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December 2005

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FOCUS December 2005

FOCUS is published by theMathematical Association of America inJanuary, February, March, April, May/June,August/September, October, November, andDecember.

Editor: Fernando Gouvêa, Colby College;fqgouvea@colby.edu

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President: Carl C. Cowen

First Vice-President: Barbara T. Faires,Second Vice-President: Jean Bee Chan,Secretary: Martha J. Siegel, AssociateSecretary: James J. Tattersall, Treasurer: JohnW. Kenelly

Executive Director: Tina H. Straley

Associate Executive Director and Directorof Publications: Donald J. Albers

FOCUS Editorial Board: Rob Bradley; J.Kevin Colligan; Sharon Cutler Ross; JoeGallian; Jackie Giles; Maeve McCarthy; ColmMulcahy; Peter Renz; Annie Selden;Hortensia Soto-Johnson; Ravi Vakil.

Letters to the editor should be addressed toFernando Gouvêa, Colby College, Dept. ofMathematics, Waterville, ME 04901, or byemail to fqgouvea@colby.edu.

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Copyright © 2005 by the MathematicalAssociation of America (Incorporated).Educational institutions may reproducearticles for their own use, but not for sale,provided that the following citation is used:“Reprinted with permission of FOCUS, thenewsletter of the Mathematical Associationof America (Incorporated).”

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February March May/JuneEditorial Copy December 15 January 15 March 15Display Ads December 20 January 28 March 28Employment Ads December 9 January 15 March 10

InsideVolume 25 Issue 9

4 Jenny Quinn Named Executive Director of AWM

5 Archives of American Mathematics Spotlight:An MAA Photographic MysteryBy Kristy Sorensen

6 What I Learned...The Frustrations of Choosing TextbooksBy Blair Madore

8 Looking Beyond the Curriculum in JamaicaBy Jon Jacobsen and Michael Orrison

9 Coffee and Mathematics, Once Again

10 Five Years at the MagazineBy Frank A. Farris

12 Mathematically Speaking: Expanding the Role of Oral Communication inMathematics ProgramsBy Stephen J. Curran, Michael N. Ferencak, John W. Thompson,and Susan M. Wieczorek

14 Lost in ShakespaceBy Stephen Abbott

17 SUMMA National Research Experience for Undergraduates Program

18 Short TakesCompiled by Fernando Q. Gouvêa and Harry Waldman

20 Our Experiences as IMMERSE FacultyBy Keith Agre, Tracy Hamilton, Jacqueline Jensen, and Keri Kornelson

22 Musings on the Two-Body ProblemBy Brian Birgen and Jean Bee Chan

23 What Does ACMS Stand For?By Robert L. Brabenec

25 Thirty Years and Counting: My Involvement With the MAABy George Bradley

26 How We Measure UpIs American Math and Science in Decline?By The Editors of The New Atlantis

28 In Memoriam

29 How We Moved Excel to the Head of the ClassBy Ed Carlin and John Holden

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The 2006 Annual Meeting of theAmerican Association for the Advance-ment of Science, to be held February 16–20, in St. Louis, MO, will feature manyoutstanding expository talks by promi-nent mathematicians. The followingsymposia sponsored by Section A (Math-ematics) are part of the special math-ematical event “Beyond Pi: Grand Chal-lenges in the Mathematical Sciences.”

Paradise Lost? The Changing Nature ofMathematical Proof (organized by KeithDevlin)

Million-Dollar Mathematics: ChallengeProblems in the 21st Century (organizedby John Ewing and James Carlson)

NUMB3RS and the Challenge of Chang-ing Public Perception of Mathematics (or-ganized by Robert Osserman and TonyChan)

Astrodynamics, Space Missions, and Chaos(organized by Edward Belbruno)

Tsunamis: Their Hydronamics and Impacton People (organized by Walter Craig,Jerry Bona, and John Mutter)

How Insects Fly (organized by Jane Wang)Arches: Gateways From Science to Culture(organized by Kim Williams)

Other symposia that will be of interestto the mathematical community include:Physics of Virtual Worlds, Frontiers in Bio-logical Imaging: From Cells to Humans,Imaging Dynamical Diseases in the Brain,Refining Einstein: The Search for Relativ-ity Violations, Science and EngineeringChallenges and Opportunities in Home-land Security, Overcoming Gender Stereo-types: Girls in Science, Engineering, andTechnology, Computer Science BehindYour Science, Expanding Universe of Digi-tal Data Collections, Evaluating Curricu-lar Effectiveness: Judging the Quality of K-12 Mathematics Evaluations, and FourEye-Opening Science Education ResearchStudies: Connecting Science and Educa-tional Research.

The above symposia are only a few of the200 or so AAAS program offerings in thephysical, life, social, and biological sci-ences. For further details about the 2006AAAS program, see the October 21st,2005 issue of Science or visit the web site

Mathematics at the AAAS Meeting, February 2006By Warren Page

at http://www.aaasmeeting.org and lookunder “Program and Events.”

AAAS annual meetings are the showcasesof American science, and they encour-age participation by mathematicians andmathematics educators. (Section A ac-knowledges the generous contributionsof AMS for travel support and SIAM forsupport of media awareness.) In present-ing mathematics-related themes to theAAAS Program Committee, I have foundthe committee to be genuinely interestedin offering symposia on mathematicaltopics of current interest. Thus, SectionA’s Committee seeks organizers andspeakers who can present substantial newmaterial in an accessible manner to alarge scientific audience. Toward this end,I invite you to attend our Section A busi-ness meeting 7:45 p.m.–10:00 p.m. Fri-day, February 17th, 2006 in the Bentonroom of the Renaissance Grand Hotel. Iinvite you also to send me, and encour-age your colleagues to send me, sympo-sia proposals for future AAAS annualmeetings.

Warren Page (wxpny@aol.com) is Secre-tary of Section A of the AAAS.

Most of the articles published in FO-CUS are written specifically for us, usu-ally by members of MAA. Occasionally,however, we will reprint articles fromother sources (with permission, ofcourse) if we feel they will interest ourreaders. By coincidence, there are threesuch pieces in this issue.

Blair Madore’s piece on choosing text-books was originally written for inter-nal use at his university as it discussedthe issues surrounding textbooks. Wethought it was interesting enough toshare with the readers of FOCUS inslightly revised form. It is the latest in-

stallment in the “What I Learned” series,though it might almost have fit into the“What’s the Best Textbook” series as well.

Frank Farris’s account on what goes onbehind the scenes at an MAA journal(specifically, Mathematics Magazine) wasoriginally written in order to share theexperience he has accumulated with fu-ture journal editors. We thought mostmembers of MAA would be interested inknowing what their editors do, and so wepresent a version of Frank’s paper here.It has been shortened a little, mostly byremoving the parts dealing with the moreboring aspects of the job.

Finally, “How We Measure Up” was origi-nally published in The New Atlantis, ajournal about technology and ethics. Wethought it presented a provocativecounter-argument to the oft-heard criesof despair about how badly our math-ematics education system is performing.

We hope our readers will enjoy the mixof articles and that some, in fact, will wishto write articles of their own. Informa-tion on how to submit articles to FOCUScan be found at: http://www.maa.org/pubs/focussubmission.html.

From the Editor

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FOCUS December 2005

Jennifer J. Quinn became Executive Di-rector of the Association for Women inMathematics (AWM) on October 1,2005. Quinn, together with an associa-tion management company, will supportthe work of the volunteer officers ofAWM. She will be actively involved withthe AWM membership at the Joint Math-ematics Meetings, the SIAM AnnualMeeting, and other events in whichAWM participates. Her duties will in-clude generating new membership, grantreporting, facilitating committee rota-tion and volunteer efforts, and carryingout new initiatives.

Barbara Keyfitz (University of Houston),President of AWM and current Directorof the Fields Institute in Toronto, says:“Following a year-long quest for a gov-ernance and staff structure in keepingwith the increased reach and responsi-bilities of AWM, we are excited to havereached this point. AWM’s capable staffunderstands and satisfies its infrastruc-ture needs, allowing the volunteer lead-ership to focus on the mission of AWM:advocacy and support for women andgirls in the mathematical sciences. Quinnwill greatly enhance these efforts.”

Quinn received her B.A. magna cumlaude from Williams College with ma-jors in mathematics and biology. Work-ing as an actuary in Chicago after gradu-ation convinced her to return to aca-demic life. She earned her M.S. in puremathematics from the University of Illi-nois at Chicago and her Ph.D. in combi-natorics, working with Richard Brualdiat the University of Wisconsin, Madison.For the past twelve years, she has taughtat Occidental College, rising to the rankof full professor and serving as chair ofher department. Quinn’s research inter-ests include graph theory, combinatorialmatrix theory, and exploring the connec-tions between partitions and quantumphysics. Her mathematical passion is forcombinatorial proof. One lifelong goalis to prove Ernst Mach correct when hesaid: “There is no problem in all math-ematics that cannot be solved by directcounting.”

Quinn writes, “I chose to pursue thisposition because of its importance pro-moting mathematics and the role ofwomen in mathematics. The major de-cisions regarding organizational opera-tions are complete; now we can refocus

Jenny Quinn Named Executive Director of AWM

on better serving and expanding ourmembership. I’m looking forward to myinvolvement in the enterprise. This is anexciting time for the AWM.”

MAA members will know Quinn as theco-author, with Art Benjamin , of Proofsthat Really Count, published by the MAAin 2003, and as co-editor, also with Ben-jamin, of Math Horizons. We are glad toreport that she will continue her workon Horizons while she helps run AWM.

Jenny Quinn

The mathematics departments ofCarleton and St. Olaf Colleges intend,pending renewed funding from NSF, tooffer again their month-long summermathematics program for eighteenmathematically-talented first- and sec-ond-year undergraduate women. By in-troducing them to new and exciting ar-eas of mathematics that they would notsee in a standard undergraduate curricu-lum, and by honing their skills in writ-ing and speaking mathematics, the pro-gram leaders endeavor to excite thesewomen on to advanced degrees in themathematical sciences, and, more impor-tantly, to increase each woman’s confi-dence in her own abilities and connectthem all into a supportive network tocarry them through their undergraduateand graduate education.

At the heart of the program are two de-manding, intense courses under the su-

pervision of female faculty who are ac-tive in research and renowned for theirteaching. In past summers we have hadthe following instructors: Judy Kennedy(Topological Dynamical Systems), EricaFlapan (Knots and Chemistry), LauraChihara (Algebraic Coding Theory),Karen Brucks (Low-Dimensional Dy-namical Systems), Margie Hale (FuzzyLogic), Rhonda Hatcher (Game Theory),Katherine Crowley (Morse Theory) andothers.

Besides the coursework, participants takepart in a variety of mathematical events:panel discussions on graduate schoolsand careers, colloquia on a variety of top-ics, recreational problem-solving, andvisits from at least one REU organizerand the organizer of the Budapest Semes-ter. The mathematical part of the pro-gram is balanced with optional weekendevents including canoeing, hiking, pic-

nics, and tubing. Past participants havereported (through program evaluationsand the list server set up for their corre-spondence) increased facility with math-ematics, bolstered self-confidence, andnew or renewed excitement towardmathematics.

If you have first- or second-year womenstudents whom you think would benefitfrom a demanding, invigorating month-long exposure to mathematics next sum-mer (June 18-July 16), please refer themto the program web page at http://www.mathcs.carleton.edu/smp or havethem contact Deanna Haunsperger atDepartment of Mathematics and Com-puter Science, Carleton College,Northfield, MN 55057(dhaunspe@carleton.edu). The deadlinefor applications is February 24, 2006.

Summer Mathematics Program for Women

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December 2005

From the Mathematical Association of America Records, Archives of Ameri-can Mathematics, Center for American History, The University of Texas atAustin.

Do you know this mathematician?

Last year the Archives of American Mathematicsreceived a valuable collection of historical documentsfrom the Mathematical Association of AmericaHeadquarters (see the January 2005 issue of FOCUSfor more details). Included in the materials are agroup of photographs from what appears to be aproduction for the Mathematics Today film series inthe 1960s. This series was developed by theIndividual Lectures Project and the Committee onEducational Media in order to provide visuallearning aids appropriate for those with a casualinterest in mathematics, college mathematicsstudents, and professional mathematicians. Twenty-four 16mm films were produced altogether, in bothcolor and black and white, and they were availablefor purchase or rent from the Modern Learning Aidsdistribution company. One of these photos is on thecover of this issue of FOCUS, and another is on thispage.

Our problem? We aren’t able to identify the subjectsin these fascinating shots. If you can help, get incontact with Kristy Sorensen, the archivist, atk.sorensen@mail.utexas.edu. Perhaps with the helpof the readers of FOCUS we can find out more aboutthe story of this project and what became of it. Wewill report on the answers we get in a future issue.

The Mathematical Association of America Recordsinventory can be found online at: http://www.l ib .u texas .edu/ ta ro /u tcah/00328/cah-00328.html.

The Archives of American Mathematics is located atthe Research and Collections division of the Centerfor American History on the University of Texas atAustin campus. Persons interested in conductingresearch or donating materials or who have generalquestions about the Archives of American Mathematics should contact Kristy Sorensen, Archivist, k.sorensen@mail.utexas.edu,(512) 495-4539. Feel free to visit us on the web at: http://www.cah.utexas.edu/collectioncomponents/math.html

Archives of American Mathematics Spotlight:

An MAA Photographic Mystery

By Kristy Sorensen

AAM at JMM!

Don’t miss a special exhibit from the Archives of American Mathematics at the Joint Mathematics Meetings in San Anto-nio. The AMS-MAA Archives Committee has arranged for an exhibit of “selections from the Archives of American Math-ematics.” When you visit the exhibit hall, don’t just look at books; come see a representative sample of the resources on thehistory of modern mathematics available at the Archives.

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FOCUS December 2005

Most semesters I am be-sieged with textbook orders justwhen I am at my busiest. Thefurthest thing from my mind isnext semester’s courses andtheir textbook needs. And yetsomehow I have to make timeto make a wise choice of a text-book. A great textbook canmake a course great. A medio-cre textbook may not affect acourse at all. But a poor text-book can destroy a course. Andso I have started looking forbooks as early as possible.

In Fall 2003, I was teaching ad-vanced calculus, a course thatis often considered the majorobstacle to completing the math majorfor most students. At other schools thiscourse might be called real analysis orintroductory analysis. We study topicsthat include the axioms for the Realnumbers, limits of sequences, the Heine-Borel theorem, the Bolzano-Weierstrasstheorem, limits of functions, continuityand uniform continuity. This is materialthat I love but students sometimes hate.Having a good textbook can be crucialto the success of this course.

I started looking for the right book earlythe spring before and continued search-ing throughout the semester. I first con-sidered two textbooks used in the pastby other members of the department: In-troduction to Analysis, by E.D. Gaughan,and Analysis With an Introduction toProof, by S.R. Lay.

Two years earlier, I had taught AdvancedCalculus II and out of consideration forthe students’ pocketbooks we used thesame text, Lay, that they had used in Ad-vanced Calculus I with another instruc-tor. It had cost nearly $100 and I couldn’tbear to make them shell out a similar fig-ure for a different book. This seemed likea good idea at the time, but there wereproblems.

Lay had a number of typographical er-rors. In this advanced class, students readand present material from the text. Anysmall error, even a poorly worded sen-tence, can become a major obstacle totheir comprehension. Of course, over-coming such errors is part of what theylearn in the course, but I wished theycould spend the majority of their timeon mathematical obstacles, not typo-graphical ones. Eventually, we found acrucial error in one proof. To resolve itwe turned to Gaughan. In that book wefound a theorem with a correct proof, butthe theorem was weaker than the one inLay. Was the stronger theorem false? No.It turned out that an earlier edition ofGaughan had the stronger theorem anda correct proof. How did it get edited outin more recent editions? Go figure.

For me, the only redeeming value of thesetexts was the excitement that finding er-rors generated in the students. It keptthem engaged in the course, if not ex-actly in the way I had intended.

So for my Advanced Calculus course Igave up on those books and looked at anumber of other texts offered to me bybook representatives. Some looked ok.Others I feared were too much like the

flawed books I mentioned above. FinallyI settled on a great looking book: An in-troduction to Analysis by G.G. Bilodeauand P.R. Thie. It was in a textbook seriesthat included a number of textbooks I

respected, so I had hopes itwould not be full of subtleerrors that we would findlater.

Unfortunately, we never gotto find out. Just as I placedthe textbook order, the pub-lisher pulled the textbookfrom the market, citing aproblem with copyright. Iwas furious and immenselyfrustrated. I was back tosquare one, and with littletime to make my decision.One can send in late, evenvery late, textbook orders,and the bookstore will comethrough. But they can’t helpif the book is not available,

as I had just learned.

I asked a colleague for new ideas and wasshown a lovely little book by Ken Ross,Elementary Analysis: The Theory of Cal-culus, from Springer-Verlag. How had itescaped me? Springer publishes somegreat books but they do not beat downmy door like reps from other companiesdo. Ross was almost perfect. It was veryreadable, written in the mathematicalstyle I like, and comparatively inexpen-sive (only $40). Its one flaw was immense.It dealt with everything in terms of se-quences and, from my point of view,didn’t deal well with the standard topicof limits of functions. Since everythingelse was so good I was willing to try andcompensate.

The students and I loved the book. Ross’ssequence-based approach really simpli-fied a lot of material and allowed the stu-dents to progress more easily.

Of course it wouldn’t be a good Ad-vanced Calculus course without a gooddose of epsilon-delta, so I created someadditional materials and exercises. Some-times I would give epsilon-delta proofsand then show students Ross’s sequencebased proof. Comparing two proofs gave

What I Learned About…

The Frustrations of Choosing Textbooks

By Blair Madore

Blair Madore and his students display analysis textbooks.

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December 2005

the students more insight and a littlemore time to understand the theorem.

The real test for Ross was advanced cal-culus II in the spring of 2004. Almost theentire course consisted of students read-ing and presenting material. This is chal-lenging for them and they didn’t findRoss easy, but we found no real errors.Ross is excellent so far. Best of all, thebook served students for two semestersfor only $40.

Don’t misunderstand me. Price is noteverything. I once picked a book justbecause it was cheap ($30) and it ruinedmy course. I would gladly pick Ross at$80 or even $100 dollars. But $100 is theceiling for me and the students. I am veryprice conscious. A publisher that took upthe motto “The very best books for thevery best price” and really meant it wouldearn this customer’s loyalty.

What have I learned from all this?

1. Look for books early. It takes time.Ask colleagues, look for reviews, anddiscuss books at conferences.

2. Always begin by checking out offer-ings from respectable and non-pushy publishers such as Springer-Verlag, Dover, and the professionalsocieties (AMS, MAA, SIAM).

3. Pick the best book regardless ofprice.

4. Price is not an indicator of qualityin textbooks.

5. Picking textbooks will never be easy.

Blair Madore is Assistant Professor ofMathematics at SUNY Potsdam. He origi-nally wrote this article for the campusbookstore to present at a board meetingspecifically about the difficulties for facultyin making textbook orders.

MAA Announces Search for

Director of Publications

The Mathematical Association of America (MAA) is seeking a highly qualified per-son for the position of Director of Publications. A candidate should have a significantrecord of work in publications in the mathematical sciences; a Ph.D. or other ad-vanced degree in a mathematical science or related field is preferred. The positionrequires successful experiences in some of the following areas: book publishing; jour-nal production; administration including financial management; editorial/reviewingexperience; mathematical writing not limited to research publications; and electronicpublications. Interest and experience with the use of the internet in publications,grants, personnel management, and marketing experience are desirable. Appoint-ments may be made for two or three years, with the option of renewal for multipleyears.

The Director will oversee a staff of six located in the headquarters office and numer-ous editors. S/he oversees publication of three journals, three magazines, nine bookseries, and a variety of columns and articles. Electronic publications include all ofthese types of materials as well as the MAA Mathematical Sciences Digital Library(MathDL). The Director’s duties include personnel management, financial adminis-tration, acquisitions, production, grant proposal writing and project management,and marketing. The Director reports to the Executive Director. S/he is a key memberof the MAA’s staff leadership team, and will work closely with the Executive Directorand other staff members, national officers, section officers, committee chairs, andothers in strategic planning and program development.

The MAA, with nearly 30,000 members, is the largest association in the world de-voted to college level mathematics. Membership includes college and university fac-ulty and students, high school teachers, individuals from business, industry, and gov-ernment, and others who enjoy mathematics. The Director of Publications is respon-sible for ensuring that publications encompass the interests of all major constituen-cies of the MAA, embrace all areas of mathematics, and are easily available to all ourmembers and the larger community who are interested in mathematics, especiallyexpository mathematics and materials for faculty and students.

The deadline for submission of applications is January 21, 2006. Interviews will beheld during the months of January and February. It is expected that the new Directorwill begin work by July 2006, earlier if possible. The position is located at the nationalheadquarters of the MAA in Washington, DC. Salary will be based upon the candidate’scredentials or current salary for a reassignment position. The MAA offers a generousbenefits package.

Candidates should send a resume and letter of interest to:

Ms. Julie KramanMathematical Association of America

1529 18th Street, NWWashington, DC 20036.

Applications may be submitted electronically to jkraman@maa.org. References willbe requested after review of applications. Applications from individuals fromunderrepresented groups are encouraged. Additional information about the MAAand its publication programs may be found on MAA’s website: http://www.maa.org .AA/EOE.

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FOCUS December 2005

In August 2004, we had theopportunity to travel to Ja-maica to lead a pilot workshopfor Jamaican high school mathteachers. The workshop fo-cused on the importance ofmathematical context in theteaching of mathematics. Itwas sponsored by the GibraltarInstitute, a Jamaica-based non-governmental organization ledby Trevor Campbell (PomonaCollege) and Reginald Nugent(Cal State Pomona), Jamaica’sCollege of Agriculture, Scienceand Education, and Harvey Mudd Col-lege.

The workshop participants shared nu-merous challenges, some of which areuniversal, such as students’ attitude to-wards work, high pupil/teacher ratio,math phobia, and limited parental sup-port. Other challenges are more specificto Jamaica (and other developing na-tions), such as lack of equipment andmaterial, illiteracy, and a curriculum fo-cused on a national exam. Indeed, anexpression many teachers lamented hear-ing from their government and admin-istrators in response to low test scoreswas, “If they’ve not learned it, you’ve nottaught it.” Moreover, student motivationis often lacking. “Why should I do maths,when I can sell to tourists and make moremoney?” is a question that one teacheroften hears. These frustrating conditionspropelled Jamaican nationals Campbelland Nugent to collaborate with us andhost the workshop “Unlocking Barriersin Mathematics Education: A Mathemat-ics Innovation Programme.”

The focus of the workshop was on theimpact that a solid understanding ofmathematical context can have on learn-ing for students of mathematics. Al-though the challenges the teachers facewith regard to class size and lack of re-sources are substantial, we felt that deep-ening the instructors’ knowledge ofmathematics would have a positive im-

pact on their student’s learning. By gain-ing some “big picture” ideas, the teach-ers could have a sense for how the math-ematics they teach is related to the math-ematics their students might learn in thefuture. Additionally, we sought to con-nect the teachers to several interestingand lively current areas of mathematicalresearch that use, in an essential way,many of the tools taught in their curricu-lum. For example, Orrison discussed vot-ing theory from an algebraic perspective.They saw how mathematics can be usedto predict, detect, and analyze paradoxi-cal results that arise in voting. We alsoexplored the connections between thenatural numbers, integers, rational num-bers, real numbers, and complex num-bers.

“Feeling comfortable with real numbershelps you point out the special role thatfractions play in mathematics, while afamiliarity with complex numbers helpsto highlight some of the subtleties asso-ciated with real numbers,” said Orrison.“It may sound obvious, but knowing thenext step in a mathematics curriculumhelps an instructor to prepare studentsto take that next step.”

Jacobsen discussed iterating maps andconnections to chaotic dynamics andfractals. While none of the teachers hadseen fractals before, they all appreciatedthe mathematics behind the images andthe power it could have in the classroomsetting. Students can see how simple

rules yield complex behavior, and howbasic algebra can be used to shed lighton the situation. There is also a sense ofexploration, where students can change

parameters or rules and explorethe dynamic and fractal land-scape.

"Dynamical systems provide afascinating framework to exciteand motivate students to thinkabout mathematics and how itmay be used to model complexphenomena. I also tried to high-light the experimental side ofmathematics, that math is alive,"said Jacobsen.

A final goal of the workshop wasto begin the creation of a coregroup of Jamaican high school

math teachers who can benefit from aglobal network of researchers activelyengaged in exploring ways to break downthe barriers that students face in learn-ing math. The response to the workshopwas very positive. Here are some samplecomments:

The hardest question to answer in anymathematics class is, “Why is this impor-tant?” I’ve never been able to give what Ifeel is a satisfactory response. Having par-ticipated in this workshop I now feel moreconfident that I can provide the perfectanswer.

This workshop opens the door for math-ematics teachers to begin to look at math-ematics as not just a subject that it taughtformally but mathematics itself is what theuniverse is living, today, yesterday, andtomorrow.

I realize more clearly that mathematics isfun, power and life. I am empowered to bemore of an ambassador for the subject andtransfer this zeal to my students.

Given the success of the workshop, weare making plans to lead similar work-shops for mathematics teachers in South-ern California.

Looking Beyond the Curriculum in Jamaica

By Jon Jacobsen and Michael Orrison

Jon Jacobsen jacobsen@math.hmc.eduMichael Orrison orrison@math.hmc.eduare Assistant Professors of Mathematicsat Harvey Mudd College.

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December 2005

Coffee and Mathematics, Once Again

In May 1996, the UNC Charlotte Mathdepartment moved to its new home, theE K and Dorrie Fretwell building, witheager anticipation. We would occupymost of the third floor and use dedicatedrooms for reading journals, keeping ourbook library, holding seminars, housingweb servers, and we would be able toenjoy modern “computerized” class-rooms. Two years later our lives got evenbetter. The large student lounge on theground floor had not been successful.Manned with vending machines andnot-very-comfortable chairs, it attractedvery little business. Then someone gotthe idea of converting it into a Starbucks-style coffee shop. Jazzman opened in2002 and never looked back. Jazzman isbranded by Sodexho (the food servicecompany on campus at the time). WhenSodexho lost the catering contract toChartwells in May of 2003, Jazzman be-came Ritazza, but little else changed.Serving breakfast sandwiches, bagels,freshly made salads, soups and sand-wiches for lunch and dinner along withdesserts, it became the hottest spot oncampus. A large coffee menu, comfort-able chairs and sofas, and an outdoordining patio all contributed to its suc-cess as well

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FOCUS December 2005

What do the editors of MAA journalsdo? What is so different about editingexpository mathematics? After my fiveyears as editor of Mathematics Magazine,I have strong opinions about these mat-ters. The goal of most mathematics jour-nals is to print the very latest results fromthe forefront of research. The goal ofMathematics Magazine is to remind usall why we loved mathematics in the firstplace, with stimulating articles and notesaccessible to advanced undergraduates.

Receiving and handling manuscripts

Everyone who takes time to prepare andsubmit a manuscript to an MAA journaldeserves to be treated with respect. Af-ter all, without the creative output of ourauthors, there would be no journal toedit. On the other hand, not every au-thor deserves a great deal of the editor’stime. Woody Dudley’s excellent bookMathematical Cranks prepared me forthe range of imaginative thinkers I en-countered.

When a manuscript is submitted to theMagazine, my able assistant, MarthaGiannini, acknowledges it promptly, in-cluding a general word to explain that ittakes at least several months to evaluatea manuscript. We ask authors to wait forour office to contact them. A certainamount of the material submitted looksreasonable at first glance, but on furtherexamination can be seen to be unsuit-able for the journal. Perhaps the piece istoo technical, written for the wrong au-dience, or substantially duplicates some-thing that has already appeared. (Manywell-meaning authors have rediscoveredgems that were printed decades ago.)There is little point in sending thesemanuscripts to referees. However, sincethe author has taken the care to submitthe piece, he or she deserves a respectfulletter, explaining, in as much detail astime permits, why the manuscript willnot be given further consideration.

My reactions to these authors are as vari-ous as the manuscripts that fall into thiscategory. If there is any way that I can

help steer an author in the right direc-tion, I try to do so. Sometimes, I haveoccasion to use the template I call “Re-ject Terse,” which omits the phrase, “Ihope that this news will not discourageyou from future submissions.” In anycase, I hope that the author will feel thatsomeone spent some time with themanuscript. Every editor can tell amus-ing or distressing tales of cranks, but evenwhen I hope that a particular author willnever again submit any manuscripts toany journals ever, I try not to sound dis-missive.

As I gained experience with the Maga-zine, I was able to see more quickly whichsubmissions should be rejected withoutreview. My experience is that only abouthalf of what I receive is evaluated by(usually two) referees.

Referees

I use a large pool of referees, which hasits benefits and pitfalls. For instance, earlyin my editorship, I added about thirtyyoung referees from Project NExT to mydatabase, even though this meant that Ihad to interpret their analysis in context:These kind young people seldom recom-mended against publication, seeming tofeel that every manuscript could be saved.Perhaps every manuscript can be saved,with enough work. In my instructionsto referees, I say, “It happens very oftenthat an author has a good idea for a pa-per suitable for the Magazine, but pre-sents it in a way that does not meet ourexpository criteria. When thinking ofyour overall recommendation, pleasemake an assessment of the attractions ofthe manuscript as it might appear afterall expository problems are solved.”

I ask referees to fill out two forms, Com-ments for Editor and Comments for Au-thor. On the form intended for my eyesonly, I ask them to mark an overall rec-ommendation as to whether I shouldprint or not print a suitably revised ver-sion of the paper. I ask them to base thisrecommendation on the accuracy andattraction of the mathematical content,

as well as the expository style. I make itclear that novelty is not a prerequisite forpublication in the Magazine, but if oneis going to write about something thatmany people know, one had better writeit in an extremely interesting new way.

It is a lamentable truth that no one re-ally knows everything that has appearedin MAA publications, but some refereescome close. It is distressing, but ulti-mately a great relief, when I send off apiece, thinking that it is extremely prom-ising, and hear back that “essentially thesame thing appeared in 19xx.” There areexcellent electronic tools we can all useto research the past history of any givenmathematical idea that has appeared inprint — JSTOR, Google Scholar, andArXiv come to mind. Even so, an experi-enced person can easily trump someonearmed only with the internet. For in-stance, it remains extremely difficult tolearn whether a particular idea mighthave appeared in a past Problems columnin one of the MAA journals.

On the Comments for Authors form, I askreferees to give constructive criticism. Ifrequently find myself telling an authorthat, while the paper is not suitable forthe Magazine, it probably ought to bepublished somewhere, especially after itis improved according to the referees’reports. A letter of rejection is not so badwhen it helps an author improve themanuscript.

The confidentiality of referees is pro-tected, except in an exceptional case thatI call the “arranged marriage.” When anauthor has learned so much from areferee’s report that he or she feels in-debted as if to a coauthor, I can inquirewhether the referee feels comfortablebeing unveiled. I believe I have arrangedfour such marriages over my editorship;three were quite happy occasions and thefourth ended well after some mediation.

In the world of narrow disciplinary re-search mathematics, the tastes of the ref-erees and editor should not matter allthat much. In pure mathematics — asopposed to, for instance, the humanities— there is an excellent chance that ourentire community will agree on the valueof a new discovery. In our MAA jour-nals, where the highest value is commu-

Five Years at the Magazine

By Frank A. Farris

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nicating mathematics, decisions requirea human touch. Since the most impor-tant question I ask is whether the pieceis likely to interest readers, nothing canbe done to isolate decisions from mytaste. That said, I am aware in every de-cision that I have been trusted to use mybest judgment to offer the best, most use-ful material possible.

Acceptance, Revision, Rejection

When evaluating a manuscript at thisstage, I will have a folder on my desk con-taining the original manuscript and atleast two referee reports. I think of thephrase from our editorial guidelines: TheMagazine has a higher duty to its read-ers than its authors. And I try to figureout what to do.

The occasional no-brainer is welcome:Both referees love the piece and it readslike a dream; into the Magazine it goes.More often, both referees see potentialin the piece, but each has a long list ofrecommendations for necessary revi-sions. Combining their insights withwhat I found by working through thepiece, I decide whether it could eventu-ally fly. A common outcome is a lettersuggesting that a suitably revised versionmight be accepted. It is quite impossibleto predict what authors are able to do,even with what I think is excellent andspecific advice, so I warn authors that Icannot guarantee that their revised pa-pers will appear in the Magazine. Since Ireceive four to five times as many manu-scripts as I can print, I have learned tobe cautious in soliciting revisions.

There is wide variety in the quality ofauthors’ revisions. Sometimes I am dis-appointed to see that an author has re-mained married to an existing word-pro-cessor file, making only a few cosmeticchanges instead of the requested thor-ough revision. Sometimes the new ver-sion is evidently perfect for the Maga-zine; writing an acceptance letter issimple. In many cases, I ask one of theoriginal referees and one new one to re-view the piece before I make a final deci-sion. I have faced a number of awkwardsituations where I encouraged a revisionand had to turn down the final version,despite evidence that the author had triedvery hard to comply with my suggestions.

This is why editorial work is not for thefaint-hearted.

Steps to Publication

Almost every acceptance letter containsa list of additional changes that must bemade before publication, even if themanuscript has already been revisedmore than once. It would probably sur-prise many people to learn just howmany versions of a manuscript go backand forth before its final appearance inprint. When putting an issue of theMagazine together, I start with authors’final versions of manuscripts and workthem over in depth to prepare final edi-tions. I ask myself: Does it begin well? Isthe organization optimal? Could it beshortened? I am not shy about propos-ing changes at this stage.

Occasionally, authors have found myeditorial hand to be a bit heavy. (“Youchanged my words!”) More often, au-thors express gratitude for improvementsto their piece. This can be a tricky inter-change; editing an author’s work is a dis-tinctly intimate act. On the whole, I havevery much enjoyed this contact with au-thors, whom I find to be a remarkablycreative bunch, striking in the variety oftheir ideas and ways of expressing them.

Some mathematics journals require thatmanuscripts be published in the order inwhich they were received. Such a policywould not be appropriate for MAA jour-nals, which offer a balance of subjects inan effort to represent the many branchesof our field. Once I have selected piecesthat seem to hang together to make anissue, I submit the issue by mailing a largeenvelope to Managing Editor HarryWaldman at MAA headquarters. Thishard copy catches up with the electronicfiles at the compositor’s office — IntegreTechnical Publishing in New Mexico —and the composition begins.

A few weeks later, the authors and I re-ceive electronic page proofs. We scruti-nize these, hoping to maintain theMagazine’s reputation for printing re-markably few errors. I have almost amonth to work on this first set of pagesbefore returning them to Washington. Aset of revised proofs arrives a few weekslater and we go through one more round

of checking. (Martha Giannini holds therecord for the most impressive proof-reading feat: During our first year, shenoticed that the page numbers on odd-and even-numbered pages were set inslightly different fonts!)

Along with the revised pages, I typicallysend in what used to be called “camera-ready copy” for last-minute items suchas Allendoerfer citations and problemsand solutions for the Putnam, USAMO,and IMO competitions. Paul Campbell’sReviews column also goes in at this timeand, if possible, the image for the cover.Just before the compositor sends the filesto the printer (from New Mexico to Ver-mont), there is one last chance to makeadditions. About ten days later, the“bluelines” arrive. These are actually fi-nal digital page proofs, representing thelast chance to find and correct errors.Occasionally, I have cried, “Stop thepresses!” and asked Integre to prepare acorrected page or two. After that, it takesabout three weeks to see the issue in itsfinal form, which, of course, is im-mensely satisfying to the weary editor.

Would I do it all again?

Yes. Editing an MAA journal is a greatjob. It does take over one’s life, but thebenefits are vast. One learns lots of newmathematics, meets hundreds of people,almost all of whom are delightful toknow, and feels deep satisfaction in serv-ing a remarkable Association.

On my computer desktop, I keep a fileof kind comments about my editorship;I paste these in randomly without re-cording who said them. When theworkload becomes overwhelming, I’llglance through and appreciate how thesepeople found time to say something nice.Here are three samples: “My eye is not ofthe eagle variety — that’s why you arethe editor and I am a mere ink-stainedwretch.” “I appreciate your prompt re-sponse. Also, I can tell my wife that I’mnot the only mathematician who workson weekends.” “If you go through all ofthis with every paper in the Magazine,you deserve sainthood. If it’s only mypaper, I apologize.”

Frank Farris will finish his term as editorof Mathematics Magazine this month.

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Recently, a group of mathematics fac-ulty at the University of Pittsburgh atJohnstown (UPJ) collaborated with amember from the communication de-partment to develop a course that ad-dressed the speaking demands facing ourmajors upon graduation. Initially theidea stemmed from a new general edu-cation requirement to incorporatespeech into the curriculum of all majors.

However, upon development of thecourse, we realized that not only was thisa valid university requirement but a nec-essary major requirement for the success-ful job and academic goals of our futuregraduates. Thus, we designed a coursemodeled after a standard public speak-ing class but utilized mathematically re-lated topics.

Despite the similarity of the two courses,we felt the technical nature of mathemat-ics posed a specialized demand on thecontent and design of the course. As aresult, the lecture materials and speechdesigns incorporated examples and lan-guage appropriate to mathematics. Inturn the speeches themselves likewisecontained varying degrees of technicallysophisticated language which was to beadapted for the audience’s assumed de-gree of mathematical understanding.

During the creation of this course, wepondered several fundamental questions:What occupations do our students pur-sue upon graduation? How well have weprepared them for these societal roles?How might we improve their future jobmarketability? What changes in our cur-riculum are necessary to address theseneeds?

Despite having addressed the students’needs in our individual courses, wehoped to broaden our focus to includethe mathematics curriculum as a whole.We turned to the CUPM CurriculumGuide 2004 and disappointedly foundmore information relating to servicecourses than to courses intended for

mathematics majors. Included in theguide was one statistic that really jumpedout at us from a 1997 survey of the 1994–1996 graduates in the mathematical sci-ences. Of students earning bachelor de-grees in mathematical sciences, 92% en-ter the workforce directly after gradua-tion.

As we thought about our recent gradu-ates and where they have ended up, werealized that UPJ Mathematics majorsalign very closely with this statistic. It isinteresting to note that among the fac-ulty in the mathematics department atUPJ, there is very little experience in thevery workforce in which our studentseventually find themselves. Despite this,our students seem to adapt well to theirnew environments. Nevertheless, thequestion remains: How can we providethe best possible education for our stu-dents to prepare them for what awaitsthem in the outside world?

With the dearth of practical business ex-perience in our mathematics depart-ment, it is fortunate that our colleaguefrom the communication departmenthas such experience. Due to this ‘outside’influence, we concluded that creating ateam taught interdisciplinary course wasone of the better things we could havedone. As CUPM 2004 points out, em-

ployers list goodcommunicationskills as one ofthe most impor-tant skills form a t h e m a t i c smajors. Despitethis, disciplinespecific oralcommunicationtraining is al-most com-pletely absentfrom most un-d e r g r a d u a t em a t h e m a t i c scurricula.

The preliminary results of a recent sur-vey of UPJ mathematics departmentalumni seem to confirm both the de-mand for excellent communication skillsin the workplace and the lack of suchlearning opportunities in our under-graduate mathematics program. Nearly95% of the responders indicate that oralcommunication skills are important, ifnot crucial, to their effectiveness in theworkplace. Several commented specifi-cally that communication skills areweighed heavily when hiring, when mak-ing or receiving evaluations, and whenconsidering, or being considered for, pro-motion. Further comments indicatedthat it is important to be able to com-municate a complicated idea not just indetail, but also in a simplified fashion.Recognizing the technical familiarity ofthe audience is paramount to determin-ing both the level of detail and the levelof rigor that the speaker should use inthe explanation.

Problems We Faced

Most realize that over the past 10 to 20years an emphasis has been placed uponwriting within the mathematics curricu-lum. Clearly, writing within the curricu-lum is extremely important and can bean effective pedagogical tool in learningand understanding mathematics. But

Mathematically Speaking: Expanding the Role of Oral Communication

in Mathematics Programs

By Stephen J. Curran, Michael N. Ferencak, John W. Thompson, and Susan M. Wieczorek

From left to right: John Thompson, Susan Wieczorek, StephenCurran, and Michael Ferencak.

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speaking within the curriculum actuallyhas its roots further back as attested byveterans of the “Texas method” devel-oped by R.L. Moore.

Still, the type of oral communication re-quired in a Moore method approach re-ally does not address the core aspects ofcommunicating technical material to anaudience of varying technical expertise.The emphasis of most oral communica-tion in mathematics classes is on enhanc-ing and developing technical under-standing. Although this is a necessaryconsideration, mathematics classesshould focus on the technical under-standing of the material while still ad-dressing the employment expectationsfor our students to communicate math-ematics information to audiences ofvarying levels of expertise. This has com-pelled us to make changes in how weteach presentation techniques to our stu-dents today.

Although this course remains in its earlystages of modification, we have come torecognize its tremendous importance.First and foremost, it acknowledges theneed for students to present comfortablyto audiences of diverse technical train-ing in a variety of presentation environ-ments and situations. Second, it in noway eliminates any of the major require-ments of the discipline since it is takenin addition to the regular mathematicsmajor course load and is intended as adiscipline specific substitute for Intro-ductory Public Speaking, a course thatmight normally be taken as a humani-ties elective.

The Course Itself

This newly created course satisfies bothgeneral education and future graduationneeds of our mathematics students. It isimportant to keep in mind that it is fun-damentally a class on public speaking. Itincludes five speeches ranging from acommemorative speech of a mathema-tician that one might give to a general,non-mathematical audience to a moretechnical speech appropriate for an MAASection meeting.

An example of this is our Applied Prob-lem Solving Speech. In this speech of

persuasion, we gave student groups anapplied max/min problem and askedthem to identify an appropriate scenariowherein they presented their solution tothe problem as if they were project teammembers in, or outside consultant to,some industry. Both the speaker and theaudience were to assume appropriateroles with the target audience being pri-marily managers and supervisors. Suchan audience would have some basic fa-miliarity with the mathematical conceptsbut would be more interested in the bot-tom line, as it were.

This speech is exactly the type of work-place situation that the majority of ourundergraduate mathematics majors facerepeatedly throughout their careers. Yetexplaining technical information to anon-technical or semi-technical audi-ence, and doing so in the form of a per-suasive speech, is a skill whose acquisi-tion is rarely, if ever, addressed in eithermathematics or communication cur-ricula.

Mathematically, the most challengingspeech for the students was the GroupConcept Introduction Speech. The goalwas for a small group of students topresent an introduction to a mathemati-cal idea or concept about which neitherthey nor the audience was to have priorknowledge but one where the audiencewas assumed to be mathematically adept.

As noted above, this resembles a grouppresentation at a mathematical confer-ence for post-undergraduates. Thisspeech forced the students to research atopic unfamiliar to them and to presenttheir findings by applying group presen-tation skills.

Naturally, the mathematicians deter-mined that the proper order for thespeeches should be from least technicalto most technical in terms of both thesubject and the level of rigor appropri-ate to the presentation (prescribed by theaudience). This, of course, was utterlywrong. In direct contrast, the most chal-lenging presentation from a publicspeaking perspective was the persuasiveApplied Problem Solving Speech.

Our students were in fact overwhelmedby the presentational demands of the lat-ter speech too early in their learning pro-cess. This supports the notion that thiscourse must be developmentally orga-nized from least to most difficult in pre-sentational skills instead of least to mostdifficult in mathematical technicality.

Again, fundamentally, this is a speakingcourse with progressively more and moredifficult presentational expectations. Stu-dents simply felt much more comfort-able presenting more difficult technicalconcepts than they did adapting to ahigher level of rhetorical argument. Con-sequently, we plan to rearrange the or-der of the speeches to end with the per-suasive one and begin with the instruc-tional demonstration of a concept ortheorem from calculus (this particularspeech experience being most useful tostudents who become graduate teachingassistants or high school educators).

Concluding Remarks

As many of us wrestle with increasing thenumber of mathematics majors, we mustrealize that our programs need to be rel-evant to what our students want to doupon graduation. Despite many of ourdesires to send students on to graduateschools, the vast majority will not utilizetheir education in this manner.

In light of this, is it appropriate that allof our communication time is investedin making technical presentations totechnical audiences? An oral communi-cation course that includes oral presen-tations to audiences with lower levels ofmathematical understanding seemsmore appropriate for our students andtheir future professional endeavors. Thiscourse addresses the practical needsstressed not only by academia but alsoby the professional job markets open tomathematics majors today.

Susan M. Wieczorek is in the Departmentof Communication, and Stephen J.Curran, Michael N. Ferencak, and John W.Thompson are in the Department ofMathematics of the University of Pitts-burgh at Johnstown, in Johnstown, Penn-sylvania.

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As the train pulls into Cardiff station Ibegin to wonder just how it happenedthat a well-meaning mathematician likemyself has ended up in Wales attendinga theater conference. My mind flashesback to a phone call several years back— it’s a colleague in our theater depart-ment innocently asking if I would cometalk to her cast about the mathematicsin an interesting new play by TomStoppard called Arcadia. Sure, why not?What harm could come of that? But it’snot just an interesting play, it’s an intoxi-cating one. And soon I am having lunchwith cast members, then closing my of-fice door to read Stoppard plays, and be-fore I realize it the director and I are co-teaching “Stoppard and Science” duringMiddlebury’s one-month winter term.But I’m still OK. It’s winter term after all,a four-week semester custom-made forthis sort of whimsical pursuit into newinter-disciplinary lands. Nothing more.

Then came a conspiracy of events farbeyond my control. Michael Frayn’sCopenhagen takes the 2000 Tony Awardfor Best Play, David Auburn’s play Proofwins the 2001 Pulitzer Prize and A Beau-tiful Mind dominates the Oscars in 2002.The vortex that is formed at the inter-section of mathematics and art over-whelms my pathetic defenses and I ampulled in, dashed about, and depositedhere at the Cardiff train station car park,waiting for a shuttle to take me to the“Theaters,” excuse me, “Theatres of Sci-ence” conference at the University ofGlamorgan in nearby Pontypridd.

“I’m Steve Abbott” I say to a slightly moresenior gentlemen waiting next to me whojust looks the part, so to speak.

“Hi. Christopher Innis,” he replies withthe appropriate British accent, though itturns out he teaches in Toronto. “Wherehave you come from?”

“Arcadia,” I say. Oh dear. In addition toanswering the wrong question, I’ve putmy best credentials on the line and it is

everything I can do to stifle the panicwelling up inside me.

“One of the best plays of the 20th cen-tury,” he says. Extraordinary. Stoppard’swild ride through Euclid, Fermat, New-ton, and Fourier is on someone’s veryshort list, and now I can’t stop wonder-ing who this person is and whether heknows what he is talking about.

Day 1

The conference has started when we ar-rive and I settle in for a presentation onhow medical dissection in the Renais-sance became a form of public theater.Afterwards I head off to attend a work-shop where a young Canadian play-wright named Vern Thiessen presents ascene from his play, Einstein’s Gift, aboutchemist Fritz Haber whose ground-breaking work produced both the fertil-izer that fed Europe and the gas that poi-soned thousands of soldiers in WWI.These workshops turn out to be a high-light of my week. Actors offer rehearsedreadings, sometimes a scientist of theappropriate sort is available to explicatetechnical details, and what follows is aprocess of open and honest feedback be-tween playwright and audience abouthow to make the script do what it is sup-posed to do.

At lunch I make it a point to seek outKirsten Shepherd-Barr whose earlymorning talk on Copenhagen I hadmissed. A respected theater scholar, itturns out that for several years she hasbeen teaching a course on science playsmuch like the one I am scheduled to co-teach in the upcoming term. I also meetPaul, a young Brit with degrees in bothphysics and the dramatic arts, as well asa gaggle of jet-lagged graduate studentswho have recently completed a scienceand theater course at NYU. Everyone isexceedingly pleasant to the rogue math-ematician among them, and from theiranecdotes it is safe to conclude that thenumber of scholars, scientists, and art-

ists gravitating toward the intersection oftheater and science has hit critical mass.

After lunch, I head off to another work-shop for a new play called Comet Hunter,by Chiori Miyagawa. This play tells thestory of early nineteenth-century as-tronomers William and CarolineHerschel, and what is especially notableand satisfying is that, as objects of scien-tific study, the stars and planets manageto keep hold of their romantic identityin this script. Still, even in the artisticallyfriendly confines of celestial mechanics,it becomes eminently clear that bridgingthe gap between C.P. Snow’s two cultures— the sciences and the humanities — isgoing to be harder than it looks. One byone, the scientists-turned-playwrights inthe audience begin asking if, in a full pro-duction, might we be able to use someprojection to actually see the images inthe telescopes on stage and thus betterunderstand what the scientists are doing.“No,” the artists say, “this is not a lecture!Even if it sounds like a foreign language,the vocabulary of astronomy can stillwork as an artistic device.” And so it goes.It is a worthy debate. Although, my senseand sympathies are firmly with the art-ists on this point, I find myself puzzlingover why plays that expose audiences totheories of, say, politics are not automati-cally dismissed as “lectures” or “peda-gogical demonstrations.”

Day 2

The conversation picks up again the nextmorning at the keynote address by CarlDjerassi. Djerassi is a distinguishedchemist and prolific novelist who, amongnumerous other achievements, wasawarded the National Medal of Sciencein 1973 for the first synthesis of a steroidoral contraceptive; i.e., he pioneered theinvention of “the pill.” Women’s repro-ductive issues pepper Djerassi’s earlynon-fiction, and then in 1997 he wroteThe Immaculate Misconception, a playthat explores the politics of in vitro fer-tilization. Djerassi has since written two

Lost in Shakespace

By Stephen Abbott

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other full length plays. One is called Cal-culus, which is about Newton, Leibnizand their famous debate over the prior-ity of the discovery of calculus. The otheris called Oxygen, which is about Priestly,Lavoisier, Scheele and the debate over(you guessed it) the priority of the dis-covery of oxygen. This latter play is co-authored with chemist and Nobel Lau-reate Roald Hoffman.

As he seems to be on most points,Djerassi is strongly opinionated aboutwhat constitutes a good “science play”and maintains that, first and foremost,real scientific content must be included.He explicitly makes the point that, forinstance, Proof does not qualify under hisdefinition. The fireworks between artistsand scientists start again but it quicklybecomes clear that we have gravitated tothe wrong question. To put it bluntly, awarning label such as “Caution: contains10% real mathematical science” isn’t go-ing to reveal much about the script it-self, and most of us recognize this.

What does emerge, for me at least, and Iwill confess that this is mostly the prod-uct of my own need to organize a tre-mendous amount of new material, is ashort list of categories into which mostscience plays can be loosely classified. Inaddition to the squabbles over credit,there is an interesting group of plays thattake up the changing moral issues gen-erated by scientific discovery.Durenmatt’s The Physicists (nuclear dev-astation, 1962) and Stevenson’s Experi-ment with an Airpump (embryonic re-search, 2000) are fine examples. A thirdtype consists of plays that look at realhistorical scientists as dramatic charac-ters. Alan Turing is the subject ofWhitmore’s Breaking the Code as well asWilson’s Lovesong of the Electric Bear, andRichard Feynmann is the subject of sev-eral recent plays. Brecht’s Galileo is an-other example, although this script alsopoints to a distinct class of plays that fo-cus on the conflict of science with estab-lished institutions, especially the church.Another popular example of a play in thisgenre would be Inherit the Wind, which,incidentally, Djerassi would have to ex-clude from his bibliography of scienceplays.

In the afternoon I make a special pointto see Chistopher Innis’ talk. I have donea bit of research on my new friend fromthe train station and it turns out he hasauthored some of the leading survey textsin modern drama. “A bit of a rock star,”was how one graduate student put it.Innis begins by offering us a list of cat-egories of science plays roughly like myown (I am delighted by this, by the way),and then proposes a new, modern cat-egory consisting of scripts in which thestructure of the play reveals or reflectsthe science it discusses. Arcadia is his ar-chetype for this phenomenon, and theargument is compelling. Principles ofthermodynamics are superimposed ontothe romantic shenanigans of the charac-ters (“the actions of bodies in heat”), theso-called “butterfly effect” from non-lin-ear dynamics is illustrated in Bernard’sdoomed attempt to reconstruct details ofLord Byron’s visit to the Croom estate,and the self-similar quality ofThomasina’s fractals is reflected in thedeep parallels that exist between the twotime periods that make up this remark-able play.

If Arcadia occupies sacred ground in thecanon of science plays, then it shares itwith Frayn’s Copenhagen, a play that alsoexploits the power inherent in the merg-ing of form and content. In this latterplay, it is the principles of quantum me-chanics being applied to the debate overHeisenberg’s behavior during WWII.The question under investigation in thiscase is Heisenberg’s 1941 visit to Bohr inCopenhagen and what precisely moti-vated Heisenberg to seek out his oldfriend and mentor who was then livingunder German occupation. Over andover again the experiment ofHeisenberg’s visit is carried out, and eachtime the wave-function collapses arounda different measurement that ultimatelysheds light on something like an uncer-tainty principle for human introspection.

Thoughtfully comparing Frayn andStoppard’s work to the new plays I amreading this week has the effect of instill-ing a heightened sense of reverence forthe art of play writing itself. Arcadia andCopenhagen each include a significantamount of technical detail and each

probes deeply into the theories theypresent for rich and rewarding meta-phors. But amid the science and thestagecraft there is also, in both of theseplays, an undeniable instinct for goodstorytelling. Frayn’s play has the feel of asuspenseful mystery and in Stoppard’scase we find wit, romance and ultimatelyheartbreak. There are glimpses of thiskind of synthesis in the plays beingworkshopped at the conference but it isanother matter to sustain the trick fortwo full acts. This evening’s reading is awork in progress called RememberingMiss Meitner that falls into the debate-over-proper-credit category. Femalephysicist Lise Meitner meets Otto Hahnand Manne Siegbahn in the afterlife tohash over who was really responsible forthe discovery of nuclear fission. Theproblem is that this play looks likeCopenhagen—three scientists in theafterworld arguing about what happenedin the real world — but it simply can’tsound like Copenhagen, and that is itsundoing.

Every night after the final readings theconference organizers turn the cafeteriainto a rather well lit pub. I am desperateto get rid of the jet lag that has me con-fusing midnight in Wales with 7pm backhome, but even after several beers of theconsistency of motor oil I still end up inmy tiny dorm room cot staring at theceiling tiles. To add to the trouble, thereis a regular nightly chorus of what I as-sume to be a horde of Welsh revelers. Thefirst night I made the best of things bygetting some work done on the com-puter, but now my batteries are dead andthere is no way to recharge without aconverter that, of course, I do not have.

Day 3

Whatever confidence as a budding the-ater scholar I have been acquiring dur-ing the week is momentarily shatteredwhen I walk into my first talk this morn-ing on “Extended Minds and ConsciousArtifacts.” It is as though I have gone tosleep and woken up at a different con-ference. “Are the mind and world sepa-rate or continuous?” the speaker asks inhis opening statement. Well, let’s see. Itake the question to mean “separate or

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connected” but either way, I am going tosay that the mind is supported in thebrain. Final answer. But apparently not—or at least not according to the theory of“extensionism” that puts forth the propo-sition that not only is the mind globallysupported across all physical boundariesbut that it can also propagate forwardand backward in time. Following thisargument we end up at the remarkableand somewhat charming conclusion thatwhen standing in front of a self-portraitof Rembrandt, we are in fact in an intel-lectual presence — his, even! Flummoxedby this, I look around the room to see ifanyone else sees a naked emperor but itis all poker faces at the moment. “Veryinteresting,” says an audience member.“This is very much like my theory of‘Shakespace’” which he goes on to explainas a kind of alternate Shakespearean re-ality, closed under the operation of dra-matic readings, I am assuming.

Still looking for a hint as to whether Ihave missed some key metaphorical leap,I work my way over to Mr. Shakespace,and as we break for the next talk I askhim for his opinion on what we havebeen hearing. “Well it is a little old-fash-ioned don’t you think? I mean the ideathat the mind lives inside a skull is a bitof straw man at this point.” Feeling asbrainless as the Scarecrow himself, I haveno choice at this point but to follow himinto the next room to hear his talk on“transversal power,” and I don’t faremuch better here. These are very smartpeople, to be sure, but the jargon hasgrown too thick and in my frustration Ibegin to conjure up images of math talksI have heard where one is subjected toseveral pages of definitions en route to ahalf-page theorem.

After lunch things return to earth a bitwith some interesting talks on quantummechanical theories of art. TomStoppard’s sometimes off-putting spy-thriller Hapgood from 1985 comes acrossas a play ahead of its time in these con-versations, whereas Copenhagen wastransformative. The scholars and practi-tioners at this conference are well-versedand enamored with the concept of theobserver being a part of the system be-ing observed, and I learn how this prin-ciple is being thoughtfully explored in

drama and dance performances wherethe audience interacts with the cast in away that alters each performance. Themore I listen, the more it occurs to methat the scientific avenues at work reallygo in both directions. With each addi-tion to the growing canon of scienceplays, the insights of Newton, Darwin,Bohr or Turing find a new voice and anew audience. But what is absolutelyclear is that this is not just a case of the-ater performing a dutiful public serviceby mining the mathematical sciences forworthy stories to tell. Since my fatefulencounter with Arcadia years ago, I havebeen following mathematical and scien-tific threads on my way to the moral andhumanistic truths that lie at the centerof the best plays of this genre. This is thereal heart of the matter, it seems to me.What makes a science play successful iswhen the mechanisms by which art andscience seek out their respective truthsare working in tandem, each one enrich-ing a part of the picture for the other.

For our last night in Wales, we are treatedto an incongruous “banquet” in the samecafeteria where we have been eating forthe week. The staff, which has been im-peccably congenial all week, is dressed intraditional Welsh attire but the band inthe corner didn’t get the memo and isplaying Sinatra tunes. After dinner, weleave campus for literally the first timeto go see a new, very post-modern playabout Nikola Tesla that concludes with amind-numbing arc of electrons across a10 foot Van de Graaf generator at theback of the stage. Heading back to myroom after the show I discover that thecarousing Welsh teenagers I have beenhearing every night are in fact the Ameri-can conference delegates who, like me,have been unable to sleep. With completedisregard for the talk I am giving in themorning, I settle in for some significantlyless formal conversations about extendedminds and transversal power. Let’s justsay the whole thing goes down muchsmoother with a wine chaser.

Day 4

Having nearly completed my first theaterconference, I am now in a position to saythat the differences between a math con-ference and this one are in many respects

superficial. The theater crowd possessesmore social dexterity — they dress bet-ter (who doesn’t?) and they don’t writeon the napkins. Another interesting phe-nomenon is that, for the most part, pre-senters read their papers rather than de-scribe what is in them. I had been tippedoff to this by my art historian wife andwas prepared to follow suit, but now thatthe day has come I decide to be true tomy extemporaneous roots and try toteach a little mathematics. It occurs tome that although the hard sciences haveplayed a major role during the week,mathematics has been left largely on thesidelines. Arcadia is the one exception buteven here the thermodynamics oftenovershadows the fractals. Auburn’s Proofhas received no positive reviews, the con-sensus being that one could just as easilywrite the mentally ill father as a geniuscomposer rather than mathematicianand nothing much would change.

The audience is rather thin when my turncomes to present my talk on “Gödel,Escher, Stoppard.” Not only am I com-peting with “Soft Dark Matter” in thenext room and “Meme Theory” twodoors down, but my guess is that very fewof my compatriots from the previousnight have made it out of bed. This is allfine with me, actually, because it is sud-denly clear that my talk is far too ambi-tious for a twenty-minute time slot onthe morning of the last day.

Essentially, I attempt to explain Godel’sIncompleteness Theorem by taking eachpart of Godel’s argument and finding adramatic parallel in the self-referentialconstructions of Tom Stoppard’s plays.In my own defense I will say that this re-ally is a fascinating exercise but it is notfor the squeamish and definitely does notgo well with a hangover. The silver lin-ing — and I find this to be true when-ever I do something mathematical out-side of a math class — is that my few stal-wart audience members are genuinelydelighted to be learning, or at least be inthe presence of, some serious mathemat-ics. Routinely, well-educated people willsay quite publicly how poor they are atmathematics without realizing that pro-fessing one’s ignorance about any othersubject is considered bad social form. Onthis particular morning however—and

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December 2005

in fact throughout the entire week—weare all keenly aware of just how much westand to learn from each other and thisputs us all at our passionate and respect-ful best.

The final curtain of the final talk falls inthe late morning. As hugs and e-mailaddresses are being passed about, I optout of the tour of Tintern Abbey andcatch the early shuttle to the train sta-tion thinking I might make it back toLondon in time to see another play thatevening. To my great delight, standing onthe platform are Chris Innis and KirstenShephard-Barr, and the long rockingtrain ride to London gives us one morechance to take on Snow’s cultural divide.Chris and Kirsten talk about their latestprojects, and I tell everyone why I thinkthey might be wrong about Proof. Kirstenwas one of the brave souls who had madeit to my talk that morning, and she ear-nestly asks if I can give her the punch-line one more time.

“Well, the idea is that you develop thisvery deterministic, rule-driven notion ofwhat is meant by mathematical proof,” Isay again. “You essentially create a theo-rem proving machine, and then you askwhether it can supply proofs for everytrue mathematical statement that it iscapable of expressing. But it turns outthat it can’t. There are always truths thatyour machine just can’t derive.” There isno shock on anyone’s face, of course. Thisis a conclusion my artful friends havelong ago made their peace with, but theyare nonetheless delighted to hear it com-ing from me. “What’s really interesting,”I add, “is not just the result itself but thereason why it is true.” And here I get asconceptual as I can. “What happens isthat you keep making this theorem-prov-ing machine stronger and stronger bygiving it more rules to employ, enablingit to reach farther and farther into thespectrum of true mathematical state-

ments. But then this extraordinary thinghappens. As soon as the machine hits acertain critical strength, it acquires theability to be introspective. Suddenly themachine no longer just talks about math-ematics — it can also talk about itself —and this opens up a whole new crazyworld.”

As the train clicks along its parallel trackson the way to Shakespace, I role this im-age around in my head and decide that Ilike it a great deal because what it says isthat there aren’t two cultures after all. Youcan’t have one side of the brain withoutthe other. You can’t have science withoutart. You can try to build a machine thatonly knows mathematics but eventually,when it gets smart enough, it acquires alittle self-awareness and all of the poetrythat comes with it.

Stephen Abbott teaches at MiddleburyCollege.

SUMMA National

Research Experience

for Undergraduates

Program

The MAA, through its StrengtheningUnderrepresented Minority Math-ematics Achievement (SUMMA) pro-gram, supports the participation ofmathematics undergraduates fromunderrepresented groups in focused andchallenging research experiences to in-crease their interest in advanced degreesand careers in mathematics.

We invite mathematical sciences facultyto apply for grants to host an MAA Stu-dent Research Program on their owncampuses for six weeks in summer 2005.These grants will support stipends forone faculty researcher and a minimumof four local minority undergraduates,as well as costs for student room andboard. Deadline for proposals is Febru-ary 21, 2006.

Additional details are available at http://www.maa.org/nreup.

The MAA booth at a recent meeting of the Society for the Advancementof Chicanos and Native Americans in Science (SACNAS), held in Den-ver September 29 – October 1. SACNAS focuses on mentoring students.There were 279 booths in all, making this the largest exhibit turn-out inSACNAS history. The conference had 2212 general attendees; 1103 ofwhich were students. 485 of those students presented posters at the meet-ing.

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FOCUS December 2005

NCTM Defines “Highly Qualified”

It is a requirement of the “No Child LeftBehind” act that schools hire “highlyqualified” teachers. But the definitiongiven in the law is fairly minimal: teach-ers who have a bachelor’s degree and fullstate certification or licensure. NCTMhas just issued a position paper arguingthat “teaching mathematics demandsmuch more,” and offering their own defi-nition of what it means to be “highlyqualified.” Their summary statement is:

Every student has the right to be taughtmathematics by a highly qualified teacher— a teacher who knows mathematics welland who can guide students’ understand-ing and learning. A highly qualifiedteacher understands how students learnmathematics, expects all students to learnmathematics, employs a wide range ofteaching strategies, and is committed tolifelong professional learning.

The statement also specifies that

NCTM expects that high school teacherswill have completed mathematicscoursework equivalent to that required fora major in mathematics. Middle schoolteachers should have acquired the depthand proficiency in mathematics equivalentto at least an undergraduate minor inmathematics. Elementary teachers, re-source teachers, and all others charged withproviding instruction in mathematicsshould have completed the equivalent ofat least three college-level mathematicscourses that emphasize the mathematicalstructures essential to the elementarygrades

The position paper, which includes amore detailed discussion of the qualifi-cations for teaching mathematics, can befound online at http://www.nctm.org/about/pdfs/position/qualified.pdf.

Tom Banchoff Honored for hisTeaching at Brown University

Thomas Banchoff, a longtime memberof the MAA and veteran of the Brown

University faculty, has received one of hisuniversity’s highest honors for innova-tion and excellence in undergraduateteaching. He will serve a three-year termas a Royce Family Professor of TeachingExcellence, through June 30, 2008.

Banchoff has given Brown Universitystudents “extraordinary instruction, en-couragement and mentoring,” said RajivVohra, dean of the faculty. He was hon-ored for the “thoughtfulness and adapt-ability” that he brings to teaching, “in-corporating new instructional technolo-gies, broadening perspectives by reach-ing across departmental boundaries, andenriching the academic experience” ofhis students.

The Royce Family Professorships wereestablished in March 2004 by a $5.5-mil-lion gift from Brown alumnus andtrustee Charles M. Royce. The professor-ships are intended to recognize, rewardand encourage innovation and excellencein teaching among the Brown Universityfaculty. Each carries a $20,000 annual sti-pend in addition to the recipient’s regu-lar salary and provides a $20,000 annualteaching excellence fund to developteaching aids and support scholarly ac-tivities, including employment of under-graduate assistants.

NAS Warns U.S. Could Lose Lead inScience and Technology

A National Academies panel composedof scientists, educators, and businessleaders has warned that the nation couldlose its lead in the sciences and technol-ogy to China and India. Compared to theU.S., the panel reports that China andIndia are graduating, for example, five tonearly ten times more engineers annu-ally. The U.S. graduated 70,000 engineersin 2004.

The U.S. response, the panel recom-mends, should be to double the Federalinvestment in research over the nextseven years; to fund more scholarshipsand fellowship in the sciences; and toannually train thousands more science

and math teachers. The report can beaccessed at http://books.nap.edu/catalog/11463.html.

Undergraduate Paper CompetitionOffers Cash Prizes and Publication

Cryptologia — a scholarly journal deal-ing with the history and technology ofcommunications intelligence specializ-ing in the mathematics of cryptology —is sponsoring two undergraduate papercompetitions. The winners will receive$300 and have have their papers pub-lished in Cryptologia.

The journal has a record of investigatingtechnical and mathematical cryptologyas well as intelligence history, fosteringthe study of the many aspects ofcryptology — technical as well as histori-cal and cultural. Editor-in-Chief BrianWinkel, Dept of MathSci, United StatesMilitary Academy, West Point, and aneditorial board of scholars in cryptologywill disseminate worthwhile papers tomathematicians, security specialists,computer scientists, historians, politicalscientists, and teachers. For more infor-mation, see the journal’s website at http://tandf.co.uk/journal/titles/01611194.asp.

GE and IBM Foundations UnveilProjects to Improve Math and ScienceLearning

Two major U.S. corporations say theywill be investing millions of dollars inAmerican school programs that theyhope will improve math and sciencelearning. The General Electric Founda-tion will distribute $100 million in grantsover the next five years to raise math-ematics and science scores in up to fiveschool districts.

One county can already call itself lucky.The school district of Jefferson County,Kentucky, is the first to receive a $25 mil-lion grant. The district plans to use themoney for a new district-wide curricu-lum and professional development forteachers.

Short Takes

Compiled by Fernando Q. Gouvêa and Harry Waldman

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December 2005

The IBM International Foundation willpay college tuition costs for up to 100 ofits employees who want to train as mathand science teachers. In order to partici-pate in the “Transition to Teaching” pro-gram, its employees have to have abachelor’s degree in math or science (ora higher degree in a related field), teach-ing experience, and at least 10 years ofemployment at IBM.

American Institute of Mathematics Of-fers Five-Year Fellowship

The American Institute of Mathematics,Palo Alto, CA, is offering five-year fellow-ships to mathematically worthy candi-dates. This fellowship funds a researcher— at $4,000 a month — and may be usedanywhere that is consistent with the re-search goals of the recipient.

AIM’s aim is to provide the fellowshipto an individual with the potential tomake a lasting impact on mathematics.The deadline for applying is December31. See http://www.aimath.org/fellows fordetails.

Design Science Receives Grant to MakeMath Accessible in MS Word and AdobePDF

Design Science has received a NationalScience Foundation grant to continueresearch in making mathematical con-tent accessible to people who are visu-ally impaired. The aim is to increasemathematics accessibility to MicrosoftWord and Adobe PDF documents. Thecompany is also striving to improve itsspeech-generation algorithms.

The need for easily accessible mathemat-ics was highlighted in this year’s U.S.Department of Education announce-ment, “Raising Achievement: A New Pathfor No Child Left Behind.” It asked insti-tutions to provide sensible and informedapproaches to testing students with aca-demic disabilities.

“The prevalence of Word and PDF docu-ments in science and education makesbringing math accessibility to these for-mats the next logical step,” said a DesignScience spokesman. The organization’s

goal is to develop a “robust, market-readysystem.”

Next Spring: Zeta Functions All the Way

On May 15-26, 2006, on the campus ofthe Institute for Advanced Study inPrinceton, NJ, the Program for Womenin Mathematics will sponsor mathemat-ics sessions under the rubric “Zeta Func-tions All the Way.” There will be twocourses for undergraduate and graduatestudents; seminars; and a variety ofmentoring activities. Junior and seniorwomen mathematicians will be involvedas lecturers, TA’s, and mentors.

The advanced course will be given byKate Okikiolu (University of California,SD) on “Spectral zeta functions in geom-etry.” Audrey Terras (UCSD) will teach“Zeta and L-functions of graphs.” The in-troductory course on zeta functions willbe given by Giuliana Davidoff and Mar-garet Robinson (Mount Holyoke Col-lege).

Enthusiastic women students andpostdocs are encouraged to visit http://www.math.ias.edu/womensprogram/ formore information.

National School and BusinessPartnership Awards

The National School and Business Part-nerships Award program will be sendingmoney to what they call “six exemplaryschool-business partnerships” next year.Each of these school-business partner-ships will receive $10,000.

The National School and Business Part-nerships Award “supports and recognizesthe efforts of schools and businesses thatimprove the academic, social or physicalwell-being of students,” says the pressrelease from the Council for Corporate& School Partnerships. The Council,chaired by former Secretary of EducationRichard Riley, “serves as a forum for theexchange of information, expertise andideas to ensure that partnerships betweenschools and businesses achieve their fullpotential for meeting key education ob-jectives.” It was founded by The Coca-Cola Company in 2001. For more infor-

mation, including application forms, seehttp:// www.corpschoolpartners.org.

Sources

NCTM: Education Week, NCTM web site.Banchoff: Brown University. NAS Re-port: NASSMC Briefing Service, http://books.nap.edu/catalog/11463.html.Cryptologia: Taylor & Francis,Cryptologia editors. GE and IBM: Edu-cation Week; see http://www.edweek.org/ew/articles/2005/09/28/05ibm.h25.html.AIM Fellowship: email communication,AIM web site. Design Science: emailcommunication, http://www.dessci.com/en/company/press/releases/ IAS Programfor Women: email communication. Na-tional School and Business PartnershipAwards: email press release.

The MAA has received funding to pro-vide support for institutions or groupsof institutions that wish to initiate or ex-pand undergraduate mathematics con-ferences. Conferences may assume anyformat that accomplishes the primaryobject of the grant, which is to provideundergraduate students the opportunityto present mathematical results and tobetter expand their knowledge of thewide range of theory, history, and appli-cations of the mathematics sciences.

The requests for funding will be reviewedthroughout the year. It is anticipated thatmost awards will be between $1,000 and$4,000, but smaller and larger requestswill be considered.

More detailed program information, in-cluding guidelines for conference orga-nizers and sample proposals, are avail-able through the project website, http://www.maa.org/rumc.

MAA Regional

Undergraduate Math-

ematics Conference

Program

20

FOCUS December 2005

The IMMERSE (Intensive Mathemat-ics: a Mentoring, Education and ResearchSummer Experience) program at theUniversity of Nebraska - Lincoln (UNL)is a summer program, funded by an NSFMCTP (Mentoring Through CriticalTransition Points) grant, which is de-signed to bring together early-career fac-ulty, graduate students, and pre-gradu-ate students for an intensive six weekprogram. The activities included coursesfor the pre-grads in algebra and analy-sis, problem sessions led by the graduatestudents, invited speakers, and panel ses-sions with the goal of preparing the pre-grads for graduate school. This article isa description of the IMMERSE programthrough the eyes of the early-career fac-ulty participants.

What is IMMERSE?

IMMERSE was designed with a ladder-like structure of participation, with par-ticipants in each group serving as men-tors for those earlier in their careers andreceiving mentoring from the more ex-perienced participants. The pre-gradu-ate students accepted into the IMMERSEprogram were selected primarily fromschools without Ph.D. programs, butthey all planned to begin a Ph.D. pro-gram in the fall. For the pre-graduates,the goal of the program is to increasetheir level of preparation for their gradu-ate program and to give them a view ofthe atmosphere of graduate school. TheUNL graduate students mentor the pre-graduates by overseeing problem sessionsand answering questions about life ingraduate school. This gives the currentgraduate students mentoring experience.The four early-career faculty (the authorsof this article) were also selected from in-stitutions that do not have Ph.D. pro-grams. We functioned as instructors andmentors to the pre-grads and graduatestudents, while pairing up with a researchmentor from the UNL faculty to workon research and receive career guidance.

Two early-career faculty members wereassigned to teach the algebra course,

while theother pairtaught thea n a l y s i scourse. Ratherthan concen-trating solelyon materialfrom standardt e x t b o o k s ,each coursewas focusedaround read-ing a relativelyrecent re-search paper.In this way,the paperserved as aguide for discussing mathematical ideasthat will be seen in graduate level coursesin algebra and analysis. The early-careerfaculty also gave advice on graduateschool, based on their own experiences,to the pre-graduates. We were therebyable to gain experience in mentoring stu-dents, encouraging students to pursuegraduate mathematics, and teachinggraduate level mathematics. These willbe valuable assets to incorporate intoworking with our own students when wereturn to our home institutions.

Our Experience

We arrived in Lincoln two weeks priorto the arrival of the pre-graduate stu-dents. During those first two weeks, wefinalized the preparations for the courses,decided on speakers to invite through-out the program, planned panel discus-sions, and developed a daily schedule forclasses and problem sessions. The sched-ule turned out to be an intense one forthe students, with both algebra andanalysis holding 90 minute lectures and90 minute problem sessions four days perweek. This provided the students withextensive access to both the graduatementors and the early-career faculty. Thepreparations during these two weeks alsoincluded discussing which mathematicalconcepts were relevant to the research

paper we were using as the center for ourcourses, writing homework assignments,and exploring different methods whichcould be used to co-teach a graduate levelcourse.

We were all new to the practice of team-teaching, and we chose different peda-gogical approaches. One pair of us de-cided to alternate lectures, with each per-son being responsible for certain topics.The other pair decided to more com-pletely “team-teach” by jointly preparingfor most lectures. One person would takethe lead in the presentation, while theother interjected important supplementsto the material being presented. All of uswanted to intersperse lectures on newmaterial with discussions about the re-search papers as the course progressed,but we did this in different ways. One pairdecided to have groups of studentspresent the important parts of the re-search paper at different points in thecourse. The other pair decided to con-duct class discussions of the theoremsand proofs. We felt the different ap-proaches were good for the students, sothat they would be exposed to differentstyles of presentation, and required toadjust their learning styles accordingly.

As part of the IMMERSE program eachof us was paired with an experienced re-

Our Experiences as IMMERSE Faculty

By Keith Agre, Tracy Hamilton, Jacqueline Jensen, and Keri Kornelson

IMMERSE participants, summer of 2005. Photograph by MarilynJohnson of the University of Nebraska-Lincoln.

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December 2005

searcher at UNL. The initial two weeks that we were in Lincolnwere also intended to provide time to begin these research con-nections, which ranged from an exchange of ideas to active pur-suit of a research project. Our research mentors were all talentedmathematicians and willing mentors, but some of these pairingswere less productive due to their other obligations. Some hadplanned extensive out-of-town trips during the program, whichslowed the research progress. Because of these absences, this partof the program didn’t work exactly as the organizers planned.However, at least two of us made significant progress on a newproject, while another continued work on an existing problem.

The IMMERSE program provided a great opportunity to interactwith very bright students who will be going on to graduate pro-grams. We were delighted to find that of the 17 pre-graduate par-ticipants, 11 were women. We were able to give some (hopefullysound) advice to students about what graduate school is like, cop-ing strategies that we employed, and some warnings about thedifficulties that they may face in their academic and personal liveswhile in graduate school. In one such discussion, we were remind-ing the students that there are many successful routes throughgraduate school. One of the IMMERSE pre-graduate students said,“My graduate school experience is going to be unique. Based ondecisions that I make, my experience will be different from any-one else’s.” One student commented that he was amazed by howmuch he had learned in such a short period of time. He was espe-cially impressed by the amount of assistance he received from otherpre-graduate students.

All in all, the IMMERSE program is appropriately named — it isan Intensive experience for both the pre-graduate students andthe early-career faculty. We spent many hours preparing lecturesand homework assignments, and many more visiting with the stu-dents during breaks. The students also spent many hours, both inclass and out, doing mathematics. As with any intensive experi-ence, however, they formed friendships and support networks(read: Dutch Blitz teams) that enabled them to cope with the stressand work even harder than they thought they could.

While participating in the program meant a long stay in Lincoln,away from our home institutions and family, the interactions withthese amazing and talented pre-graduate and graduate studentsmade the experience lively and invigorating. The opportunity toembark upon new research projects gave our research programs aboost of new energy as well. We have learned a great deal from thestudents about mentoring, and about concerns students have whenthey are preparing to start their graduate careers. The studentsalso expressed that the experience was worthwhile, with most feel-ing more prepared for their graduate programs than they wereupon their arrival in Lincoln. As one student put it, “IMMERSEprovided an opportunity to review a great deal of material andlearn many new things. I gained confidence, too! I feel ready forthe fall semester.” Comments like this are what made IMMERSE arewarding experience for all of us.

Keith Agre is an assistant professor at St. Cloud State University.Tracy Hamilton is an assistant professor at California State Univer-sity Sacramento. Jacqueline A. Jensen is an assistant professor at SamHouston State University. Keri Kornelson is an assistant professor atGrinnell College.

Participants must be U.S. citizens or permanent

residents and intend to enroll in a Mathematics

graduate program (which offers a Ph.D. degree) for

the Fall 2006 semester.

For more information, visit us on the web at

www.math.unl.edu/immerseor write to us at

Nebraska IMMERSEDepartment of Mathematics

University of Nebraska-Lincoln

203 Avery Hall

Lincoln, NE 68588-0130

adonsig1@math.unl.edu

Deadline for applicationMarch 1, 2006

University of Nebraska-LincolnAn equal opportunity educator and employer with a comprehensive plan for diversity

Intensive

Mathematics: a

Mentoring,

Education and

Research

Summer

Experience

June 28—August 9, 2006

An NSF-funded research and mentoring

experience in algebra and analysis

for beginning graduate students in

mathematics.

There is a $3,000 stipend, plus up to

$500 for travel. Room and board are

provided on campus.

22

FOCUS December 2005

A curious thing happened on our wayto lunch at the 2005 Joint MathematicsMeetings at Atlanta. As components ofmathematical couples, we discussed thechallenge of finding geographically closepositions for ourselves and our partners.This challenge is informally called theTwo-Body Problem. In a moment of en-thusiasm, we decided to share ourmusings and urge institutions to helpsolve the Two-Body Problem for math-ematical couples. Such a solution wouldbenefit both hiring institutions and themathematics profession.

Between bites of our sandwiches, weidentified several known solutions. Theyare: (1) The partners find two positionsin the same institution; (2) they find twopositions at different but nearby institu-tions; (3) one partner finds a position inan academic institution, while the othera position in nearby business, industry,or government (BIG); or (4) they sharea single position at one academic insti-tution.

For the hiring institution, one clear ben-efit of any solution is stability. Once aviable solution has been found, thedaunting prospect of returning to the jobmarket tends to keep the couple in place.In fact, smaller and isolated colleges canbecome attractive “fixed points.”

A similar benefit is that “happy workersare productive workers.” When concernabout employment is minimized, thepartners can focus more effectively ontheir work. They become more involvedin their institutions and protective of thesolution they have found. They tend tobe active on hiring committees and will-ing to mentor new members. Even if thedynamics of a department become cha-otic, the partners are motivated to takeleadership roles to improve the depart-ment. Often these members have an in-creased loyalty to their own institutionand are more likely to stay put even ifone partner becomes distinguished in afield of study.

The advantages of solution (1) are thatcommuting difficulties are minimized,partners can work on related projects,and they share all aspects of professionallife. The institution can sometimes at-tract higher quality members by hiring acouple because these mathematicians arenot simply looking for the highest pay-ing or most prestigious positions.

When partners hold positions at differ-ent but nearby institutions as in solution(2), communication between the two in-stitutions naturally increases. In practice,the couple connects two disjoint institu-tions so that members at both institu-tions can share opportunities and col-laborate on projects, making a positiveimpact in the profession.

Finding one position at an academic in-stitution and one at a BIG institutionleads to better placement of students intointernships, more real-world applica-tions in the classroom, and mutual ap-preciation between academia and BIG.While the more rigid work schedule ofthe BIG institution may create pressureon the academic partner, a higher BIGsalary can help ameliorate that problem.

Solution (4), partners sharing one singleacademic position, will allow both part-ners to devote more time to research andother creative activities. A benefit is theincrease in specialties represented amongthe faculty. The “same” faculty membermight teach abstract algebra, differentialequations and statistics. By hiring acouple with partners from different re-search areas to fill a shared position, asmall college can feature more special-ties and have better qualified facultymembers for advanced courses.

Are there drawbacks to hiring a couple?If the partners are in the same depart-ment and their relationship sours, theentire department will be affected. Witha shared position, the handling of a dis-solution is even more difficult. Problemsmay also arise when one member of the

couple is a good fit for the department,but the other is not.

Problems aside, an increasing number ofinstitutions realize the benefits of hiringa mathematical couple. There was a timewhen anti-nepotism rules meant thatmathematical couples in the same de-partment were rare, but currently aninstitution’s best interests lie in develop-ing policies about mathematical couples.For example, the University of KansasDomestic Partner AccommodationGuideline includes the following:

“With two-career couples becoming thenorm rather than the exception inacademia, we are willing, indeed eager,to investigate possibilities for domesticpartner accommodations when such ac-commodations will increase our numberof quality faculty and staff.”

As members of two-career couples our-selves, we encourage others to be persis-tent and creative when searching for po-sitions. Make the institution an offer itcannot refuse. Once a couple accepts anoffer of two positions, performanceabove and beyond normal expectationswill encourage other institutions to ex-plore the value of mathematical couplesin the future.

Institutions can help solve the Two-BodyProblem. A solution will empower bothpartners to reach full career potential. Ifinstitutions seek opportunities to offerpositions to couples, they will be richlyrewarded with loyalty, dedication, andstability.

Brian Birgen is Assistant Professor ofMathematics at Wartburg College inWaverly, IA. Jean Bee Chan is Professor ofMathematics at Sonoma State Universityin Rohnert Park, CA.

Musings on the Two-Body Problem

By Brian Birgen and Jean Bee Chan

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December 2005

In the early seventeenth century,Johannes Kepler believed that in doingmathematics, he was thinking thethoughts of God. Was he right? Doessuch a question even make sense in 2005?

Like all other academic disciplines, math-ematics has a core of concepts and meth-ods that are independent of the worldviews of individual mathematicians. Infact, some mathematicians have regardedthat core as the entire discipline. For ex-ample, writing in 1927, David Hilbertarticulated his vision that mathematicscould become a “presuppositionless sci-ence.” Hilbert’s vision, though, seems torequire a very narrow assignment of theboundaries of mathematics, one that in-cludes formal axiom systems, definitions,and deductive reasoning, but not muchelse. Other mathematicians have pre-ferred a broader definition of the disci-pline, one that incorporates the philoso-phy and history of mathematics, math-ematics education, its role in contempo-rary culture, its connections with otherdisciplines, and much more.

Scholarly work in these broader areas,though, is often influenced by worldviews. One group of mathematicians thathas embraced these broader aspects ofmathematics and sought to explore howworld views might impact scholarship inthese areas is the Association of Chris-tians in the Mathematical Sciences(ACMS). Some of the questions ACMSmembers have explored include the fol-lowing.

• What is the nature of mathemati-cal objects? Are they social construc-tions? Do they exist in the mind ofGod? Are these perspectives recon-cilable?

• Mathematicians often describe theirsubject as “beautiful.” What is theconcept of beauty used here? Howdoes it relate to other concepts ofbeauty including the theologicalnotion of the “beauty of God”?

• How did Enlightenment thinkers seethe role of mathematics in humanculture? Are we as mathematicianscomfortable with such an under-standing of mathematics? Now thatthe Enlightenment perspective hasfallen out of favor, how may ourculture’s perspective on the role ofmathematics change? What respon-sibility do we as a mathematics com-munity have in shaping this perspec-tive?

• Does a theological perspective pro-vide any helpful insight into the is-sue of the “unreasonable effective-ness” of mathematics?

ACMS was organized in 1977 and nowhas more than 300 members. ManyACMS members are mathematics facultyat Christian liberal arts colleges, whereintegrative questions such as those listedabove are encouraged. There are alsomembers from secular colleges and uni-versities, high schools, and industry, aswell as graduate students and a growingnumber of teachers of computer science.ACMS members do not believe that thereexists a distinct Christian mathematics,but rather that dual knowledge of faithissues and mathematics enriches and in-forms both areas. A familiar analogue isthe way that the separate disciplines ofgeometry and algebra supplement eachother in analytic geometry.

The main activity of ACMS is a four dayconference, held every two years fromWednesday evening until Saturday noonof the week following Memorial Day.The 15th conference was held in May2005 at Huntington University in Indi-ana, and the 16th conference will be atMessiah College in Pennsylvania fromMay 30 until June 2, 2007. These confer-ences offer a chance for about 100 del-egates to share several days together. Ac-tivities include invited talks by featuredspeakers, shorter papers by ACMS mem-bers on a wide variety of topics, manyopportunities for informal discussion,and a time of common worship.

The following list of past featured speak-ers and their topics illustrate the diver-sity of interests within ACMS. DonaldKnuth (at Calvin College in 1987) spokeon the writing of his book Surreal Num-bers and his efforts to develop a book onBible study, while Tom Banchoff (atMessiah College in 1989) spoke on hisinvolvement with students in computerrepresentations of four dimensionalspace and on the background of EdwinAbbott Abbott, the author of Flatland.Joseph Dauben (at Westmont College in1993) presented material from his bookson Georg Cantor and AbrahamRobinson, and Owen Gingerich (atWheaton College in 1997) spoke abouthis special interests in the history of as-tronomy, arising from his joint appoint-ment at the Smithsonian AstrophysicalObservatory and Harvard University. BillDunham (at Gordon College in 1999)spoke about some of Euler’s results, in-cluding geometry in addition to the moreusual topics from analysis and algebra,while Paul Zorn (at Point Loma NazareneUniversity in 2003) presented examplesof material he encountered during histime as editor of Mathematics Magazine.

The Proceedings from every conferencehave been published and are available forpurchase. The tables of contents may beperused at the website (http://www.acmsonline.org), where one mayalso find directions for ordering a copyof the Proceedings or for becoming anACMS member. The organization re-cently began an online journal for articlesdealing with the integrative issues men-tioned earlier. The texts of twenty sixpapers from previous conferences arealso included on the website. In addition,several ACMS members authored thebook Mathematics in a Postmodern Age,published by Eerdmans in 2001. (It wasreviewed in the MAA’s Read This onlinebook review column; see http://www.maa.org/reviews.) Another publica-tion is the Bibliography of Christianityand Mathematics (1910–1983), whichwas compiled in 1983 and is presently

What Does ACMS Stand For?By Robert L. Brabenec

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being revised and enlarged by GeneChase at Messiah College.

Every January, in conjunction with theJoint Mathematics Meetings, ACMSsponsors a dinner followed by a talk of ageneral nature. In Atlanta in 2005, TomBanchoff spoke about his involvementover a period of ten years with SalvadorDali on the use of computer graphic sys-tems to enhance artistic representationof multidimensional images. When theJoint Meetings include a Sunday, as theywill in San Antonio in 2006, ACMS alsoprepares an early morning non-denomi-national worship service for interestedparticipants.

ACMS members are also involved in thegeneral program of the MAA. David Lay

(University of Maryland) played a lead-ing role in the reform of the linear alge-bra curriculum and the writing of an in-fluential textbook on this topic. WayneRoberts (Macalester College) has longbeen involved in calculus reform, serv-ing as editor of the 5 volume Resourcesfor Calculus publications. CharlesHampton (College of Wooster) is activeas an officer in the SIGMAA for the Phi-losophy of Mathematics. RobertBrabenec (Wheaton College) and AlHibbard (Central College) are MAAauthors. Francis Jones (Huntington Uni-versity) was chosen for a MAA sectionteaching award. Judith Palagallo (Univer-sity of Akron) serves on the editorialboard of the MAA series Classroom Re-source Materials and began theMentoring Women in Mathematics pro-

gram. Fernando Gouvêa (Colby College)is, among other things, editor of FOCUS.Andrew Simoson (King College) haspublished a dozen articles in MAA jour-nals and Francis Su (Harvey Mudd Col-lege) has served on the editorial boardfor the Spectrum book series.

The website mentioned above containsadditional information about the ACMSorganization. Anyone interested in itsprograms is welcome to participate in itsactivities.

Robert L. Brabenec is Professor of Math-ematics at Wheaton College in Illinois. Hewas one of the founders of ACMS.

Do you have lots of issues of theMonthly taking up space on your book-shelves? Before you put them in the re-cycling you might consider the follow-ing. Two issues of the Monthly appear ina new booklist from the Los Angeles rarebook dealer, Michael Thompson. Each ofthe issues — volume 59, number 8 (1952)and volume 62, number 9 — contains anarticle by W. V. Quine on the simplifica-tion of truth functions. The articles areof interest because they were precursorsof Quine’s later work on the Quine-McCluskey method of logical circuitminimization. The asking price is $1250for the pair. (Thanks to JerryAlexanderson.)

Save the Monthlies

At the Joint Mathematics Meetings, the History of Mathematics SIGMAA will be sponsoring a special presentation byEdwin L. Barnhardt, Director of the Maya Exploration Center, and Christopher Powell, a senior research associate of theCenter. They will discuss a new line of research on what is known as “Maya Sacred Geometry,” examining how the Maya usedproportions derived from nature in their art and architecture. The talk will be on Thursday, January 12, from 9:30 am to 10:50am. (This talk was not listed in the October issue of FOCUS.)

Shapes of Sacred Space

Additions to the Joint Mathematics

Meetings Program

NUMB3RS and Math, The “We AllUse Math Every Day” Program, Orga-nized by Linda Beheler, Texas Instru-ments. Thursday, 5:00 p.m. - 6:30 p.m.“We all use math every day...” Thesewords open the weekly introduction tothe hit CBS show, NUMB3RS in whichan FBI agent and his math professorbrother solve crimes using math to fig-ure out clues and drive the investigation.These words are also the title of a TI pro-gram in partnership with CBS to pro-mote student interest in math. The pro-gram includes weekly online activitiesthat correspond to the math in each epi-sode of NUMB3RS and a special teacherkit. See how to use NUMB3RS to helpexcite students about the real world rel-

evancy of math, receive a teacher kit, andmeet a cast member from NUMB3RS.Autographs and photo session followsthe event. Cast member to be announcedprior to show. The session is sponsoredby Texas Instruments, The Mathemati-cal Association of America, and theAmerican Mathematical Society.

Jacob Fox of MIT, winner of the 2005Morgan Prize, will speak on “RamseyTheory on the Integers, Rationals, andReals,” at the Research in Mathematicsby Undergraduates session Friday 6:00pm to 6:20 pm. Darren Narayan is thesession organizer.

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December 2005

I first got involved with the MAA inApril of 1974. This was the end of mysophomore year at Allegheny College, aliberal arts college in Meadville, Pennsyl-vania. Because of our three term calen-dar, I had already completed calculus I,II and III, an introductory analysis classbased on the Moore Method, and linearalgebra. I was enrolled in abstract alge-bra, and had decided to major in math.It was exciting to meet students and fac-ulty from colleges all over the region andhear interesting and understandablemathematical talks!

In January of 1975, the faculty decidedto take two seniors and two juniors (in-cluding me) to the Joint Meetings inWashington, DC. It was a wonderful ex-perience. We drove to the meetings inRich Lundgren’s orange VW bus (called“The Pumpkin”), playing bridge all theway. It was exciting to be in Washing-ton, which I had visited only once before.I roomed with Ben Haytock, one of myprofessors at Allegheny. I also met KathyTaylor, who was already teaching atDuquesne. Kathy is a past winner of theMAA service award from her section. Wedid some sightseeing, including the Na-tional Gallery, the zoo, and many of themonuments. After this meeting, I knewI wanted to become a professor of math-ematics and become involved with theMAA.

The 1976 spring meeting of the Allegh-eny Mountain Section was held at WestVirginia University. I gave a talk basedon my senior project under the directionof Dick McDermot. I was nervous, butit was definitely a valuable experience.

During my graduate years at NotreDame, I maintained my membership inthe MAA, even though neither my fel-low students nor the faculty were muchinterested in the organization. I lookedforward to getting a teaching position ata school that valued excellence in teach-ing and supported involvement in the

MAA (if only Project NEXT had beenaround then!). I was therefore verypleased to accept Duquesne’s offer for atenure- track position to begin in the fallof 1981, and to be able to return to myhome town and the Allegheny MountainSection.

The faculty at Allegheny were (and stillare) very much involved with the Section,as were (and still are) the faculty atDuquesne. Attending the annual sectionmeeting was a very high priority for me.In a few years, I was asked to become Stu-dent Program Coordinator for the Sec-tion. I have been told that our Sectionwas one of the first to start including pro-grams for students and having studentsgive talks.

This appointment was the start of my fif-teen years as an officer of our Section. Ialso served as newsletter editor, co-direc-tor of short and minicourses, and Gov-ernor of the Section. My first fall sec-tion officers meeting was at Clarion Uni-versity. Ben Freed’s wife provided a verynice meal for us at the conclusion of themeeting. This allowed the officers timeto get acquainted on a personal level andto be fortified for our trip home.

The next year, I asked if people wouldlike to come to my home for the meet-ing, since it was centrally located in thesection, and I would provide the meal.Everyone enjoyed the relaxed atmo-sphere of meeting in someone’s home.The meeting was very productive, andpeople ate my cooking with no com-plaints. My mother graciously providedhomemade pies, which were the hit ofthe meal. For my remaining years as anofficer, and for one year after my termended I continued to host the fall meet-ing of the officers.

I was privileged to be one of the orga-nizers of the last section meeting we hadat Duquesne. Since coming to Duquesne,I have missed only one section meeting.

Ironically, it was the meeting at which Iwas honored with an award for outstand-ing service by our section.

Because of my involvement with the sec-tion, Dick McDermot, founder of theSection Summer Short Course, and MAAaward winner for distinguished serviceto the section, nominated me to the na-tional Minicourse Committee. I servedon that Committee for 8 years, chairingit for 3. I am now serving on the Com-mittee on Sections, the Committee onProfessional Development, and the Co-ordinating Council on Meetings. I alsohave been organizing on-site receptionsfor GLBT members of the MAA at ournational meetings.

My many years of involvement with theMAA have been rewarding. I have metso many wonderful, dedicated, andfriendly people. I (and in some cases mypartner, my parents , sister, and brother-in-law) have seen much of the countryby attending the Joint Meetings andMathFest.

The MAA is a vital and vibrant organi-zation. Of course, the national staff isvery dedicated, but it is because so manypeople volunteer their time and energythat makes the organization work. If youhaven’t been active in your section, I urgeyou to become so. If you have, consideran appointment to a national commit-tee. The organization will be grateful,and you will find it to be one of the mostexciting parts of your career.

Last spring the position of Section His-torian became vacant, and I was askedto take that position. I am very glad toonce again be involved in the affairs ofthe section. Oh, and Mom, could youplease make a couple of pies for ourmeeting?

George Bradley is Associate Professor ofMathematics at Duquesne University inPittsburgh, PA.

Thirty Years and Counting: My Involvement With the MAA

By George Bradley

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As if coordinated to provoke headlines,top executives at three of the nation’sleading technology firms recently issuedbleak appraisals of the American educa-tion system, criticizing especially howAmerican students are taught scienceand mathematics. Microsoft ChairmanBill Gates minced no words at a summitof the nation’s governors: until highschools are redesigned, he declared, “wewill keep limiting, even ruining, the livesof millions of Americans every year.” Thechief executives of Intel and Cisco Sys-tems shortly followed suit, suggestingthat America’s lackluster schools will in-creasingly force companies to look over-seas for talent.

Of course, these concerns are hardly new.But the somber prognoses from theheights of high-tech have added high-profile urgency to recent press reportsabout the declining performance of U.S.students in science and math comparedto other nations, and the potential riseof China as a technological and eco-nomic superpower. Leading U.S. mediaoutlets have featured major stories on theconsequences of China’s rise forAmerica’s future, like the recentNewsweek cover story by Fareed Zakariaappealing for a “massive new focus” onscience and technology in the U.S., lestAmerica “find itself unable to producethe core of scientists, engineers and tech-nicians who make up the base of an ad-vanced industrial economy.” In such amedia atmosphere, one could be forgivenfor having concluded that the UnitedStates is drifting unawares into an edu-cational backwater while the rest of theworld paddles furiously past it.

The truth is more complex. Cross-na-tional studies of scientific and math-ematical ability, interpreted rightly, tella complicated story, giving reason toquestion how well the tests measureAmerica’s real educational standing inthe world. The two tests cited most fre-quently in press reports are the Programfor International Student Assessment(PISA) and the Trends in International

Mathematics and Science Study(TIMSS). PISA, undertaken by the Or-ganization for Economic Cooperationand Development (OECD), most re-cently spanned 41 countries and tested15-year-olds on mathematical word-problems. The latest TIMSS, in 2003,comprised more traditional, textbook-style math and science problems and wasadministered to fourth- and eighth-grad-ers in 25 countries by an internationalteam of researchers based in Boston andAmsterdam. The Department of Educa-tion funded both studies in the U.S., withhelp from the National Science Founda-tion.

Both tests have repeatedly been invokedby sensationalists seeking to cast theUnited States as unprepared for the high-tech, global economy. When the latestPISA results were released toward the endof last year, for instance, the ChristianScience Monitor ran with the headline“Math + Test = Trouble for U.S.Economy,” and concluded that thestudy’s emphasis on “real-life” math skillsmakes it an accurate and “sobering” pre-dictor of students’ performance in “thekind of life-skills that employers careabout.” Federal officials expressed con-cern about the test results, too. “If wewant to be competitive, we have somemountains to climb,” said Deputy Edu-cation Secretary Eugene Hickok.

To be sure, the results of neither TIMSSnor PISA should send American educa-tors and policymakers rushing to thechampagne. In most math areas testedby PISA, the gap between the average U.S.student and the average student in thehighest-scoring countries—often Fin-land, the Netherlands, Singapore, Japanand Hong Kong—was roughly equiva-lent to the gap between the United Statesand low-scoring countries like Uruguayor Mexico. Where 44 percent ofSingapore’s students reached the TIMSS“advanced international benchmark,”only 7 percent of U.S. students did. And,in general, the longer students had re-mained in the U.S. school system, the

worse they performed relative to theirpeers abroad.

The first question that must be asked ofsuch broad results, however, is whetherthe tests themselves accurately representthe countries’ student populations. Inter-national surveys such as these are notgiven to every student in each participat-ing country; the tests’ organizers pick outstatistical samples that are supposed torepresent each country’s entire studentpopulation. Even so, schools—especiallyin the United States—sometimes declineto participate in the tests, potentiallyskewing the sample. As far as accuratesampling is concerned, early incarnationsof the tests were not encouraging. In thefirst TIMSS general achievement test,conducted in 1995, only 5 of 21 partici-pating countries met the study’s guide-lines for conducting representativesamples. While most countries partici-pating in the latest studies have dramati-cally improved their overall sampling, theUnited States remains a notable excep-tion. Only 73 percent of U.S. studentschosen to be sampled were actuallytested, a figure below the “minimum ac-ceptable” rate of 75 percent. In mostother countries, that number was wellover 90 percent. If the omitted 27 per-cent of U.S. students were even slightlyabove or below average, their exclusioncasts serious doubts on the accuracy ofthe U.S. sample.

The studies also inevitably confront largedifferences between countries’ schoolsystems. “In Cyprus, students taking theadvanced mathematics test were in theirfinal year of the mathematics and scienceprogram; in France, the final year of thescientific track; in Lithuania, the finalyear of the mathematics and sciencegymnasia; in Sweden, the final year of thenatural science or technology lines; andin Switzerland, the final year of the sci-entific track of gymnasium,” ProfessorIris Rotberg of George Washington Uni-versity wrote in Science concerning the1995 TIMSS assessment, which testedhigh-schoolers. “In contrast, students in

How We Measure Up

Is American Math and Science Education in Decline?

By The Editors of The New Atlantis

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several countries, including the UnitedStates, attended comprehensive second-ary schools. The major differences in stu-dent selectivity and school specializationacross countries make it virtually impos-sible to interpret the rankings.” In TIMSS,especially, tests are conducted by grade-level rather than by age. In elementaryand middle school, where topics are of-ten covered and learned over the courseof a few weeks, the risk of comparing stu-dents at incommensurate stages of theireducation is great.

Broad curricular differences have prob-ably had a role in deflating U.S. scores.TIMSS and PISA use the same test inevery participating country, and the ma-terial that makes it onto the test is se-lected through a winnowing process thatleaves the tests considerably narrowerthan any single country’s general cur-riculum. Countries that include largeamounts of material in their typical cur-ricula are therefore at a disadvantagecompared to those countries that focustheir curricula more intensely on fewersubject areas. Regardless of its other mer-its or failings, the American strategy ofrepeated exposure to a broad range ofsubjects—American textbooks are thebulkiest in the world—is likely to lenditself to unduly poor performance onstandardized tests, as full understandingof any single concept takes longer to de-velop.

Demographics and culture are alsothought to confound the results of cross-national comparisons. In the UnitedStates, the tested students come fromevery socioeconomic rung, while othercountries sometimes lack some rungsbecause of cross-border employment.For example, much of the labor force inHong Kong (which is treated on the testsas an independent entity) is made up oftens of thousands of low-paid Filipinohousehold workers whose children liveand are educated in the Philippines; inlight of the extensive literature tying so-cioeconomic indicators to educationalachievement, this cross-border employ-ment surely affects both countries’ scores.A similar situation obtains in other placeswith significant immigration and cross-border commerce, as Gerald Braceypoints out in a 1997 article in the jour-

nal Educational Researcher. “Each morn-ing thousands of Malaysians enterSingapore to sweep streets, pick up gar-bage, and do other low-level jobs. Theyreturn to their homes at night, relievingSingapore of having to educate the chil-dren of poor laborers,” Bracey writes. “Ifone reads the [domestic] educational re-search literature, one is struck by thelengths—the extreme lengths—that re-searchers go to to ensure that samples intheir studies are comparable....The re-search community would never accepttest results in this country that simplycompared scores in an inner-city slumand an affluent suburb as if they werecomparable,” he writes. The opposite cir-cumstance holds in the United States:Students from all socioeconomic rungsare educated and scored on these tests.

Amid this deluge of confounding factors,the inference that the U.S. education sys-tem is going down the tubes is an unjus-tified logical leap. The United States isstill pumping out tremendous numbersof new Ph.D.s in the sciences—more, infact, than our economy can presentlyabsorb, as there is a well-reported dearthof jobs for newly-minted science Ph.D.s.The same is true in engineering: Accord-ing to a recent National Science Foun-dation report, the number of engineersgraduating from U.S. schools will con-tinue to grow into the foreseeable future,outstripping the number of availablejobs. Of these new engineers and Ph.D.s,an increasing number are foreign-born—but increasing even faster is thepercentage of those who decide to stayin the United States. Federal researchfunding for scientific research and devel-opment has consistently risen in abso-lute terms and as a fraction of discretion-ary spending—and industry researchdollars have risen dramatically on top ofthat, to the tune of 7 percent per year inreal terms—according to calculations bythe Consortium for Science, Policy andOutcomes at Arizona State University.(Alarmist media reports often use GDP,against which research spending hasfallen, as a comparative baseline.) Andcountries that have “outperformed” theUnited States in educational studies formany years—a number of Europeancountries top this list—still fail to rivalthe U.S. in any measure of research pro-

ductivity. When Bill Gates and othersseem to appeal for school reform in theU.S., perhaps they are merely providingtheir companies with political cover anda post hoc justification for employingforeign engineers who, while not bettereducated than U.S. workers, are often sig-nificantly cheaper.

Nevertheless, there remains good reasonto worry about what the global economyportends for those American studentswho really are badly educated. In onlyone other OECD country (New Zealand)are internal educational inequalitiesworse than in the United States, accord-ing to a recent analysis by researchers inEngland and Italy. Where these inequali-ties lie is no mystery. The gap in testscores between white and ethnicallyAsian students on the one hand and blackand Hispanic students on the other is awell-known attribute of U.S. schools andis noted ruefully in nearly all cross-na-tional studies. Two University of Penn-sylvania researchers recently aggregatedscores from a number of cross-nationalstudies and found that white students inthe United States, taken alone, consis-tently outperform the predominantlywhite student populations of severalother leading industrial nations. “Thereis compelling evidence,” they write,” thatthe low scores of [black and Hispanic stu-dents] were major factors in reducing thecomparative standing of the U.S. in in-ternational surveys of achievement. Ifthese minority students were to performat the same level as white students, theU.S. would lead the Western G5 nationsin mathematics and science, though itwould still trail Japan.” In PISA, for in-stance, white students performed abovemost European countries, whereas blackstudents performed on par with studentsin Thailand. So while the performanceof minority groups in the U.S. does re-fute the alarmist assertion regarding anacross-the-board decline in U.S. schools,it does so in a particularly unfortunateway—namely, it suggests that someAmerican minority groups will be shutout of high-paying jobs as companieslook for better-educated workers over-seas. Although the most recent TIMSSsaw the white-black score gap closeslightly, it is almost certain to remainshockingly large in the near future.

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None of this is to say that other coun-tries are not catching up technologically,nor that the United States is safe fromcompetition in even a single technologi-cal sector. China is without doubt themost aggressive challenger. In the mid-twentieth century, Japan’s economy grew55-fold over the course of thirty yearsthrough stringent government control;observers of Japan’s rise will rememberthe key role of its Ministry of Interna-tional Trade and Industry, which em-ployed many of the nation’s brighteststars and guided the economy on a care-fully directed path of technologicalgrowth. China’s strategy has been simi-lar, though its tremendous size has ne-cessitated delegation of heavy-handedeconomic control to regional govern-ments in what scholars have termed “lo-cal state corporatism.” It has simulta-neously harnessed the power of marketsin a way Japan did not. Regional govern-ments lavish tax breaks on high-tech in-dustries (many of them funded fromoverseas) and pump millions intoChina’s new universities—which arepoised to graduate more Ph.D.s than theUnited States by 2010, according to someprojections. Nearly all of China’s topleaders are scientists and engineers bytraining: President Hu Jintao is a hydro-electric engineer, Premier Wen Jiabao isa geological engineer. Their predecessors,Jiang Zemin and Zhu Rongji, were bothelectrical engineers. The technocratssteering China’s ship of state are work-ing hard to modernize scientific educa-tion in their country.

But the United States need not worry—not yet. The U.S. is by no means in tech-nological decline, though China and In-dia will inevitably pose challenges inyears to come. Although not a crisis, thiscompetition should motivate the U.S. toimprove its science and math education,especially for poor and minority studentswho might lose out in a globalized, high-tech economy. If sensationalists musttake up a cause, it should be the plight of

Mathematics FacultyStony Brook University’s Department of Mathematics is accepting applications for faculty needed for positions in the secondary teacher preparation program, involving bothundergraduate and graduate students.Required: Must have doctorate in Mathematics or Mathematics Education. Must have strongpotential for creative leadership in mathematics education, including research and publications.Administrative experience; familiarity with NCTM and NCATE standards; secondary schoolmathematics teaching experience; and experience teaching pedagogy courses highly desirable. Initial duties include teaching two courses per semester and some administrative duties.Research also expected. Teaching duties will decrease as administrative duties increase to full leadership of one of the components of the teacher preparation program (currently about 20 undergraduates and 20 graduates per year). Salary and rank commensurate with experience. Applications will begin review on January 15, 2006.To apply, please send CV and at least three letters of reference to: Math Education SearchStony Brook University, SUNY Stony Brook, NY 11794-3651

AA/EOE. Visit www.stonybrook.edu/cjo for employment information.

Ruth Aaronson Bari, professor emeritusof mathematics at George WashingtonUniversity, died on August 25. She was87. Born in Brooklyn, NY, she learned tolove mathematics at the local college,from which she received a bachelor’s de-gree in 1939. Her plans to obtain her PhDat Johns Hopkins were delayed by WorldWar II and the arrival of three daugh-ters, but she returned to Johns Hopkinsand eventually received her degree in1966, at age 47. Her research work wasin graph theory and was well received.She joined the GWU faculty that sameyear, and remained until her retirementin 1987. In addition to her mathemati-cal research, she was deeply interested inmathematics teaching. She was a mem-ber of MAA for 38 years.

In Memoriam

Hans Samelson, the well-known topolo-gist and differential geometer who wasat Stanford since 1960, died September22 in Palo Alto. He was 89. Samelson wasa student of Heinz Hopf at the ETH inZurich. After coming to the Institute forAdvanced Study, he taught at Wyoming,Syracuse, and Michigan before comingto Stanford. He retired in 1986, but re-mained active, publishing both new re-search and historical articles, most no-tably one on Brunellischi’s dome in Flo-rence. Samelson was the author of twopopular textbooks, one on linear algebraand one on lie groups and algebras. In1981-82 he served as Section Chair of the(then) Northern California Section ofthe MAA.

those students and not a hyped-up“threat” of China or the “impending de-cline” of technological innovation hereat home.

Reprinted with permission from The NewAtlantis: A Journal of Technology and So-ciety, Number 9, Summer 2005, pp. 111-116. See http://www.TheNewAtlantis.com.A follow-up article is planned for the Win-ter 2006 issue of the same journal.

Have You Moved?

The MAA makes it easy to change youraddress. Please inform the MAA Ser-vice Center about your change of ad-dress by using the electronic combinedmembership list at MAA Online (http://www.maa.org) or call (800) 331-1622,fax (301) 206-9789, email:maaservice@maa.org, or mail to theMAA, PO Box 90973, Washington, DC20090.

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December 2005

Picture this—

You want to teach your students a simplelesson in data handling by holding theirattention long enough to look at corre-lations between the class members’ handspans and height. Your young charges(aged 14) are enthused by the exercise oftaking measurements, and then sit qui-etly (for a while) as they await your black-board demonstration of what the datalooks like.

And they wait…

And wait…

Finally, your graphs are complete andyou happily begin discussing the corre-lations shown in your carefully drawnbox and whisker diagram and histogram,when the bell rings signaling the end ofclass.

That may happen once, you may think,but experienced teachers will know notto eat up valuable instruction time withdrawing graphs such that they never getto the meat of the matter, i.e. the actualdiscussion of data interpretation.

What then does the more experiencedteacher do? There certainly is no short-age of mathematical and statistical soft-ware packages that could be used to gen-erate these diagrams in keystrokes. Alas,these software packages typically comenot only with relatively hefty purchaseprices but also time-consuming learningcurves. More likely, the practical short-cut would be to omit the relatively excit-ing exercise of using such spontaneousdata and to limit dataset size as much aspossible. “But where’s the fun in that?”you may ask, or likely your students will.

Why not use a much simpler tool likeMicrosoft Excel?

That’s exactly the question that each ofus came to ask, from our varying per-spectives — one of us is a mathematicsteacher on the front lines of instruction,and the other a manager of a worldwide

company that develops cross-platformmathematical and statistical compo-nents, among other technical softwareproducts.

From the developers’ perspective, it’s ap-parent that teachers are not the only oneswho are too time-pressed to masterelaborate mathematics and statistics soft-ware packages. That’s why the Numeri-cal Algorithms Group (NAG) devotedmany development hours in 1998 to cre-ate statistical software that is built intothe widely familiar and easy-to-use Ex-cel platform, the NAG Statistical Add-Insfor Excel, which enable the use of thesepowerful tools without any program-ming. All of the statistical algorithmscould be accessed via the function wiz-ard just like any other standard Excelfunction, with results being immediatelyupdated whenever input cells were al-tered.

From the developers’ perspective, it wasquite delightful to learn that the NAGStatistical Add-Ins were being used insome local Oxford schools, and consul-tations were begun in the spring of 2004on how to improve the product as an in-structional tool. There was just one tinyproblem — from the view of experiencedinstructors these Statistical Add-Ins forExcel were of only modest value as ateaching tool.

The completely different places that wewere coming from made for some veryinteresting conversations. The develop-ers were keen to add functionality andfished for input on the importance ofimproving the standard deviation func-tions, average functions, etc. However,from a teaching perspective, it was thepresentations, not the functions, whichwere lacking and holding up the Statisti-cal Add-Ins from being useful in theclassroom.

For example, bar graphs drawn in Excelare simplistic visual representations ofdata that are not mathematically correct,and in fact, if students presented themat exam time, they would fail because

they had left gaps between bars, or didn’tproperly indicate scales. Then there werea number of graphs critical to the cur-riculum that Excel could not generate atall — cumulative frequency graphs andbox whisker diagrams, for example.What was needed was a way to teach Ex-cel to draw correct continuous bar chartsthat teachers could use to demonstratehow to describe datasets. Similarly, scat-ter graph production in Excel needed tobe changed so that two points marked inthe same place would not overwrite eachother, but rather appear with one pointmoved to the side. The software alsoneeded to help teachers make the distinc-tion between discrete and continuousdata. It would need to generate outputto a frequency table to save teachers ‘tally-time’.

It was apparent from a teaching perspec-tive what would be needed to make Ex-cel a valuable teaching tool. Before col-lecting teachers’ input, the key develop-ers had imagined that it was importantto have software that produced the algo-rithm but meticulously avoided givingthe student an easy way to do the home-work. It became obvious that while thedevelopment team could solve the prob-lems, the teachers were the ones whoknew how Excel functions would need tolook and feel. Further, only the teachersknew whether the questions that the soft-ware helped ask were in the right se-quence, from a teaching perspective, andwhether they were helpful in terms ofhow students’ minds usually work ingrappling with the subject matter.

Earlier this year, the first result of thesecollaborations between developers andteachers was released to the wider world— NAG Schools Excel Add-In (N-SEA,http://www.nag.com/n-sea/), and was re-cently made part of the UK’s “e-Learn-ing Credits”, which are funds set aside forUK schools to spend on educational soft-ware.

Although the curriculum (for ages 14–16) only requires that students learn withrelatively small datasets, between 30 and

How We Moved Excel to the Head of the Class

By Ed Carlin and John Holden

30

FOCUS December 2005

50, it is anticipated that as N-SEA be-comes more widely used in the UKschools, there will be impetus to workwith the potentially more meaningfuland valuable interpretation of larger-sized datasets, particularly those nowavailable through a UK initiative calledthe CensusAtSchool project (http://www.censusatschool.ntu.ac.uk). TheCensusAtSchool project is part of an in-ternational effort to generate a world-wide database with data of particularinterest to school-aged children such asstudent heights and weights, which canbe used in Information and Communi-cations Technology courses (ICT) to en-hance instruction in data handling. Itenables teachers to discuss datasets withmany hundreds of thousands of datum,but practically speaking, can only be ac-cessed with statistical instruction sup-port software such as N-SEA.

Hopefully, members of the Mathemat-ics Association of America will write thenext chapter of this story. NAG’s NorthAmerican branch has recently releasedthe NAG Schools Excel Add-In (N-SEA)

to U.S. and Canadian instructors of highschool advanced placement and intro-ductory college-level courses, in hopesthat they will find it as helpful as theirUK counterparts have. There is reasonto think that this will be the case. In-structors in the UK, US and Canada aresimilarly adept with Excel software andfamiliar with its limitations in the class-room. Moreover, the time pressures thatteachers in the UK face are mirrored inNorth America, and these realities typi-cally preclude the use of elaborate math,science and statistical software in theclassroom.

However, N-SEA customization for theneeds of MAA members is needed. Al-though the end point in mathematics,science and social science courses thatprovide statistical instruction are actu-ally quite similar on both sides of theAtlantic, there are distinct approaches invarious curricula. The Numerical Algo-rithms Group is poised to fine-tune N-SEA software to match the special needsof North American curricula, which arecommunicated by the first generation of

North American N-SEA users. Based oninput from UK teachers, the next gen-eration of N-SEA will also include bubblesort algorithms and first fit bin packingalgorithms. Equivalent input from USand Canadian N-SEA users is similarlywelcomed. For more information, con-tact info@nag.com, 630–971–2337.

Ed Carlin has been an Advanced SkillsTeacher in Mathematics at the WallingfordSchool in Oxfordshire, UK for the past 7years. John Holden is Sales Manager forNAG (http://www.nag.com), a 30-year-old company serving over 10,000 sitesworldwide, including many leading aca-demic centers. NAG is dedicated to pro-viding cross-platform mathematical, sta-tistical and data mining components andtools for developers as well as 3D visual-ization application development environ-ments. It operates worldwide with officesin Chicago (USA), Oxford (UK), and To-kyo (Japan). Questions can be forwardedto Ed Carlin and John Holden viainfo@nag.com.

Chair, Department of Mathematics, Physics, and Computer ScienceThe Misher College of Arts & Sciences at University ofthe Sciences in Philadelphia invites applications for theposition of Chair, Department of Mathematics, Physics,and Computer Science to begin July 1, 2006. The suc-cessful candidate will have excellent interpersonal and lead-ership skills and will have the vision and ability to bring thedepartment to a new level of recognition and achievement.

The Department of Mathematics, Physics, and ComputerScience (MPCS) consists of 15 full time faculty and one fulltime staff member. MPCS currently offers the BS degree incomputer science and minors in mathematics, physics,computer science, and statistics. The faculty is committedand highly motivated to advancing the department. Plansinclude the creation of new majors and programs. The fac-ulty also participates in the interdisciplinary BioinformaticsBS and MS program and collaborates actively with otherundergraduate and graduate programs.

The new Science and Technology Center will house the department and provide a significant opportunity for thegrowth of its programs.

The Chair will provide leadership and will be responsible for the recruitment and development of faculty to achievethe teaching, research and service missions of the depart-ment. The Chair will also develop and administer budgetsand participate in leadership and planning at the collegeand university levels.

The candidate must have a PhD in an area relevant to thedepartmental disciplines, and a distinguished record ofteaching, research and service. Preference will be given tocandidates with administrative experience.

The application should include a CV, a letter of applicationthat addresses the candidate’s philosophies of teaching,research and departmental administration, and also contactinformation for at least three references. Electronic submis-sions are preferred at math@usip.edu. Alternatively, sendto: MPCS Chair Search, Misher College of Arts &Sciences, University of the Sciences in Philadelphia,600 S. 43rd St., Philadelphia, PA 19104. For questions contact Judeth Kuchinsky (j.kuchin@usip.edu, 215-596-8593). Evaluation of applications will beginNovember 1, 2005, and continue until the position is filled.

USP, founded in 1821 as the Philadelphia College ofPharmacy, is a unique health science university of 2800 students, with undergraduate andgraduate programs in the naturalsciences, pharmacy, and otherhealth related areas. Located inthe University City district, USP isclose to several major universitiesand many biotechnology andpharmaceutical corporations.

Consult the USP web site at http://www.usip.edu for additional information. AA/EOE