THE NEWSLETTER OF THE MATHEMATICAL ASSOCIATION OF AMERICA

June 1996 Rochester Reinstates Mathematics Student Volume 16, Number 3 Ph.D. Program Takes Top Prize in Department agrees to overhaulits Westinghouse Science In this Issue undergraduate teaching The University of Rochester, which announced Competition the closure of its Ph.D. program in mathemat• ics last fall (FOCUS, February 1996) has de• Jacob Lurie, an eigh• 4 More Melissa cided to reverse that decision. Ithas announced teen-year-old math• Letters a comprehensive proposal developed jointly ematics student at by the administration and key faculty in the Montgomery Blair 7 Who Teaches mathematics department, with input from other High School in the departments. the Teachers? Washington, D.C. area, claimed the top As part of the rescue package, the mathematics prize in the annual 9 A Russian faculty has agreed to a sweeping review of the courses it offers to undergraduates not major• Westinghouse Sci• Teacher in ing in mathematics, and of the department's ence Talent Search America linkages with the research specialties of fac• this spring. The Westinghouse search is gener• ulty in other departments. Discontent with the ally regarded as the nation's most prestigious science competition. This year was the fifty• department's non-majors undergraduate teach• 12 Contributed fifth in its history. Papers in ing was said to be a factor in the original deci• sion to drastically reduce the size of the It is relatively rare for a mathematician to win San Diego department and end the Ph.D. program. the top prize. Lurie, who this fall starts his col• The department will also develop a new Ph.D. legiate education at Harvard where he intends 14 Employment program in mathematics. to study mathematical logic, took as the theme Opportunities for his competition entry John Conway's sur• The new plan is enabled in part by resources real numbers. provided by the Department of Physics and Lurie is no stranger to the professional math• Astronomy, which will contribute through fu• ematics community, nor is his Westinghouse ture joint appointments with mathematics. success the first time he has found himself the PresidentThomas H. Jackson said that the new center of media attention. He was the youngest arrangement meets both the financial and in• member of the six-person U.S. team who scored structional quality goals outlined in the "Re• a perfect forty-two points in the thirty-fifth naissance Plan" for the college, announced The Mathematical International Mathematical Olympiad in Hong last November. Association of America Kong in 1994. 1529 Eighteenth Street, NW "I am happy to say that the Renaissance Plan By any standards, Lurie is an early developer. Washington, DC 20036 led to a series of unprecedented conversations At age three he was adding numbers in his head. See Rochester on page 3 He finished calculus in the eighth grade. He was just sixteen at the time of his IMO success. The Mathematical Association of America Second class postage paid at 1529 Eighteenth Street, NW Washington. DC and In addition to the honor and the recognition, additional mailing offices Washington, DC 20036-1385 Lurie's Westinghouse triumph brings him a $40,000 scholarship toease his passage through Harvard. FOCUS June 1996 FOCUS Editorial FOCUS is published by the Mathematical Association of America six times a year: February, April, June, August, October, and How Others See Us December. Angus Campbell was the chair of the Mechanical Engineering Editor: KeithJ. Devlin, Saint Mary's College of California, devlin@ stmarys-ca.edu Department at Big State University. A widely read man, he regu• larly attended seminars in English, history, biology, psychology, Associate Editor: Donald J. Albers, MAA anthropology, astronomy, economics, practically every subject you can think of-with Associate Executive Director and Director one exception: mathematics. of Publications and Electronic Services, [email protected] When he had first arrived at Big State fifteen years earlier, he had gone to the mathemat• Managing Editor: Harry Waldman, MAA, ics seminars as well. But after a few years he finally gave up. Nothing those folks said [email protected] seemed to have any relevance for him. And what is more, he could never understand enough to come away with the sense that he had learned anything whatsoever. Production Specialist: Amy Fabbri, MAA, [email protected] But then, one day, he received a notice from the Mathematics Department announcing Copy Editor: Nancy Wilson, Saint Mary's a talk on "The Mathematical Theory of Gears." College of California, nwilson@stmarys• "At last," he thought, "a mathematics talk that interests me." ca.edu Letters to the editor should be addressed to: And so, when the day came he went along. Sitting in the front row of the seminar room Keith Devlin, Saint Mary's College of in eager anticipation, he watched as the speaker took out his notes. The speaker cleared California, P.O. Box 3517, Moraga, CA his throat and began. 94575; e-mail: [email protected]. "The theory of gears with a real number of teeth is well known. So today ..." Subscription and membership questions should be directed to the MAA Customer Service Center, 1-800-331-1622; e-mail: [email protected]. The FOCUS subscription price to individual members of theAssociation is$6.00, included in the annual dues. (Annual dues for regular members, exclusive of annual subscription The above opinions are those ofthe FOCUS editor and do not necessarily represent the prices for MAAjournals, are $68.00. Student official view ofthe MAA. and unemployed members receive a 66 percent discount; emeritus members receive a 50 percent discount; new members receive a 40 percent discount for the first two New MAA Board ofGovernors Members membership years.) Copyright © 1996 by the Mathematical Association of America (Incorporated). Educational institutions may reproduce articles for their own use, but not for sale, provided that the following citation is used: "Reprinted with permission of FOCUS, the newsletter of the Mathematical Association of America (Incorporated)." David A. Sanchez Manuel P. Berriozabal Martha J. Siegel Second class postage paid at Washington, Texas A&M University University of Texas at Towson State University DC and additional mailing offices. Governor Ex-Officio San Antonio Secretary Postmaster: Send address changes to the Governor At Large MAA, P.O. Box 90973, Washington, DC 20090-0973; e-mail: [email protected], or call1-800-331-1622(U.S. and Canada only); (301) 617-7800 (outside U.S. and Canada). For advertising information, contact Joseph Watson, MAA, 1529 Eighteenth Street NW, Washington, DC 20036; e-mail: jwatson@ maa.org; (202) 387-5200. ISSN: 0731-2040 Printed in the United States of America. Katherine P. Layton Paul Zorn Beverly Hills High School St. Olaf College Governor At Large Governor Ex-Officio 2 June 1996 FOCUS

Rochester from page 1 The new proposal includes the following ments on improving the teaching of un• key developments: dergraduate mathematics, especially cal• between math faculty and the administra• culus, for non-math majors. tion, and between math faculty and their • Faculty in the Department of Physics and colleagues in other departments," Jack• Astronomy have agreed to two future joint •The mathematics department has elected son said. "That,in tum, led to the Depart• appointments with the Department of a new chair, Douglas Ravenel, who is ment of Physics and Astronomy's offer to Mathematics. This effectively provides charged with implementing the instruc• promote linkages by joint appointments, funding for one additional position to the tional program and the renewed linkages and a new dedication on the part of the mathematics department, as well as pro• with other departments. mathematics faculty to strengthen under• moting tangible linkages between these Commenting on the plan, President Jack• graduate instruction and their ties to other fields. sonsaid, ''This is a solution that fully meets departments, inconcert withallof ourother • Mathematics faculty have offered to the goals of the Renaissance Plan-the efforts." develop a plan for a smaller, high quality bottom line, as before, is that we will in• "The mathematics department fully sup• Ph.D. program, which they can operate crease the quality of our programs within ports this plan," commented Joseph with a reduced number of faculty. (The our overall budget targets-and, obvi• Neisendorfer, department chair. "It pro• Renaissance Plan had called for the num• ously, it is a happier solution for the math• vides both an opportunity and a challenge ber of tenure-track mathematics faculty to ematics faculty. to the mathematics department. We are decline from twenty-one to ten, with the "It will add luster to our undergraduate enthusiastic about the prospect of intro• ultimate addition of four to five non-ten• program and work to enhance intellectual ducing some significantinnovations which ure track faculty to teach undergraduate cooperation across disciplines while promise to diversify and enhance the un• mathematics courses for non-math majors. implementing a Ph.D. program of distinc• dergraduate experience in mathematics. I Under the new proposal, the mathematics tion. I am pleased that their active coop• am grateful that the administration has departmental size would be set at an ulti• eration-and that of the Physics and provided us with the opportunity to do this mate target of fifteen tenure-track faculty Astronomy Department-now enables us within the context of a graduate program members and there would be no hiring of to move forward in this direction." of high quality." non-tenure track faculty for instructional purposes.) The new Ph.D. program is to He added that Charles E. Phelps, univer• "This is an important development for the be developed during the next six months sity provost, and Richard N. Aslin, vice University," added mathematics profes• and will be available to doctoral students provost and dean of the college, have also sor Douglas Ravenel. "I am glad to see it in the fall of 1997. endorsed the new proposal, as has the is renewing its commitment to mathemat• Executive Committee of the university's ics, a subject lying at the heart of modem •Mathematics faculty have agreed to form board. science. Excellence in math at all levels is a committee to work with other depart- a vital asset for any research university."

David M. Wells Carl C. Cowen Peter E. Moore Bernard Sohmer Allan C. Peterson Pennsylvania State Purdue University Nothern Kentucky The City College University ofNebraksa University, New Indiana Section University (CUNY) at Lincoln Kensington Kentucky Section Metro New York Nebraska-SE South Allegheny Mountain Section Dakota Section Section

James T. Smith Darryl McCullough Janet Heine Barnett Charlotte J. Chell San Francisco State University of Okla• University of South• Carthage College University homa, Norman ern Colorado Wisconsin Section Northern California Oklahoma-Arkansas Rocky Mountain Section Section Section 3 FOCUS June 1996

More Melissa Letters Dear Dr. Devlin, Icompleted a twenty-four-year high school In my editorial in the April 1995 FOCUS, I told the story of my then sixteen-year-old math teaching career two years ago and daughter Melissa, whose extremely high intelligence was scholastically hindered by had the good fortune to be allowed to teach a learning disability. With a measured cognitive ability in the 99.9 percentile, at the high in an exceptional school fifteen of those school she was earning low grades, and a professional diagnosis of her learning disabil• years. I had several Melissas in my classes. ity notwithstanding, she was regarded by most ofher teachers as simply a lazy, not-too• bright student. My wife and I removed her from the school and enrolled her at the One Melissa closely resembled yours. selective four-year college where I work. whereupon she immediately ran up a 4.0 Julianne wasn't quite as mathematically GPA. precocious, but in her world of geology and civil engineering, she had few equals. Following my editorial, letters poured in from FOCUS readers all across the nation, Her father was assistant head of the con• telling ofsimilar tales of woe, and in the October FOCUS I printed a number ofthem. struction team for Chicago's celebrated Letters continued to come in, and as I travel around to MAA section meetings around Deep Tunnel project which gathers and the country, members tell me ofcases they know of. Here, for one last time, is another stores excess runoff rainwater and later selection of letters on the issue. pumps it into the waterways. Julianne worked summers on Deep Tunnel as an -Keith Devlin engineering assistant, gofer, and assistant on tours of visiting engineering dignitar• ies down in the hole. Once, in an emer• gency, she led a tour for a group of Japanese civil engineers. Hair tucked in a hard hat Dear Dr. Devlin, and clad in hip boots and the usual con• I read your editorial in the April 1995 tion which he therefore failed to answer struction coat, no one suspected a "mere" FOCUS with interest. We, too, have a child and for which he lost all credit. What ap• sixteen-year-old school girl was in charge who was identified during his pre-college palled me even more than his teacher's (answering technical questions, etc.). Back days as "learning disabled." In some ways lack of cooperation with respect to spac• above ground, she took off the hat and our stories have similarities, but there are ing for the tests, however, was his insis• shook out her hair. Before the coat was significant differences as well. I am a pro• tence that if the proof was not the one in off, the excited murmurs and applause fessor of mathematics, albeit not at a pres• the "answerbook," it was wrong. Our ere- . began. The mayor even heard of this ex• tigious institution, nor am I president of a ative son and his similarly inclined class• ploit. national mathematical association. Welive mates were repeatedly penalized for proofs Back in school, in my honors level third• in a small Ohio town which has a pretty that were not exactly as the author had year algebra-trigonometry class, Julianne average high school. Our son Tom is not stated them, even if they were logically just couldn't quite keep up. She had time mathematically gifted, but he does have correct! to do only half the homework problems. average intelligence and shows some un• Her class participation was a teacher and usual, even brilliant, insights at times. There is no doubt that similar scenarios are repeated many times over in this coun• student's dream, always on track and of• Other parents may have taken more seri• try. Because of my encouragement, Tom ten revealing everyone's unspoken diffi• ously the school's repeated admonition culty. She pleaded for more time on tests. that he did not belong in college prepara• believes that he is good at mathematics and did not let the D's and C's he received By now I knew my customer, and by co• tory classes. However, we all persevered in that class dampen his enthusiasm for incidence, we both had lunch scheduled and he happily has his bachelor's degree the very next period. So Julianne and I in speech communications. the subject. Few other parents would be able to evaluate such reasoning, and the slipped into a neighboring physics lab It is Tom's high school experience in a judgment of the teacher is what would where we sat while she finished her ex• geometry class which I recalled as I read stand instead. You are not alone in your ams and I finished peanut butter sand• your story. Tom's writing was large and observation and concern. Although there wiches. Her scores were exemplary. A few awkward. In Englishclass he compensated are certainly some excellent, knowledge• colleagues complained, but the school by typing his work. but math teachers had able, and cooperative high school teach• principal supported me completely. Stu• a challenge reading what he wrote, I'll ers, we still have a good deal of work to do dents who knew also thanked me. What readily admit. His IEP indicatedthat teach• to prevent more of these tragedies. more could a teacher want? Julianne had ers were to be sure he had sufficient room the wit to write an award-winning science and time in which to do his work. The Thanks for sharing your experience. fair research report and also use it for an geometry tests unfortunately had limited Sincerely, honors level English class research report. space for proofs and the teacher made no Her idea; no one else ever discovered that Delene Perley concession to requests for more space. I ploy. What handicap? Wooster, Ohio rememberwell one test where Tom's proof In his letter (October 1995 FOCUS, p. 4), took up the space of the entire next ques- Dave Connor makes a very cogent obser-

4 June 1996 FOCUS vation; I fear it won't go away. To a grow• berg and Wilson (1992) have demon• times are engaged by parents who feel that ing extent mathematics, like intelligence, strated, the ten most commonly used stan• theirchildis misunderstoodor unrealized. is becomingoperationallydefinedin terms dardizedtests do not align well with school Such occurrences take place when you of the national and international exams mathematics curricula that are conceptu• teach prior to the college level. administeredin schoolsand colleges,ACT, ally based. Roger Pinkham, in his letter, stated, "I SAT,AP,AHSME, and the many state tests In his letter, Dr. Green wrote,".. .I, too, am spendan enormousamountoftime directly devised with the cooperation of NCTM a mathematician and do not wish to ap• and indirectly ironing outthe wrinkles put and its state affiliates to measure school pear too pushy in solving this problem." in their minds by some poorly prepared and teacheraccountability. Test results are As a mathematics educator who is not a high school teacher." No doubt there are taken as measure ofeducational progress, research mathematician, I urge mathema• such teachers and I appreciate Roger's which directly affect budgets and teacher ticians such as Dr. Green and yourself to patience in rectifying the situation. At the salaries. School systems demand "teach• become more "pushy!" Without such a same time, FOCUS needs to recognize the ing for the test." One very real reason why push from the research mathematics com• excellencewhichexists in secondary math other nations excel in international com• munity, I hold little hope for the prospect instruction. parisons is the fact they hide all but the of a widespread move away from school brightestwhen such tests are administered. When one of the math teachers in my de• mathematics as a sequence of rote proce• In the USA, a participating school is very partment left our high school to teach at dures and toward school mathematics as a likely to treat such a test as just more in• the college level, he was inundated by stu• means of making sense of things. terruption and administeritto everyone in dents who responded to his teaching. His the building, special education on up. We Sincerely, competence and skills of communication reveal oureducational bumps and bruises; were appreciated by his students. Thomas G. Edwards everyone else hides theirs.... I wonder at Assistant Professor ofMathematics The Mathematics Department of the Uni• the fate of a Melissa in Japan. I'd wager Education versity of Arizona has had a program in they would deny having any. Wayne State University place whereby they use high school teach• Candor like yours is exceptionally rare, Detroit, Michigan ers to teach their beginning math courses. Dr. Devlin, and yourcourageis admirable. They have been pleased with the results Don't stop. indicating that high school math teachers exhibit strong pedagogical skills. Many Sincerely, Dear Keith, of these skills are consonant with the rec• ommendations of David S. Moore in his Larry Freeman I need to address an issue which has ap• Chicago, Illinois FOCUS article "The Craft of Teaching." pearedalmost incidentallyin FOCUS over a few issues. It has to do with the perspec• A September 1995 issue ofU.S. News and tive of the high school mathematics WorldReportconsidered the best colleges teacher. There has been no specific article and universities in the nation. It listed Dear Dr. Devlin, dealing with this topic, but references have Dartmouth College as the best teaching I have been following the case ofMelissa been made which have left me a bit un• school. Dr. John Rassias, a brilliant lan• and the resulting letters in FOCUS (Octo• easy. guage instructor at Dartmouth, is widely recognized for his teaching techniques. ber 1995, pp. 2, 4-5) with more than a When the U.S. International Mathemati• However, in a conversation with this passing interest. You see I was a high cal Olympiadteamwon first placein Hong writer, he indicated that teaching at the school mathematics teacher for twenty• Kong in 1994, a statement was made that pre-college level is more challenging and four years and am now a professional one could not infer the existence ofexcel• demanding than teaching at the university mathematics educatorinvolveddirectly in lent secondary instruction as a contribut• level. It may very well be that the best teacher education. I am well aware of the ing factor. This was an accurate statement. teaching is occurring not at Dartmouth or frustrations involved in attempting to However, one logically could not disclaim Saint Mary's, but at the pre-college level. change the status quo. it either. We should remain agnostics in In defense of the secondary teachers, not this regard. It is not important where the best teaching is taking place, but that we all teach well. only are they a product of a post-second• Your editorial about Melissa was touch• Ken Ross stated as much: "I believe that ary education that we provide, but they ing and thoughtful. Undoubtedly you were we are all in this together and that we need often work under tremendous pressures correct in many of your analyses of the to work together to maintain momentum that support the teaching of mathematics problem. The teacher involved certainly and establish better mathematics educa• in ways that are more procedural than could have been incorrect in her proce• tion for all." conceptual. A chiefculprit here is the pro• dures. However, such statements as "On liferation ofstandardizedtesting inAmeri• top of that, Melissa's father is a profes• Philip D. Evanstock can schools. It is all too easy for some sional mathematician....How coulda high Mathematics Chair school administrators to equate a strong school mathematics teacher get it so Trevor G. Browne High School mathematics program with high scores on wrong?...do nothing to solve the prob• Phoenix, Arizona standardizedtests. Unfortunately, as Rom- lem." High school math teachers some-

5 FOCUS June 1996 Dear Professor Devlin, Dan Kalman Appointed MAAAssociate I read your editorial about your daughter's experience in high school mathematics. You ask, "What if there are hundreds and Executive Director thousands" of students having similar The MAA is pleased to announce that Professor Dan Kalman has been appointed experiences. As far as the experience of Associate Executive Director for the MANs Member Services and Programs Depart• being taught that "mathematics was about ment. He has received a leave of absence, beginning in July, from American Univer• the mastery of dull, mindless, algorithmic sity where he is assistant professor of mathematics. procedures," I believe that is today the universal experience of American high Kalman has served as associate editor of Mathematics Magazine, program chair and school students. (Of course there are ex• second vice chair of the MAA's Southern California Section, and as a member of ceptions, but I don't believe they can add various national committees. He is a prolific author and has written articles for MAA up to even 5% of the whole.) I don't en• journals, including three for Math Horizons. In 1994 Kalman was awarded the pres• tirely understand how that isaccomplished tigious George P61yaAward for the article "Six Ways to Sum a Series," published in in the geometry course. But to see that it is the College Mathematics Journal. being done in the algebra courses, one need Professor Kalman received his Ph.D. and M.A. from the University of Wisconsin, only read some widely used high school Madison, and his B.S. from Harvey Mudd College. Prior to joining the faculty at text. Each new section is preceded or fol• American University, he served as an applied mathematician at The Aerospace Cor• lowed by a statement of that section's ob• poration in southern California. Kalman also taught mathematics at Lawrence Uni• jectives, which are almost all algorithmic versity,the University of Wisconsin, Green Bay,andAugustanaCollege, South Dakota. in nature. There often are some objectives that refer to "thought" or "understanding," but they are few and non-operational; they are not needed for doing almost all of the homework exercises and they arenot tested think some, because you have to discuss when I took most of a year off from my for in the class tests. issues-though you can mostly repeat research work to teach at a branch of the University of Maryland. I got into conver• I returned to college teaching eight years arguments the teacher discussed. But in sations with one professor of education, ago, after a long time in a government lab. math class you're not supposed to think. and, coincidentally, with a young assis• I teach at Temple University, which is You're supposed to memorize the proce• tant professor of psychology. The latter something like a state university serving dures for solving different problems, and was a student of Skinner's, I believe, and the Philadelphia area primarily. The stu• try to recognize the words that tell you he spent a lot of time trying to convince dents are mostly of working class or lower which procedure to use for which prob• me that one must not speak of "mental middle class background and they vary lem. states" or "thought" or "understanding." widely in ability; admission standards are Up to now, the only answer I've gotten is The professorof education's specialty was not high. When I started teaching them I "yes." math ed; and he told me the current view was rather happy with them. I found them was that educational objectives should be conscientious and hardworking, if often Melissa was unfortunate in being involved completely "objective," i.e., behavioral. mathematically weak. (Each class also with the school's bureaucracy (the special One should not say, "This lesson's pur• contained quite bright students.) It took education director), and fortunate in hav• pose is to bring the student to under• me several years to realize what they were ing you to rescue her.But as far as I can see stand ... ," rather,"This lesson's purpose is working hard at. Itsimply did not occur to all students who don't have an individual to make the student able to do the follow• me, for years, that they were filtering out outstanding teacher, and who don't go to ing ...." all my exposition of ideas and explana• a special school like Bronx High School of Science, are being taught not to think in tions of reasoning and trying their best to Of course a much bigger factor may be math class. Those to whom abstract learn what they thought the courses were that it makes it easier to pass students who thought is more onerous than pleasurable about: certain procedures for solving cer• have learned very little. tain problems. Their effort went into simply accept that. Those who have previ• Incidentally, "mastery of... mindless... memorizing mathematical words and ac• ously come to enjoy thinking don't sim• procedures" is not itself a mindless pro• tivities. ply stop thinking-though they may simply be turned off from mathematics. I cess. Like memorizing a long list of unre• I finally formulated a question which I get bright students in the "core" math lated words, it may need real mental effort. started asking high school teachers I am course who have been avoiding math in And training people to do it may perhaps acquainted with: college; when they are finally forced to prepare them for their future (low-level) careers. Is the following a correct description? In take some, they do think about it and some• times ask, "Why is that so?" high school, students are taught that for Sincerely, English class you have to think, because How did this style of teaching math come Seymour Haber you have to make up and write composi• about? One factor that may have helped Merion, Pennsylvania tions. And in social studies you have to some is an educational theory I heard about 6 June 1996 FOCUS Who Teaches the Teachers? Jack Price

A colleague in the mathematics depart• ics community addition, many universities have estab• ment mumbled to me the other day that as awholeisbe• lished faculty development centers that the new students were worse prepared ginning to un• stress good teaching as well as alternatives than ever. He wanted to know, "What are derstand the to full-time lecturing. those teachers doing out there?" I'm cer• importance of The bottom line is this:Weexpect the teach• tain that his comments are not unique. teaching and ers we prepare to prepare in tum excellent (As a matter of fact, I don't believe that teacher educa• mathematics students. Therefore we must they are entirely true. Our high schools tion. The Asso• make certain that the teaching we in the are graduating more better-prepared stu• ciation for colleges and universities show them in our dents who go to college.) My less-than• Mathematics Teacher Educators was mathematics and mathematics education helpful answer was, "Who prepared their formed specifically to improve mathemat• classes is a model of what we want them to teachers? ics teacher education. The Mathematics and do. So what is part of the answer to why As with many universities, our mathemat• Education Reform Network, the Math• teachers aren't better prepared? Perhaps, ics departmentdraws many students from ematical Sciences Education Board, the in the words of the great philosopherPogo, the high school classrooms of teachers American Mathematical Society, and the "We have met the enemy and he is us." we have prepared. The Professional Stan• MathematicalAssociation ofAmericahave This was reprintedfrom the January 1996 dards for Teaching Mathematics is testi- . all recognized that mathematics teaching issue ofthe NCTM News Bulletin. mony to the idea that what students learn at all levels must be improved. The recent Recognition and Rewardsbooklet produced is intimately connected to how they are Jack Price is president of the National taught. If some teachers are not doing by the Joint Policy Board for Mathematics promotes teaching as an important aspect Council ofTeachers ofMathematics. The well, is it because they are simply emu• e-mail address for NCTM is infocentral of the retention, tenure, and promotion lating what they have learned from us? It @nctm.org. is encouraging to see that the mathemat- policies of colleges and universities. In

Workshop for Women Graduate Students and Postdoctoral Mathematicians Over the past eight years, the Association of their careers. The workshop will also approximately the last five years, whether for Women in Mathematics has held a include a panel discussion on issues of ca• or not she currently holds a postdoctoral series of workshops for women graduate reer development and a luncheon. An in• or other academic position. All non-U.S. students and recent Ph.D.s (referred to as troductory dinner and discussion period citizens must have a current U.S. address. "postdocs" below) in conjunction with will be held on the Thursday evening prior All applications should include a curricu• major mathematics meetings. to the workshop. All mathematicians (fe• lum vitae, a concise description of re• male and male) are invited to attend the search, and a title of the proposed talk! Supported by the Officeof NavalResearch Saturday program even though funding is poster.All applications should also include and the AWM, the next workshop in the provided only for twenty women graduate at least one letter of recommendation; in series will be held in conjunction with the students and postdocs. Departments are particular, graduate students should in• annual Joint Mathematics Meetings (Janu• urged to help graduate students and clude a letter of recommendation from ary 8-11, 1997) in San Diego, California, postdocs obtain some institutional support their thesis advisors. Nominations by other on Saturday, January 11, with an intro• to attend the workshop and the associated mathematicians (along with the informa• ductory dinner on Thursday, January 9. meetings. tion described above) are also welcome. We invite each participating graduate stu• We also seek volunteers to lead discussion Send five complete copies of the applica• dent to presenta posteron her thesis prob• groups and to act as mentors for workshop tion materials (including the cover letter) lem and each postdoc to present a talk on participants. Ifyou are interested in volun• toWorkshop Selection Committee,AWM, her research. The AWM will offer fund• teering, please contact the AWM office. 4114 Computer & Space Sciences Build• ing for travel and two days' subsistence ing, University of Maryland, College Park, for up to twenty participants. Participants To be eligible for funding, graduate stu• MD 20742-2461; (301)405-7892; e-mail: will have the opportunity to present and dents must have begun work on a thesis [email protected]. The application discuss their research and to meet with problem. "Postdoc" refers to any mathema• deadline is September 1.Applications via other women mathematicians at all stages tician who has received her Ph.D. within e-mail or fax are not acceptable.

7 FOCUS June 1996 Vivienne Malone-Mayes, Pathfinder Etta Z. Falconer and Lee Lorch She was the first the organizations specifically devoted to the problems of minorities and women, Vivienne Malone-Mayes was born in Black elected to there she was too. With skill, integrity, Waco, Texas, February 10, 1932, and died the Executive steadfastness, and love, she fought racism there on June 9, 1995. She leaves a daugh• Committee of the and sexism her entire life, never yielding ter,Patsy Mayes-Wheeler of Dallas, Texas, AWM and served to the pressures or problems which beset and other family members. on the Board of Directors of the National Association of Mathematicians (oriented her path. She leaves a lasting influence. In An excellent student all her life, Vivienne toward the Black community in the math• her premature death we have all lost. In• graduated from a segregated Waco high ematical world). She was a member of the spired by her life, we are bereaved at the school at sixteen years of age. She earned AMS, the NCTM, and the MAA, and was loss of a loving and beloved friend. a B.A. in 1952 and an M.A. in 1954, both elected a director-at-large for the Texas Memorials can be sent to the Vivienne from Fisk University in Nashville, Ten• Section of the MAA. In addition, she Lucille Malone-Mayes Scholarship Fund, nessee. At Fisk, she had courses from Dr. served as director of the High School Lec• c/o LaNelle McNamara, 501 Franklin Evelyn Boyd Granville, one of the first ture Program for the Texas MAA. Ave., Suite 501, Waco, TX 76701. two African American women to receive the Ph.D. in mathematics. She returned to Her last attendance at the Joint Mathemat• A longer version of this memoriam ap• Waco to serve as chair of the Mathematics ics Meetings was in 1993 in San Antonio. peared in the November-December 1995 Department at Paul Quinn College (1954• This was a particularly joyous reunion. It issue ofthe AWM Newsletter. 61). Seeking as always to expand her brought Vivienne together with Gloria knowledge, she applied to take some Hewitt, the two of us, and, above all, with Etta Z. Falconer and Lee Lorch met courses at Waco's Baylor University, only Evelyn Boyd Granville whom she had not Vivienne Malone-Mayes at Fisk Univer• to be rejected explicitly on grounds of race seen in many years but whose inspiration sity. Etta Falconer teaches at Spelman (1961). The University of Texas at Austin, she never forgot. College inAtlanta, Georgia and is associ• already required by federal law to deseg• She was in the struggle to make the path ate provost for science. Her e-mail ad• regate, admitted her. Overcoming major, smoother for those who followed. She dress [email protected]. Lee Lorch consistent obstacles of both subtle and made her presence in the national math• is professor emeritus at York University in blatant race and gender discrimination, in ematics community felt and respected. In North York, Ontario, Canada. His e-mail 1966 she became the fifth African Ameri• address is [email protected]. can woman to receive the Ph.D. in math• ematics (the second Black and the first Black woman to receive the Ph.D. in math• MAA President Ross Appoints Task Force ematics from the University of Texas). She later observed that "it took a faith in schol• on Publishing Education Material arship almost beyond measure to endure the stress of earning a Ph.D. degree as a MAA President Ken Ross has announced the formation of a task force to stimulate black, female graduate student." Her the• the submission to MAA publications of excellent expository material on collegiate sis, supervisedby Dr. Don Edmonson, was mathematics teaching and learning. The intention is to create a working relationship titled A structure problem in asymptotic between the experts on education in the MAA and the editors of the various MAA analysis. Part of this work was published publications which will lead to the increase of submissions of quality material on in the Proceedings ofthe American Math• education. Motivation for establishing the task force came from the demise of UME ematical Society, vol. 22 (1969) under a Trends at the start of this year. different title. Later her research interests shifted to summability theory in which she The task force has been charged to develop-jointly with the editors of the three published jointly with Dr. B. E. Rhoades. MAA journals, FOCUS, MAA Online, and MAA Notes-mutually acceptable pro• cedures for accomplishing its goals. This will include determining how best to in• She became in 1966 the first Black faculty form prospective authors what kinds of articles journal editors would like to receive. member at Baylor University, the institu• The task force may also provide any assistance editors might request in processing tion which had rejected her as a student and reviewing such material. only five years previously. There she spent the rest of her teaching career, retiring The task force, which former UME Trends Editor Ed Dubinsky has agreed to chair, because of ill health in 1994. is to complete its work by the end of 1997. Other members include the chair of the Coordinating Council on Education, the chair of the Coordinating Council on Pub• Throughout the years, she maintained a lications, and the editor of each of the Monthly, Mathematics Magazine, the College high level of activity in mathematical, Mathematics Journal, FOCUS, MAA Online, and the MAA Notes series. community, and religious organizations.

8 June 1996 FOCUS

very democratic, par• ARussian Teacher ticularly that children of "proletarians" would begiven unlimitededu• inAmerica cational opportunities. Andrei Toom Children of manual workers and poor peas• Part Oneof Two ants really were given privileges to enter all This article originallyappearedinthe June kinds of schools, and 1993 issue ofthe Journal of Mathematical professors who gave Behavior and then in the Fall 1993 issue them bad grades might ofAmerican Educator. It appears here in be accusedof anti-revo- slightly different form, presented in two lutionary activity. Only Andrei Toom at the blackboard. installments. The second installment will a generation later, Rus- appear in the next issue ofFOCUS. sia had thousands of hastily coached engi• "criticized bourgeois society." Mark I am a Russian mathematician and teacher. neers and scientists of proletarian descent. Twain, Jack London, Ernest Seton, O. For nearly twenty years I did research and One of these "proletarian scientists," an Henry, Edgar Allan Poe, Paul de Kruif, taught students at Moscow University. academician named Lysenko, gave fan• Ernest Hemingway, and Ray Bradbury Now I have moved to the United States, as tastic agricultural promises that he never were among my favorite authors. have many other Russians. This article is kept. However,Lysenko impressed Soviet I vividly remember reading a book about about some of my experiences of teaching rulers from Stalin to Khrushchev because a scientist who proved that insects have both in Russia and America. they also were pseudo-educated. A major no reason; they only have instinct. What branch of biology, namely genetics, was The Evil Empire declared a "bourgeois pseudo-science" he actually proved was that the behavior of insects was effective only in situations Americans' ideas about Russia are as con• because Lysenko was against it. tradictory as Russia itself. For many years usual for them. When the experimenter Soviet Russia was perceived as "The Evil The ambitions of pseudo-educated "pro• artificially arranged unusual situations, the Empire." On the other hand there was a letarian scientists," their haughtiness to• insects did the same standard movements Sputnik movement in America which ward bourgeois science, their pretensions although they evidently could not be of claimed that the Russian educational sys• of superiority because of having had poor any use in that new situation, because it tem was much better than the American parents and being led by "the world's tru• was different from those to which the in• one. Obviously these images did not fit est teaching" (that is, Marxism) caused a sects had become accommodated through together. A lot of effort is needed to give lot of industrial and ecological disasters. evolution. I was impressed. I understood the real picture. I am just going to make a However, Communists never admitted the that propaganda tried to tum us into some few comments to explain my background. true causes of these disasters; all of them kind of insects. I thought then and think were attributed to some "enemy" sabo• now that it is a most important duty of a Communist rule in Russia emerged from tage. A number of alleged "enemies" were teacher of humans to teach them to be the collapse of the obsolete Tzarist autoc• arrested and reportedly confessed. Masses humans, that is, to behave reasonably in racy, under which most people were de• of people, although declared "educated" unusual situations. When I taught in Rus• prived of education. Early Communists by that time, believed these reports. But sia, I was thanked most explicitly for this. enthusiastically sang the "International" disasters continued, and to explain them But I met a lot of resistance from some of which claimed, "Who was nothing will away theauthoritiesneeded more andmore my American undergraduate students, become everything." Nobody ever knew "enemies." Meanwhile Russia became the especially when I tried to give them some• what it meant exactly, but many were ex• world leader in wasted resources and pol• thing unexpected. On tests, they wanted cited. Many Russian revolutionaries sin• luted environments. Chernobyl isjustone to do practically the same as what they cerely believed that it was their mission to example. had done before--only with different nu• redress all the social injustices immedi• I was eleven when Stalin died. For many merical data. This is why I decided to write ately, but ignorance crippled all their ef• this article. forts. A telling example is described in the years all Soviet people, especially young• novel Chapayev by the Russian writer sters, had been indoctrinated that they Productive Thinking Furmanov. The hero Chapayev, a Red should never doubt the Communist tenets. I always believed that really good educa• Army commander, insists on giving an All media had been filled with verbose tion is the most valuable contribution that official certificate of competence in medi• praises to Stalin who was called "the great• intellectuals of a country can make toward cine to a poorly educated man, naively est genius of all times and all peoples." its democratization. Remember that the thinking that having such a certificate re• However, much of Russian and foreign great French Revolution was prepared by ally makes one a doctor. literature was available, including Ameri• the Age of Enlightenment. It was evident that the worst features of Soviet rule were Communists made promises that looked can authors. Foreign authors were pub• lished under the pretext that they connected with the power of the pseudo- 9 FOCUS June 1996 educated who got their certificates for study of sciences, but they expected intel• problems. When I advised Ph.D. and other being "proletarians," but cared only for lectual efforts of me, and it was important. students, I gave them problems that inter• their careers. Understandably Soviet au• ested me, and we solved them together. Later my school teacher of mathematics, thorities always were suspicious about The main pressure that students put upon Alexander Shershevsky, helped me a lot. independent thought and real intellectu• teachers was to tell them something new. He strived to become a mathematician, als. but could not obtain a research position Wheneverthe purpose oflearningwas real In return, good teaching, intended to de• because in his student years he had gotten competence, it had nothing to do with good velop real competence of students, always into some political trouble. (The trouble standing with the authorities, who were had a flavor of resistance to Soviet au• must havebeen minor,otherwise we would feared and despised by intellectuals. thorities, as it involved realism, open• never have seen him again.) I was espe• Grades were just a nuisance like any ex• mindedness, and critical thinking. When cially impressed by his responsible atti• traneous control. For example, when I a good mathematics teacher tried to move tude to his mission. He urged me to attend taught in the college organized by his students to think independently, he was informal classes in mathematics at Mos• Kolmogorov, I simply gave an A to every aware that his real influence went far be• cow University.The main business of these student because all of them deserved A yond mathematics: he tried and succeeded classes was solving nonstandard problems. according to average Russian standards to keep alive the critical spirit. Learning Students werefree to drop in and out. Using and I wanted to save them the trouble of recipes without thinking was associated this I changed several groups until I found dealing with the authorities. But they knew with the Communist tyranny; learning to a teacher, Alexander Olevsky, who I liked perfectly well that we expected much more solve nontrivial problems was associated most. Every year students at Moscow of them than of the average students and with independence and criticism. For this University arranged acompetitionfor high they worked very hard. reason, for example, George Polya's writ• school students in solving problems. Each Every advanced school where independent ings on teaching were perceived in Russia problem was new and unlike others and and creative thought was cultivated be• as books on open-mindedness and critical demanded a nontrivial idea and a rigorous came a breeding ground for political dis• thinking rather than juston the teaching of proof to solve. There were five problems sent. The mathematics department of mathematics. We knew that P6lya was not and five hours to solve them. Typically Moscow University was no exception. alone. He referred to other scientists, for everyone who solved at least one problem From time to time there were political example to Max Wertheimer's notion of was rewarded. In this way I got several clashes there and I took part in them. This "productive thinking." prizes. This convinced me that I could caused me problems with the Soviet au• succeed as a mathematician. When I In the years of Khrushchev's liberalism, thorities and eventually led to my emigra• moved from high school to the mathemat• some new foreign books also became tion. ics department of Moscow University, available in Russia. Russian thinkers read solving problems naturally led me to re• very attentively all the foreign authors they Emigration search. could find.Many valuable ideas came from In 1989, quite by chance, I was allowed to Americans: authoritarian personality Everyone ShouldBe a Teacher accept an invitation to Italy. Once there, I decided not to go back. I would accept all (Theodor Adorno); group pressure From my first year in the university I took the invitations I had to other universities. (Solomon Asch); obedience to authority it for granted that a competent mathema• From Rome I went to Rutgers University, (Stanley Milgram). Eric Berne's Games tician should participate in the teaching of then to other American universities. Fi• People Play moved us to see which dirty mathematics because I had excellent ex• nally I got a regular position at Incarnate games our rulers played with us. Thomas amples tofollow.The famous Kolmogorov Word College, where I am now, but it Kuhn's book about scientific revolutions organized a mathematical college affili• would be premature to write about my was about ideological revolutions for us. ated with Moscow University, and I taught experiences here. Milton Rokeach's idea of open and closed there. Academician Gelfand organized a minds opened our minds. John Holt'scriti• School by Correspondence, and I in• It is a common opinion that the United cism of American schools made us under• structed its teachers. In the computer club, States of America supports democracy. stand that our schools deserved much I headed the teaching program. Democracy always was connected in my harsher criticism. Aleksandrov, Arnold, Boltyansky, mind with good education for all people, My parents belonged to artistic circles, and Dobrushin, Dynkin, Efimov, Kirillov, and I knew that American thinkers also pressure of censure was a constant theme Postnikov, Sinai, Tzetlin, Uspensky, the believed in this connection. Thus when I of conversations. If trimming a tree went Yaglom brothers, and other first-class came to this country, I expected to have too far, they would say with regret, "Look mathematicians were willing to lecture and rich opportunities to teach students to think how we have edited this tree!" Exact sci• to communicate with students. A lot of critically, independently, and creatively, ences provided the greatest available de• new and original problems from all and to solve nonstandard problems with• gree of independence from authorities, and branches of mathematics and at various out hindrance from authorities. levels of difficulty were invented for all my parents spoke with envy about math• My first experience in teaching in this kinds of students from young children to ematicians who could afford to say the country did not contradict this expecta• graduate students and young profession• exact truth and even be paid for it rather tion. It was proposed that I give a course als. Now I was among those who invented than punished. They could not guide my called "Analysis of Algorithms" to gradu-

10 June 1996 FOCUS ate students of the computer science de• them with good grades. partment of Boston University. The text• Cryptology and book Introduction to Algorithms by But in the next year when I came to a huge Cormen, Leiserson, and Rivest was ex• state university and started to teach the so• Mathematics: A cellent. The department applied to me a called business calculus ("Calculus II for wise rule-to give full freedom to the lec• Business and Economics") to undergradu• Dynamic Partnership turer-and I used it to the benefit of my ates, I got into an absolutely new situa• students as I understood it. In one semes• tion. All my ideas about teaching students Allegheny College, Meadville, PA ter I covered most of that rich book. I be• to think became completely out of place. July 8-12, 1996 lieve that the mathematical introduction Never before had I seen so many young The speaker will be Dr. Richard Shaker. was especially useful: I filled many gaps people in one place who were so reluctant Fees are $150 for the registration and in my students' former education. My nine• to meet challenges and to solve original $130 for room and board (Sunday teen students came from alloverthe globe, problems. All they wanted were high evening, July 7, through Friday lunch, and most of them collaborated with each grades and they wanted to get them with a July 12). For further information, con• other in an excellent way.After every lec• conveyor belt regularity. Suppose that a tact George Bradley, Dept. of Math and ture, they came to one room, discussed the worker at a conveyer belt gets inspired by Computer Science, Duquesne University, problems that I gave them, and solvedthem some interesting idea and tries to imple• Pittsburgh, PA 15282; (412) 396-5115; together. Some problems I gave them were ment it into his work. You can guess that e-mail: [email protected]. from the book, some were invented by me. he will get into trouble. This is what hap• I tried to miss no opportunity to make my pened to me when I started to teach Ameri• students think and they accepted it. Also can undergraduates. I will describe my Science Linkages there was no problem with grades. The experience in the next article in this series. department gave me carte blanche and I Andrei Toom is an associate professor at used it benevolently: almost all of my stu• in the Community Incarnate Word College in San Antonio, dents learned a great deal and I rewarded Texas. AAAS Workshops These workshops are directed at educa• AudienceAsserts Discriminatory Grading tors in schools, colleges, community• based organizations, and churches. Each Persists workshop is a day and a half. The regis• tration fee for each is $125 for the entire Dave Boliver, Pat Kenschaft, Fran Most complaints from the audience were workshop or $15 to attend the network• Rosamond of male professors favoring males, while ing reception held on the first day. The at least one was of a female professor fa• A skit staged during the Joint Mathemat• registration fee includes meals and many voring males with higher grades for the ics Meetings portraying gender discrimi• useful publications and giveaways. For same work and one of a female professor nation is all too common in real life, more information, please contact Patricia favoring females with higher grades for according to its audience members. A. Thompson, project assistant at the the same work. We, the leaders of the pro• sue Institute; (800) 351-7542. Meant to open mathematicians' eyes to gram, noted that much of the undesirable the perception of gender discrimination, behavior portrayed in this and other skits AAAS Intouch with Preschool Science the skit, put on by the Committee on the may be attributable to general insensitiv• Workshop is designed for individuals Participation of Women, had a male and ity, social ineptness, loyalty to friends, or interested in adding hands-on science ac• female answering testquestions essentially thoughtless cultural patterns. "Micro-in• tivities to their preschool programs. the same way, yet the woman received a equities" smack of moral turpitude and Radisson Hotel Metrodome lower grade. When the male offered to go should not be overlooked. As one method Minneapolis, MN with her to the professor, she declined, of fighting this type of micro-inequity, we June 13-14 and saying that his grade would likely be low• suggest that if both students agree to have ered while hers would never be raised. their papers copied, the incident can be re• AAAS Headquarters Eventually, the female drops out of the opened after the students are graduated and Washington, DC doctoral program when she is told no one "safe." Pairs of papers can be saved and October 3-4 on the senior faculty will become a accumulated by a department chair after AAAS Teaching Science to Students female's dissertation advisor. the perpetrator has been warned. with DisabilitiesWorkshopis designed for teachers and community leaders who The house audience was instructed to dis• Dave Boliver teaches at the University of work with disabled youth. cuss the skit in groups and report back. Central Oklahoma. Pat Kenschatj teaches Members, including undergraduates, at Montclair State College (e-mail: AAAS Headquarters graduates, and faculty, reported and cor• [email protected]). Washington, DC roborated similar events in their recent Frances Rosamon teaches at National June 5-6 experiences. University.

11 FOCUS June 1996 used in the classroom, and how to teach assignments, and projects would be wel• MAA Contributed history of mathematics courses. To con• come. tinue the theme of this institute, this ses• Environmental Mathematics • sion invites contributions from individuals Papers inSan Diego Getting it into the Curriculum who have taught history of mathematics The MathematicalAssociationofAmerica in innovative ways or who have used his• Thursday afternoon and Friday afternoon and the American Mathematical Society tory in their classes to support current Ben Fusaro,* Florida State University, will hold their annual joint meetings from changes in curricula, pedagogy, and the Dept. of Mathematics, Box 3027, Talla• Wednesday, January 8, 1997 through Sat• mathematical preparation of teachers. hassee, FL 32306; (904) 644-9717; fax: urday, January 11, 1997 in San Diego, Teaching the Practice of Statistics at (904) 644-4053; e-mail: fusaro@ California. The complete meetings pro• math.fsu.edu gram will appear in the October 1996 is• All Levels sues of FOCUS and theAMS Notices. This Friday morning and Saturday morning Patricia Kenschaft, Montclair State Uni• versity preliminary announcement is designed to K. L. D. Gunawardena,* University of alert participants about the MAA's con• Wisconsin, Oshkosh, Department of Math• We invite presentations that apply math• tributed papers sessions and their dead• ematics, Oshkosh WI 54901-8631; (414) ematics to the environment. We seek pa• lines. 424-1056; fax: (414) 424-7317; e-mail: pers that can serve as the basis for Please note that the days scheduled for [email protected] classroom modules, and precalculus mod• eling is especially welcome. Our goal is to these sessions remain tentative. The orga• Anne D. Sevin, Framingham State Col• develop materials that will appeal to the nizers listed below solicit contributed pa• lege, and Chitra Gunawardena, Univer• environmental awareness of our students pers pertinent to their sessions; proposals sity of Wisconsin Centers-Fox Valley should be directed to the organizer whose and convince them that mathematics is name is followed by an asterisk (*). For This session will present papers related to effective in solving problems that they, additional instructions, see Submission teaching the practice of statistics at all and society at large, believe are impor• Procedures below. levels, especially in courses beyond the tant. (Sponsored by the Committee on introductory course. For this session, the Mathematics and the Environment.) Sessions generally must limit presenta• organizers invite papers which focus on Needed Connections: Preparation of tions to ten minutes, but selected partici• teaching statistics to mathematics majors, pants may extend their contributions up to use of technology in statistics courses, and Teachers K-12 twenty minutes. Each session room con• innovative teaching techniques. Submis• Friday morning and Saturday afternoon tains an overhead projector and screen; sion of proposals via e-mail is preferred M. M. Lindquist,* Columbus College, blackboards will not be available.Youmay by the organizers. request one additional overhead projec• Dept. of Math, 14 Seventh St., Columbus, tor, a 35mm slide projector, or a 112-inch Interdisciplinary Courses-Integrat• GA 31901-5465; (706) 568-2255; fax: or 314-inch VHS VCR with one color ing Mathematics and Other (706) 323-6531; e-mail: Iindquist maryts monitor.Persons needing additional equip• Disciplines cc.csg.peachnet.edu ment should contact, as soon as possible, Saturday afternoon C. Patrick Collier, University of Wiscon• but prior to October 24, 1996, Donovan sin-Oshkosh, and Albert D. Otto, Illinois Agnes M. Rash,* St. Joseph's University, H. Van Osdol, Department of Mathemat• State University ics, University of New Hampshire, 5600 City Ave., Dept. of Math and Compo Science, Philadelphia, PA 19131-1395; There are many types of connections Durham, NH 03824; e-mail: needed to prepare students to become [email protected]. (610) 660-1562; fax: (215) 473-0001; e• mail: [email protected] mathematics teachers: connections among The Uses of History in the Teaching of many stakeholders-the schools, the Sandra Fillebrown, St. Joseph's Univer• Mathematics mathematics and education departments, sity and the community as they plan and imple• Saturday morning and Saturday afternoon The mathematical community is being ment programs; connections within math• Florence Fasanelli, * Mathematical Asso• challenged to make mathematics more ematical topics, between mathematics and ciation of America, 1529 Eighteenth relevant to students in other disciplines other disciplines, and with applications; Street,N.W., Washington DC 20036-1385; and to make explicit the ways in which connections between initial preparation, (800) 741-9415; fax: (202) 265-2384; e• mathematics can be of use in other fields induction, and continued professsional mail: [email protected] of study. Integration of mathematical development. Papers should address pro• Victor J. Katz, University of the District knowledge with other disciplines is one grams that are taking a new look at con• of Columbia, and V. Frederick Rickey, way to enhance learning. This session in• nections. vites papers on experiences in teaching Bowling Green State University Innovations in Teaching courses that fully integrate mathematics An NSF-supported MAA Institute on the with another discipline. Of particular in• Linear Algebra History of Mathematics and Its Use in terest would be papers on courses team• Wednesday and Friday afternoons and Teaching has dealt, for two summers, with taught with members of other departments. Thursday evening the history of mathematics, how it can be Papers detailing course syllabi, readings, David C. Lay,* University of Maryland, 12 June 1996 FOCUS

Department of Mathematics, College Park, forum for sharing innovations in teaching courses. Projectdirectors who have imple• MD 20742; (301) 405-5136; e-mail: abstract algebra. Although any talks fit• mented reform developmental algebra [email protected] ting this description are encouraged, those courses are encouraged to share key as• Steven J. Leon, University of Massachu• which address one or more of the follow• pects of their programs and results to date. setts, Dartmouth ing categories are particularly solicited: Submission of proposals via electronic use of models or visualization; use of com• mail is preferred by the organizers. This sesssion will focus on (1) geometric puter software; and successful pedagogi• Research in Undergraduate Math• visualization in linear algebra; (2) use of cal techniques. Where appropriate, each ematics Education technology in the course; and (3) instruc• presenter is encouraged to provide the tional strategies. Papers may treat more context, tools, method, and effect of the Wednesday morning and Friday morning than one of these areas, if appropriate. innovation being discussed. M. Kathleen Heid,* Pennsylvania State Talks on visualization should show how University, 171 Chambers Building, Uni• to introduce, motivate, or develop a topic Innovations in Courses Before Calcu• versity Park, PA 16802-3205; (814) 865• (or topics) using transparencies, physical lus: Implementing the Crossroads 2430; fax: (814) 863-7602; e-mail: models or other visual aids, or computer/ Standards [email protected] supercalculator activities. Instructional Thursday afternoon and Saturday after• David M. Mathews, Central Michigan strategies should be innovative and suc• noon cessful methods for organizing or present• University Ray E. Collings, * Dekalb College, Cen• ing the course. We solicit research papers which address tral Campus, Dept. of Math, 555 N. Indian questions concerning the teaching and Establishing and Maintaining Under• Cr., Clarkston, GA 30021-2396; (404) learning of undergraduate mathematics. graduate Research Programs in 299-4162; fax: (404) 298-3836; e-mail: Both theoretical and empirical investiga• Mathematics [email protected] tions utilizing qualitative or quantitative Wednesday morning and Friday morning Janet Ray, Seattle Central Community methodologies are welcome. To the great• Emelie Kenney,* Siena College, Depart• College est extent possible, reports should be situ• ment of Mathematics, Loudonville, NY In 1995 the American Mathematical As• ated in and advance understandings about 12211-1462; (518) 783-2440; e-mail: sociation of Two-Year Colleges the teaching and/or learning of mathemat• [email protected] (AMATYC) released its "Crossroads" ics' and should be set within appropriate theoretical frameworks. We are especially Joseph Gallian, University of Minnesota• standards. Papers should present stan• interested in reports on completed stud• Duluth dards-based course content, methods, and student performance resulting from fac• ies. (Sponsored by the AMS-MAA Com• In recent years, there has been a growing ulty efforts consistent with Crossroads mittee on Research in Undergraduate interest in undergraduate research in math• philosophy. (Co-sponsored by AMATYC Mathematics Education (CRUME).) ematics. We seek papers that address suc• and the MAA Committee on Two-Year The Use of Hand-held Technology in cesses and difficulties in establishing, Colleges.) maintaining, funding, and assessing un• the Teaching and Learning of Math• dergraduate research programs of allkinds, Development Programs That Work ematics especially academic year programs. De• Thursday afternoon and Saturday after• Thursday morningand Saturday afternoon scriptions and analyses of any efforts that noon Marcelle Bessman, * Jacksonville Univer• support and encourage the involvement Mercedes McGowen,* William Rainey sity,Department of Mathematics, Jackson• of students in mathematics research, in• Harper College, Math-1200 W. ville, FL 32211; (904) 745-7300; fax: cluding informal programs, mentoring Algonquin Road, Palatine, IL 60067-7398; (904) 745-7573; e-mail: mbessma@junix. individual students, conferences and meet• (847) 925-6526; fax: (847) 925-6049; e• ju.edu ings involving students, REU programs, mail: [email protected] and non-REU formal programs are wel• V. J. Rammamurthy, Northern Florida come. Jacqueline B. Giles-Giron, Houston Com• State University, Bert K. Waits, Ohio State munity College University Innovations in Teaching In many colleges and universities, devel• Abstract Algebra Computers and graphing calculators can opmental algebra courses constitute a sig• be used as tools for exploration of math• Wednesday morning and Friday afternoon nificant portion of the course offerings. ematical concepts and constructs as well Al Hibbard, * Central College, Dept. of Substantial revisions in precalculus and as for "discovery of mathematical truths." Math/ComputerScience, Pella, IA 50219• calculus courses, coupled with the recently Through integrated use ofthis technology 1902; (515) 628-5133; fax: (515) 628• published AMATYC Standards, have the classroom becomes a laboratory for 5316; e-mail: [email protected] spurred efforts to rethink the developmen• instruction and learning. For this session tal mathematics curriculum as well. We the organizers invite papers which focus Ellen Maycock Parker, DePauw Univer• invite papers describing significant on uses of hand-held technology in the sity, Krystina Leganza, Ball State Univer• changes in content and/or pedagogy in the mathematics classroom. (Sponsored by the sity teaching of developmental mathematics MAA Committee on Computers in Math- The purpose of this session is to provide a

13 FOCUS June 1996 ematics Education.) [email protected] Assessment for Better Learning: As• Calvin C. Moore, University of Califor• El\1PLOYMENT sessing Teaching and Learning in a nia at Berkeley, and Morton Lowengrub, Climate of Change Indiana University OPPORTUNITIES Reform activities in mathematics depart• Thursday morningand Saturday afternoon Rates for FOCUS Employment Advertise• ments have led to changes in curriculum, Bonnie Gold,* Wabash College, Depart• ments are $95.00 per column inch (one inch in equipment needs, sometimes in staff• minimum), billed to the nearest 1/2 inch. ment of Mathematics, Crawfordsville, IN ing, and hopefully in how and what math• 47933; (317) 361-6306; e-mail: All advertisements are set with a one-line ematics students learn. How do [email protected] headline, centered, boldface, consisting of administrators see these changes? What the institution name, unless additional head• Annalisa Crannell, Franklin & Marshall are their roles and responsibilities in rela• line information is provided. College, Ahmed Zayed, University of tion to these changes? What are a All invoices include a tear sheet. Advertis• Central Florida department's responsibilities in informing ing Copy Deadlines: The first of the month, As we experiment with new ways of teach• the administration? Presentations are two months prior to publication. FOCUS is sought from mathematician-administra• published in February, April, June, August, ing, we need to find new and more effec• October, and December. tive ways to assess how well our students tors and from chairs or faculty who have are learning, and, correspondingly, how been successful in their efforts with ad• Advertisers should contact: Joseph Watson, ministrators. The Mathematical Association of America, well we are doing as teachers. This ses• 1529 18th St., NW, Washington, DC 20036; sion will discuss methods of evaluation (202) 387-5200; fax: (202) 265-2384; e-mail: which go beyond traditional examinations [email protected] and evaluationforms. Especially welcome are papers which directly use this assess• ment to improve teaching and student learning. (Sponsored by the Committee SUBMISSION PROCEDURES Butler County Community College onTeaching UndergraduateMathematics.) Butler County Community College invites ap• FOR CONTRmUTED plications for a full-time tenure-track position New Directions in Student Assessment teaching mathematics, beginning August 1996. Wednesday afternoon and Thursday af• PAPER PROPOSALS Applicants must have a Master of Science or ternoon Master of Arts degree with a minimum of 24 graduate/dual level credit hours in mathematics. After you have selected a session to Richard Vandervelde,* Hope College, Experience teaching mathematics at the college Department of Mathematics, Holland, MI which you wish to contribute a paper, level is desirable. Salary is commensurate with 49422-9000; (616) 395-7123; e-mail: forward the following directly to the experience. organizer, indicated above with an [email protected] Teachingduties range from developmental math• asterisk (*): ematics to elementary differential equations. Jay M. Jahangiri, Kent State University • the name(s) and addressees) of the Other duties include participation incollege com• Many students develop math anxiety as a author(s); and mittees, curriculum development, and student result of the old-fashioned exams which advising. • a one-page summary of your paper. are "do or die" situations. Assessing stu• Located on 323 acres of rolling hills, under tall dents' performances with respect to criti• The summary should enable the oak trees, Butler County Community College, cal thinking, mathematical communi• organizer(s) to evaluate the appropriate• chartered in 1965,is the first community college cation skills, and the use of technology ness of your paper for the selected ses• in Western Pennsylvania. Fully accredited by the Middle States Association of Colleges and demands assessment techniques dramati• sion. Consequently, you should include Schools, Butler County Community College pro• cally different from those many institu• as much detailedinformation as possible vides many occupational programs as well as tions and instructors have traditionally within the one-page limitation. transfer programs. relied on. We invite contributed talks from Yoursummary must reach the designated Submit resume, transcripts, and three letters of persons regarding new (and old) innova• organizer by Friday, September5, 1996. reference by June 17, 1996, to Dr. R. M. tive evaluation techniques which are ef• Sanderson, Box 1203, Butler, PA 16003-1203. Organizers will acknowledge receipt of fective in this new environment. Butler County Community College is an EEO/ all paper summaries. Ifan organizer ac• AA employer. How Mathematics Departments and cepts your paper, you will receive infor• Upper Level Administrators Work Ef• mation on how to submit electronically fectively an abstract for your paper. All abstracts Wednesday morningandFriday afternoon must be submitted by Thursday, Octo• Univ. of Papua New Guinea ber 2, 1996. Abstracts received after the Lida K. Barrett,* United States Military Lecturers in applied maths and computer science. deadline will not be published in the Rewarding, challenging posts for versatile edu• Academy, Mathematical Sciences Dept., booklet of abstracts which will be avail• cators. Ph.D. or near. Start 7/96 (preferred) or 11 West Point, NY 10996-1786; (914) 938• able in the meetings registration area 97. Details: Prof. Arganbright, Maths, UPNG, 2559; fax: (914) 938-2409; e-mail: during the conference in San Diego. Box 320, University PO, NCD, Papua, New Guinea. E-mail: [email protected]. 14 June 1996 FOCUS Calendar National MAA Meetings - Spring 1998 Southwest Missouri State Lutheran College, Seguin, TX University, Springfield, MO August 10-12, 1996 Annual Joint Sum• - Spring 1998 Southern Methodist Uni• mer Meetings, University of Washington• NEBRASKA-SOUTHEAST SOUTH versity, Dallas, TX Seattle, Seattle, WA. Board of Governors DAKOTA - April 18-19, 1997, Wayne TEXAS - Spring 1997TexasLutheran Col• Meeting August 9, 1996 State College, Wayne, NE lege, Sequin, TX January 8-11, 1997 Eightieth Annual NEW JERSEY - November 6, 1996, Lu• WISCONSIN - April 11-12, 1997, Uni• Meeting, San Diego, CA. Board of Gov• cent Technologies, Murray Hill, NJ versity of Wisconsin-River Falls, River ernors Meeting January 7, 1997 - April 1997, Middlesex County College Falls, WI January 7-10, 1998 Eighty-first Annual NORTH CENTRAL - October 18-19, Meeting, Baltimore, MD. Board of Gov• Other Meetings 1996, University of Minnesota, Duluth, ernors Meeting January 6, 1998 June 22-26,1996 Art and Mathematics MN Sectional MAA Meetings Conference (AM96), SUNY-Albany, NORTHEASTERN - June 7-8, 1996, NY. Speakers include John Horton EASTERN PA & DELAWARE - Novem• Hampshire College, Amherst, MA Conway, Martin Golubitsky, and Benoit ber 1996, Delaware State College, Dover, Mandelbrot. Forinformation,contact Nat - November 22-23, 1996, Univ. ofMassa• DE chusetts-Boston, Boston, MA Friedman, Dept. of Math and Statistics,SUNY, Albany, NY 12222; INDIANA - October 26, 1996, Rose• NORTHERN CALIFORNIA - February (518) 442-4621; fax: (518) 442-4731; e• Hulman Institute of Technology, Terre 22,1997,University ofSan Francisco, San mail: [email protected]. Haute, IN Francisco, CA July 29-August 2,1996 PCALC Course, - Spring 1997 Franklin College, Franklin, OHIO - October 25-26, 1996, Denison precalculus and calculus topics using the IN University, Granville, OH TI-82 and CBL with an introduction to LOUISIANA-MISSISSIPPI - Feb 28• the TI-92, LaSalle University, Philadel• OKLAHOMA-ARKANSAS -April 4-5, March 1, 1997 Millsaps College, Jackson, phia, PA. Contact Charles Hofmann; 1997, University of Central Oklahoma, MS (215) 951-1136; fax: (215) 951-1805; e• Edmond, OK mail: [email protected]. MD-DC-VA-Novemberl-2,1996,Hood SEAWAY - November 8-9,1996, SUNY College, Frederick, MD August 5-9, 1996 CAS-CAL Course, College at Geneseo, Geneseo, NY calculus enhanced with computer sym• METRO. NEW YORK - May 3, 1997 SOUTHEASTERN -March 13-15,1997, bolic algebra using the TI-92 and CBL, Mercy College, Dobbs Ferry, NY GeorgiaInstituteofTechnology/Spellman Montgomery County Community Col• MISSOURI - Spring 1997 Missouri West• College, Atlanta, GA lege, Blue Bell, PA. Contact Roseanne ern State College, St. Joseph, MO Hofmann; (215) 641-6405; e-mail: SOUTHWESTERN - Spring 1997 Texas [email protected]. Technology College Short Course Program The Technology College Short Course Program, organized by Bert Waits and Frank Demana from Ohio State University, is offering week-long courses at several colleges in twenty-two states this summer. Each short course participant will learn hands-on how to use the new TI-92 hand-held symbolic algebra computer and/or the TI-83 or TI-85 graphing calculator to enhance the teaching and leaming ofcollege and university mathematics. Mathematics reform materials consistent with the calculus reform movement, MAA recommendations, and the AMATYC Standards will be the focus of appropriate short courses. Applications, problem solving, pedagogy, implementation issues, and testing issues will be featured in all short courses. The Calculator-Based Laboratory (CBL) system will be used to collect data and connect mathematics with science. Offered are the following courses. • DEV Mathematics in the foundation using the TI-83 and CBL (includes pre-algebra, beginning algebra, intermediate algebra, and data analysis) • ALGT College algebra, trigonometry, and data analysis using the TI-83 and CBL • PCALC-CALC Precalculus and calculus using the TI-83 or TI-85 and CBL • CAS-CALC Calculus enhanced with computer algebra using the TI-92 To get information on dates and locations, contact Ed Laughbaum, Ohio State University, Department of Math, Room 342 Math Tower, 231 W 18th Ave., Columbus, OH 43210; (614) 292-7223; fax: (614) 292-0694; e-mail: elaughba@ math.ohio-state.edu. 15 The singular solution for a multi-function world.

r----,TM START One calculator DOING to handle algebra EXTRAORDINARY through calculus. THINGS Another for finance. And a computer program to perform statistical computations. Whoa. Wouldn't it be extraordinary Math. Graph-Table split screen allows if one calculator could meet so you to trace the graph many diverse needs, and and scroll the table still be easy to use? simultaneously. Well, now one does just that. Presenting the TI-83 Graphing Calculator. Statistics. Display The revolutionary results ojhypothesis tests graphically TI-83 handles a host of functions and numerically. for a variety of college subjects. For Calculate conjidence instance, the TI-83 allows your students to intervals. differentiate graphs with a variety of line styles, analyze data sets of up to 999 elements, and solve for different variables interactively. Plus, the TI-83 handles inferential statistics and the most popular financial functions with ease. Because it's based on the popular TI-82, there's no learning curve either. In fact, the two can be used side-by-side in class. The affordable, portable TI-83. In a multi-function world, there simply is no equal. Finance. Financial junctions include Time-Value-oj-Money, cash flows, and ~TEXAS amortization. INSTRUMENTS For more information about the TI-83, call 1-800-TI-CARES (U.S. and Canada), send e-mail to: [email protected] or visit us on the Internet at http://www.ti.eomkale IH021996