FOCUS August/September 2001

FOCUS is published by the Mathematical Association of America in FOCUS January, February, March, April, May/June, August/September, October, November, and December. August/September 2001 Editor: Fernando Gouvêa, Colby College; [email protected] Volume 21, Number 6 Managing Editor: Carol Baxter, MAA Inside [email protected] Senior Writer: Harry Waldman, MAA 4Orthogonal Latin Garage Doors [email protected] By Gary Gordon and Liz McMahon Please address advertising inquiries to: Doris Griffin; [email protected] 6 Duke University Featured in MAA Exhibit for Congress President: Ann E. Watkins, California State University, Northridge 7MAA Writing Prizes Announced at MathFest 2001 First Vice-President: Barbara L. Osofsky, Second Vice-President: Frank Morgan, 8Four Forums Will Address Mathematics at the Secretary: Martha J. Siegel, Associate Secretary: James J. Tattersall, Treasurer: School/College Transition Gerald J. Porter Executive Director: Tina H. Straley 10 Quantitative Literacy: Everybody’s Orphan By Bernard L. Madison Associate Executive Director and Director of Publications and Electronic Services: Donald J. Albers 12 Travel Grants for ICM 2002, Beijing, China FOCUS Editorial Board: Gerald Alexanderson; Donna Beers; J. Kevin 13 Clay Mathematics Institute Announces Long Term Fellows, Colligan; Ed Dubinsky; Bill Hawkins; Dan Olympiad Scholar, IMO Awards Kalman; Peter Renz; Annie Selden; Jon Scott; Ravi Vakil. 14 MAA National Election Results Letters to the editor should be addressed to Fernando Gouvêa, Colby College, Dept. of Mathematics, Waterville, ME 04901 or by 15 Short Takes email to [email protected]. Subscription and membership questions 17 From the Sections should be directed to the MAA Customer Service Center, 800-331-1622; e-mail: 18 Evaluating Undergraduate Programs: Indicators of [email protected]; (301) 617-7800 (outside U.S. and Canada); fax: (301) 206-9789. Departmental Health By John A. Dossey and Kenneth J. Travers Copyright © 2001 by the Mathematical Association of America (Incorporated). Educational institutions may reproduce 20 A Different Pencil: Use Technology Wisely articles for their own use, but not for sale, By Dick Jardine provided that the following citation is used: “Reprinted with permission of FOCUS, the newsletter of the Mathematical Association of America (Incorporated).” On the cover: Gary Gordon and Liz McMahon's garage doors are painted according to a Periodicals postage paid at Washington, DC mathematical scheme. See page 4 for the article. and additional mailing offices. Postmaster: Send address changes to FOCUS, Mathematical Association of America, P.O. FOCUS Deadlines Box 90973, Washington, DC 20090-0973. November December January ISSN: 0731-2040; Printed in the United States Editorial Copy September 14 October 14 November 15 of America. Display Ads September 24 October 29 November 26 Employment Ads September 24 October 29 November 26

2 August/September 2001 FOCUS

USA Mathematical Olympiad Team Ties Russian Team for Second Place

T he 2001 USA USA Mathemati- Mathematical Olym- cal Olympiad piad team, composed Team and repre- of six gifted young sent the United mathematicians, States at the IMO. faced off in the Inter- “We are very national Mathemati- proud of their cal Olympiad (IMO) achievement,” against the best high- said Titu An- school students from dreescu, head 82 counties and came coach of the US Team. “It is the re- in second to the team The US IMO team pictured here with Titu Andreescu, Director of the American Math- from China. sult of many years ematics Competitions. Left to right: Dong Shin, Gabriel Carroll, Reid Barton, Tiankai of hard work . All Liu, Oaz Nir and Ian Le. Photograph courtesy of the Clay Mathematics Institute. Mathematical Olym- the students and piad teams of the the coaching staff USA have done very well in International American Mathematics Competitions, an gave their best, and we can see the results. Mathematical Olympiad competitions official program of the Mathematical As- Congratulations to them all.” since first entering in 1974. In twenty- sociation of America presented by the seven years of competition, USA teams Akamai Foundation. The first exam is IMO participants were treated to several have won three times and finished in the taken by more than 350,000 students. The gala events, including the Opening Cer- top five twenty-two times. In 1994, all six USA Mathematical Olympiad, the last of emonies on July 4 presented by the members of the USA team achieved per- the exams, involves only 180 students. Akamai Foundation, and Closing Cer- fect scores, an unprecedented accom- emonies at the Kennedy Center and a lav- plishment by any other team. ish dinner at the National Building Mu- seum, both presented by the Clay Math- During the first two weeks of July at ematics Institute. George Mason University, 475 high- school students from 83 countries com- The Akamai Foundation was the present- peted in the International Mathematical ing sponsor of the IMO 2001 USA, with Olympiad. The students were allotted the National Science Foundation, U.S. nine hours to solve six difficult problems Department of Education, Wolfram Re- that are regarded as challenging by most search, Texas Instruments, and the Na- professional mathematicians. As evi- tional Security Agency all as title spon- dence of the difficulty of the IMO prob- sors. The Clay Mathematics Institute was lems, only four of the 475 students re- asked in May 2000 to participate as a part- ceived perfect scores, Reid Barton and ner by planning and executing the clos- Gabriel Carroll of the USA and Liang Andrew Wiles speaking at the closing ing ceremonies in conjunction with their Xiao and Zhiqiang Zhang of China. ceremonies of the International Math- annual meeting. The University of Ne- ematical Olympiad. Photograph cour- braska-Lincoln and George Mason Uni- Barton, a member of four USA Math- tesy of the Clay Mathematics Institute. versity were academic sponsors. ematical Olympiad teams, distinguished himself by becoming the first IMO con- For additional details on participants, testant to win four gold medals. In addi- The twelve students with the highest results, problems, photos, and history of tion to Barton and Carroll, Ian Le and scores are named winners of the USA the International Mathematical Olym- Tiankai Liu of the USA also won gold Mathematical Olympiad and they are piad, go to the following web sites: http:// medals. Oaz Nir and Dong Shin, the honored at ceremonies held in Washing- www.maa.org, http://imo.wolfram.com, other two members of the USA team, ton, DC hosted by the Mathematical As- http://www.claymath.org/events/ won silver medals. sociation of America, the National Acad- olympiadevent.htm, and http:// emy of Sciences, the National Science www.imo2001.org/. The USA team is selected through a se- Foundation, and the US Department of quence of three examinations of the State. The top six performers make up the

3 FOCUS August/September 2001

Orthogonal Latin Garage Doors Then we tried a more symmetric square, pictured on the left below. Trial and error By Gary Gordon and Liz McMahon produced a square orthogonal to it. (Al- though it is always possible to relabel the squares so that the first row in each square When we moved into our new house on the other to obtain ordered pairs, each is 1, 2, 3, 4, we liked the two squares given in the fall of 1986, the roof was gray, the one of the n2 possible ordered pairs ap- below better.) siding was gray and the two garage doors pears precisely once. (To see these or- were white. In addition, the weather in dered pairs clearly, superimpose one ar- Easton, Pennsylvania is frequently gray, ray on the other and then slide one of 1234 at least during the winter. The four of us the arrays a bit to the left.) (two mathematicians and our two daugh- 2143 ters) came to the same conclusion: the Latin squares are important in all sorts 3412 exterior of our house needed something of applications in experimental design, colorful to cheer up the neighborhood. geometry and graph theory, and they 4321 arise naturally as group multiplication The Project tables. The subject of Latin squares is more than 200 years old; amateurs at- The two wooden garage doors are con- tempting to design whist tournaments 1342 structed in horizontal sections, with four did much of the early development. Al- 4213 sections making up a door. Each section most any text on combinatorics treats this has four raised rectangular panels, so each topic; in fact, a pair of orthogonal 4 x 4 2431 door has 16 panels arranged in a 4 x 4 Latin squares decorates the cover of van 3124 grid. The doors need to be painted every Lint and Wilson’s interesting text A few years, so we soon hit on an obvious Course in Combinatorics. It is possible to solution to our gray lives: Paint the doors find a pair of n x n orthogonal Latin some color that wasn’t white. squares for every n except 2 and 6. Euler It is not hard to show that there can be at conjectured that no orthogonal Latin most three pairwise orthogonal 4 x 4 Latin squares, and, in general, at most n-1 We talked about the particulars of such a squares exist when n is congruent to 2 painting project and came up with a few mod 4, but in 1959, this conjecture was pairwise orthogonal n x n Latin squares. This maximum number is achieved constraints. First, do something math- disproved when a pair of 10 x 10 orthogo- ematical. Since both adults in the house nal Latin squares was found at the Uni- whenever there is a projective plane of are mathematicians and we frequently versity of North Carolina by Parker, Bose order n. All known projective planes have order n = pk for some prime p and some have students over for various activities, and Shrikhande. A nice, short introduc- integer k 1, so these are the only values this seemed important. Second, don’t do tion to the topic can be found at http:/ ≥ of n where the full complement of or- something that would completely alien- /buzzard.ups.edu/squares.html. thogonal squares is known to exist. Since ate us from our neighbors. We were rea- The field remains an active area of re- sonably sure painting rectangles on the search, with many interesting open prob- we only have a two-car garage, our work doors solid colors would keep us within lems waiting for new approaches. was done. Is there a third Latin square that is orthogonal to the two given above? Find the bounds of semi-normal neighbor- hood behavior. Third, do something col- For our purposes, we needed a pair of it! orful. This was the motivation for the orthogonal 4 x 4 Latin squares. Algo- The Paint project to begin with. Finally, choose col- rithms exist for finding orthogonal pairs ors that we could live with for a long time. of Latin squares using projective planes, We also needed the colors to be easy to but, because we wanted one of the doors We were now ready to plan the painting. Rebecca and Hannah (our daughters) felt distinguish. to have nice symmetry, we used trial and error. We first tried the square below, but very strongly about the colors they liked The Math unfortunately, we showed that no other and the color combinations they would not allow. This restriction banished any Latin square is orthogonal to it. We decided to paint the panels of the oranges or yellows. Also, the colors had doors to make a pair of 4 x 4 orthogonal to look good together, and not be too dif- ferent (this restriction banned blue and Latin squares. A Latin square is an n x n 123 4 array, where each member of the array is red as two of the colors). Rebecca’s favor- one of the numbers from 1 to n, so that 234 1 ite color was teal and purple was Hannah’s favorite, so those two colors were in. Then each number between 1 and n appears 341 2 exactly once in each row and each col- we took a short trip to our local hardware umn. Two n x n Latin squares are orthogo- 412 3 store and made final choices for the re- maining colors, staying on the blue side nal if, when you superimpose one array

4 August/September 2001 FOCUS of the spectrum. Our helpful salesman mixed the paints after feigning interest in a short lecture in combinatorics.

When the time came to paint, each of us was responsible for painting their favor- ite color. The correspondence between number and color (and painter) was

Purple Hannah Light Blue Liz, who calls it Carolina blue Dark Blue Gary Teal Rebecca

The painting took two days, including a primer and two coats for most of the col- ors. We applied masking tape to each Another view of the orthogonal Latin garage doors. bounding edge of each rectangle (a non- trivial task, as there are 128 such edges second door. Then they can check that not the only mathematicians who have on the two doors). The hardest part of this property holds for the other three decorated their house in a mathematical the project was applying and removing colors, if they want, or they can take our theme, but we are fairly certain that we this tape from the doors; Rebecca and word for it. are the only ones on our block. Hannah were less interested in this part. Most people who study the doors find the There are other possible themes we (or The Reactions symmetry on the left door. There is also you) could explore. We could mow crop symmetry on the right door, but it’s circles in our lawn, or paint the Fano con- We love our doors! More fun has been harder to see. Sarah McMahon (a histo- figuration on the front door. Finally, all the reaction of other people, which has rian at Bowdoin College, and the sister of us can all find inspiration in the ideas been almost uniformly positive. (On the and sister-in-law of the authors) realized of the mathematician Carl Frederick other hand, would you approach a that the positions of each individual color Gauss. The great Gauss once suggested stranger and tell them their garage doors on the right door are the same up to ro- the following enormous project: By cut- are hideous?) tation, reflection or both rotation and re- ting down a massive number of trees in flection. She was very excited when she Siberia, he hoped to give the largest proof The reactions to the project began while discovered that pattern. ever of the Pythagorean Theorem. The we were painting. One neighbor stopped goal of such a project was also to impress by and asked “What are you doing?” We Te enagers like the doors; most comments the neighbors, but on a grand scale. Pre- gave a fairly short explanation, and he are on the order of “They’re really cool!” sumably, such a figure would be visible seemed satisfied and allowed that it or “I think they’re funky.” Our favorite to extraterrestrials, who would then as- seemed a good family project. A passing reaction was last Halloween, though. A sume that intelligent life existed on Earth. driver slowed down long enough to shout trick-or-treating teen said, “Your garage We have no plans to undertake this “My daughter thinks it’s the coolest!” and doors are really nice. I heard there is a project. a British neighbor said “Actually, it’s mathematical pattern to them.” Maybe rather neat,” (read this with a British ac- next year we’ll pass out reprints instead cent). An artist (who was selling us a car) of candy. Liz McMahon ([email protected]) got out his sketchbook to write the pat- and Gary Gordon ([email protected]) terns down. The Moral teach at Lafayette College and live in an easy to recognize house in Easton, PA. People understand the Latin square prop- Neighbors are surprisingly tolerant of Their research interests include combina- erty quickly; it’s easy to see that each color mathematical home improvement. With- torics, algebra and geometry, and their appears once in each row and column on out painting numbers, equations or theo- teaching includes courses outside of the each door. It’s harder to explain orthogo- rems, we helped spice up the street and mathematics curriculum. They have plenty nality; we tell them to focus on the posi- we also made it much easier to give di- of non-mathematical interests, including tions of the purple rectangles (for ex- rections to our house: “look for the col- biking and indoor rock climbing with their ample) on one door and to find the cor- orful garage doors.” One of us offers a daughters Rebecca and Hannah. They are responding positions on the other door. prize for anyone (excluding mathemati- also involved in Lafayette’s REU program They can see that all four colors appear cians) who can figure out the pattern; no in mathematics, to which they invite the in these corresponding positions on the one has claimed it yet. We are certainly applications of interested undergraduates.

5 FOCUS August/September 2001 Duke University Featured in National Academy MAA Exhibit for Congress Elects 72 New Mem- bers, Including Six Each year, the Council on National Mathematicians Science Funding (CNSF) sponsors an exhibition and reception that show- The National Academy of Sciences cases research projects supported by the (NAS) announced in May the election of National Science Foundation. This past 72 new members of the Academy. The spring, 30 booths displayed a wide size of this year’s class, 20% larger than range of scientific research and educa- in the past, reflects, according to NAS tion projects, and university research- Home Secretary Stephen Berry, “the ers and educators were on hand to de- changing nature of science and the birth scribe their work to interested members of new areas.” Six new sections have been of Congress and their staffs. In the past Pictured left to right: Jennifer Baucom, Elena added to the NAS’s existing 25: compu- exhibits focused mostly on basic re- Strauss, Milena Mihaylova, Congressman David tational biology, computer and informa- Price and David Smith. search, but now they are balanced be- tion science, environmental sciences, hu- tween research and education. man ecology, immunology, and systems all mathematics faculty at Duke Univer- neurobiology. The NAS expects to elect sity and PIs of the featured projects. The This year, the MAA, a member of CNSF, 72 members every year for the next 6 showcased three educational projects be- booth featured three students from East years. ing carried out by faculty at Duke Uni- Chapel Hill High School, in Chapel Hill, NC, Jennifer Baucom, Elena Strauss, and versity. One of these projects is Duke This year’s class includes six mathemati- University’s Post CALC Project, which is Milena Mihaylova, who had used mate- cians: Leo Breiman (Statistics, U. C. Ber- developing online mathematics materi- rials in an Advanced Math Topics course keley, Emeritus), Robion C. Kirby (Math- taught by Tomberg. Preceding the ex- als for high school students who have fin- ematics, U. C. Berkeley), Gregory A. ished a year of calculus but still have time hibit, the Duke faculty, high school stu- Margulis (Mathematics, Yale), Donald G. left in their high school careers. The ma- dents and MAA Executive Director, Tina Saari (Economics and Mathematics, U. terials feature a wide range of applications Straley visited with members of Congress C. Irvine), Leslie G. Valiant (Computer of mathematics, from the modeling of and their staff persons to tell them about Science and Applied Mathematics, the Duke projects and the importance of musical sounds to the spread of epidem- Harvard), and Efim I. Zelmanov (Math- ics. Materials available at the table also NSF funding. The MAA/Duke exhibit ematics, Yale). The Academy also elected described MathDL, the MAA Mathemati- proved to be very popular. Many Repre- several Foreign Associates, including sentatives, Senators, and staff persons cal Sciences Digital Library project, and Jacob Palis of the Instituto de Matemática other curriculum materials being devel- stopped by specifically to visit it. The Pura e Aplicada in Rio de Janeiro, Brazil. oped at Duke. young people were a big hit and were in- strumental in bringing people to the Presenting at this year’s exhibit were Lang MAA table, and they did a great job of Moore, David Smith, and Jim Tomberg, explaining the project.

ICMI Study on Teaching and Learning of Mathematics at the University Level Featured in Special Journal Issue

The International Commission on ruary 2000, volume 31, number 1) of the Studies have dealt with many issues in Mathematical Instruction recently spon- International Journal of Mathematical mathematics education, such as assess- sored an ICMI Study on the “Teaching Education in Science and Technology. The ment (1993), gender equity (1996), the and Learning of Mathematics at the Uni- papers deal with a wide range of issues, role of the history of mathematics (1999), versity Level.” In addition to a book that from “Redesigning the Calculus Se- and teaching geometry (1998). ICMI’s is forthcoming from Kluwer Academic quence at a Research University: Issues, forthcoming (twelfth) Study, on “The Press, the study produced several inter- Implementation, and Objectives” to “A Future of the Teaching and Learning of esting research papers. These have been Metacognitive Intervention in Math- Algebra,” was the subject of an article in collected in a special issue (January-Feb- ematics at University Level.” Past ICMI the December 2000 issue of FOCUS.

6 August/September 2001 FOCUS

MAA Writing Prizes Announced at MathFest 2001

Carl B. Allendoerfer Awards of expository articles accessible to under- Ezra Brown graduates and published in Math Hori- “Three Fermat Trails to Elliptic James N. Brawner zons. The awards are named for Trevor Curves” “Dinner, Dancing, and Evans, a distinguished mathematician, College Mathematics Journal, Vol. 31 Tennis, Anyone?” teacher, and writer at Emory University. No. 3, May 2000, pp. 162-172. Mathematics Magazine, Vol. 73, No.1 February 2000, 29-36. Lester R. Ford Awards The George Pólya Awards, established in 1976, are made to authors of exposi- Rafe Jones and Jan Pearce Keith Kendig tory articles published in the College “A Postmodern View of Fractions and “Is a 2000-year-old Formula Still Mathematics Journal. The awards are the Reciprocals of Fermat Primes” Keeping Some Secrets?” named for George Pólya, a distin- Mathematics Magazine, Vol. 73 American Mathematical Monthly guished mathematician, well-known No. 2, April 2000, 83-97. Vol. 107, No. 5, May 2000, pp. 402-415. author, and professor at Stanford Uni- versity. The Carl B. Allendoerfer Awards, estab- E.R. Scheinerman lished in 1976, are made to authors of “When Close is Close Enough” Merten M. Hasse Prize expository articles published in Math- American Mathematical Monthly ematics Magazine. The awards are Vol. 107, No. 6, June–July 2000 Francis Edward Su named for Carl B. Allendoerfer, a dis- pp. 489-499. “Rental Harmony: Sperner’s Lemma tinguished mathematician at the Univer- in Fair Division” sity of Washington and President of the The Lester R. Ford Awards, established in American Mathematical Monthly Vol. Mathematical Association of America, 1964, are made to authors of expository 106, No. 10, December 1999 1959–60. articles published in the American Math- pp. 930–942. ematical Monthly. The awards are named Trevor Evans Awards for Lester R. Ford, Sr., a distinguished The Merten M. Hasse Prize, established mathematician, editor of the American in 1986, honors a noteworthy exposi- Ira Rosenholtz Mathematical Monthly, 1942-46, and tory paper appearing in an Association “One Point Determines a Line” President of the Mathematical Associa- publication, at least one of whose au- Math Horizons, November 2000, tion of America, 1947-48. thors is a younger mathematician. The Volume 8, No. 4 pp. 20–24. prize is named after Merten M. Hasse, George Pólya Awards an inspiring and dedicated teacher, and James Tanton aims to encourage younger mathema- “A Dozen Areal Maneuvers” Chip Ross and Jody Sorenson ticians to take up the challenge of ex- Math Horizons, Volume 8, No. 3 “Will the Real Bifurcation Diagram position and communication. September 2000, pp. 26-30, 34 Please Stand Up!” College Mathematics Journal, Vol. 31 For citations, biographical sketches of The Trevor Evans Awards, established by No. 1, January 2000, pp. 2-14. the prize winners, and responses, see the Board of Governors in 1992 and first online at http://www.maa.org/ awarded in 1996, are made to authors news/mfawards01.html.

Proof wins Pulitzer and several Tony Awards Have You Moved? David Auburn’s play Proof, which was The play received the 2001 Pulitzer Prize The MAA makes it easy to change your reviewed a year ago in FOCUS (August/ for Drama, and shortly afterwards re- address. Please inform the MAA Service September 2000, p. 8), has won the ceived Tony Awards for Best Play, Best Center about your change of address by Pulitzer Prize and several Tony Awards. Actress (Mary Louise Parker), and Best using the electronic combined member- The play, which had a successful run off- Director (Daniel Sullivan). For more ship list at MAA Online (www.maa.org) Broadway early last year and then moved about the play, check out its web page at or call (800) 331-1622, fax (301) 206- on to an even more successful run at the http://www.proofonbroadway.com/. 9789, email: [email protected], or mail Walter Kerr Theater on Broadway, is a to MAA, PO Box 90973, Washington, DC dramatic mystery about the daughter of 20090. a brilliant but unstable mathematician.

7 FOCUS August/September 2001

Four Forums Will Address Mathematics at the from the MAA. (See page 7 of the 2001 School/College Transition Spring/Summer Catalog.) This forum is sponsored by the National Over the next six months, four national Lynn Steen (former MAA President) of Council on Education and the Disci- forums will address issues in precalculus St. Olaf College will keynote “Rethinking plines at the Woodrow Wilson Founda- mathematics, including arguments that the Preparation for Calculus.” In addition tion with financial support from The Pew significant reforms are needed in school to Narayan, members of the Steering Charitable Trusts. The Mathematical Sci- and college mathematics. The forums will Committee are Nancy Baxter-Hastings ences Education Board is hosting the fo- focus on three major topic areas: quanti- (Dickinson College), Steve Dunbar (Uni- rum with the cooperation of the MAA. tative literacy, college algebra, and prepa- versity of Nebraska), Sheldon Gordon ration for calculus. Since mathematics in (SUNY at Farmingdale), Christopher Reforming College Algebra these areas is taught in both school and Hirsch (Western Michigan University), college, articulation issues will be part of and Jo Ann Lutz (North Carolina School The third forum, “Reforming College all the discussions. for Science and Mathematics). Algebra,” will be held February 7–10, 2002, at the ExxonMobil Conference Among the motivations for holding these Achieving Quantitative Literacy Center in Arlington, Texas. The hypoth- meetings are the changes in school math- esis here is that the traditional college al- ematics prompted by the NCTM Stan- The second forum, “Quantitative Lit- gebra course should be changed. To what dards and the impact of technology. Three eracy: Why Numeracy Matters for it should be changed is not clear. College of the four forums are invitational events, Schools and Colleges,” will be held De- algebra courses are serving both as gen- but the proceedings of each of these will cember 1–2 at the National Academy of eral education courses and as prerequi- be published, and all four forums are de- Sciences in Washington, DC. This invita- site courses for subsequent courses such signed to initiate a broader discussion tional forum for approximately 100 per- as finite mathematics and calculus. Con- within the collegiate mathematics com- sons will be the center of an effort to start sequently, the topic of this conference munity. a national conversation on the growing reaches over into both the precalculus importance of numeracy in all aspects of discussion and the quantitative literacy Preparation for Calculus American life. discussion.

Chronologically, the first forum is “Re- We all now live in a world awash with “Reforming College Algebra” is being thinking the Preparation for Calculus.” It data, and daily civic discourse teems with organized by Don Small of the US Mili- will be held October 4–6 at the offices of quantitative measures. Education for tary Academy. He is being advised by the the National Science Foundation (NSF) quantitative literacy is simultaneously MAA Task Force on the First College- in Arlington, Virginia. Approximately fifty more necessary and more difficult. School Level Course. Support is from the participants will be invited to this NSF- and college curricula, dominated by tra- ExxonMobil Foundation. This forum will supported workshop which is being or- ditional disciplinary offerings, face a be keynoted by Arnold Packer, director ganized by a Steering Committee chaired daunting challenge of adapting to meet of the SCANS 2000 Center at Johns by Jack Narayan of SUNY at Oswego. The this growing educational need. Nowhere Hopkins University. Dr. Packer is a purpose of the workshop is to rethink the is this more evident than in mathematics former Assistant Secretary of Labor and preparation for calculus given that: (1) curricula. The purpose of the forum is to co-author of Workforce 2000. school mathematics has changed in re- examine the relationship between quan- sponse to the NCTM Standards; (2) col- titative literacy and mathematical com- AAAS Symposiums lege expectations have changed; (3) tech- petence and to address how this relation- nology is providing tools for teaching and ship bears on the aims of education in Finally, two complementary ninety- learning; and (4) college algebra courses high school and college. minute symposiums have been scheduled are changing. as a part of the Annual Meeting of the The discussion was initiated by the pub- American Association for the Advance- The workshop aims to develop some lication of a book, Mathematics and De- ment of Science (AAAS) in Boston, Feb- principles for reforming precalculus mocracy: The Case for Quantitative Lit- ruary 14–17, 2002. One symposium is courses and to provide cohesion for indi- eracy, containing a case statement pre- “Articulation in Mathematics: Smooth- vidual reform projects in order to have a pared by a National Design Team led by ing the Road from School to College,” and larger impact on the mathematics com- Lynn A. Steen and twelve responses to the second is “Living with Data: Achiev- munity. Problems and needs will be iden- that case statement. In addition, several ing Quantitative Literacy.” tified to give funding agencies direction. issue papers have been commissioned. The workshop proceedings will be com- The papers and proceedings of the forum The Articulation symposium is being piled and submitted for publication as a will be published and distributed widely. organized by Bernard L. Madison and volume in the MAA Notes series. Mathematics and Democracy is available will have three speakers. Stephanie Pace

8 August/September 2001 FOCUS

Marshall, President of the Illinois Math- Letters to the Editor ematics and Science Academy, will speak on the report of the National Research Not a Klein Bottle Fat Nerds Typo Council’s Committee on Advanced Sci- ence and Mathematics Courses in Ameri- I noticed the caption on page 4 of the There is a typo in the URL for the Lon- can High Schools. Dr. Marshall was a latest FOCUS issue incorrectly describes don Times piece about mathematicians member of this Committee which re- the Oberwolfach sculpture as a “Klein as “fat nerds” on p. 26. It should be http:/ viewed Advanced Placement courses, In- Bottle,” when it is actually Boy’s surface, /www.thetimes.co.uk/article/0,,2- ternational Baccalaureate courses, and an immersion of the real projective 61352,00.html. The hyphen between “2” courses for dual college and high school plane. If the readers of FOCUS are in- and “6” got lost. credit. terested in seeing more images of Boy’s surface, I would recommend these web Norman Richert Joan Ferrini-Mundy, Chair of the NCTM sites: Mathematical Reviews Standards Impact Research Group and principal author of the 2000 NCTM The Geometry Center: Due to production problems at our end, Standards, will describe educational http://www.geom.umn.edu/zoo/ the May-June issue of FOCUS contained characteristics of graduates of NCTM toptype/pplane/boy/ a great many typos and other errors. We’d Standards-based mathematics programs. like to apologize to our readers and to The third speaker, David Lutzer, will re- A student page at Smith College: thank the many readers who contacted us port on the results of the 2000 CBMS http://math.smith.edu/~jposson/ with corrections. survey of undergraduate mathematical sciences. Dr. Lutzer was director of this My very own site: With respect to the note about students survey. http://www.ipfw.edu/math/Coffman/ viewing mathematicians as “fat nerds”, let steinersurface.html me add that a discussion of the research The Quantitative Literacy symposium is in question can be found in J. S. Berry and being organized by Lynn A. Steen. Three Adam Coffman S. Picker, “Your pupil’s images of Math- speakers will address some of the issues Indiana University Purdue University ematicians and Mathematics”, Math- in education for quantitative literacy that Fort Wayne ematics in School, 29 (March 2000), 24– are the subject of the National Academy 26. of Sciences forum described above. The three speakers are Joan Leitzel, President of the University of New Hampshire, Ri- chard Schaeffer, President of the Ameri- can Statistical Association, and Arnold Packer, described above as the keynoter of the college algebra conference.

Ed Burger is Pólya Lecturer

T he MAA has speaker, talented teacher, and effective exposition that the MAA seeks to encour- named Ed Burger writer. (He has even written for FOCUS age, the award provides funds for the of Williams College – see our December 2000 issue.) Dubbed Pólya Lecturer to give talks at several as the Pólya Lec- the “ambassador of mathematics” by the meetings of the Sections of the MAA. turer for 2001–02 President of Williams College, Burger is and 2002–03 aca- an engaging and entertaining speaker Each MAA Section is entitled to a Pólya demic years. Burger, who is sure to be a big hit with MAA Sec- Lecture approximately once every five who received one of tions throughout the country. years. For more information, including a last year’s Deborah list of past Pólya Lecturers, visit http:// and Franklin Ed Burger The George Pólya Lectureship was cre- www.maa.org/awards/polyalecturers.html. Tepper Haimo ated in 1991. Named for George Pólya, a Awards for Distinguished Teaching of renowned teacher and writer who em- Mathematics, is well known as a dynamic bodied the high quality of mathematics

9 FOCUS August/September 2001 Quantitative Literacy: Everybody’s Orphan By Bernard L. Madison

The world is awash with data, and civic lower). Moreover, the US has the highest Numeracy, or quantitative literacy, is nei- discourse teems with quantitative mea- underachievement rate (58% compared ther mathematics nor statistics, and it is sures. Political arguments use, misuse, to a median for other countries of about not watered-down mathematics. It is a confuse, and spin various rates of change. 20%). Here, “underachievement rate” is way of thinking that uses and enhances Statistical analyses of how voters thought defined to be the percent of high school tools from mathematics and statistics to they voted have filled recent newspapers. graduates whose performance on literacy describe or understand everyday occur- Risk factors are quoted for tire failures, tasks is below the minimum level needed rences. As such, numeracy becomes in- truck crashes, and lung cancer. However, to cope adequately with the complex de- dispensable to an informed citizen and many (if not most) US citizens do not mands of daily life. In contrast, the US is conceptually and operationally difficult understand the analyses of these quanti- second only to Canada in the percentage because of its use in so many different tative concepts. (36%) of adults aged 30-34 who have contexts. some postsecondary degree. This indi- The heavy and increasing use of quanti- cates that many of the 3 out of 5 US high One major difference between quantita- tative ideas and language in civic dis- school graduates that do not meet the tive literacy and mathematics is that course means that quantitative literacy, or OECD standard for literacy have some quantitative literacy is richly contextual numeracy, is needed by all. However, postsecondary degree or certification. while mathematics students are asked to numeracy education is claimed by no dis- rise above context and learn mathemat- cipline and suffers accordingly in the dis- Much of the responsibility for traditional ics. The power of mathematics is in its cipline-dominated school and college education for quantitative literacy has abstractness and generality. The theory curricula. This is the basic premise of a rested on the mathematics curriculum in is that the students will be able to use the national conversation on quantitative lit- schools and colleges. In fact, quantitative mathematics in various contexts, but, as eracy and mathematics sponsored by the literacy and mathematical literacy have we know, this is enormously difficult. National Council on Education and the been considered by many as one and the Neither of the arts of applying math- Disciplines (NCED) at the Woodrow same. ematics and communicating mathemat- Wilson Foundation. The yearlong discus- ics is easily learned, so contextual use of sion will center on a national forum, With the advent of computing power over mathematics as in quantitative literacy Quantitative Literacy: Why Numeracy the past few decades, analysis of data be- requires educational attention. Matters for Schools and Colleges, to be held came manageable, and the discipline of at the National Academy of Sciences on statistics flourished. So, since much of the By and large, college mathematics facul- December 1–2, 2001. (See the Four Fo- public discourse on quantitative matters ties have considered quantitative literacy rums article on page 8 of this issue of FO- concerns statistical measures, statistics someone else’s problem, often believing CUS for more details.) has a share of the responsibility for quan- that quantitative literacy is remedial at titative literacy. Some data analysis and the college level. That may have been the The literacy rate in the US, which is the statistics have entered the school curricu- case in the distant past when numeracy result of our policies of universal educa- lum, spurred on by the NCTM Standards, was roughly equivalent to simple arith- tion, has been a source of national pride. and some colleges and universities have metic, but it is no longer the case in our Some international survey evidence instituted courses in quantitative literacy data-laden and quantitative-measure shows that we are slipping badly, however, or a requirement in quantitative literacy happy society. Even college graduates and the biggest culprit may be quantita- that can be satisfied by various combina- who major in some mathematically in- tive literacy. tions of courses, some mathematics and tensive subject, say science or engineer- some not. But according to various re- ing, may have trouble understanding the The International Office of Economic ports current education for numeracy is context-laden quantitative language of Cooperation and Development (OECD) not sufficient. public discourse. Many of these have fol- considers that literacy has three compo- lowed the calculus-driven sequence for nents: prose literacy (interpreting words), Quantitative literacy is discussed in a new their mathematics and have applied, of- quantitative literacy (using arithmetic publication, Mathematics and Democracy: ten with difficulty, that mathematics in and proportional reasoning), and docu- The Case for Quantitative Literacy, pub- the context of their major discipline. No ment literacy (interpreting tables, charts, lished by NCED in May 2001. The book, wonder they have difficulty in all the rich and graphs). The OCED International containing a case statement for quanti- contexts in which mathematical concepts Adult Literacy Survey, conducted from tative literacy written by a National De- occur in the daily press—in health re- 1994–1998, placed the US literacy rate as sign Team led by Lynn A. Steen and twelve ports, federal budget analyses, sports re- second lowest of 18 European/North responses to that statement, is available ports, drug effectiveness studies, crime American countries (only Poland is from the MAA.

10 August/September 2001 FOCUS statistics, and a thousand other places. ideas of calculus or to cover the contexts the writing/literature situation and the for calculus problems. numeracy/mathematics situation is that Mathematics, as traditionally taught, is literature faculty expect their students to being challenged as appropriate for lit- Can we develop a sequence of school and write well while mathematics faculty of- eracy, not only by those worrying about early college mathematics that will simul- ten ignore the numeracy of their students. quantitative literacy but also by those taneously prepare students for advanced If numeracy and mathematics goes the worrying about scientific literacy. In 1985, work in mathematics and prepare them way of writing and English, then educa- the year of the last visit of Halley’s Comet, to be quantitatively literate citizens? Most tion for numeracy will be external to AAAS initiated Project 2061 to analyze school college preparatory mathematics mathematics programs, even if not in a what science all Americans should know. sequences consist of algebra, geometry, coordinated program across the curricu- (Halley’s Comet will return in the year and trigonometry. Students who are not lum. 2061.) The first publication was Science headed for a college curriculum needing for All Americans in 1990. This year, calculus or who may have no need for Two models of teaching writing are WAC Project 2061 released a new book, Designs calculus (other than as a general educa- (writing across the curriculum) and WID for Science Literacy, which basically is a tion course) are usually steered toward (writing in disciplines). Mathematics and how-to book on designing a K-12 cur- calculus because that is the route that statistics in disciplines is pervasive in uni- riculum to achieve scientific literacy— leads to credentials for college entrance. versities now, as students encounter what science everyone should know. School sequences that are not calculus mathematics and statistics in economics, bound are usually weaker, but they need social sciences, sciences, and engineering. Most educators would agree with Designs not be. As long as the calculus-driven se- The lack of coherence and connections assertion that there can be some thinning quence is the road to entry into selective of these encounters prevents achieving of the curriculum in science and math- colleges, it will be the choice of parents broader, more generally applicable quan- ematics. Agreement on which are the top- and competitive students. Even an alter- titative understanding. If “across” implies ics that could go would be less likely. native track that is stronger for general more coherence and less discipline- Among the long list of mathematics top- education, particularly quantitative lit- bound approaches than does “in,” then ics Designs considers expendable are fac- eracy, would not compete well with cal- mathematics and statistics across the cur- toring quadratics and polynomials. Most culus and its reputation as being a good riculum would approximate education mathematicians would consider such measure of student achievement. for quantitative literacy. omissions absurd, but they look at the world through a different lens than does What other disciplines share responsibil- Education for quantitative literacy ap- Project 2061. Again, traditional math- ity with mathematics and statistics for pears to be a difficult problem, beset with ematics is being challenged, and the days quantitative literacy? Certainly econom- dilemmas within the context of tradi- of automatic acceptance of much of what ics, the physical and biological sciences, tional discipline-dominated curricula. we have traditionally taught are over. and engineering. The social and behav- But a numerate citizenry is critical for ioral sciences are increasingly quantita- today’s democracy, and citizens need a Several questions are being posed in this tive; and even the humanities have quan- high degree of literacy to seek out infor- national conversation about quantitative titative components. Unfortunately, mation, critique it, and use it. Lynn Steen literacy, and these questions deserve the many of the quantitative concepts and has written that an innumerate citizen is attention of the US mathematics faculty. measures used in disciplinary courses are as vulnerable today as the illiterate peas- Such attention will certainly help find tightly tailored to those disciplines, not ant of Gutenberg’s time was in the 15th good educational answers, but it may also context-free as in mathematics, but con- century. School and college mathematics help keep mathematics a vital, growing text-bound to a discipline, so transfer of curricula have a major role to play in collegiate discipline. learning to different contexts is difficult. numeracy education. The mathematics What may be necessary is that institutions community must join this national dis- What mathematics is most important for coordinate quantitative learning across cussion. quantitative literacy? Much of the con- the curriculum, analogous to the writing tent of the calculus-driven sequence across the curriculum programs. Bernard L. Madison is MAA Visiting would not be considered effective in Mathematician during 2001, on leave from achieving quantitative literacy. The ma- The analogy between quantitative literacy the University of Arkansas. His e-mail is jor reason cited is the context-free nature and writing is fairly strong. Writing in [email protected]. of this sequence and its emphasis on al- college has gained a status distinct from gebraic and calculus techniques. One of the traditional disciplines, most notably the aims of calculus reform was to move English and the other humanities, over towards more contextual calculus prob- the past several decades, primarily be- lems. That effort has been met with only cause it was critical for success in many limited success, mainly because of the areas and not successfully taught in any dilemma of choosing either to cover the single discipline. One difference between

11 FOCUS August/September 2001 Travel Grants for ICM 2002, Beijing, China terms of a proposal submitted to the Na- tional Science Foundation (NSF) by the Society. The American Mathematical Society gram, if funded, will be administered by has applied to the National Science Foun- the Professional Services Department, Should the proposal to the NSF be dation for funds to permit partial travel AMS, P.O. Box 6248, Providence, RI funded, the following conditions will ap- support for U.S. mathematicians attend- 02940. You can contact them at ply: mathematicians accepting grants for ing the 2002 International Congress of [email protected], 800-321-4267, ext. 4105 partial support of the travel to ICM 02 Mathematicians (ICM 02) August 20-28, or 401-455-4105. may not supplement them with any other 2002, in Beijing, China. In anticipation NSF funds. Currently, it is the intention of the availability of funds, the AMS is This program is open to U.S. mathema- of the NSF’s Division of Mathematical preparing to administer the selection pro- ticians (those who are currently affiliated Sciences to provide no additional funds cess, which would be similar to previous with a U.S. institution). Early career on its other regular research grants for programs funded in 1990, 1994 and 1998. mathematicians (those within six years of travel to ICM in 2002. However, an indi- their doctorate), women, and members vidual mathematician who does not re- Applications for support will be printed of U.S. groups underrepresented in math- ceive a travel grant may use regular NSF in the September issue of the Notices, and ematics are especially encouraged to ap- grant funds, subject to the usual restric- forms will be available on the AMS ply. ICM-02 Invited Speakers from U.S. tions and prior approval requirements. website (at http://www.ams.org/ institutions should submit applications, careersedu/icmapp.html) beginning Au- if funding is desired. All information currently available about gust 1, 2001. All completed application the ICM 02 program, organization, and forms must be mailed to the AMS by Applications will be evaluated by a panel registration procedure is located at http:/ October 31, 2001. This travel grants pro- of mathematical scientists under the /www.icm2002.org.cn/.

AWM Sponsors Essay Scientific Societies Present Public Contest Service Awards The Association for Women in Math- ematics is sponsoring an essay contest for Three major scientific societies pre- the House Committee on Science, and middle school, high school, undergradu- sented their 2001 Public Service Awards Chair of its Subcommittee on Environ- ate, and graduate students. The essays at a ceremony at the Rayburn House Of- ment, Technology and Standards. should be brief biographies of contem- fice Building in Washington, DC, on porary women who are pursuing a career Wednesday, May 16. The honorees were Dr. Lane is a former Director of the Na- in the mathematical sciences. The biog- Congressman Vernon Ehlers (R-MI) and tional Science Foundation. He was instru- raphies should be based primarily on an Dr. Neal Lane, former Assistant to the mental in raising science research and interview with the woman in question, President for Science and Technology. education to a high priority in the Clinton and should be between 500 and 1000 The awards, for committed and sustained Administration. The FY 2001 Federal words long. Winners will receive a prize, efforts in support of science, are given budget, in which science agency budgets and their essays will be published online jointly by the American Astronomical received much larger increases than in at the AWM web site. The AWM is also Society, the American Mathematical So- recent years, reflected Lane’s efforts. Cur- seeking volunteers who are willing to be ciety, and the American Physical Society, rently, Lane is University Professor and interviewed by students wishing to write which collectively represent more than Senior Fellow at the James A. Baker III essays for the contest. Women mathema- 100,000 scientists and mathematicians. Institute for Public Policy at Rice Univer- ticians wishing to volunteer should con- sity. tact the contest director, Victoria E. Congressman Ehlers, one of two physi- Howle, at the address below. cists in Congress, has been a champion Past recipients of the AAS-AMS-APS for science research and education Public Service Award include Senators Essays for the contest should be submit- throughout his congressional career. Re- Bill Frist (R-TN) and Joseph Lieberman ted to Victoria E. Howle in plain text for- cently he has concentrated on K-12 sci- (D-CT), and Dr. Harold Varmus (former mat, either by email at ence and mathematics education, intro- director of the National Institutes of [email protected] or in hard copy to ducing several bills to facilitate improve- Health). For more information on the Victoria E. Howle, Sandia National Labs, ment in science and mathematics learn- award, visit the AMS web site at http:// MS 9217, P. O. Box 969, Livermore, CA ing and teaching. Congressman Ehlers is www.ams.org/government/ 94551. For more information, visit the a member of the House Committee on pubservaward01.html. AWM web site at http://www.awm- Education and the Workforce, as well as math.org/biographies/contest.html.

12 August/September 2001 FOCUS Clay Mathematics Institute Announces Long Term Fellows, Olympiad Scholar, IMO Awards

The Clay Mathematics Institute, a on the winners, check online at http:// non-profit foundation dedicated to in- www.claymath.org/awards/ creasing and disseminating math- clayresearchaward.htm. ematical knowledge, recently an- nounced the names of four Long Term At the other end of the spectrum, the Prize Fellows, two Research Award American Olympiad Scholar award winners, one Olympiad Scholar, and goes to the student with the most in- four winners of its IMO Award. By genious and elegant solution to a prob- awarding these Fellowships to research lem on the USA Mathematical Olym- mathematicians and the Olympiad piad. This year’s award went to Michael and IMO awards to high school stu- Hamburg, an 11th grader from South Roman Bezrukavnikov Alexei Borodin dents, the CMI continues its extensive Bend, Indiana. Michael was one of only support for mathematics at many dif- 9 out of the 270 finalists to answer ferent levels. Problem 6 on the exam correctly. His solution, which was virtually a “proof The CMI Long Term Prize Fellows are without words,” won unanimous praise all young (under 30) research math- from the judges. (The proof can be seen ematicians who have already contrib- online at http://www.claymath.org/ uted profound new ideas and had ma- awards/cmiolympiadscholar.htm.) jor achievements in mathematical re- CMI’s award includes a cash prize and search. The Fellows are each hired by placement at an exclusive two-week CMI for terms ranging from one to five “mathematics boot camp” in Washing- years, depending upon factors includ- ton, DC this June. ing age and experience. Current Fel- Sergei Gukov Mircea Mustata lows are on the cutting edge of research In July, CMI announced that its CMI- universe around us. “Mathematical ranging from exploration of the intrica- IMO Award would go to the four students achievements have always blazed trails in cies of the theory of numbers to error who had perfect scores in the 2001 Inter- science and philosophy that eventually correction in quantum computation. Fel- national Mathematical Olympiad (see ar- filter down to everyday life in the form lows carry out this research at whatever ticle on page 3): Liang Xiao and Zhiqiang of new technologies and even social out- location they believe will best advance Zhang from China, Reid Barton and looks,” he said. The main point, however, their work. Gabriel Carroll from the United States. is simply that these are among the best young mathematicians, and CMI’s sup- This is actually the second year in which The mission of The Clay Mathematics port should allow them to fulfill their CMI is naming Long Term Fellows, but Institute is to increase and disseminate early promise as researchers. As David it is the first year in which the awards have mathematical knowledge, to educate Eisenbud of the University of California been made public. This year’s Fellows are mathematicians and other scientists at Berkeley pointed out, “The Fellows are Roman Bezrukavnikov (age 27, ap- about new discoveries in the field of the most brilliant people in their field, pointed for one year), Alexei Borodin (age mathematics, to encourage gifted stu- and these awards will give them the free- 25, appointed for four years), Sergei dents to pursue mathematical careers, dom to expand their talents.” Gukov (age 23, appointed for five years), and to recognize extraordinary achieve- and Mircea Mustata (age 29, appointed ments and advances in mathematical re- The CMI has also recently announced the for three years). The CMI also announced search. 2001 winners of the Clay Research Award, last year’s Long Term Prize Fellows: which recognizes outstanding achieve- Manjul Bhargava (age 27 at time of ap- To learn more about CMI, visit their web ment in mathematical research. This pointment, appointed for five years), site at http://www.claymath.org, year’s winners, announced at the closing Dennis Gaitsgory (age 26, appointed for which also contains more information ceremonies of the International Math- three years), Daniel Gottesman (age 30, about the awards and winners, including ematical Olympiad in Washington, DC, appointed for one year), and Terence Tao photographs. were Edward Witten of the Institute for (age 24, appointed for three years). Advanced Study at Princeton and Stanislav Smirnov, a senior lecturer at the CMI President Arthur Jaffe (of Harvard Royal Institute of Technology in University) pointed out that the work of Stockholm and a researcher at the Swed- Photographs courtesy of the Clay Math- the award winners has the potential to ish Royal Academy of Science. For more ematics Institute change how we view ourselves and the

13 FOCUS August/September 2001 MAA National Election Results Undergraduate Student Poster Session

The results from this year’s MAA elec- diana Section to San Diego Joint Mathematics Meetings tions are in. Ronald L. Graham has been being a member Tuesday January 8, 2002 elected President-Elect. As per the MAA of various com- 4:30 PM to 7:30 PM bylaws, he will serve as President-Elect for mittees and Organized by Mario U. Martelli a one-year term, beginning after the Janu- councils. He is a Claremont McKenna College ary meeting in 2002 and concluding at the distinguished end of the January meeting in 2003, at research math- s has been the case in several recent which point he will begin a two-year term ematician spe- A years, there will be an undergraduate stu- as MAA President. Carl Cowen has been cializing in Op- dent poster session at the forthcoming elected First Vice President and Joe Gallian erator Theory, Joint Mathematics Meetings in San Di- has been elected Second Vice President. but he also has a ego, CA. These sessions have been very Both will serve two-year terms beginning deep concern Carl Cowen successful in the past, and students and at the end of the January meeting in 2002. for mathematics their teachers are encouraged to take ad- education. “While this is the ‘New Golden vantage of this opportunity. Ronald Gra- Age of Mathematics’ and NSF sees math- ham has had ematics playing a central role in progress To participate, send title and half-page many roles in science in the coming years,” he observes, abstract to Mario Martelli either by e- within the “our children’s mathematical education is mail ([email protected]) or MAA, rang- in crisis, a shortage of qualified teachers by regular mail (Mario Martelli, Math- ing from a looms, and fewer graduates choose careers ematics Department, Claremont term as First in mathematics, especially women and mi- McKenna College, Claremont, CA 91711, Vice President norities. MAA works at the center of this Tel. 909-607-8979). Please include the in 1982–83 to ferment!” He emphasized the importance following information: author(s) participation of cooperation name(s), presenter(s) if not all authors in several between the will attend, affiliation, address, phone committees MAA and other number and e-mail of all presenters, and Ronald Graham and editorial organizations of the advisor(s). Clearly indicate the pre- boards. He in order that senter, who should keep in touch with has been a Hedrick Lecturer, a Pólya Lec- these issues Prof. Martelli and receive all information turer, and a Presidents’ Lecturer. He has may be success- regarding the poster. Make sure that your won both the Lester R. Ford Award and the fully addressed. submission does not arrive later than Carl Allendoerfer Award; both for exposi- December 10, 2001. Notification of ac- tory writing. Joe Gallian has ceptance will be e-mailed within 20 days also had a wide after the abstract has been received. Let Outside the MAA, Graham has been Presi- range of activi- the organizer know if you did not receive dent of the American Mathematical Soci- ties within the Joe Gallian it. Apply early! Space is limited and will ety and had many other roles within the MAA, but per- be filled up on a first-come, first-serve AMS. He is the winner of several awards, haps he has basis. The session is reserved to under- and has given invited talks at all sorts of been most visible as a lecturer and as a co- graduates. First year graduate students meetings, from the International Congress director of Project NExT. may submit posters on work done while of Mathematicians to the American Asso- undergraduates. Poster contents should ciation for the Advancement of Science. His statement on challenges facing the not be purely expository. Each poster will MAA highlighted the importance of pro- be evaluated by a panel of judges and the One of Graham’s goals as President will be viding leadership in increasing public best posters will receive monetary prizes to address issues such as the preparation awareness of mathematics, attracting new provided by the MAA, AMS, CUR and of students for the increasingly varied members at the graduate and undergradu- NSA. Tri-fold self standing 48" by 36" mathematical opportunities available in ate level outside academia, and offering table-top poster board will be provided. the emerging high technology economy, professional development opportunities. Additional material or equipment is the the development of appropriate curricu- “Project NExT has been enormously suc- responsibility of the presenter. Let the lar material, and increased outreach to the cessful with the generous support of the organizer know if an electrical outlet is broader public. Exxon/Mobil Foundation,” he notes. “The needed for your presentation. MAA must make this program self-sustain- Carl Cowen has also had many roles within ing.” See you in San Diego on January 8! the MAA, from being Governor of the In-

14 August/September 2001 FOCUS Short Takes the theme of the teaching and learning The idea is that while frontline math- of proof in mathematics. This newsletter ematical research problems are out of mainly contains bibliographical informa- reach for non-specialists, the methods Carnegie Foundation Studies tion, not only references to new material, used by research mathematicians are ac- Teacher Education but also old references pointed out by cessible to almost all young people. De- readers which do not appear in the bib- veloping the habits of mind used by The Carnegie Foundation for the Ad- liographical portion of the site.” The working scientists and mathematicians is vancement of Teaching has started a five- newsletters are available at http:// of immense and lasting value to all stu- year study of teacher education. They www.cabri.net/Preuve/. dents, no matter what they do with their want to find out how teacher education lives. classes are taught, how aspiring teachers Also worth noting is the Newsletter of the learn, and how their work is evaluated. International Study Group for the History Since this kind of work is unfamiliar to The project is part of a broader effort in and Pedagogy of Mathematics, often many students and teachers, the involve- which the foundation is looking at the known as “HPM.” The HPM newsletter ment of mathematicians is crucial. Math- training of lawyers, engineers, doctors, used to be published on paper and mailed ematicians will serve as online mentors social workers and clergymen. Many edu- to HPM members, but that has become whose role is to help students and teach- cation specialists welcomed the new too expensive, resulting in the move to ers ask themselves the right questions, study, feeling that the comprehensive in- publication on the web. You can find it point them to available resources, help formation it will generate may be of great on the Americas Section Web Site at them build their mathematical back- value to continuing attempts to improve http://www.sju.edu/~ambruso/ ground when necessary, and help them teacher education. For more information hpm/Welcome.html. navigate their path through the problem on the Carnegie Foundation program, solving and research process. visit their website at http:// Maryland Ph.D. Program Gets National www.carnegiefoundation.org/TeacherEd/ Attention for Success with Minorities The project is actively seeking mathema- index.htm. ticians who might be interested in taking n its February 16 issue, the Chronicle of part in this effort. For more information, Plus: An Online Magazine I Higher Education published an article visit their web site at http:// on Mathematics entitled “A University Beats the Odds to www2.edc.org/makingmath/, email to Produce Black Ph.D.s in Math” (page [email protected], or contact Jean Benson, here is much mathematical material T A14). The article features Ray Johnson Making Mathematics, Education Devel- on the internet. One of the most inter- and the University of Maryland program. opment Center, Inc., 55 Chapel Street, esting is Plus Magazine, at http:// The Chronicle returned to the subject in Newton, MA 02458; (617) 969-7100. plus.maths.org.uk. The magazine, which its March 16 issue (page B12), and also is targeted at those who are 16 or older posted an interview with Ray Johnson on Achieve, Inc. Announces Mathematics and have an interest in mathematics, in- its (subscribers-only) web site. All this Package for Middle School cludes a wide range of articles and news attention is due to Maryland’s success in items. It’s definitely worth adding to one’s attracting African-American students chieve Inc., a nonprofit group backed collection of bookmarks. Plus started life A and in supporting them all the way to the by political and corporate leaders, has as PASS Maths in 1997, published by the Ph.D. announced a plan to put together a pack- Department of Applied Mathematics and age of services aimed at improving math- Theoretical Physics at the University of More information on the program can be ematics achievement in the middle school Cambridge. It now runs under the aegis found in a book chapter by Duane A. grades. The plan was sparked by Ameri- of the Millennium Mathematics Project Cooper, “Changing the Faces of Math- can 8th graders’ disappointing perfor- —a group that incorporates elements of ematics Ph.D.s: What We Are Learning at mance on the TIMSS study. (See our May/ the DAMTP, the Cambridge Department the University of Maryland,” in Chang- June issue for an analysis of the study’s of Pure Mathematics and Mathematical ing the Faces of Mathematics: Perspectives results.) The package to be produced by Statistics and the School of Education. on African Americans, M. Strutchens, M. Achieve will include an 8th grade test that When FOCUS went to press, Plus had Johnson, W. Tate, eds. (Reston, Va.: will show states how they compare with been nominated for a Webby Award for NCTM, 2000). international standards, professional de- Science. Visit them to see if they won. velopment programs for teachers, and a EDC Announces Making Mathematics buyer’s guide to textbook and curricular Other Internet Newsletters Project materials. Achieve plans to work with the College Board to offer the package to the he internet has made it very easy to T aking Mathematics is an NSF-funded 14 states that have joined the Mathemat- publish electronic newsletters, and a great M project of the Education Development ics Achievement Partnership. Achieve’s number of them have sprung up. An in- Center in Newton, MA. The project home page is at http://www.achieve.org; teresting one is the Newsletter on Proof, brings together mathematicians with sec- you can read more about their plans to which is described as “a newsletter pub- ondary students and teachers to work on lished every other month, dedicated to research-like problems in mathematics. Short Takes continued on page 16

15 FOCUS August/September 2001 address mathematics in middle school at ference in Toulouse, France, entitled Tom Banchoff Receives their website: http://www.achieve.org/ “Fermat, quatre cents ans apres,” will Honorary Degree achieve/achievestart.nsf/pages/partnr. mark the event in October. For more in- formation, check their website at http:// Tom Banchoff, who was president of NExT News borel.ups-tlse.fr/Fermat/index.html. the MAA in 1999–2000, received an hon- orary Doctor of Science degree from In a recent ad in the op-ed section of John H. Marburger III may be Bush Rhode Island College in recognition of the New York Times, ExxonMobil dis- Science Advisor his contributions to mathematics educa- cussed their involvement with mathemat- tion. Banchoff, a mathematician with ics and science education. MAA’s Project President Bush announced that he in- deep interests in education and in the use NExT, which has been funded by tends to nominate John H. Marburger, III of technology to communicate math- ExxonMobil for many years, is one of two as Director of the Office of Science and ematical ideas, teaches at Brown Univer- projects that are highlighted in the article. Technology. Marburger is currently the sity in Providence, RI. He described the You can access the ad online at http:// Director of the Brookhaven National event as a rare case of “a minor prophet www.exxonmobil.com/news/opeds/ Laboratory and President of Brookhaven being honored in his own country.” 120401.pdf. Science Associates. He is presently on a leave of absence from the State Univer- San Francisco Exploratorium MAA has continued to seek funding for sity of New York at Stony Brook where Highlights Mathematics Project NExT, with the hope of allowing he served as President and Professor from the project to fully fund all participants. 1980 to 1994 and as a University Profes- This October, the Exploratorium, a sci- Recent donations of $15,000 from the sor of Physics and Electrical Engineering ence museum in San Francisco, will open Education Advancement Foundation and from 1994 to 1997. Marburger, who is a a new exhibition entitled Mathematica: $25,000 from the Dolciani-Halloran graduate of Princeton University and re- A World of Numbers and Beyond. The ex- Foundation will fund 16 NExT fellows for ceived a Ph.D. in Applied Physics from hibition, designed by Charles and Ray 2001-02, and efforts are underway to se- Stanford University, will need Senate con- Eames, explores mathematics as a tool, a cure more funding. firmation before he can take up the job. science, and a work of art. The ideas, im- His statement about his nomination can agery, and history of mathematics will be Happy Birthday, Fermat be found on the BNL web site at http:// portrayed by an array of demonstrations, www.bnl.gov/bnlweb/pubaf/pr/ devices, and other materials. The exhibi- This year marks the 400th anniversary bnlpr_JHMstatement.htm. tion will open on October 6. See their web of the birth of Pierre de Fermat. A con- site at http://www.exploratorium.edu for more information.

16 August/September 2001 FOCUS

From the Sections

Oklahoma, Section; the first Chairman from Arkan- (Sec-Treas sas. 1966-1970), John Jobe, In 1965, Professor George M. Ewing, of Oklahoma the University of Oklahoma, made a State Univer- motion to change the Section’s name to sity, (Sec- the Oklahoma-Arkansas Section in rec- Treas 1978- ognition of the regular participation of 1991). Front Arkansas people. The motion was sec- row from the onded by R. B. Deal and passed without left shows a negative vote. Robert McMillan, For 68 years the Secretary-Treasurers Oklahoma have been from Oklahoma. John Watson Christian is the first to be elected from Arkansas. University, All Secretary-Treasurers were from either (Sec-Treas Oklahoma University or Oklahoma State Pictured above are the Secretary-Trea- 1996-2001), and John Watson, Arkansas University until 1996 when Robert surers of the OK-AR Section of the Tech University, (Sec-Treas 2001- ). McMillan was elected. He was the first MAA. Collectively they represent 27 from a private university. Professor Deal years of service in this position from as The Section began in 1933 and was has been active in the OK-AR Section and early as 1966 to the current Secretary- known as the Oklahoma Section. Arkan- a member of the MAA for 57 years. He Treasurer in 2001. sas did not have a section and many presented a paper at the section meeting members of the mathematics commu- in March of this year. The OK-AR Sec- Top left (back row) shows Stan Eliason, nity met with the Oklahoma Section. In tion home page is at http:// University of Oklahoma, (Sec-Treas 1956 Professor O. P. Sanders, University www.uca.edu/divisions/aca- 1991-96), Harold Huneke, University of of Arkansas, was elected Chairman of the demic/math/maa/maa.htm.

Award for Distinguished Service to D’Ambrosio and Yong Mathematics: Call for Nominations Share Kenneth O. May Prize he Committee on the Yeh-Gin Gung tion should be no more than two pages T he fourth Kenneth O. May Prize, and Dr. Charles Y. Hu Award for Distin- in length, and should include justifica- T awarded by the International Commis- guished Service to Mathematics is seek- tion. Send nominations to the Commit- sion on the History of Mathematics, went ing nominations for this award. The tee on Distinguished Service to Math- to Ubiratan D’Ambrosio of Brazil and Gung-Hu Award is the MAA’s most pres- ematics, c/o Martha Siegel, Towson Uni- Lam Lay Yong of Singapore for their tigious award for service. It is awarded versity, Stephens Hall 302, 8000 York many publications and scholarly contri- for service to mathematics that has been Road, Towson, MD 21252, or by email to butions on the study of non-Eurocentric widely recognized as extraordinarily suc- [email protected]. To be considered for mathematics. The prize was awarded at cessful. The contribution should be such the next award, nominations should the 21st Intenational Congress on the as to influence the field of mathematics reach the committee by November 30, History of Science, held in Mexico in July. or mathematical education in a signifi- 2001. Questions should be addressed to Past recipients of the K. O. May Prize in- cant and positive way on a national scale. Henry Alder, the chair of the Commit- clude Dirk J. Struik, A. A. Youschkevitch, Recipients of this award must be mem- tee, at [email protected]. For more on Christoph J. Scriba, Hans Wussing, and bers of the Association who reside in the the award and a list of past winners, vist René Taton. The award is named for Ken- United States or Canada. MAA Online at http://www.maa.org/ neth O. May, the founder Historia awards/gunghu.html. Mathematica, the official journal of the Any member of the MAA can nominate International Commission on the History candidates for the award. The nomina- of Mathematics.For more information on the ICHM, see http://elib.zib.de/IMU/ ICHM/index.html. 17 FOCUS August/September 2001 Evaluating Undergraduate Programs: Indicators of Departmental Health

By John A. Dossey and Kenneth J. Travers set of indicators for use by mathematics dicators, the kinds of data to collect in departments as they undertake self-as- the light of these issues, how to go about sessment activities. For details of this collecting data, how to organize the col- he teaching of undergraduate math- T project go to: http://www.mste.uiuc.edu/ lected data, and, finally, how to commu- ematics in the first two years is currently indicators with an updated website, full nicate and use the information gathered. in a state of transition. At the department reports, as well as illustrative data, to be The mathematics departments were lo- level, the student population is changing, available on-line at the site in December cated at a community college (CC), a both in its composition and in the math- 2001. newly founded (1989) comprehensive ematics that has been taken prior to col- state university (SU), and a Level I re- lege. Student goals and aspirations for What are education indicators? search university (RU). The choice of enrolling in mathematics courses are dif- three such very different kinds of insti- ferent and more diverse than ever before. We are all familiar with the use of eco- tutions was deliberate. It permitted one At the same time, the needs of the tradi- nomic indicators to describe the health to see how self-assessment plays out in tional partner disciplines of mathemat- and direction of the nation’s economy. three very different kinds of institutions. ics are also changing to reflect disciplin- These indicators—for example, the Dow- ary advances and the impact of technol- Jones Industrial Average—reflect “perfor- Surveys were developed to provide data ogy on teaching and learning across the mance characteristics” of the economy. relative to five different facets of under- disciplines. Recommendations based on Even when these data have complex rela- graduate programs: institutional and de- recent research on how humans learn call tions with other aspects of the economy, partment goals and priorities, curricu- for changes in instructional programs they provide “benchmarks” —compari- lum, instructional staff, classroom prac- and learning environments. As math- sons of the condition of the economy tices, and student issues. For more infor- ematics departments attempt to deal with with itself over time. Sets of these indica- mation on the survey’s instruments these issues, there are demands from cen- tors and associated benchmarks help in- themselves, refer to the URL listed above. tral administration, government and form judgments of the economy’s funding agencies, the public, and students strength and of the direction of its move- Story Lines Emerging From the Data themselves that mathematics depart- ment (for example, prediction of more ments become both more responsive to likely economic trends on the basis of the Comparisons of the data from the three the needs of their various constituencies past performance of the economy). institutions provide some interesting and more accountable for their actions. similarities and differences. The first is Indicators also have a corresponding role that, across the institutions, the depart- Most mathematics department chairs, to play in education. As Shavelson and his ments have been responsive to keeping curriculum committees, and concerned colleagues (see Shavelson, R., McDonnell, their curricula up-to-date through sylla- faculty recognize that providing quality L., Oakes, J., Carey, N., with Picus, L. bus revisions and new textbook adop- programs involves far more than simply (1987). Indicator Systems for Monitoring tions across the courses normally taught offering courses. Syllabi must be devel- Mathematics and Science Education. Santa in the first two-years. However, one in- oped, qualified instructors (tenure or ten- Monica, CA: RAND, 1987) have stated: teresting fact emerged from this analysis. ure-track faculty, adjuncts, teaching as- It appears that departments tend to con- sistants, etc.) must be identified and as- Education indicators are single or compos- sider the revision of course goals and con- signed, and decisions must be made ite statistics that reflect important aspects tent, then choose a text in the following about such matters as class size, use of dis- of the education system (as economic indi- year, and come out with a new syllabus cussion sections, selection of textbooks, cators reflect aspects of the economy). They in the following semester or year. This, and inclusion of technology (graphing are expected to tell a great deal about the along with other responses, indicates that calculators, computer algebra software, entire system by reporting the condition of there is at least the core of a curricular etc.). particularly significant features of it…. [An planning process. education indicator] should provide insight In the current climate of change and ac- into the ‘health’, quality or effectiveness of Other data collected at the institutional/ countability, mathematics departments the system; and it should be useful in the departmental level provide demographic are searching for ways to make decisions educational policy context (Shavelson, et overviews of the departments and help that are educationally sound. However, al, 1987, p. 8). situate the department and its programs the stark reality is that the sources of data, in the overall milieu of the university at at both the local and national levels, for As part of the Illinois Indicators Project, large. They provide a background against this kind of decision-making are either three mathematics departments each car- which the departmental directions can be nonexistent or largely ineffective. In or- ried out an extensive assessment of its compared and contrasted with the der to help address this problem, the Na- lower division (first two years) math- institution’s direction and overall mis- tional Science Foundation funded the In- ematics programs. The assembled data sion. dicators Project at the University of Illi- provided an opportunity to identify is- nois at Urbana-Champaign to develop a sues in the development of program in- A second major story line deals with in- 18 August/September 2001 FOCUS struction. The instructional staff was only about one-third that proportion of All in all, the surveys and reporting meth- asked to describe the extent to which they the state university and research univer- ods developed in the project, the man- make use of instructional technology sity instructors reported calculator use. ners of comparing and contrasting the across those courses commonly found in Hence, it appears that relatively similar results, and the development of a data the first 2-years and how they made use, use of lectures, question-and-answer ap- base for different levels of institutions if at all, of a variety of pedagogical ap- proaches, homework, and individual provide a basis for other departments to proaches in teaching these courses. Their working time in classes characterize in- consider. Other departments may wish to responses are summarized in Table 1 be- struction at these three campuses. examine themselves and look for ways of low. responding to calls on their campuses for Pictures and stories also emerge showing departmental self-evaluations or for jus- Other questions dealt with the use of spe- contrasts in the types of assessment em- tifications of departmental existence in cific teaching strategies. The data were ployed, different patterns of interaction this age of value-added accountability. quite similar with respect to the frequency between instructors and their students, with which instructors used lecture, ques- and other issues of classroom climate. John A. Dossey is Distinguished University tion and answer approaches, homework, Questions to students about the degree Professor of Mathematics Emeritus at Illi- and individual working time in classes. to which their instructors are responsive nois State University and former chair of However, substantial differences were to their needs and seem to have an aware- the Conference Board of the Mathemati- found in the use of group work, guided ness of their needs as students in differ- cal Sciences (CBMS). Kenneth J. Travers is discovery activities, and calculator or ing majors reveal general student satis- Professor of Mathematics Education and computer demonstrations. For example, faction across the board. These data are Director of the Office for Mathematics, Sci- around 40% of the comprehensive uni- somewhat different from what one hears ence, and Technology Education at the versity and research university instructors in the lore and myths repeated about University of Illinois at Urbana- report using group work while only mathematics department instructional Champaign. around 10% of the community college staff and their interactions with their stu- instructors did so. However, while 100% dents. of the community college instructors re- ported use of calculators in their classes,

Technology Instructional Approaches School Course Graphing Computers Small Written Project/Lab Calculator Group Assignments Assignments Work CC College Algebra Used Always Not Used Used Rarely Not Used Not Used SU College Algebra Used Always Not Used Not Used Used often Not Used RU College Algebra Used Always Not Used Not Used Not Used Not Used CC Math for Used Often Used Rarely Used Rarely Used Rarely Used Often Elem. Ed SU Math for Used Rarely Used Often Used Often Used often Used Rarely Elem. Ed RU Math for Used Often Used Often Used Always Used Always Used Always Elem. Ed. CC University Used Always Not Used Used Rarely Used Rarely Used Rarely Calculus SU University Used Often Used Always Used Rarely Used Often Used Always Calculus RU University Used Often Used Often Used Often Used Often Used Often Calculus (for all categories, depends on version)

Table 1. Uses of technology and various instructional approaches at three kinds of campuses

19 FOCUS August/September 2001 A Different Pencil: Use Technology Wisely tors with their calculators; few under- stood the special role of eigenvalues in By Dick Jardine analyzing mathematical relationships.

This is a confession. I am guilty of the problem, y' = y + 1, y(0)=2, that our stu- Keeping the last lesson in mind, we owe crime of “bludgeoning our students with dents can solve exactly more quickly than it to our students to allocate course time technology,” to quote Gary Sherman of they can iterate to obtain the numerical to the learning of technology. Our stu- Rose-Hulman. Gary was offering some approximation. It is not difficult to find dents have too many demands on their caveats in a talk about implementing cal- a differential equation that students can- time to do otherwise. We can develop culus reform. Before being aware of re- not solve analytically, for example y' = et2, carefully designed worksheets which can form, I had long been an advocate of the y(0)=2, but can solve readily using the aid in the learning process (many are use of computer technology in math- numerical method. Additionally, a com- available on the WWW. Just search on the ematics education. puter algebra system can easily generate CAS or calculator you’d like to use and a slope field for the latter problem, lead- you’ll be overwhelmed with the quantity In the mid-80s, I wrote Pascal programs ing to a complete demonstration of ana- and quality of the work that has been for the Apple II and TERAK (can you lytical, numerical, and graphical solutions done so that you “do not have to reinvent believe an 8-inch floppy disk!) micro- of mathematical problems. Require stu- the wheel”). computers to demonstrate concepts for dents to generate one slope field by hand my probability and statistics course. I and they will quickly appreciate the ad- Allocating an appropriate amount of used the computers in my classroom as vantage of using the computer and cal- classroom time for demonstration is im- an electronic blackboard to display vari- culator. portant. Assigning group activities that ous discrete and continuous distributions can be done in a laboratory setting dur- and to compute the associated probabili- A second lesson learned is that we must ing class hours or outside of class, as ties, in the same way that I used the TI- be careful not to overwhelm our students graded and ungraded homework is essen- 83 Plus in my class last semester. I con- with technology at the expense of their tial. Early in the semester, maximum use tinue to advocate the use of technology learning mathematics. Recalling Gary should be made of available computer in the teaching of mathematics, but Sherman again, this lesson is better ex- laboratories and computer-equipped would like to offer some “lessons learned” pressed with an analogy: “Do not fall in classrooms. so that others do not make the same mis- love with the technological backpack at takes I have made. the expense of the mathematical hike— In addition to allocating time in the mathematics atrophies!” course, be sure to allocate plenty of prepa- Make perfectly apparent to your students ration time toward developing the appropriate use of technology. Dur- At the start of a differential equations worksheets, web pages, and other tech- ing a recent elementary statistics class, I course I taught five years ago, I spent far nology-based learning activities. The time demonstrated the use of the TI-83 to plot more time at the beginning of my course spent must be worth the increment in the histogram of a data set and then had demonstrating how to use the new com- learning made possible by the technology. students produce a similar histogram as puter algebra system (CAS), getting the Experience reduces the time spent in a group activity. After class, a student CAS to work on our campus network, completing subsequent activities, but noted that she could have just as easily and making the CAS work on the variety many of us have the shared experience of done the plot by hand rather than push of student and classroom computers on spending way too much time developing all the buttons required to generate the campus than I spent doing the math- a learning activity that was technologi- graph on the calculator. She was right! I ematics. It followed that the mathemati- cally dependent. Also, in addition to the had failed to make clear to the class that cal content of the course suffered appre- primary technology-based lesson plan, since the data was now in the machine, I ciably. always have a back-up plan for when the could not only plot histograms but also technology fails. do a wide variety of other graphs and Additionally, I have taught in an environ- analyses of the data with ease, far faster ment in which undergraduates were ex- Invariably, the network will go down, than anyone could do with paper and pected to learn not only a CAS, but also batteries will die, the projector bulb will pencil. Our students must be clearly in- the use of an advanced spreadsheet and burn out, the monitor will go blank, the formed of the advantages that technol- the use of a high-end graphing calcula- software will not load as it did when you ogy offers, so that they do not just see it tor. Some students were up to the chal- last checked it, some student will find just as a “high-tech” way of doing the same lenge, but many were overburdened with the right wrong keystroke to push to en- old thing. “technological backpacks” that were too sure the calculator or computer demon- full. As a result, the depth of the math- stration fails. All of those crises have hap- In one reform calculus text, the authors’ ematical learning suffered in the process pened to me. Technology fails sometimes. first example of the use of Euler’s method of learning how to do the mathematics Plan on it. to solve a differential equation is not only with technology. Most of our students done incorrectly, but also is applied to a could generate eigenvalues and eigenvec- In students’ evaluations of my courses,

20 August/September 2001 FOCUS they report that my modest web pages that each of us must decide based on the ematics so that your students, like mine, facilitate their learning. But crafting ef- needs of our particular students. learn that technology is not a panacea, but fective CAS worksheets and web pages is can be a wonderful partner in doing a time-consuming activity, and creating There’s an old saying that a turtle never mathematics. them is an artistic endeavor that is devel- makes progress unless it sticks its neck oped only with a significant commitment out. I will continue to attempt to stay on Dick Jardine is an assistant professor at of time on the part of the instructor. the leading (hopefully, not “bleeding”) Keene State College, with interests in using edge of the use of technology in teaching the history of mathematics to enhance I often think I spend far too much time mathematics to my students. My neck is mathematical learning and using technol- on technology-based activities when I prominently out, because I owe it to my ogy appropriately to facilitate mathemati- could be creating paper and pencil dis- students to keep it out. Don’t be guilty cal learning. In his spare time, he runs the covery activities for students to explore of the offense cited by Gary Sherman, but roads and trails of New Hampshire and and learn mathematics. It’s a trade-off use technology wisely in teaching math- plays the guitar badly, but with a smile.

ExxonMobil and NSF Join MAA in Supporting Teacher Preparation

Several national reports have called for nents have not been determined, the pro- the principal author of the MET report. better preparation of school mathemat- gram will include workshops, mini- Bernard L. Madison, MAA Visiting ics teachers. These same reports have rec- courses, and electronic networking sup- Mathematician, is directing MEFT from ognized the major role that collegiate port for college faculty who design or the MAA offices. mathematics faculty should play in this teach courses for future teachers. Com- improvement. To help address this need, ponents will also promote providing pro- MEFT planning will have two major pub- the MAA is developing a multi-year, mul- fessional development opportunities for lic components. In September, the Lead- tifaceted program to aid college faculty school teachers through college and uni- ership Team will convene a conference of in teacher preparation and support. versity mathematics departments. approximately forty K-12 teachers, col- lege faculty, and curriculum developers With funding from the ExxonMobil The general strategy for MEFT, includ- to advise on the components of MEFT. Foundation and the National Science ing a year of planning, came from a Sep- The second component will be a pilot Foundation, the MAA is spending a year tember 2000 gathering at the MAA of ap- workshop to be held January 9–14, 2002, planning a program with the central pur- proximately thirty leaders in mathemat- following the Joint Mathematics Meet- pose of helping collegiate mathematical ics education. The planning Leadership ings in San Diego. The workshop, Teach- sciences faculty teach better courses for Team consists of Judith Covington, Vir- ing Future Teachers, will be directed by future teachers. The program, called ginia Bastable, Ed Dubinsky, Glenda Ed Dubinsky and have Deborah Ball and Mathematicians Educating Future Teach- Lappan, and Alan Tucker (Chair). Hyman Bass as faculty. ers (MEFT), will be outlined in a proposal to be submitted for funding near the end MEFT originated in the MAA Commit- Based on the experience of the Septem- of 2001. tee on the Mathematical Education of ber 2000 and September 2001 confer- Teachers (COMET), as did the MET re- ences, the MET report, and Teaching Fu- The Mathematical Education of Teachers, port, which was later shifted to CBMS to ture Teachers: A Pilot Workshop, MEFT the CBMS report about to be issued, secure broader support. The idea for will have a solid foundation. This foun- makes recommendations on the content MEFT came from Ed Dubinsky and Olaf dation work should result in a program and nature of courses for prospective Stackelburg. Judith Covington is Co- to provide continuing support and en- teachers, emphasizing the mathematics Chair of COMET, and Ed Dubinsky and couragement for collegiate mathematics of teaching. The MAA program is to fol- Glenda Lappan are members. Virginia departments to become more fully en- low through on the MET report and to Bastable is a former K-12 teacher who gaged in teaching future teachers and help college faculty members implement directs SummerMath for Teachers at supporting them after they graduate. such courses. Although all the compo- Mount Holyoke College. Alan Tucker was

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