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Complete Issue 17, 1998 Humanistic Mathematics Network Journal Issue 17 Article 30 5-1-1998 Complete Issue 17, 1998 Follow this and additional works at: http://scholarship.claremont.edu/hmnj Recommended Citation (1998) "Complete Issue 17, 1998," Humanistic Mathematics Network Journal: Iss. 17, Article 30. Available at: http://scholarship.claremont.edu/hmnj/vol1/iss17/30 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]. ISSN 1065-82 Humanistic Mathematics Network Journal Isssue #17 May 1998 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 Harvey Mudd College address, e-mail address, and a brief summary of content. In addition, your telephone number (not for publication) would Associate Editors be helpful.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 text, Stephen Brown with annotations as to where you would like them to fit State University of New York, Buffalo within the text; these should be original photographs, or drawn in dark ink. These figures can later be returned to JoAnne Growney (poetry) 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 Essays and other communications may also be transmitted Southern Oregon State College by electronic mail to the editor at [email protected], or faxed to (909) 621-8366. The editor may be contacted at (909) Harald Ness 621-8867 if you have further questions. University of Wisconsin Center The Journal uses the programs Microsoft Word and Page- Maker for the Macintosh. If you used either of these pro- Frances Rosamond grams to prepare your paper, it would be very helpful to us National University, San Diego if you sent a copy of your file on diskette along with the printed copies of the paper. Gian-Carlo Rota Massachusetts Institute of Technology Note to Librarians Julian Weissglass Humanistic Mathematics Network Journal issues #8–#17, ISSN#1065-8297, are the successors to the Humanistic Math- University of California, Santa Barbara ematics Network Newsletter, ISSN#1047-627X. Production Managers Subscriptions Linley E. Hall The Humanistic Mathematics Network Journal is distrib- Harvey Mudd College uted free to all libraries and individuals who request copies and subscriptions. Please address subscription requests to Thomas D. Werner Prof. Alvin White. Harvey Mudd College Cover "He breathes 4D geometry:" the cover features diagrams from Randal J. Bishop's "The Use of Realistic Imagery to Represent the Relationships in a Four-Dimensional Coordinate System" which show how one can create a photograph of objects in 4D space. Publication of the Humanistic Mathematics Network Journal is supported by a grant from the EXXON EDUCATION FOUNDATION. Humanistic Mathematics Network Journal #17 May 1998 From the Editor Robert Davis: In Memoriam 1 Problems That Matter: 23 Carolyn A. Maher, Teaching Mathematics as Robert Speiser Critical Engagement Jeffrey Bohl Randal Bishop Plunges Into 3 4-D Space Book Review: The Courage 32 C. Ernesto S. Lindgren To Teach Sandra L. Keith The Use of Realistic Imagery 5 to Represent the Relationships On Solving Equations, 35 in a Four-Dimensional Negative Numbers, and Other Coordinate System Absurdities: Part I Randal J. Bishop Ralph A. Raimi Thinking About the Preparation 12 The Poetics of E=MC2 43 of Teachers of Elementary Richard A. Schwartz School Mathematics Jane Wenstrom, Kathleen Death, Trial and Life 45 Martin, Susan King Prem N. Bajaj Platonism and All That 16 The Smarandache Semantic 48 Bob Burn Paradox Anthony Begay Real Data, Real Math, All 17 Classes, No Kidding In Future Issues... Martin Vern Bonsangue The poems located throughout the journal are by sixth and seventh grade students taught by Margarel Schaffer at Hale Middle School in Los Angeles, CA. From Newsletter #1 Dear Colleague, This newsletter follows a three-day Conference to Examine Mathematics as a Humanistic Disci­ pline in Claremont 1986 supported by the Exxon Education Foundation, and a special session at the AMS-MAA meeting in San Antonio January 1987. A common response of the thirty-six mathemati­ cians at the conference was, "I was startled to see so many who shared my feelings." Two related themes that emerged from the conference were 1) teaching mathematics humanistically, and 2) teaching humanistic mathematics. The first theme sought to place the student more centrally in the position of inquirer than is generally the case, while at the same time acknowledging the emo­ tional climate of the activity of learning mathematics. What students could learn from each other and how they might come to better understand mathematics as a meaningful rather than arbitrary disci­ pline were among the ideas of the first theme. The second theme focused less upon the nature of the teaching and learning environment and more upon the need to reconstruct the curriculum and the discipline of mathematics itself. The reconstruc­ tion would relate mathematical discoveries to personal courage, discovery to verification, mathemat­ ics to science, truth to utility, and in general, mathematics to the culture within which it is embedded. Humanistic dimensions of mathematics discussed at the conference included: a) An appreciation of the role of intuition, not only in understanding, but in creating concepts that appear in their finished versions to be "merely technical." b) An appreciation for the human dimensions that motivate discovery: competition, cooperation, the urge for holistic pictures. c) An understanding of the value judgments implied in the growth of any discipline. Logic alone never completely accounts for what is investigated, how it is investigated, and why it is investi­ gated. d) A need for new teaching/learning formats that will help discourage our students from a view of knowledge as certain or to-be-received. e) The opportunity for students to think like mathematicians, including chances to work on tasks of low definition, generating new problems and participating in controversy over mathematical is­ sues. f) Opportunities for faculty to do research on issues relating to teaching and be respected for that area of research. This newsletter, also supported by Exxon, is part of an effort to fulfill the hopes of the participants. Others who have heard about the conferences have enthusiastically joined the effort. The newsletter will help create a network of mathematicians and others who are interested in sharing their ideas and experiences related to the conference themes. The network will be a community of support extending over many campuses that will end the isolation that individuals may feel. There are lots of good ideas, lots of experimentation, and lots of frustration because of isolation and lack of support. In addition to informally sharing bibliographic references, syllabi, accounts of successes and failures .. the network might formally support writing, team-teaching, exchanges, conferences .... Alvin White August 3, 1987 From the Editor I want to welcome the new Production Managers Linley Hall and Tom Werner. Their skill and knowledge are evident from the appearance of this issue. I am grateful for their past experience and their willingness to offer their time and ability. We are all saddened by the death of friends and colleagues: Jim Leitzel, who gave guidance and inspiration to the Project NExT Fellows; Bob Davis, who is the subject of an article in this issue; and Bob Menges, Professor of Education at Northwestern University and an inspiration and friend to many. They will be missed. An exciting event at the National Council of Teachers of Mathematics in Wash- ington, D.C. in April was the gathering of many teachers, professors and others who are involved in projects supported by the Exxon Education Foundation. The whole landscape of mathematics education has been beautified by the sup- port of the EEF. On the occasion of the 40th anniversary of the Foundation, Allyn Jackson re- viewed the work of those who have been supported. Her review appeared in the program of the NCTM in April 1995, and is reprinted in issue #12 of this Journal (October 1995). If you would like copies of that issue, please let me know. Robert Davis: In Memoriam A recurring theme throughout Bob Davis’s writings Education at Cornell before moving to the University was the difficulty of using words. He wrote extremely of Illinois in 1972. There he was Professor of Educa- carefully, often with poetic eloquence. As his chapter tion, Associate Director of the computer-based Edu- heading “Neither Words nor Pictures” indicates, cation Research Laboratory, and Director of the Cur- mathematics seems to lie somewhat beyond the reach riculum Laboratory. At Illinois he continued his fun- of images and language, no matter how precise we damental work on mathematical cognition, especially try to be. The same holds true, he emphasized, of most through a series of important studies of learners’ math- ideas worth writing about. Bob’s subtlety was daunt- ematical thinking and problem solving. This theoreti- ing to some readers, like his hesitation to make snap cal orientation, based on key ideas of cognitive sci- pronouncements, his discomfort lest a major issue ence, informs his later work. become flattened by superficial thoughts or words. Facts and dates can never sum a person up, but still He also served on the Research Advisory Cominittee they tell us something.
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