pi. Taken together, these examples from the early history of calculus should reveal the genius of one of the greatest mathematicians of all.

977: 11:30am-12:00n Anthula Natsoulas, anatsou@utnet.utoledo.edu, University of Toledo, Toledo, Ohio **Mathematics, Prophecy, and Divination: Ifa, Oracle of the Yoruba of Nigeria**

Ways in which mathematical concepts from the basis for traditional divination systems will be presented. Emphasis will be on that of the Ifa Oracle of the Yoruba people of Nigeria in West Africa. The presenter will demonstrate the use of an Ifa divination board and make suggestions for classroom applications.

1005: 12:00n-1:30pm Terry Goodman, goodman@cmsu1.cmsu.edu, Central Missouri State University, Warrensburg, Missouri, Ann McCoy, Emily Combs, Karen Kennedy, Clinton Middle School, Clinton, Missouri, **Four Score and Seven Ways to Integrate Mathematics and History**

From Pythagoras to the Pilgrims and from 300 bc to the present, participants will engage in a variety of activities that are designed to integrate mathematics and history. Historical mathematics topics as well as the role mathematics has played in the history of our country will be emphasized.

1022: 12:00n-1:30pm Jane Beattie-Scott, janescott@usca.edu, University of South Carolina–Aiken, Aiken, South Carolina & Kim Robinson, Clayton College and State University, Morrow, Georgia, **Secret Codes: Historical Vignettes and Their Mathematics**

What do a Roman conqueror, a Scottish queen, a World War II radio operator, and a modern-day mail carrier have in common? Secret codes! Participants will progress through history using mathematics to enjoy the puzzles of codes. Bring your graphing calculator to make some of the mathematics quickly accessible. The TI-83 will be used on the overhead.

1025: 12:30-1:00pm Roberto Torres-Hernández, robert@sunserver.uaq.mx, Universidad Autonoma de Queretaro, Queretaro, Mexico & Gerardo Sousa-Aubert, Universidad Autonoma de Queretaro, Queretaro, Mexico, **Descartes, the Quadratic Equation and the Teaching of Analytic Geometry**

At first the speakers will present the Descartes geometrical method to solve a kind of quadratic equations and then work the method with modern analytic geometry tools. Finally, they will discuss the possible genesis of this procedure and some heuristic aspects of it. Handout available.

1047: 12:30-1:30pm John Mahoney, mahoneyj@sidwell.edu, Benjamin Banneker Academic High School, Washington, DC **Benjamin Banneker's Mathematics -- in His Own Handwriting!**

Benjamin Banneker, a self-taught African American mathematician, kept a journal containing a number of mathematical puzzles and other examples of mathematics. With the aid of computer enhancement, Banneker’s writing will be presented along with explanations of the ingenious mathematical techniques he used. Handout available.