**History and Pedagogy of Mathematics**

April 19, 2008

MAA Carriage House, 1781 Church St NW, Washington, DC

All are welcome to this meeting at the MAA's new Carriage House. Registration $40 payable at the door. Registration includes the cost of lunch.

9:15 - 10:00 am

Amy Ackerberg Hastings, University of Maryland University College

**"The Acknowledged National Standard": Charles Davies, A. S. Barnes. and Textbooks as Teaching Tools**

Book historians have added a number of dimensions to our understanding of texts in the history of science and mathematics, including how readers and publishers participate alongside authors in the transmission of knowledge, how patterns of use indicate intellectual reception, and how textbooks communicate scientific ideas to popular audiences. However, promotion has been at least as important a factor as pedagogical and intellectual superiority in determining which objects have become widely established instruments for teaching mathematics and science. This talk explores the evolution of the textbook into a commercialized teaching tool by concentrating on how the partnership of Charles Davies (1798-1876) and Alfred Smith Barnes (1817-1888) shaped mathematics instruction in the United States. Davies parlayed his reputation as a professor at the United States Military Academy at West Point into a successful career of defining himself primarily as a producer of textbooks. Barnes, his publisher, organized the books into graded series and utilized aggressive marketing techniques. Together, the men sought to enlarge their audience of American students and laid claim to national status as the standard for the nascent mathematics textbook industry. This talk is based upon the first chapter of *Tools of American Mathematics Teaching, 1800-2000*, a forthcoming book prepared jointly with Peggy Aldrich Kidwell and David Lindsay Roberts, and will include a few highlights from the entire volume.

10:15 - 11:30 am

Alain Touwiade, President, Washington Academy of Sciences, Historian, Smithsonian Institution

**Leafing through History: An Imaginary Walk through an Ancient Library**

This will be an overview of ancient scientific books, their writing, their illustration, their production, and their history, with a presentation of some important mathematical collections. The talk will be illustrated with images of ancient books, from papyrus to 16th and early 17th-century printed works.

11:45 am - 12:15 pm

Florence Fasanelli, American Association for the Advancement of Science

**Some Frontispieces in the Michalowicz Collection at American University**

These frontispieces dating from 1647 to 1792 played an important role in the design of the mathematics texts that accompanied them by portraying images of the works that followed. Who made them and why as well as where and how will be discussed as we look carefully at the pages.

12:15 - 1:30 pm Catered lunch, included in registration fee

1:30 - 2:00 pm.

Peggy Aldrich Kidwell, National Museum of American History, Smithsonian Institution

**The Chinese Tangram, Mathematical Recreations, and Mathematics Education in the United States**

The tangram is a flat, seven-piece puzzle consisting of asquare, a rhombus, and 5 isosceles right triangles of differing size. Invented in China in the late eighteenth century, the tangram may well have been the first mathematical recreation that could be described as a global fad. The puzzles reached the United States from Europe 1817. In this same period, there was considerable emphasis on teaching arithmetic and even the elements of geometry to young children. At mid-century, Unitarian minister and textbook author Thomas Hill proposed using simplified tangrams in introductory geometry, and designed a set of puzzle pieces and pattern cards for school use. Hill's cards were only modestly successful, but fit nicely with the general growth in apparatus for elementary mathematics teaching at the time, as well as kindergarten apparatus being developed in Germany by Friedrich Froebel. Tangrams have been a mathematical recreation, sometimes used in mathematics teaching, ever since.

2:15 - 3:00 pm

Betty Mayfield and Kimber Tysdal, Hood College

**Women and Mathematics in the Time of Euler: Undergraduate Research in the History of Mathematics**

Last summer we supervised a group of four undergraduate students in research that focused on women and mathematics in 18th century Europe. We structured our program like a traditional REU, with speakers and field trips and collaboration as well as individual research projects. We will report on our experiences and on what our students learned about the history of mathematics.

3:15 - 4:00 pm

Maryam Voulis, University of New Haven

**History of Arab Cryptanalysis**

This presentation will discuss the contributions of medieval Muslim scientists to cryptography and cryptanalysis.

4:15 - 5:00 pm

Ilhan Izmirli, American University

**Are Proofs Necessary in Mathematics? A Brief History**

This talk will trace the idea of proof from Babylonian to Greek, medieval, and modern mathematics to Lakatosian ideas. It will also address the role of proof in mathematical pedagogy.

5:15 - 6:00 pm

Bob Stein, California State University, San Bernardino

**The Math Wars and Culture**

In recent decades, attempts to improve mathematics education in the US have been marked by fundamental differences that flare up as "math wars." We will consider those differences in terms of Hofstede's dimensions of culture and their implications for mathematics education. The talk will be illustrated with personal experiences, notably with the California Mathematics Framework revision of 1997.