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March 2000 THE NEWSLETTER OF THE MATHEMATICAL ASSOCIATION OF AMERICA Math Spans All Dimensions April 2000 is Math Awareness Month Interactive version of the complete poster is available at: http://mam2000.mathforum.com/ FOCUS March 2000 FOCUS is published by the Mathematical Association of America in January. February. March. April. May/June. August/September. FOCUS October. November. and December. a Editor: Fernando Gouvea. Colby College; March 2000 [email protected] Managing Editor: Carol Baxter. MAA Volume 20. Number 3 [email protected] Senior Writer: Harry Waldman. MAA In This Issue [email protected] Please address advertising inquiries to: 3 "Math Spans All Dimensions" During April Math Awareness Carol Baxter. MAA; [email protected] Month President: Thomas Banchoff. Brown University 3 Felix Browder Named Recipient of National Medal of Science First Vice-President: Barbara Osofsky. By Don Albers Second Vice-President: Frank Morgan. Secretary: Martha Siegel. Treasurer: Gerald 4 Updating the NCTM Standards J. Porter By Kenneth A. Ross Executive Director: Tina Straley 5 A Different Pencil Associate Executive Director and Direc­ Moving Our Focus from Teachers to Students tor of Publications and Electronic Services: Donald J. Albers By Ed Dubinsky FOCUS Editorial Board: Gerald 6 Mathematics Across the Curriculum at Dartmouth Alexanderson; Donna Beers; J. Kevin By Dorothy I. Wallace Colligan; Ed Dubinsky; Bill Hawkins; Dan Kalman; Maeve McCarthy; Peter Renz; Annie 7 ARUME is the First SIGMAA Selden; Jon Scott; Ravi Vakil. Letters to the editor should be addressed to 8 Read This! Fernando Gouvea. Colby College. Dept. of Mathematics. Waterville. ME 04901. 8 Raoul Bott and Jean-Pierre Serre Share the Wolf Prize Subscription and membership questions 10 Call For Papers should be directed to the MAA Customer Thirteenth Annual MAA Undergraduate Student Paper Sessions Service Center. 800-331-1622; e-mail: [email protected]; (301) 617-7800 (outside 11 The Anneli Lax New Mathematical Library U.S. and Canada); fax: (301) 206-9789. By Don Albers Copyright © 2000 by the Mathematical Association of America (Incorporated). 12 Short Takes Educational institutions may reproduce articles for their own use. but not for sale. 13 Secretary Riley Responds to Open Letter provided that the following citation is used: "Reprinted with permission of FOCUS. the 14 Employment Opportunities newsletter of the Mathematical Association of America (Incorporated)." About the Cover: This first ever four-color cover of FOCUS depicts a portion of the Periodicals postage paid at Washington. DC paper version of the poster for Math Awareness Month. April 2000. To see the "real" and additional mailing offices. Postmaster: interactive electronic version of the poster, go to http://mam2000.mathforum.com. Send address changes to the MAA. P.O. Box The concept and the design of the poster are due to Tom Banchoff of Brown Univer­ 90973. Washington. DC 20090-0973. sity and Davide Cervone of Union College. copyright Thomas Banchoff Productions. ISSN: 0731-2040; Printed in the United States Inc. of America. FOCUS Deadlines May/June Aug/Sept October Editorial Copy March 22 July 14 Display Ads April 4 July 28 August 21 Employment Ads March 30 July 21 August 10 2 March 2000 FOCUS "Math Spans AU Dimensions" During April Math Awareness Month "Math Spans All Dimensions" is the the MAA has that charge. Based on their whose work connects in some way to the theme for Math Awareness Month 2000, experience with the experimental MAA theme of dimensionality. The people who sponsored by the Joint Policy Board for electronic journal Communications in have agreed to participate go way beyond Mathematics, comprised of representa­ Visual Mathematics, MAA president Tom the expected mathematicians and physi­ tives of the MAA, the AMS, and SIAM. Banchoff and his collaborator Davide cists to include an author of children's As in recent years, mathematics depart­ Cervone of Union College have raised the books (Madeleine L'Engle, author of A ments nationwide are being encouraged concept of a poster to a new level. Wrinkle in Time), a choreographer (Julie to organize a wide range of activities to Strandberg of Brown University), and This year's Math Awareness Month focus attention on mathematics during the even a cartoon character (Geri, one of the poster exists in two forms. The first is a month of April. JPBM has been promot­ characters created by Pixar Animation, paper poster which will be distributed to ing mathematics in this way since 1991, who appears in Toy Story If). As one mathematics and mathematical sciences when the first Math Awareness Week had might expect, Edwin A. Abbott, author departments in colleges and universities. "Mathematics: It's Fundamental" as its of Flatland, gets a prominent place also. The second (for some, this is the real theme and highlighted applications in poster) is an electronic poster that can Clicking on the images on the poster industry, technology, and science. Last be accessed on the web at http:// takes one to pages giving more informa­ year, the week was expanded to a month, www.mam2000.mathforum.com. tion on the person pictured and on the and a web site at the Math Forum (http:// mathematics involved, so that the poster www.mathforum.com/mam/past.html) The central image of the poster starts as itself becomes a useful beginning point provided support for and reports on the a string of zero-dimensional points, then for Math Awareness Month activities. many activities organized to bring a becomes a I-dimensional curve, then greater awareness of the importance of expands to a two-dimensional strip, Production and distribution for the Math mathematics to teachers and students at which then expands to a 3-dimensional Awareness Month 2000 poster has re­ all levels and to the general public. cornucopia. Extensions beyond the third ceived support from Wolfram Research, dimension are accessible only by com­ Inc .• Each year one of the organizations in the puter. Around the poster are clickable JPBM takes the responsibility for the windows, each "inhabited" by a person design of the MAM poster, and this year Felix Browder Named Recipient of National Medal of Science By Don Albers Felix Browder, who is a University Pro­ to the U.S. when he was five years old. fessor at Rutgers University, has been He says that he was a bookish child and named a recipient of a 1999 National liked all subjects. He attributes his inter­ Medal of Science. He was cited for pio­ est in mathematics to reading E.T. Bell's neering work in nonlinear functional Men ofMathematics when he was in sev­ analysis, opening up new avenues in non­ enth grade. He describes that book as a linear problems, and for being a leader "marvelous piece of historical fiction." in the scientific community to broaden Browder earned his doctorate at the age the range of interactions among disci­ of 20 from Princeton in 1948. Before plines. joining Rutgers University, he spent Browder, 72, is one of three brothers, all twenty-three years at The University of of whom are mathematicians. His Chicago, including a twelve-year stint as younger brothers, Andrew (Andy) and chair of the department. William (Bill), have spent most of their In 1999 he became President of the careers at Brown University and American Mathematical Society.• Princeton University, respectively. Both Bill and Felix have served as presidents Don Albers is the Associate Executive of the American Mathematical Society. Director and Director of Publications Felix Browder Browder was born in Moscow and came and Electronic Services for the MAA. 3 FOCUS March 2000 The Curriculum Revisited: Updating the NCTM Standards A Proposal By Kenneth A. Ross By Sol Garfunkel The National Council of Teachers of Responses received from the ARGs in Mathematics (NCTM) published the Cur­ 1997-98 were weighed by the writers as In a 1989 study and follow-up analysis riculum and Evaluation Standards for they produced Principles and Standards ofCBMS reports, the late Gail Young and School Mathematics in 1989, with fol­ for School Mathematics: Discussion I noted that the number of students tak­ low-up documents on standards on teach­ Draft, released in October 1998, at which ing mathematics courses above the level ing (1991) and assessment (1995). After time the ARGs were asked to review the of calculus in departments of mathemati­ gathering reactions from members and draft. According to the NCTM, the cal sciences had been steadily declining. others, the Council made a decision early ARG's reviews were central to the set of We also demonstrated that a great deal in 1996 to proceed with updating the reactions NCTM solicited and received of mathematics instruction at this level Standards and targeted the year 2000 for from a wide range of audiences. The feed­ is taking place in departments other than release of the next document. back was synthesized into a set of key mathematics. I am sure that there are issues used both to guide the writers as many reasons for this trend, over several In shaping the updated document, NCTM they revised the document and as the fo­ of which we have no control. However, sought the views of many different cus of a review sponsored by the National there is one area in which we have al­ groups, especially the mathematical sci­ Research Council. The full set of com­ most complete control, namely the en­ ences community. One of the first out­ ments was also available to the writers try-level undergraduate curriculum. reach actions of NCTM was to request electronically to allow easy access to the that the presidents of the Conference The central importance of mathematics feedback on particular topics or sections. Board of the Mathematical Sciences ap­ in our increasingly complex and techno­ point or designate a committee to serve The final Principles and Standards for logical world is undeniable, and the pos­ as an Association Review Group (ARG) School Mathematics document will be sibilities for new applications almost end­ to provide input to the process.
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