Humanistic Mathematics Network Journal Issue 26 Article 26 6-1-2002 Complete Issue 26, 2002 Follow this and additional works at: http://scholarship.claremont.edu/hmnj Recommended Citation (2002) "Complete Issue 26, 2002," Humanistic Mathematics Network Journal: Iss. 26, Article 26. Available at: http://scholarship.claremont.edu/hmnj/vol1/iss26/26 This Full Issue is brought to you for free and open access by the Journals at Claremont at Scholarship @ Claremont. It has been accepted for inclusion in Humanistic Mathematics Network Journal by an authorized administrator of Scholarship @ Claremont. For more information, please contact [email protected]. INVITATION TO AUTHORS EDITOR Essays, book reviews, syllabi, poetry, and letters are wel- Alvin White comed. Your essay should have a title, your name and ad- Harvey Mudd College dress, e-mail address, and a brief summary of content. In addition, your telephone number (not for publication) ASSOCIATE EDITORS would be helpful. Susan Addington If possible, avoid footnotes; put references and bibliogra- California State University, San Bernadino phy at the end of the text, using a consistent style. Please put all figures on separate sheets of paper at the end of the Stephen Brown text, with annotations as to where you would like them to State University of New York, Buffalo fit within the text. These should be original photographs, high quality printouts, or drawn in dark ink. These figures JoAnne Growney (poetry) can later be returned to you if you so desire. Bloomsburg University Two copies of your submission, double-spaced and prefer- Joel Haack ably laser-printed, should be sent to: University of Northern Iowa Prof. Alvin White Humanistic Mathematics Network Journal Sandra Keith Harvey Mudd College St. Cloud State University Claremont, CA 91711 Richard Montgomery If possible, please include a copy of your file on disk with Southern Oregon State College your submission. The HMNJ is produced using Microsoft Word for the Macintosh as well as Adobe PhotoShop, but Harald Ness most file formats are acceptable. Essays and other commu- University of Wisconsin Center nications may also be transmitted by e-mail to the editor at [email protected] or faxed to (909) 621-8366. The editor may be contacted at (909) 621-8867 if you have further questions. Frances Rosamond National University, San Diego NOTE TO LIBRARIANS Humanistic Mathematics Network Journal issues #8–#26, Bill Rosenthal ISSN#1065-8297, are the successors to the Humanistic Math- Muhlenberg College ematics Network Newsletter, ISSN#1047-627X. Julian Weissglass SUBSCRIPTIONS University of California, Santa Barbara In the future this publication will be available online at http://ww2.hmc.edu/hmnj PRODUCTION STAFF Fessica L. Nelson, Mary E. Sullivan Katherine E. O. Todd-Brown, Stephanie K. Wong, Steven G. Avery Harvey Mudd College COVER The Ancient of Days Striking the First Circle of the Earth by William Blake. This image appeared in black and white in Humanistic Mathematics Network Newsletter #4, the first printed issue of this publication. Publication of the Humanistic Mathematics Network Journal has been supported by a grant from the EXXONMOBIL FOUNDATION. Humanistic Mathematics Network Journal #26 June 2002 From the Editor Comments on Zal Usiskin’s Article in the 1 Book Review: The Teaching Gap 39 HMNJ for May, 2001 by James W. Stigler and James Hiebert Bob Stein Review Part II: Contrasting U.S. and Japanese Beliefs about Mathematics Loopy 3 Teaching George W. Hart Michael L. Brown History of Mathematics, an Intuitive 6 Review of JoAnne Growney’s 44 Approach “My Dance is Mathematics” Alejandro R. Garciadiego Sally Lipsey Humanizing Mathematics: The Humanistic 12 Portfolio Assessment in Liberal Arts 45 Impression in the Course for Mathematics Mathematics Teaching Mike Kenyon Ada Katsap Divisibility: A Problem Solving Approach 50 A Brief Look at Mathematics and Theology 19 Through Generalizing and Specializing Philip J. Davis Rene Zazkis Pat’s Prologues: A Radio Talk Show 25 Equation Story 54 Patricia C. Kenschaft Whitney Perret Notes on Formal Constructivism 28 Does a mathematical/scientific world-view 55 D. Joyner & P. Lejarraga lead to a clearer or more distorted view of reality—purposive musings inspired from “Calculus” 30 readings in The URANTIA Book, The Sarah Glaz Cosmic Family, Volume I, and elsewhere. Jeru Marcy’s Dots: A Problem on a National Test 32 Revisited Special Section: On the Publication of the 59 P. Baggett & A. Ehrenfeucht 26th Issue of the HMNJ Sandra Keith Aphorisms 33 Philip Davis Lee Goldstein Annalisa Crannell Marion Walter When is a Math Problem Really “Real”? 35 Reuben Hersh Michael E. Goldberg Larry Copes JoAnne Growney Sandra Keith Stephen Brown Comments and Letters In Future Issues... From the Editor When newsletter #1 was published in 1987 it was an act of hope. That hope has been ful- filled by the support and good will of many readers, authors and friends worldwide as well as several program officers of the Exxon Education Foundation and its successors. I am grateful to all. I am also grateful to the presidents and deans of Harvey Mudd College, the chairs of the math department, and the technical staff for their support and encouragement. My gratitude also extends to the generations of Harvey Mudd students who have created the format, typed the articles to be sent to the printer, and performed the essential tasks that converted the authors’ ideas into print. The journal is in library collections all over the world. Future issues of HMNJ will be on the website created by the college at http://www2.hmc.edu/hmnj/ Although HMNJ will continue as an online publication, this last printed issue is a special occasion that should be marked. Thanks to the Exxon Mobil Foundation for support all of these years. Special thanks to Bob Witte, my program officer for most of the years, and to the other helpful officers of the Foundation. Also, special thanks to everyone who supported the journal with their articles and advice. Starting and editing the journal has been rewarding and educational. I learned a few things and met (by mail and in person) many wonderful people. My apologies to colleagues, friends and others whose articles could not be included or fully printed in the hard-copy journals. I look forward to continuing our associations and friend- ships through meetings and correspondence. History of Mathematics, an Intuitive Approach Dr. Alejandro R. Garciadiego Dept. of Mathematics Faculty of Sciences Universidad Nacional Autonoma de Mexico ABSTRACT ate themselves from the event they are reporting on. The main goal of this essay is to discuss, informally, an intuitive approach to the history of mathematics Of course, in most cases, the term history is misused as an academic discipline. The initial point of depar- by professional reporters. Often, for example, TV ture includes the analysis of some traditional defini- sports commentators discuss player's individual tions of the concept of 'history' taken from standard records while narrating a baseball game. These statis- dictionaries. This concise dissection attempts to sug- tics include the player's batting average, number of gest the complexity of the discipline. times at bat in the game, number of stolen bases, etc. Sometimes, the commentators also narrates the KEY WORDS: HISTORY, HISTORY OF MATHEMAT- player's background. They mention the college the ICS, HISTORIOGRAPHY, METHODOLOGY, CHRO- player attended; where he played in the minor NOLOGY. leagues, his previous professional teams and so on. The commentator may also discuss some of the The term 'history' is familiar to almost everyone, and player's qualities as a human being (e.g., generosity, most people believe they know its meaning intuitively. sportsmanship). Then, the sportscaster may try to ex- The lay person sometimes thinks of history in terms plain why the player was motivated to become a pro- of dates, names, places and of colorful anecdotes on fessional. After the commentator has finished with interesting characters. History provides a record of these statistics and anecdotes, he often says: '... and, where someone lived and what he did. In short, his- ladies and gentlemen, ... the rest is history'. tory is the repository of the past. But what exactly is the history of mathematics as an academic discipline? This popular expression 'and, ladies and gentlemen, ... the rest is history'- suggests that once the informa- The events that took place yesterday are now part of tion or anecdote has been revealed to the audience, history. Photographs are history: they reflect the way the rest of the account is common knowledge and re- we once were. History is studied in elementary school, quires no further explanation. Or, perhaps, the phrase especially that of student's native countries. Teachers, '... the rest is history' is synonymous with '... the rest is who often seem old enough to have taken part in some unimportant' or '... the rest is well-known'. In fact, the of the historical events, teach -over and over again- term 'history' may suggest that something is not of anecdotes, names, places, dates, and so on. Historical current concern or lacks importance (e.g., My youth movies, TV programs and books are popular. The is history) [2, p. 614]. media affects the way people understand history as a discipline. Unfortunately, sometimes the public's History, however, is much more than long lists of data. knowledge of important historical issues is derived Think back to your student days. Did your teacher from the popular media (especially movies), and not demand knowledge that was more substantial and from professional sources. Thus, their understanding profound that mere factual information contained in of these events can be distorted. a list of data, especially on a test? Sometimes they asked essay questions which required some explana- Unlike the word mathematics, the term history is used tion of historical events.