THE WSLETTER OF T HE MATHEMATICAL ASSO IATIO

Volume 17, Number 1 MATHFEST 97 In this Issue World Class at Work! COntributed P. 3 Mathfest 97 Special Sessions aper Sessions 15 Teaching Math on the World Tours Wide Web Minicourses 17 Penonal Opinion

19 ICMI Study in History DETAILS START ON PAGE 3! 20 Workshops

22 Classlfleds

The Mathematical Association of America Second class postage paid at 1529 Eighteenth Street, NW Washington. DC and A Sharper FOCUS additional mailing offices Washington, DC 20036-1385 MAA Online is becoming the medium of choice for members to keep up to date on MAA activities. As a result, FOCUS will be leaner in the months to come. FOCUS will continue to provide you with essential infor• mation and interesting, infonnative articles, but the overall message as the MAA contin• ues to move into the electronic age is Get on line to MAA Online. -Keith Devlin, Editor FOCUS April 1997 FOCUS Editorial FOCUS is published by the Mathematical Association of America six times a year: The 5 Percent That Can Help the 60 Percent February, April, June, August, October, and Can three vectors in the Euclidean plane be linearly independent? The answer is yes, accord• December. ing to 48% of a of 25 students questioned one to three semesters after they had completed a differential equations and linear algebra course followed by a linear algebra Editor: Keith J. Devlin, Saint Mary's College of California; devlin@ stmarys-ca.edu course. Of those same students, 36% were unable to give an example of three independent vectors in Euclidean three-space, 68% could not give a correct definition of linear indepen• Associate Editor: Donald J. Albers, MAA dence, 58% could not define the span of a set of vectors, and 60% could not give an example Associate Executive Director and Director of a subspace of a vector space. Incidentally, these were students who had passed both of Publications and Electronic Services; courses; indeed, their average grades in the two courses were 3.05 and 2.91, respectively (A [email protected] = 4, B = 3, C = 2, D = I). Managing Editor: Harry Waldman, This data was supplied by mathematics education expert Guershon Harel at the start of a MAA;[email protected] presentation made at the Joint Mathematics Meetings in San Diego in January. Pretty discour• Production Editor: Amy Fabbri, MAA; aging, don't you agree? [email protected] Harel's point was not that we should give up trying to teach linear algebra to our students• Copy Editor: Nancy Wilson, Saint Mary's though one can imagine that being a natural reaction to such depressing data. Rather, he said, College of California; nwilson@stmarys• we should reflect on what it takes to ensure that our students achieve genuine understanding. ca.edu Although the students in Harel's sample had been able to pass the course, indeed to pass it with a solid grade, they had learned almost nothing of substance. Their success was based on Advertising Coordinator: Joseph learning how to manipulate symbols according to various rules, without any understanding Watson, MAA; [email protected] of what those symbols referred to. To put it plainly, they had not understood the fundamental Letters to the editor should be addressed to concepts of linear algebra. Keith Devlin, Saint Mary's College of The blind use of symbolic manipulation was vividly illustrated by the response given by one California, P.O. Box 3517, Moraga, CA 94575; [email protected]. of Harel's students, when faced with a matrix equation AX = 0, where A is a matrix and X a column vector. The student first rewrote the equation as xlAI + ... + xnAn = 0 (where the Subscription and membership questions Ai are the columns of A) and then solved to give XI = [x2A2 + ... + xnAnl/AI. should be directed to the MAA Customer Service Center, 1-800-331-1622; e-mail: When asked what dividing by AI meant, the student simply pointed to the expression he had [email protected]. Send address changes to written and said, "It's just this over this." Pure syntax. Of course, it would be easy for those the MAA, P.O. Box 90973, Washington, DC of us in the business (of mathematics education) to shrug, smile, shake our heads, or wring 20090-0973; e-mail: [email protected], or our hands in despair at the sheer depth of misunderstanding displayed by this answer. If call1-800-331-1622(U.S. andCanadaon1y); Harel's class was in any way unusual, such a response might be acceptable. But as we all (30 I) 617-7800 (outside U.S. and Canada). know-or should know-it was not an unusual class in any way, except perhaps in being questioned on their knowledge after the ink on the final exam had dried. As Walter Cronkite The FOCUS subscription price to individual used to say as he signed off on the CBS Evening News each night, that's the way it is. members of the Association is $6.00, included in the annual dues. (Annual dues for regular Well, if that is indeed the way it is, then we need to do something about it. What on earth is members, exclusive of annual subscription the point of our putting weeks of effort into trying to teach some basic (and very useful) prices for MAA journals, are $68.00. Student mathematics, if those efforts do not result in any real learning? Unless we are content to go and unemployed members receive a,~6 through a meaningless ritual each semester, we have two choices. We either give up or we percent discount; emeritus members receive figure out how to do it right. a 50 percent discount; new members receive a 40 percent discount for the first two Figuring out how to do it right will require that those of us who earn our daily bread by membership years.) teaching university mathematics and our summer airline ticket by publishing theorems (Coke) take a good hard look at what "the math ed crowd" down the corridor (Pepsi) have discovered Copyright © 1997 by the Mathematical about the way students learn. Yes, I know, 95% of the math ed literature is verbose junk and Association of America (Incorporated). we Coke-folk don't have the time. But 95% of published mathematical research is symbolic Educational institutions may reproduce articles for their own use, but not for sale, junk, and we never let that get in our way, did we? In both cases, the good 5% is what counts. provided that the following citation is used: That 5% of good math ed stuff can help that 60% of college students whom our present "Reprinted with permission of FOCUS, the methods measurably fail. For teaching linear algebra, start out by looking at some of Harel's newsletter of the Mathematical Association own work. (Some of it is about to be published by the MAA.) In his San Diego talk, Harel of America (Incorporated)." stressed the importance of motivating mathematical concepts within the student's own frame of reference-of providing the student with an intellectual need for the concept. Second class postage paid at Washington, DC and additional mailing offices. For Harel is on the faculty at Purdue University, by the way. advertising information, contact Joseph Watson, MAA, 1529 Eighteenth Street NW, Washington, DC 20036; (202) 387-5200; e• mail: jwatson@ maa.org. ISSN: 0731-2040 The above are the opinions of the FOCUS editor, and do not necessarily represent the official views of the MAA. 2 MATHfEST97 World Class Mathematics at Work!

iscover the people, the theorems, the applications and the art of Review the detailed mathematics by attending Mathfest 97, August 1-4 in Atlanta, DGeorgia. Strengthen and energize your mathematical vocation by descriptions of lectures, attending lectures, contributed paper sessions, minicourses, short courses, and special sessions. And, of course, you won't want to miss the opportuni• sessions, and other ty to share and discuss ideas with colleagues at your national meeting. events in the following Several special events are planned for Atlanta. Attend the lectures and special sessions that pay Tribute to Paul Erdos, the world-renowned math• pages. Register by ematician whose itinerant life style and tremendous productivity won him legendary status. Leading this tribute are two lectures by Ronald L. Graham, using the form on who was a close-friend and colleague of Erdos for many years. Another page 13. Information special event is the Earle Raymond Hedrick Lecture Series with this year's lecturer, Elliott H. Lieb of . He will begin with a on Mathfest 97 also presentation entitled "Why Is The Material World The Way It Is? A Mathematical View of the Stability of Matter." Back by popular demand is may be accessed the theatrical performance of Colin C. Adams and Edward B. Burger, "Casting About: About Casting." If you missed it in Seattle, here's your via MAA Online second chance. Rounding out Mathfest 97 are many activities developed specifically for students. at www.maa.org.

3 Tribute to Paul Erdos MAA will pay tribute to the • AWM-MAA Invited Address: master , Paul Suzanne Lenhart University of Tennessee & Oak Ridge National Laboratory "Applications of Optimal Control to Various Population Models" ErdSs, with a collection of Saturday, 8:45 am-9:35 am Invited Addresses and Special Sessions that reflect on his life, • Hedrick Lecture Series: Elliotl H. Lieb Princeton University his mathematics, and the Lecture 1: "Why Is The Material World the Way It Is? impact he had on individuals A Mathematical View of the Stability of Matter" and the profession. Erd& died Saturday, 9:50 am-l 0:40 am Lecture 2: liThe Origins of Entropy" at age 83 in September of Sunday, 9:50 am-l 0:40 am 1996, but will be remembered Lecture 3: liTo the Edge of Quantum Mechanics" Monday, 9:50 am-l 0:40 am through the insights of his

more than 1,500 papers, • Denis Lawrence Weaire Tri nity College-Dublin his almost 500 co-authors, his "The Simulation of Foam in 2 and 3 Dimensions" Saturday, 3:00 pm-3:50 pm inspiring unsolved problems, and his unique character. • NAM-MAA Invited Address: Fern Y. Hunt National Institute of Standards and Technology Join the MAA in honoring "Fractal Dimensions, Ergodic Theory and a Peano-like Curve" Sunday, 8:45 am-9:35 am this influential mathematician

by attending the lectures and • Ronald L. Graham AT&T Bell Laboratories sessions in his honor: "Paul Erdos' Favorite Problems" Part 1: Sunday, 10:55 am-11:35 am Ronald 1. Graham will speak in Part 2: Monday, 10:55 am-l1 :35 a a two-part series on Paul Ed&' Favorite Problems; Richard A. • Pi Mu Epsilon J. Sutherland Frame Lecture: Philip D. Straffin, Jr. Beloit College Duke and Renu Laskar will "Excursions in the Geometry of Voting" lead a session on Paul Erdbs: Sunday, 8:00 pm-9:00 pm A Mathematical Nomad; • Colin C. Adams and Edward B. Burger Williams College and Andrew Granville, Carl Mathematical Play, "Casting About: About Casting" Pomerance, and other speakers Monday, 8:45 am-9:35 am will discuss Paul Ed&, Number • MAA Student Lecture: Theorist Extraordidre. Aparna W. Higgins University of Dayton "Demonic Graphs and Undergraduate Research" 4 Monday, 3:00 pm-4:00 pm Program at a Glance GENERAL INVITED SPECIAL STUDENT MINICOURSES CONTRIBUTED ACTIVITIES ADDRESSES SESSIONS ACTIVITIES PAPER SESSIONS

Registration MM-Pi Mu Epsilon 12:00 n00n-7:OO pm Student Reception F 5:30 pm-6:30 pm Board of Governors Breakfast R 8:00 am-9:OO am I Board of Governors Meeting 9:00 am-5:OO pm o "Georgia on My Mind" A Mathfestival y 7:00 pm-IO:OO pm

Registration Applications of Optimal Control Undergraduate Research Student Hospitality Center Developing the Ability in History of Mathematics & Its Use in 8:00 am-4:OO pm to Various Population Models in Mathematics 9:00 am-5:00 pm Beginning College Mathematics the Mathematics Classroom, Part 1 Suzanne Lenhart Yewande Olubummo Majors to Write Proofs, Part A Charles Pierre, Elinor Berger Exhibit Hall MM & PME Student 1:00 pm-2:50 pm 8:45 am-9:35 am 1:00 pm-2:50 pm Dan Fendel, Diane Resek 9:00 am-5:OO pm Paper Sessions 1:00 pm-2:50 pm Usi~ Technology to Implement S 1:00 pm-5:00 pm Student Hospitality Center Hedrick Lecture 1: NExT Trends in Research the rossroad Standard In 9:00 am-5:00 pm Why Is the Material World Julianne Rainbolt, Knot Theory & Applications College Math Courses, Part 1 A the Way It Is? Frederick J. Wicklin in the Sciences, Part A Cheryl Stratton, Jean Bevis 1:00 pm-2:50 pm Pi Mu Epsilon Council Meeting Elliott H. Lieb 1:00 pm-2:50 pm Stefanos Gialamas T 9:30 am-12:30 pm 9:50 am-IO:40 am 1:00 pm-2:50 pm The Incorporation of Statistics MM Awards Session Standards in School in Non-Statistics Mathematics U Mathematics Courses, Part 1 10:55 am-11 :25 am The Simulation of Foam in 2 & 3 Dimensions Billy Rhoades Cathy A. Godbois, Eric Y. Leung R 4:00 pm-6:00 pm Investing for Retirement Seminar Denis Lawrence Weaire 4:00 pm-6:00 pm 4:00 pm-6:OO pm 3:00 pm-3:50 pm Innovative Teachin~ldeas for o Undergraduate Mat ematics, Part 1 MM Section Officers Meeting Mohammad H. Ahmadi, A 4:00 pm-6:OO pm Tingxiu Wang 4:00 pm-6:00 pm y MM 25-Year Member Reception & Banquet 6:00 pm-l0:OO pm

Registration Fractal Dimensions~ Ergodic Paul Erdos: AMathematical Student Hospitality Center Developing the Ability in Usi~ Technology to Implement 8:00 am-4:00 pm Theory & a Peano- ike Curve Nomad 9:00 am-5:00 pm Beginning College Mathematics the rossroad Standard in Fern Hunt Y. Richard A. Duke, Renu Laskar Majors to Write Proofs, Part B College Math Courses, Part 2 8:45 am-9:35 am MM & PME Student MM Student ChapterslPME 1:00 pm-2:50 pm Dan Fendel, Diane Resek Cheryl Stratton, Jean Bevis Paper Sessions 1:00 pm-2:50 pm Advisor's Breakfast 1:00 pm-2:50 pm Hedrick Lecture 2: 1:00 pm-5:00 pm 8:00 am-9:15 am The Origins of Entropy Mathematics Instruction & Mathematics for Liberal Arts the World Wide Web Knot Theory & Applications Students: New Goals, Methods, Elliott H. Lieb PME Banquet s Exhibit Hall Earl D. Fife, Lawrence Husch, in the Sciences, Part B & Assessments, Part 1 9:00 am-5:00 pm 9:50 am-IO:40 am 6:00 prn-ll:OO pm Stefanos Gialamas Janet Heine Barnett, Janet G. Nichols & Gene Klotz 1:00 pm-2:50 pm U Paul Erdos' Favorite 4:00 pm-6:00 pm 1:00 pm-2:50 pm Student Hospitality Center PME Frame Lecture: Problems, Part 1 Excursions in the Geometry Music & Mathematics, Part A Calculus Reform: What Works N 9:00 am-5:OO pm Meeting the Challenges of AN DWhat Does Not Work Ronald L. Graham of Voting Leon Harkleroad Reform in Teacher Education at Lawrence Husch PME Banquet 10:55 am-11 :35 am Philip D. Straffin, Jr. 4:00 pm-6:00 pm o Minority Institutions Through 1:00 pm-2:50 pm 6:00 prn-ll:OO pm 8:00 pm-9:00 pm Invited Address Partnerships & Collaborations Is Fuzziness a Mathematical Innovative Teachin~eas for A To Be Announced Etta Falconer. John Kenelly, Concept? Part A Undergraduate Mat matics, Part 2 y 3:00 pm-3:50 pm Genevieve Knight, William Hua (Harry) Li, Mohammad H. Ahmadi, Tingxiu Hawkins Wang Luisamaria Nicosia McAllister 4:00 pm-6:00 pm 4:00 pm-6:00 pm 4:00 pm-6:OOO pm History of Mathematics & Its Use in the Mathematics Classroom, Part 2 Charles Pierre, Elinor Berger 4:00 pm-6:00 pm Registration Castin About: About Casting NSF-Funded Middle School Student Hospitality Center Music & Mathematics, Part B The Incorporation of Statistics 8:00 am-4:OO pm Colin t. Adams, Curriculum Projects: What 9:00 am-5:00 pm Leon Harkleroad in Non-Statistics Mathematics Edward B. Burger Mathematical Background 1:00 pm-2:50 pm Courses, Part 2 8:45 am-9:35 am Will Be Needed by Teachers M Exhibit Hall Workshop: Mathematical Cathy A. Godbois, Eric Y. Leung 9:00 am-5:OO pm of These Materials? Is Fuzziness a Mathematical Hedrick Lecture 3: James D. Gates Modeling 1:00 pm-2:50 pm o 1:00 pm-2:50 pm Frank Giordano Concept? Part B Student Hospitality Center To The Edge of Mathematics for Liberal Arts Quantum Mechanics 1:00 pm-2:50 pm Hua (Harry) Li, N 9:00 am-5:OO pm Paul ErdOs: Number Theorist Luisamaria Nicosia McAllister Students: New Goals, Methods, Elliott Lieb H. Extraordinaire MM Student Lecture & Assessments, Part 2 9:50 am-I 0:40 am Andrew Granville, 1:00 pm-2:50 pm o MM Business Meeting Demonic Graphs & Janet Heine BarneN, Janet G. Nichols 11:45 am-12:15 pm Carl Pomerance Paul ErdOs' Favorite 1:00 pm-2:50 pm Undergraduate Research 1:00 pm-2:50 pm A Problems, Part 2 Aparna W Higgins Dynamical Systems & Modeling: 3:00 pm-4:00 pm y Ronald L. Graham Papers bTe Graduate Students 10:55 am-11 :35 am Jack Ha e 4:00 pm-6:00 pm 5 Special Sessions Special Sessions feature presentations or panel discussions. The speakers are invited by the organizers and selected because of their knowledge and accomplishments in the focal area of the session.

Undergraduate Research in Paul ErdOs: A Mathematical Nomad NSF-Funded Middle Mathematics Richard A. Duke Georgia Institute of Technology School Curriculum Projects: Yewande Olubummo Spelman College Renu Laskar Clemson University What Mathematical Background Th is session presents various aspects of This session includes a discussion of Paul Will Be Needed by Teachers of research in mathematics at the undergraduate Erdos, the non-stop traveler, and his impact These Materials? level. Topics include descriptions of programs, on those he met and worked with along the James D. Gates, Executive Director Emeritus National Council of Teachers of Mathematics appropriate topics for research, ways to way. Speakers include the organizers. New curriculum materials for middle implement and support a research program, Sunday, 1:00 pm-2:S0 pm school mathematics will require some and the role of undergraduate research in changes in the traditional mathematical mathematics. Mathematics Instruction and the background provided for preservice and Saturday, 1:00 pm-2:S0 pm World Wide Web inservice teachers. This session deals Earl D. Fife Calvin College with the necessary changes. Lawrence Husch University of Tennessee NExT Trends in Research Monday, 1:00 pm-2:S0 pm Gene Klotz Swarthmore College Julianne Rainbolt Michigan State University This session features invited presentations on Frederick J. Wicklin The University of Minnesota how the World Wide Web is being used in Paul ErdOs, Number Theorist In this session, participants in MANs Project mathematics education. Presenters demon• Extraordinaire NExT will share their current research strate the use of, and discuss examples and Andrew Granville University of Georgia interests and results. strategies for using today's technology to Carl Pomerance University of Georgia Saturday, 1:00 pm-2:S0 pm enhance students' understanding of mathe• This session includes talks not only on matics. (Sponsored by the MAA Committee the mathematics of Paul Erdos, but also Standards in School Mathematics on Computers in Mathematics Education.) developments from his mathematics and Sunday, 4:00 pm-6:00 pm Billy Rhoades Indiana University what he meant to the speakers personally. Other speakers include Krishna Alladi, Panelists discuss the NCTM recommendations University of Florida; and Neil Calkin, on professional, curriculum and evaluation Meeting the Challenges of Reform Georgia Tech. standards for school mathematics. Pros and in Teacher Education at Minority Monday, 1:00 pm-2:S0 pm cons of implementation and implications for Institutions Through Partnerships colleges and universities will be addressed, and Collaborations and questions will be taken from the audi• Etta Falconer Spelman College Dynamical Systems and Modeling: ence. The panelists include: Gail Burrill, John Kenelly Clemson University Papers by Graduate Students President of the NCTM; Joan Ferrini-Mundy Genevieve Knight Coppin State College Jack Hale Georgia Institute of Technology Mathematical Sciences Education Board; William Hawkins MANs SUMMA Program Interesting research in dynamical systems Henry Alder, University of California, Davis; This session addresses efforts to align instruc• and modeling will be presented by and James R. C. Leitzel, University of New tional activities with guidelines for the prepa• graduate students. Hampshire. ration of teachers of mathematics. In addition Monday, 4:00 pm-6:00 pm Saturday, 4:00 pm-6:00 pm to the organizers, presenters include Stella Ashford, Southern University-Baton Rouge (for MainSTey); Karen Norwood, North Carolina State University; and Gilbert Casterlow, North Carolina A& T University (for CCRCA). The "MainSTey" and "CCRCA" projects are funded by NSF and based at minority institutions; SUMMA provides technical assistance. Sunday, 4:00 pm-6:00 pm Contributed Paper Sessions Contributed paper sessions are organized around a pre-determined topic. Presenters are selected by the paper organizers after reviewing responses to a call for papers.

History of Mathematics and Its Use The Incorporation of Statistics in Mathematics for Liberal Arts in the Mathematics Classroom Non-Statistics Mathematics Courses Students: New Goals, Methods Charles Pierre Clark Atlanta University Cathy A. Godbois & Eric Y. Leung and Assessments Elinor Berger Columbus State University Harrisburg Community College-Lancaster janet Heine Barnett & janet G. Nichols These sessions feature papers describing As the trend toward the incorporation of University of Southern Colorado innovative ways of using the history of modeling real and student collected data Despite the reputation of liberal arts mathematics in the classroom. Some of the into the undergraduate mathematics curricu• mathematics courses as "Math for Poets," topics to be covered: investigative approach• lum expands, issues regarding the amount such courses fulfill a standard graduation es; descriptions of ways to teach history of of statistics required as a prerequisite and/or requirement and provide a final mathemati• mathematics courses using both original and the statistics topics which should be cal experience for numerous students who non-original sources; uses of the history of included in the course must be resolved. move into careers in non-technical fields. mathematics in accord with current changes How much or how little statistical back• Recently, a variety of philosophies concern• in curricula, pedagogy, the preparation of ground is required or should be included? ing the quantitative and mathematical needs teachers of mathematics, and ideas inherent Speakers will present differing viewpoints of these students have developed, along in the STANDARDS. and current practices. with new and often innovative methods of instruction and assessment. This session Part 1: Saturday, 1:00 pm-2:50 pm Part 1: Saturday, 4:00 pm-6:00 pm addresses these philosophies, and instruct• Part 2: Sunday, 4:00 prrHJ:oo pm Part 2: Monday, 1:00 pm-2:50 pm ional and assessment techniques being used to meet their goals. Using Technology to Implement the Innovative Teaching Ideas for Part 1: Sunday, 1:00 pm-2:50 pm Crossroads Standards in College Undergraduate Mathematics Part 2: Monday, 1:00 pm-2:50 pm Mathematics Courses Mohammad H. Ahmadi Cheryl Stratton & jean Bevis University of Wisconsin-Whitewater Georgia State University Tingxiu Wang Oakton Community College Calculus Reform-What Works These sessions focus on innovative Throughout our teaching careers, we often AND What Does Not Work find a new method in teaching standard uses of technology in undergraduate mathe• Lawrence Husch University of Tennessee matics courses, in particular, how changes topics in mathematics which is creative This session features reports from departments in delivery can support AMATYC Standards, or interesting. This session highlights which have implemented calculus reform in and how the classroom can become a instructors' outstanding or innovative ideas, a significant manner for an extended period learning laboratory. and their insights on teaching everyday and have made a decision to continue or material in undergraduate mathematics. discontinue that teaching method. Part 1: Saturday, 1:00 pm-2:50 pm Part 2: Sunday, 1:00 pm-2:50 pm Part 1: Saturday, 4:00 pm-6:00 pm Sunday, 1:00 pm-2:50 pm Part 2: Sunday, 4:00 pm-6:00 pm

7 Minicourses Minicourses offer four hours of focused instruction. Enrollment is limited and a separate registration fee is required. Refer to Registration Information and the Registration Form for details.

Developing the Ability Music in Beginning College and Mathematics Majors Mathematics to Write Proofs Dan Fendel & Diane Resek Leon Harkleroad San Francisco State University Over the years, people have used mathemat• The focus of this minicourse is on ways to ics in various ways to describe, analyze, help beginning college mathematics majors and create music. This minicourse explores develop the ability to write meaningful the application of mathematical areas such proofs. A key element of the approach is as number theory, probability, and group Other Sessions to have students work from their own theory to musical topics like tuning systems, Investing for Retirement Seminar conjectures, gradually attaining greater rigor. bell-ringing, and 20th century compositional Conducted by a certified financial Participants work in groups with activities technique. Emphasis will be placed on how planner, this seminar presents financial from the presenters' college and high school participants can incorporate this material in investment strategies for retirement. texts, see student work, and discuss the their classes-or even design a service Areas of discussion include saving strategies, controversies that arise from this approach. course on music and mathematics. fighting inflation's effect now and in the future, ways to approach estate planning, Part A: Saturday, 1:00 pm-2:50 pm Part A: Sunday, 4:00 pm-6:00 pm and protecting assets from inheritance Part B: Sunday, 1:00 pm-2:50 pm Part B: Monday, 1:00 pm-2:50 pm and estate taxes.

Saturday, Knot Theory Is 4:00 pm-6:00 pm. and Applications Fuzziness in the a Mathematical Sciences Concept? Stefanos Gialamas Illinois Institute of Art Hua (Harry) Li West Texas University Designed for participants who are unfamiliar Luisamaria Nicosia McAllister Moravian College with knot theory, this minicourse introduces Fuzziness is a term introduced to denote a such concepts as mathematical knots and new mathematical methodology to handle Mathfest 97 Deadlines links, knot equivalence, the Writhe number, uncertainties that cannot be determined by the linking number, Conway polynomial probabilistic and random assumptions. It is Early Bird Registration ...... June 18 and Jones polynomial. Ribbon knots and based on the theory proposed by Lotfi A. their role in DNA research will also be Zadeh in 1965. The theory offuzzy sets even• Dormitory Housing Reservations ...... June 18 presented. Participants will use strings to tually led to the discovery of fuzzy logic and create fascinating knots and links and its application to modern technology. During Renaissance Atlanta Hotel-Downtown Reservations ...... June 30 compute invariants and also will work this hands-on course, participants will be on knot and link puzzles, present results, introduced to the ideas underlying fuzzy sets, 50% Refund for Registration & and then re-create knots using laser points fuzzy numbers, fuzzy logic and fuzzy graphs. Event Tickets ...... July15 and mirrors. They will work collaboratively on assigned problems and discuss their solutions. Tour Reservations ...... July 18 Part A: Saturday, 1:00 pm-2:50 pm Part A: Sunday, 4:00 pm-6:00 pm Part B: Sunday, 1:00 pm-2:50 pm Regular Registration ...... July 20 Part B: Monday, 1:00 pm-2:50 pm Short Course Registration ...... July 20

Minicourse Registration ...... July 20 Students and faculty will be interested in presentations of student work in sessions sponsored by l/1 the MAA and PME, and in the Invited Lectures developed with students in mind. Starting with a student reception on Friday night, Mathfest 97 includes a rich array of activities for students. At Shop for new publications and products the Student Hospitality Center--{)pen Saturday through Monday-students and other Mathfest and revisit old favorites at the Mathfest attendees can meet for informal conversation, refreshments, and mathematical diversions. The 97 Exhibit Hall. This is your opportunity OJ Hospitality Center also provides programs for the student paper sessions, packets for student to review the latest books, play with innovative calculators and preview soft• ... presenters, and information on Mathfest activities of interest to students. Special information for ware programs. Meet company represen• ~ students can be found on MAA Online at www.maa.org. tatives and receive feedback that will assist you in making purchase decisions. ... MAA/Pi Mu Epsilon Student Reception In the Exhibit Hall, you'll find the Friday, 5:30 pm-6:30 pm popular MAA Bookstore. There you can select from MAA's extensive collection of MAA and Pi Mu Epsilon Student Paper Sessions books on mathematics, mathematics Saturday, 1:00 pm-5:00 pm • Sunday, 1:00 pm-5:00 pm education, and related topics. Schedule > time to browse through the 12 new titles ... Pi Mu Epsilon Banquet premiering at Mathfest 97. Purchase See the Mathfest Registration Form for ticket information. books at the meeting and you'll save money with a special discount! ~ Sunday, 6:00 pm-8:00 pm Representatives from publishers, software Pi Mu Epsilon J. Sutherland Frame Lecture firms, games and puzzle companies, edu• U "Excursions in the Geometry of Voting" cational foundations, and more will be on hand in the Atlanta Ballroom in the Philip D. Straffin, Jr. Beloit College Renaissance Atlanta Hotel-Downtown. Sunday, 8:00 pm-9:00 pm Modern political theory uses geometric models to investigate how voters' ideological The Exhibit Hall is open on ~ beliefs affect their voting power, the policy outcomes they will choose, the stability of Saturday, Sunday, and Monday those outcomes, and how the voters will form coalitions. This lecture looks at a 9:00 am-5:00 pm. selection of such models, using only ideas from plane geometry.

MAA Student Workshop Call for Student Papers "Mathematical Modeling" Students who wish to present a paper at Frank R. Giordano COMAP Mathfest 97 must be nominated by a faculty Monday, 1:00 pm-2 :50 pm advisor familiar with the work to be present• In this presentation, problems from the Mathematical Contest in Modeling are examined and ed. Students who make presentations at Mathfest 97, and who are also members of extended, and several models will be developed and refined. The discussion weaves MM Student Chapters are eligible for partial through undergraduate mathematics to include discrete, continuous, stochastic and travel reimbursement through a grant from nonlinear considerations. To keep things lively there will be opportunities for audience the Exxon Education Foundation. participation, as well as some short film clips. To propose a paper for presentation, students must complete a form and obtain the signa• MAA Student Lecture ture of a faculty sponsor. Nomination forms "Demonic Graphs and Undergraduate Research" are located on MM Online at www.maa.org Aparna W. Higgins University of Dayton under STUDENTS, or can be obtained from Monday, 3:00 pm-4 :00 pm Professor Charles Diminnie, 3306 Grand• The results of student research can have depth, breadth, and beauty. This lecture highlights view Drive, San Angelo, TX 76904 E-mail: several student research studies: investigations into the effects of the line graph operator on [email protected]. Deadline for properties of graphs; pioneering results in pebbling graphs; and, building on receipt of papers is June 27, 1997. the other two studies, an exploration of pebbling numbers of line graphs. 9 EpidemioJogy ModeHng MAA Two-Day Short Course

Co-sponsored by the Centers for Disease Control (CDC) Meet and share ideas with your peers at a July 31-August 1, 8:30 am to 5:00 pm variety of social events being held at Mathfest 97. You can reserve your tickets by This short course precedes Mathfest 97 and requires a separate registration fee. ordering through your advance registration For details, refer to the Mathfest 97 Registration Form or visit Short Course on MAA Online, www.maa.org. (see registration form). Banquet events will offer vegetarian meals if requested on the registration form. Cancellations must be Despite great strides in research and treatment, infectious diseases continue to be a major received in writing by July 15 for a 50% cause of mortality, particularly in developing countries. This course will present the basic refund. No refunds are available after mathematical models for the spread of infectious disease and provide participants with the foundations of model development and examples suitable for use in undergraduate this date. mathematics courses. Applications to human diseases such as measles and HIV/AIDS IIGeorgia on My Mind ll Mathfestival and applications to wildlife diseases such as rinderpest and brucellosis will be presented. Participants do not need any previous knowledge of epidemiology modeling as all infec• Kick-off Mathfest 97 with this celebration of tious disease models will be developed carefully from basic principles. the food and fun of the South on Friday, August 1. All participants and guests There will be four talks each day plus a lecture by an epidemiologist on "The Politics of Epidemiology Decision-Making" on Thursday and a panel discussion on "Current are invited! This event will be held in the Problems in Epidemiology" with CDC panelists on Friday. Georgia Ballroom of the Renaissance Atlanta Hotel-Downtown, 7:00 pm-10:00 pm.

Speakers Come and mingle with old friends and make some new ones before the meeting even The principal speaker, Herb Hethcote from the University of Iowa, has worked on epidemiology models and their applications for over 20 years. He will speak on several begins. Tickets are $35. topics: "Three Basic Epidemiology Models," "Epidemiology Models with Variable Population Size," "Comparison of Vaccination Strategies for Rubella," and "Modeling PME Banquet Pertussis (whooping cough) Transmission and Immunization." This annual event will be held on Sunday, Andy Dobson of Princeton University will speak on "Diseases of Wildlife: Rinderpest in 6:00 pm-B:OO pm. Tickets are $12 and $20. the Serengeti and Brucellosis in Yellowstone." After the banquet, attend the popular PME

John Glasser from the Centers for Disease Control will talk on "Evaluation via J. Sutherland Frame lecture, given this year Mathematical Modeling of Extraordinary Efforts to Control a Measles Outbreak in Dallas, by Philip D. Straffin, Jr. of Beloit College. Texas during 1990."

Linda Allen of Texas Tech University will talk on "Some Discrete-TIme Epidemic Models, MAA 25-Year Member Banquet Applications to Chlamydia and Chickenpox." The 20th annual banquet for those

Mac Hyman of the Los Alamos National Laboratory will speak on "Two Plausible Models individuals who have been members of for HIV Transmission Can Predict Qualitatively Different Epidemics." the MAA for 25 years or more. This banquet will be held on Saturday,

Registration 7:00 pm-1O:00 pm. There will be a reception prior to the banquet at 6:00 pm. To register for the MAA Two-Day Short Course refer to the Mathfest 97 Registration Form. Tickets are $35. Tours To register for tours, please complete the form at the bottom of this page and return it, with payment, to Atlanta Arrangements by Friday, July 18. This form is separate from your Mathfest 97 registration. Confirmations will be mailed directly to you and tickets can be picked up at the Mathfest registration desk. Pre-registration is advised because decisions to cancel low-enrollment tours (less than 35) will be made by Friday, July 18, 1997. Cancelled tours will be fully refunded. No refunds or exchanges will be made after July 18. Payment must be in U.S. funds drawn on U.S. banks .

• Atlanta's Famous Firsts Church you will continue past Dr. King's Afterwards, enjoy a nature walk in the Friday, August 1, 1:00 pm-5:00 pm birth home and tomb, and stop at the Fernbank Forest and take a trivia quiz $30.00 Martin Luther King, Jr. Center for Non• as you look at native foliage. Then its off Today's tour will begin at CNN Center, Violent Social Change. Next you will to SciTrek, one of the top ten physical home of the first cable television net• drive through the Atlanta University science centers in the nation. Each work, Cable News Network (CNN). complex and visit the grand Herndon exhibit here requires your participation Here you can catch a glimpse of the Home, former residence of Alonzo to examine the laws of science. fast-paced excitement of a 24 hour news Herndon, founder of the Atlanta Life broadcast with an insider's studio tour. Insurance Company, the largest and • The Good Life in Then it's off to visit the fabulous new most successful black-owned business in Historic Buckhead World of Coca-Cola Pavilion, Coke Mart the world. The last stop will be the APEX Monday, August 4, 9:00 am-l :00 pm and Underground Atlanta. Coca-Cola's Museum, where you will have the oppor• $25.00 International Headquarters are located tunity to view exhibits on local black Buckhead is known today as Atlanta's in Atlanta and it is here where the history and art by national black artists. premiere residential and shopping dis• secret formula was first perfected. trict with a distinct historical identity. Here you will visit the Atlanta History • Atlanta's • The Sights and Sounds of Science Center with its regal Swan House, an African-American Heritage Sunday, August 3. 1:00 pm-5:00 pm architectural masterpiece built in 1929. Saturday, August 2, 1:00 pm-5:00 pm $29.00 Next you will stop at the Tullie Smith $24.00 The first stop will be Fernbank, the House, an Atlanta "plantation style" This tour will begin with a narrated ride largest natural science museum south of farmhouse of the 1840's. Finally, you down historic Auburn Avenue to visit The Smithsonian. Take "A Walk Through can tour the Atlanta History Museum Ebenezer Baptist Church where Dr. Time in Georgia" or view the intriguing and follow Atlanta from its humble Martin Luther King preached. From the "Spectrum of Senses." beginnings to today. ~------~ Friday, August 1 1:00 pm-5:OO pm Atlanta's Famous Firsts $30x _ = CII:: Saturday, August 2 1:00 pm-5:oo pm Atlanta's African-American Heritage $24x _ = ou. Sunday, August 3 1:00 pm-5:oo pm The Sights and Sounds of Science $29x _ = z Monday, August 4 9:00 am-l :00 pm The Good Life in Historic Buckhead $25 x _ = o Total Amount Enclosed = Name: ______Address: City, State, Zip: Phone: L-J ______Fax: L-J ______Method of Payment: 0 Check 0 Visa 0 Mastercard Credit Card # Expiration Date: CII:: II 0 Please check if you need additional assistance to fully participate in the tour program. You will be contacted by Atlanta Arrangements. ::J Make chedcs payable to Atlanta Arrangements and return this form to: Atlanta Arrangements, 2964 Peachtree Road, NW Suite 652, o Atlanta, GA 30305 • phone (404) 262·7660. Credit card orders may be sent by fax to (404) 233·2426 I- 11 Registration Information How to Register for Mathfest Minicour~hort Course Registration: Meal Information Enrollment in Minicourses and the Short £arty Bird ~1IbI: Those who register by Course is limited. Advance registration must Britan Dining Hall on Georgia Tech's campus , the early bird deadline of June 18 can take be received by July 20. You will be notified will be open Monday through Friday, 7:30 advantage of the early bird fee savings and by July 26 if a course is full. Onsite registra• am-8:00 pm and Saturday and Sunday, have their registration packets mailed directly tion will be accepted if enrollment permits. 11 :00 am-7:00 pm. Meals at the dining hall to them prior to the meeting. The packets The MAA reserves the right to cancel a must be paid on an individual basis. Meeting will be mailed July 9 and there will be no course due to low enrollment, and will pro• participants must make their own arrange• need to register once you arrive in Atlanta. vide a full refund of course registration fees. ments for an early breakfast on Saturday and Sunday. Meal prices are: Regular Registration: Those who register after June 18 but before the final deadline of Breakfast-$4.50 July 20 must pay the regular registration fees. Mathfest Housing lunch-$5.50 These registration packets will not be mailed This year MAA will make dormitory housing Dinner-$6.00 and must be picked up at the Mathfest arrangements but will not make hotel reser• Registration Desk. You may also register on• vations. A special rate has been negotiated site at the registration desk. Travel Information at the headquarters hotel, the Renaissance Air Travel : Delta Air lines has been selected The Mathfest Registration Desk is located in Atlanta Hotel-Downtown, but meeting as the official airline for Mathfest 97 and the Georgia Ballroom lobby at the Renaiss• participants must call and make their own offers special meeting fares. To take advan• ance Atlanta Hotel-Downtown. Registration reservations. Call 1-800-463-3571 for reser• tage of these savings, you must travel Delta will be open n~7:OO pm on Friday, and vations and ask for the special Mathematical round-trip from anywhere within the U.S. 8:00 affi-4:00 pm, Saturday through Monday. Association of America Mathfest meeting and Canada to Atlanta. For reservations call You may also pick up or purchase event and rate. The following rates are guaranteed Uniglobe Travel Unlimited at 1-800-444-7176 tour tickets at this location. until June 30: or Delta at 1-800-214-6760. Refer to Mathfest file number XT529. The Windsor Company has been selected by • Single/Double $99 MAA as the official Mathfest management • Triple/Quad $119 Travel from the Airport: The Renaissance firm (similar to the role AMS had in the past) The above rates are subject to applicable Atlanta Hotel-Downtown is located at 590 Windsor will coordinate arrangements and taxes at the time of the meeting. West Peachtree, NW in Atlanta. registration. Send completed .....ation forms with lui payment to: A limited number of Georgia Tech dormitory Ataxi from the Hartsfield Atlanta International rooms are reserved for Mathfest. Rooms will Airport costs approximately $18.00 one way. The WindIor CaInpany be assigned on a first corne, first 5elVe and The Airport Shuttle runs continuously from 56M General W...... Drive student priority basis. If you would like to the airport to the major downtown hotels, SuIte 1-201 regisIer for dormitory housing, please including the Renaissance Atlanta Hotel• Ainallldria, VA 22312 CHIpIete the .....iatt Iedion on the Downtown. Shuttle tickets can be purchased ~ (703) 642-9385 ...... and enclose proper at the airport. You can also take the MARTA f.Ic (703) 642-9312 paymert. Dormitofy housing re5elVations rapid rail system from the MARTA terminal in Email: IIIpIIemoIwindI nut be received by )!lie 18. the airport to the North Avenue stop, located diagonally across the street from the hotel. Make checks payable to The Windsor If sharing a dorm room with another individ• The cost is $1.50 per person one way. Company. Payments by check must be made ual who is registering for Mathfest, only one in U.s. Funds and drawn on a u.s. bank. person should submit housing registration. By Car: The hotel is easily accessible by car from Interstate 85/75. Take Exit 100, Registration forms accompanied by insuffi• The additional person should only complete Sprin&W. Peachtree. Travel West on North cient payment will be returned or a $5 a registration form for the meeting. Confirm• Avenue to Peachtree Street. Take a right onto charge will be assessed if an invoice must ations for dormitory housing will be mailed Peachtree, drive 2 blocks and make a right be prepared to collect the delinquent on June 25. The rates for dorm rooms are: onto Prescott Street. At the next block, make amount. For each invalid check or credit • Single/US per room per night a right onto West Peachtree Street. The hotel card, a $25 processing fee will be assessed. • DoubIeIS40 per room per night will be on your left. Refund Policy: Cancellations must be To Dormitory Housing: Directions to the received in writing by July 15 for a 50% dormitory housing will be included with refund of registration fees and event tickets. confirmations for dormitory housing. There will be no refunds after this date. II DEADLINES: PLEASE NOTE THAT THESE ARE EARLIER THAN LAST YEAR Early Bird Registration • June 18 Regular Registration • July 20 Dorm Reservations • July 18 50% Refund on Registration and Event Ticket Cancellation • July 15

Name ______Name to appear on badge ______Address ______Telephone ______Fax Email Affiliation Guest badge ______Guest badge ______PLEASE NOTE CHARGE PER GUEST REGISTRATION BELOW

REGISTRATION FEES The Renaissance Atlanta Hotel-Downtown Please call 1-800-468-3571 and ask for the Mathe• MATH FEST Early Regular Amount Subtotal matical Association of America Mathfest 97 special by 6/18 by 7/20 & ons~e meeting rate. The rates per night for the meeting are: D Member 0 MM 0 AMS 0 Both $140 $183 -- Single/Double $99 &Triple/Quad $119. The above D Nonmember $216 $289 -- rates are subject to applicable taxes at the time of the D Graduate Student & Others Including Emeritus Members of MM or AMS, unemployed meeting. Currently the tax rate is 13%. or lemporarily employed individuals, individuals from developing nations, Kthrough 12 teachers and librarians $ 39 $ 49 -- D Please indicate if you need additional D Undergraduate Student $ 22 $ 27 -- assistance to fully participate in D Guest $ 10 $ 10 -- Mathfest 97. You will be contacted D One Day Registration $ 99 -- by The Windsor Company. -- SHORT COURSE ON EPIDEMIOLOGY MODELING Do you want your registration packet mailed in You NEED NOT be registered for Mathfest to attend the Short Course. advance? DYes D No D Student $ 50 $60 -- If yes, please provide your mailing address if D MAA Member and Mathfest Participant $125 $140 -- different from above: D Nonmember or Mathfest nonparticipant $175 $190 -- -- MINICOURSES To register for a Minicourse, you MUST be registered for Mathfest. Packets will be mailed July 9. D Developing the Ability in Beginning College Mathematics Majors to Write Proofs $ 45 -- D Knot Theory and Applications in the Sciences $ 45 -- D Music and Mathematics $ 45 Please complete this form & return -- with payment to: D Is Fuzziness a Mathematical Concept? $ 45 -- -- The Windsor Company 5600 General Washington Drive, Suite 8-201

SOCIAL EVENTS 1V'I"'rianTidets lIiegulvTdets Alexandria, VA 22312 D "Georgia on My Mind" Mathfestival - &/or - x $ 35 -- Phone: (703)642-9385 • Fax: (703)642-9382 D 25-Year Banquet _&/or - X $ 35 -- Email: [email protected] -n D PME Banquet: PME members & family, MM Student Chapter members, METHOD OF PAYMENT MM student paper presenters - &/or - x $ 12 -- o D PME Banquet: All others _&/or x $ 20 - -- D CHECK ~ -- Make checks payable to The Windsor Company. DORM HOUSING Payment must be in U.s. Funds and drawn on a U.S. Bank. A limited number of dorm rooms have been reserved for Mathfest &will be assigned on a first come first serve and student priority basis. 3 Arrival Date:. ____ Departure Date.: ____ If you are staying in a double, register for housing on only one registra- D CREDIT CARD tion form. Provide the name of the additional person here: . The additional person Visa, Master Card, Discover, Novus should register separately, but only for the meeting. Card Number ______Card Type ______Room Type #Nights Expiration Date ______D Single _x $ 35 Signature ______D Double _x $ 40 Name on Card ______

Please note that a $25 processing fee will be applied for each returned check or invalid credit card. GRAND TOTAL ENClOSED LI __----'I D PURCHASE ORDER #____ _ Indicate method of payment at right.-+ Please enclose copy. Downtown Atlanta/Conference Vicinity

Teehwood Drive

The Renaissance Atlanta Hotel-Downtown April 1997 FOCUS Teaching Math on the World Wide Web Steven M. Hetzler and Robert M. Tardiff

The World Wide Web provides a revolu• A web page contains information that can How does one get started writing these tionary opportunity for teaching math• be displayed (and instructions to the pages? It's no harder to construct one of ematics, communicating with students, browser for displaying that information) these pages than it is to write a computer and helping them construct their own learn• just like a WordPerfect or LaTeX docu• program. All you need are hardware, soft• ing. The same software that is used to cre• ment. In all but the simplest pages, some ware, access to the Internet, time, and a lot ate and browse web pages can create and of the information may be in other files; of patience. Interested? Then check out execute interactive laboratory modules that the web page contains pointers to those our website at http://henson2.ssu.edu/ make full use of multimedia. More impor• files (hypertext links). These pointers cre• -rmtardif/focus.htm for details of how to tantly, this software can be used to orches• ate opportunities to use multimedia, and get started. trate a computer algebra system (CAS) or mathematical and other software in an other mathematical software in a natural active learning environment. The reader Both Steven H etzle r and Robert Tardiffare way. can instruct the browser to load a helper, in the Department of Mathematics and say Mathematica, to display the file. So, if Computer Science at Salisbury State Uni• Much of the software is available at little the user has M athematica, the browser can versity in Maryland. Their e-mail ad• or no cost to academics via the Internet start Mathematica, download a notebook dresses are [email protected] and and is reasonably easy to use in a Win• from the website into Mathematica, and [email protected]. dows or Macintosh environment. This then slip into the background. The result technology is not restricted to the Internet is an interactive learning environment! The where speed of the connection is a real user can toggle between Mathematica and issue. The same programs can be run on the browser or even view the two simulta• your local machine or on a Local Area neously with a Mathematica Notebook Network (LAN), where speed of connec• designed to explore topics being discussed tion is not as much of a problem. on the web page.

u.s. Department of Commerce BUREAU OF THE CENSUS Mathematical Statisticians

1he u.s. Bureau of the Census, an agency in the Department and doctoral level mathematical statisticians with a strong of Commerce, invites applications for several positions academic background and excellent communications and throughout the agency. As the primary factfinder for the interpersonal skills. Successful candidates will have Nation the Census Bureau's mathematical statisticians knowledge in a number of the following areas: sampling support a large number of ongoing surveys and censuses techniques, experimental design, time series analysis, covering demographic and economic statistics. Besides regression analysis, linear models, exploratory data analysis, the decennial census of population and housing and the statistical inference, statistical analysis, statistical computing, quinquennial census of business the Census Bureau conducts and applied probability. U.S. CITIZENSHIP REQUIRED. a large number of establishment and household surveys. These efforts provide key data to quantify our Nation's Salary range: $28,208 - $59,725 (GS 7 - 12 levels) economic and social health. commensurate with education and experience. The Federal Government provides an excellent benefit package. The Primary areas of application include design, research, and Census Bureau is an Equal Opportunity Employer. evaluation in all areas of the Census Bureau's survey and census program. This includes design and analysis of To apply send resume, names of three references, and surveys and censuses, evaluation of nonsampling errors copy of transcripts to: occurring from nonresponse, coverage and measurement error, and research to reduce these errors .. Cynthia Z.F. Clark Associate Director for Methodology and Standards These positions located in Suitland, Maryland, close to U.S. Bureau of the Census Washington, D.C., are appropriate for bachelors, masters Washington, D.C. 20233 The Census Bureau is an Equal Opportunity Employer

15 FOCUS April 1997 The Third International Mathematics and Science Study

The Third International Mathematics and calculus and two physics textbooks. well in school subjects, as well as their Science Study (TIMSS) represents the home environment. In addition students most extensive investigation of mathemat• Student Assessments in their last year of secondary school were ics and science education ever conducted. Student assessments for both mathemat• asked a series of questions about their The study is sponsored by the International ics and science contained multiple choice, future career and education plans. Association for the Evaluation of Educa• short answer, and extended response items. Teacher Questionnaires tional Achievement (lEA) and funded in International scoring rubrics for short an• the U.S. by the National Science Founda• swer and extended response items defined Teachers responded to general questions tion (NSF) and the National Center for multiple categories of correct and incor• about their academic background, official Education Statistics (NCES). Approxi• rect responses. All short answer and ex• work schedule, familiarity and use of of• mately fifty countries have participated in tended response items, as well as over half ficial documents and guides, their ideas this comparative survey of education fo• of the multiple choice items for both math• about mathematics and science, and peda• cusing upon nine-year-old students, thir• ematics and science, have been released gogical approaches to two specific situa• teen-year-old students, and students in allowing detailed in-depth discussion and tions. With respect to the specific class their last year of secondary schools. For analyses. Release items are available for from which students were tested for the oldest students, TIMSS analyses con• viewing at the TIMSS International Study TIMSS, more specific questions were sidered three groups: a cross-section of all Center web site, www.ed.gov/NCES/ asked: specific topic coverage goals, typi• students completing their last year of sec• timsslbrochure.html. cal lesson profile, assignment and use of ondary education, i.e., a "literacy" sample; homework, use of student work groups, In addition, some countries, including the mathematics specialists, i.e., those stu• types and purposes of classroom assess• U.S., participated in the performance as• dents studying or having studied calculus; ment, and characterizations of students' sessments which measured students' re• and science specialists, those students opportunities to learn specific TIMSS sponses to hands-on, practical tasks The studying or having studied physics. TIMSS items. Teacher questionnaires were admin• TIMSS performance assessments were went well beyond traditional comparative istered only to those teaching the two conducted with subsamples of the nine• assessments by including a comprehen• younger student age groups. sive analysis of textbooks and curriculum and thirteen-year-old students participat• guides; investigations of instructional ing in the main TIMSS survey. There were School Questionnaires practices; students' classroom perceptions, five tasks each for science and mathemat• interest, and motivation; and various in• ics and two tasks that combined mathemat• School administrators responded to ques• fluences on curricular organization and ics and science for a total of twelve tasks. tions about the school's staff, the locus of student learning. All curriculum analysis responsibility for various decisions, stu• data are currently available. Questionnaire Student Questionnaires dents' behavior, course offering and stu• dent tracking, instructional time, and and assessment data for thirteen-year-old Students responded to questions about the course assignment/graduation criteria. students is also currently available. Ques• type and amount of homework assigned, School questionnaires were administered tionnaire and assessment data for nine• typical classroom instructional practices, to those representing all three student age year-olds will be available in late spring their interest in and motivations for doing 1997; questionnaire and assessment data groups. for students in the last year of secondary school is anticipated to be available the beginning of 1998. Following are brief descriptions of the type of data available from the various aspects of TIMSS. What's Happening at the MAA Curriculum Analysis • Former AMS President Ronald L. Graham of AT&T Research has been appointed P61ya Lecturer for 1997-98 and 1998-99. He will be visiting sections during those two A content analysis of textbooks and state years. curriculum guides detailed the specific topics, student performance expectations, • The MAA Board of Governors has elected James R. C. Leitzel (University of New and perspectives encouraged. Curriculum Hampshire) as governor-at-large representing Teacher Education and Jeffrey Lagarias guides from at least fifteen different states (AT&T Research) as governor-at-large representing Outside Academia. and multiple texts were examined for each • Past-president Lynn Steen chairs the new joint advisory board for FOCUS and MAA ofthe three student age groups: four math• Online. ematics and three science textbooks for nine-year-olds; three general mathemat• The above are just three of the many items included in the latest report by MAA ics, one algebra, and three science text• Secretary Martha J. Siegel. The full report is available on MAA Online. books for thirteen-year-olds; and two

16 April 1997 FOCUS

what we are attempting to assess. Since PERSONAL OPINION the emergence of evaluation forms in the '70s, with their emphasis on teaching, good practice in assessment has shifted its fo• cus to examine student learning. In pur• Question 13: How Do You Rate the Instructor? suit of this goal, we have created a wide Sandra Z. Keith and Pao-sheng Hsu variety of assessment practices such as student self-evaluations, portfolios, focus Most student evaluation fonns culminate try (where all the children are above aver• groups, peer reviews, exit interviews, etc. in a Question 13, typically: age) but raises the question of exactl y what These methods allow students to articu• Overall, how do you rate the instructor? purpose is served by the low 5 on the scale. late their opinions in ways that can signifi• To see a 2.8 or 3.2 in this situation as sig• cantly improve the learning environment What's wrong here? The question is per• nifying that the instructor failed should because they address learning experiences haps intended to guide students to sum• make an observer's skin crawl. rather than fuzzy and emotion-skewed marize their responses to the previous How does one even interpret a score of2.8 attitudes reported as a number. Mathemat• questions on the survey, and in this re• ics departments have been slower than spect the function of the question may be when responses on this question are dis• crete and the class size is small? For ex• other departments on many campuses to seen as exploratory, or fonnative. How• adopt these open-ended methods, and a ever, when this question appears on a sur• ample, a teacher with many high ratings has more to lose from a few angry scores heavy reliance on Question 13 in faculty vey, there is a danger that it will be regarded evaluation processes casts mathematics as the only significant item on the survey than a teacher with middle ratings; a fact which shows up in the standard deviations. further into the Dark Ages. More danger• and interpreted with a particularly blind ously, we imply to students that they may faith in the personnel process. To receive Noted assessment authority Clifford Adelman suggests that standard deviation finish the tenn shifting the responsibility a score of 2.8 on a scale in which 1 is high of their learning onto the teacher and away and 5 low may be seen as a tenninal fail• units are at least as important as means in matters of assessment, that variation in the from themselves. Indeed, a significant ing grade for the instructor. In this situa• problem with current student evaluations tion, the question becomes inappropriately results alters the meaning of the mean. * * Yet standard deviations are rarely referred is that they fail to review with the student evaluative, or in the assessment jargon, the ways in which the student has exerted summative. to in this setting, and at any rate, it's un• clear how they could be used wisely. his or her right to learn. In this sense, we It is fairly easy to persuade oneself as an are falling short of our mission to educate. evaluator that Question 13 carries its Third, semantics. Overall, how do you rate the instructor? How does one even inter• Well-worded student evaluation fonns can weight by reflecting on student comfort have their uses when they trigger issues with the learning environment, or general pret this vague question? Students may be influenced by the other survey questions and questions that can be answered else• student satisfaction. But there are serious where in the evaluation process. However, validity problems here. related to instruction which may favor the lecture approach or devaluate refonn meth• Question 13 becomes too easily a substi• First, a substantial literature on these sur• ods and interactive styles. Or the question tute for meaningful assessment. When veys suggests that on the most general or may allow for rogue responses based on used in departmental, institutional, or sys• undefined questions, student ratings of fe• feelings not tapped by other questions. tem-wide surveys, it pressures faculty to male and minority instructors tend to be There is no way to tell how the student is emphasize student comfort or even com• lower. * There are usually enough students using the question. Admittedly, students placency over student learning, thus sub• in a class who feel free to exercise their may provide follow-up comments, but verting educational goals. It therefore has biases on this question to skew the overall even then, their brief explanations usually no place on departmental, institutional, and result. raise more questions than they answer. One system-wide surveys. Second, how are the statistics to be man• ofthe authors received the comment: "The *Basow, S. A. e.g., in "Student Evalua• aged? A teacher's score on Question 13 is class was too abstract. I learned a lot more tions of College Professors: When Gen• frequently compared with the department's from one-on-one than class." How does der Matters," Journal of Experimental average or with the average of others teach• one factor this response, or indeed, any Psychology 87, no. 4 (1995): 656-665. ing a given course (since the level or type other response into a score? The problem ** Adelman, C. Lessons of a Generation, of course taught may influence the score is that the ambiguity of the question makes on this question). If, for example, the de• it a magnet for students to remark on any Education and Work in the Lives of the partmental average is 2.3 and the teacher differences which they happen to find HighSchool Class of1972, Jossey-Bass, receives 2.8, the conclusion may be that unsettling. In the long run, an institution (1994): 41. the teacher is in the 3-range, and thus, well that uses a survey with a Question 13 may below average. In the situation of one of be vulnerable to charges of inherently dis• Sandra Keith teaches at St. Cloud Univer• the authors, the departmental average on criminatory practices. At some institutions, sity in St. Cloud, Minnesota. Her e-mail this question was indeed 2.3. Since the the question is considered non-contrac• address is [email protected]. question is rated on a scale with 3 as a tual, and is prohibited under collective Pao-sheng Hsu teaches at the University middle, the skewed mean not only sug• bargaining. of"'faine in Orono. His e-mail address is gests that we are in Lake Woebegon coun- Last and most important is the question of [email protected].

17 FOCUS April 1997 SALE SALE SALE SALE SALE SALE SALE SALE SALE SALE SALE SALE The Mathematical Association of America

GEOMETRY From Pythagoras to Einstein Series: New Mathematical Library Geometric Transformations I K.O. Friedrichs Series: New Mathematical Catalog Code: NML-16/foc Library 88 pp., Paperbound, 1965 I.M. Yaglom ISBN 0-88385-616-6 Translated by Allen Shields List: $8.00 Catalog Code: NML-08/foc MAA Member: $6.00 133 pp., Paperbound, 1962 NUMBERS & NUMBER ISBN 0-88385-608-5 THEORY List: $13.00 HISTORY MAA Member: $10.00 Continued Fractions Studies in the History of Math• Series: New Mathematical Geometric Transformations II ematics Library Series: New Mathematical Series: Studies in Mathematics Carl D. Olds Library Esther R. Phillips, Editor Catalog Code: NML-09/foc I.M. Yaglom Catalog Code: MAS-26/foc 162 pp., Paperbound, 1963 Translated by Allen Shields 320 pp., Hardbound, 1987 ISBN 0-88385-609-3 Catalog Code: NML-21/foc ISBN 0-88385-128-8 List: $12.00 189 pp., Paperbound, 1968 List: $1500 MAA Member: $8.00 ISBN 0-88385-621-2 MAA Member: $12.00 List: $l3.00 An Introduction to Inequalities MAA Member: $10.00 Mathematics: Queen and Ser• Series: New Mathematical vant of Science Library Geometric Transformations III Series: Spectrum Edwin Beckenbach "~.!!)'~;'f!IIIiiI!I:!I'''''''t,~ Series: New Mathematical E.T. Bell Bellman Library Catalog Code: QAS/foc Catalog Code: I.M. Yaglom 454 pp., Paperbound, 1987 133 pp., Translated by Abe Shenitzer ISBN 0-88385-447-3 ISBN 0-88385 Catalog Code: NML-24/foc List: $14.99 List: $12.00 237 pp., Paperbound, 1973 MAA Member: $12.99 MAA ISBN 0-88385-624-7 List: $13.00 The Role of Mathematics in MAA Member: $10.00 Science Series: New Mathematical Series: New Mathematical Library Geometric Inequalities Library Philip J. Davis Series: New Mathematical M.M. Schiffer and Leon Bowden Catalog Code: Library Catalog Code: NML-30/foc 65 1 pp., N.D. Kazarinoff 207 pp., Paperbound, 1984 ISBN 0-88385 Catalog Code: NML-04/foc ISBN 0-88385-630-1 ~t: $l3.00 132 pp., Paperbound, 1961 List: $10.00 TO order, CaII\A Member: $ .. ISBN 0-88385-604-2 MAA Member: $100 .... List: $10.00 MAA Member: $7.50 1-800-331-16],;:, P.o. Box 9112 • WASHINGTON, DC 20090-1112 . 18 April 1997 FOCUS ICMI Study on History The International Commission on Math• concern is in using history of mathemat• duct related research activities during the ematical Instruction (lCMI) is conduct• ics in mathematics education? next two years. It is planned that a book ing a study on the role of the history of 5. Do different parts of the curriculum will be published in late 1999 in the !eM! mathematics in the teaching and learning utilize history of mathematics in a differ• Study series, based on contributions to and of mathematics. This study is led by the ent way? outcomes of the conference and research International Program Committee (IPC) activities. of ten members, of whom Florence 6. Does the experience of learning math• Fasanelli of the MAA is the American ematics in different parts of the world, or The IPC for the study invites members of representative. The IPC has prepared a cultural groups in local contexts, make the educational and historical communi• discussion document in which key issue different demands on the history of math• ties to propose or submit contributions on related to the study are identified, pre• ematics? specific questions, problems, or issues sented, and discussed in a preliminary stimulated by the discussion document no 7. What role can history of mathematics manner. The document has identified the later than June I, 1997. These contribu• play in supporting special educational major questions the study will address. tions will be regarded as input to the plan• needs? These include ning of the study conference. The entire 8. What are the relations between the role Discussion Document is appearing in 1. How does the educational level of the or roles we attribute to history and the L'Enseignement math matique, the offi• learner bear upon the role of history of ways of introducing or using it in educa• cial organ of ICMI, but because the fPC mathematics? tion? wants to make it accessible to as many 2. At what level does history of mathemat• people as possible, it will also be available 9. Why would using history of mathemat• ics as a taught subject become relevant? electronically on MAA Online. If you can• ics be good for the learner? not access the web, you may obtain a copy 3. What are the particular functions of a These questions and others will be dis• by contacting Florence Fasanelli at the history of mathematics course or compo• cussed in more detail at an invited study MAA, 1529 18th St. NW, Washington, DC nent for teachers? conference to be held in France in the 20036-1385; fax: (202)453-5450; e-mail: 4. What is the relation between historians spring of 1998. Individuals will also con- [email protected]. of mathematics and those whose main Birds flock together for protection. As it turns out, so do we. Whoever said there is safety in numbers must have been talking about MAA. After all, one of your greatest member benefits is access to valuable insurance coverage. At group rates outsiders envy. We've not only done all the legwork in finding these plans. We've tailored them to the preferences of you, our members. The coverage is easy to update as your needs change. And it stays with you, even when you change jobs. To speak with a customer service representative, call 1800 424-9883, or in Washington, DC (202) 457-6820, between 8:30 a.m. and 5:30 p.m. eastern time. It's one time when the numbers are all in your favor. MAA Insurance Term life • Disability Income Protection • Excess Major Medical • Member Assistance • High-limit Accident

19 FOCUS April 1997 Teaching and Learn• WORKSHOPS ing on MAA Online MAA Online, the newsletter of the MAA Multiwavelets and their Applications on the World Wide Web, has introduced a section titled "Teaching and Learning" Allegheny College, Meadville, PA, June 16-20, 1997 which will feature columns, articles, and news related to the teaching of mathemat• This short course focuses on the construction and properties of scaling vectors, the ics. The section includes two regular col• associated multi wavelets, and their application to image compression, signal process• umns: "Research Sampler" and ing, and differential equations. For information and/or an application, contact George "Innovative Teaching Exchange." The Bradley, MathieS Dept., Duquesne University, Pittsburgh, PA 15282; (412) 396-5115; Sampler, edited by Annie and John Selden, e-mail: [email protected]. provides an overview of what is new in research on undergraduate mathematics education. The Teaching Exchange, ed• ited by Bonnie Gold, is an opportunity for DIMACS Workshops teachers to share the great ideas they have developed in their classrooms. Economics, Game Theory, and the Internet DIMACS Center, Rutgers University, Piscataway, NJ In addition to the two regular columns, April 18-19, 1997 "Teaching and Learning" contains short news stories related to mathematics edu• The Internet poses many interesting challenges for theoretical economics and game cation and pointers to other materials on theory. The highly asynchronous interactions and large degree of anonymity inherent the web, such as the Project NExT website in the Internet require that many traditional game theoretic notions of equilibrium, and a website dealing with the teaching of learning, and mechanism design, need to be reexamined in this context. Invited speak• developmental mathematics. Longer fea• ers include Herve' Moulin, WIlliam Sharkey, and Hal Varian. For further information, ture articles are also planned for the near contact Eric Friedman, Department of Economics, Rutgers University; friedman@fas• future. The URL for MAA Online is econ.rutgers.edu. For local arrangements, contact Pat Pravato, DIMACS Center; (908) www.maa.org, from which one can click 445-5929; [email protected]. WWW:http://dimacs.rutgers.eduIWorkshops/ on "Teaching and Learning" to enter this index.html section of the site. Network Design: Connectivity and Facilities Location Of course there's a lot more in MAA Online Princeton Universitiy (Nassau Inn) that's relevant to teaching, from news about April 28-30, 1997 professional development to book reviews which range from "popular" mathematics The workshop will focus on combinatorial, algorithmic, and applicational aspects of books to books about teaching mathemat• these problems. We will be especially interested in efficient approximation algorithms ics. Contributions are welcome. Send e• and their computational performance. The distinguished speaker will be Sanjeev Arora. mail to the editor, Fernando Gouvea, at For further information, contact organizers Ding-Zhu Du, [email protected] or Panos [email protected]. Pardalos, [email protected]. For local arrangements, contact Sandy Barbu; (609) 258- 4562; [email protected]. WWW:http://dimacs.rutgers.eduIWorkshopS/index.html Microsurveys in Discrete Probability Math Ph.D. Institute for Advanced Study. Princeton Unemployment Rate Falls June 2-6, 1997 The 1996AMS-lMS-MAAAnnuaISur• Probabilistic aspects of algorithms and discrete mathematics, and discrete aspects of vey of New Doctoral Recipients and Fac• theoretical probability form a broad and active field of contemporary research. The ulty Salaries (First Report) is now workshop is aimed at researchers seeking to broaden their familiarity with the field. The available. Highlights from the report are: organizers are not soliciting contributed papers, but there will be a website set up in advance of the meeting featuring profiles of participants, abstracts of talks (both the • Unemployment fornew doctoral recipi• main fifty-minute lectures and the twenty-minute presentations), and open problems; ents declined to the lowest rate since fall aU registered participants are invited to contribute to the website. These contributions 1990. should be sent to Barbara Quigley; [email protected]. Invited speakers • Doctoral recipients employed by busi- will include David Aldous, Persi Diaconis, Jim Fill Ravi Kannan, Harry Kesten, Robin ness and industry in the U.S. increased. Pemantle, Boris Pittel, Jim Propp, and Alistair Sinclair. Contact Jim Propp, Call (301) 942-9595 or e-mail [email protected]. For local arrangements, contact Pat Pravato; (908) 445-5929; [email protected] to request a [email protected]. WWW: http://dimacs.rutgers.eduIWorkshopS/index.html copy.

20 April 1997 FOCUS NSF Undergraduate Faculty Enhancement Workshop In Memoriam: J. Teaching Undergraduate Geometry, Cornell University, June 9-14, 1997 Sutherland Frame

This workshop is intended for college and university faculty who teach (or soon will J. Sutherland teach) an undergraduate geometry course-such as the courses typically attended by Frame, profes• future or in service teachers. The leaders of the workshop will be Kelly Gaddis (Buffalo sor of math• State College), David Henderson (Cornell University), Jane-Jane Lo (Cornell Univer• ematics sity), and Avery Solomon (Cornell University). emeritus, In the mornings the participants will experience a learning and teaching environment Michigan State that is innovative both in terms of content and in terms of teaching methods. The content Uni versi ty, will be the integration of geometries on plane, sphere, and other surfaces-presented died at his through problems which emphasize experiencing the meanings in the geometry. Stu• home in East dent investigations, small group learning, and writing assignments will be explored. Lansing, Michigan, on In the afternoons there will be seminars and presentations on topics related to the February 27, 1997. He was 89 years old. workshop theme, including "How to Write Good Exploratory Problems," "Using Writ• ing in Mathematics," "Curriculum Developments in School Geometry," "Using Com• Dr. Sutherland, "Sud" to all who knew him, puterTechnology in Geometry," "Formal versus Intuitive Knowing in Geometry," "What was highly active in both the MAA and the is in the 8 Undergraduate Geometry Courses at Cornell," "Non-test-basedAssessments," mathematics honor society Pi Mu Epsi• "Student Affects and Beliefs Toward Innovative Program," and "Including All Students lon. He personally installed more than fifty by Encouraging Diverse Ideas." In addition there will be ample free time for informal chapters of Pi Mu Epsilon, and in 1952 he discussions and enjoyment of the geometry of nature in and around Ithaca. created and developed the highly success• ful Pi Mu Epsilon Summer Student Paper Much ofthe housing and food expenses will be covered for all participants by the NSF. Conferences in conjunction with the MAA There may also be very limited NSF funds available to support travel costs for partici• and the AMS. He was president of Pi Mu pating faculty from institutions with limited resources. The NSF will also support Epsilon from 1957 to 1966. He was an follow-up activities by the participants after the workshop including local workshops, MAA governor for a period, and at the exchange of related classroom materials, and communication of experiences and ideas. Association's request, he organized the first Enrollment is limited. Applications will be reviewed beginning April 1. For more infor• MAA-AMS Employment Register, which mation and application procedures, contact the UFE Geometry Workshop, Dept. of he chaired from 1953 to 1958. Math, Cornell University, Ithaca, NY 14853-7901; fax : (607) 255-7149; e-mail: At the Joint Mathematics Meetings in J anu• [email protected]; WWW: http://math.comell.edu/-dwh. ary 1994, Sud was awarded the Yueh-gin Gung and Dr. Charles Y. Hu Award for Distinguished Service to Mathematics, the Undergraduate Association's most prestigious award. Posters Awarded

The Undergraduate Student Poster Session sponsored by the MAA and CUR at the January meetings in San Diego was very successful and visi• tors were truly impressed with the quality of the projects presented. A panel of three judges, Joe Gallian, Judyth Palagallo, and Phil Straffin, carefully evaluated all posters and recognized five of them with a $100 Front row: Sarah Spence, Jessica Sidman, Pilar Mara ; prize each, with money provided by Second row: Dmitry Ostrovsky, Andy Miller the MAA and CUR. The students selected for recognition were Pilar Sarah Spence (University of Richmond). Mata (California State University, Fuller• Each was also given a book kindly offered ton), Andy Miller (Wartburg College), by the exhibitors present at the meeting. Dmitry Ostrovski (Macalester College), Mario Martelli (California State Univer• Jessica Sidman (Scripps College), and sity, Fullerton) organized the session. 21 FOCUS April 1997

CLASSIFIEDS

ALABAMA dents, recruit and tutor students, and write tech• Community College of Philadelphia, 1700 Spring nology grants for introductory courses. Garden Street, Philadelphia, PA 19130. We are Troy State University Dothan Application letter, curriculum vitae, unofficial commi tted to a work force reflective of our Com• Seeks applicants for Assistant Professor of Math• munity. graduate transcripts, and three letters of recom• ematics. This is a tenure track position requiring mendation should be sent to: Search Committee, EEO/AA Employer. an earned doctorate in mathematics. The ability Math Department, One University Place, LSU• to teach both undergraduate and graduate courses Shreveport, Shreveport, LA 71115. University of Pittsburgh-Bradford in mathematics is required. Salary is commensu• Mathematics-Tenure-Track, full-time assistant LSU-Shreveport is an EEOIAA Employer. rate with training and experience. Position begins professor position to begin Fall 1997. Must be September 1, 1997 and will remain open until MISSOURI able to teach remedial, precalc and applied calc filled. Interested applicants should submit a let• level math courses. Ph.D. or Ed.D. required. ter of application, resume, transcripts, and three Cottey College of Missouri Excellence in teaching and current classroom professional references to: Ms. Janet McQueen, Assistant or Associate Professor, full-time, ten• pedagogy in the area of remedial math, academic Troy State University Dothan, P.O. Box 8368, ure track faculty starting Fall 1997; three person advising, and the ability to direct undergraduate Dothan, AL 36304-0368. department. Curriculum now includes algebra, research are essential. In order to ensure full Troy State University Dothan is an EEOIAAIA• trigonometry, statistics, precalculus, calculus and consideration, send letter of application, vita, DA employer and encourages applications from differential equations; four sections per semester official transcripts, and three reference letters by all minorities. Anyone requiring special accom• teaching load. Ph.D. and experience preferred. May I, 1997, to: Dr. Richard Melka, Math Search modations is encouraged to contact the Human ABO considered for initial appointment, but Committee, Univ. of Pittsburgh at Bradford, 300 Resource Coordinator at (334) 983-6556 Ext. 208. continuation requires doctorate. Teaching ori• Campus Dr., Bradford, PA 16701-2898. Women ented, small, private (not church- related), and minorities are encouraged to apply. AAlEOE LOUISIANA residential, two-year liberal arts college for LSU -Shreveport women. 10: I students per faculty ratio, students Department of Mathematics from 35-40 states and 18-20 countries. 80 miles Applications are invited for three anticipated ten• from Kansas City metro area, 40-140 miles for VIRGINIA ure-track Assistant Professor, denoted I thru 3, Ozark recreation areas. Our purpose is the devel• and two anticipated Instructor positions. The nor• opment of intellect and leadership in young University of Richmond mal teaching load is 12 hours per semester. women. To apply send curriculum vitae, names The Mathematics and Computer Science Depart• and phone numbers of three references, and cover ment invites applications for a one-year position Position I: Requires a Ph.D. in Mathematics or letter expressing interest to Dr. Hal Ross, Aca• as Visiting Assistant Professor of Mathematics Mathematics Education with a strong mathemat• demic Vice President, Cottey College, Nevada, beginning in August of 1997 and ending in May ics background. Candidate should be in the Missouri 64772. E-mail: [email protected]. of 1998. The teaching load is 12 hours (normally forefront of math reform and technological ad• FAX: 417-667-8103. Telephone: (417)667-8181. four courses) per semester. Candidates with Ph.D. vances; will work with area teachers to meet their in hand are preferred. The University is an equal needs and teach a variety of math courses. Posi• PENNSYLVANIA opportunity employer. tion 2: Requires a Ph.D. in mathematics and commitment to work with upper-level under• Mathematics University: University of Richmond graduate. Candidate will be active in the MAA, Community College of Philadelphia Department: Mathematics and Computer Science particularly student activities. Position 3: Re• Anticipates one full-time tenure track faculty Department quires a Ph.D. in mathematics with a strong position in the Mathematics Department effec• Contact Person: Dr. Gary Greenfield background or a Ph.D. in statistics. Expertise in tive Fall 1997. Qualifications include a Master's e-mail: [email protected] applied math is desirable. Candidate will also help Degree in Mathematics, commitment to quality determine and serve the math and statistical needs remedial and college level teaching, and interest of businesses and industries. in curriculum development. Proven record of innovative, collaborative learning strategies, and The two instructor positions require a masters technology applications a plus. Send resume and degree in mathematics. Candidates will teach three letters of recommendation by April 30, 1997 introductory courses, work with lower-level stu- to: Mathematics Department Hiring Committee,

Rates for FOCUS Employment Advertisements are $95.00 per column inch (one inch minimum), billed to the nearest 112 inch. All advertisements are set with a one-line headline, centered, boldface, consisting of the institution name, unless additional headline information is provided. All invoices include a tear sheet. Advertising Copy Deadlines: The first of the month, two months prior to publication. FOCUS is published in February, April, June, August, October, and December. Advertisers should contact: Joseph Watson, The Mathematical Association ofAmerica, 1529 18th St., NW, Washington, DC 20036; (202) 387-5200; fax: (202) 265-2384; e• mail: [email protected]

22 April 1997 FOCUS MEETINGS

National MAA Meetings College, Dobbs Ferry, NY - Spring 1998, Pima Community College, August 1-4, 1997 MathFest, Atlanta, GA MICHIGAN - May 2-3, 1997, Wayne State Tucson, AZ January 7-1 0, 1998 Eighty-firstAnnual Meet• University, Detroit, MI SEAWAY-April 18-19, 1997, Broome Com• ing, Baltimore, MD. Board of Governors - May 1-2, 1998, Western Michigan Uni• munity College, Binghamton, NY Meeting January 6, 1998 versity, Kalamazoo, MI - November 7-8, 1997, Siena College, January 13-16, 1999 Eighty-second An• MISSOURI - April 11-12, 1997, Missouri Loudonville, NY nual Meeting, San Antonio, TX. Board Western State College, St. Joseph, MO - April 1998, York University, No. York, of Governors Meeting, January 12, - Spring 1998, Southwest Missouri State Ontario, Canada University, Springfield, MO TEXAS - April 3-5, 1997, Texas Lutheran 1999. NEBRASKA-SOUTHEAST College, Sequin, TX January 19-22,2000, Eighty-third Annual SOUTH DAKOTA-April 11-12, 1997,Wayne - Spring 1998, Southern Methodist Uni• Meeting, Washington, DC. Board of State College, Wayne, NE versity, Dallas, TX Governors Meeting, January 18, 2000. NEW JERSEY - April 12, 1997, Middlesex - Spring 1999, Southwest Texas State Uni• January 10-13, 200 I Eighty-fourth An• County College, Edison, NJ versity, San Marcos, TX nual Meeting, New Orleans, LA. Board NORTH CENTRAL - April 25-26, 1997, WISCONSIN - April 11-12, 1997, Univer• of Governors Meeting, January 9, 2001 Mankato State University, Mankato, sity of Wisconsin-River Falls, River MN Falls, WI Section Meetings NORTHEASTERN - June 6-7, 1997, - April 17-18, 1998, University of Wis• Merrimack College, N. Andover, MA consin-Stevens Point, Stevens Point, WI ALLEGHENY MOUNTAIN - April 4-5, - Nov 21-22, 1997, Western New England 1997, Westminster College, New College, Springfield, MA Wilmington, PA Other Meetings OHIO-April 11-12, 1997,YoungstownState - April 1998, Clarion University of PA, June 6-8, 1997 Annual Meeting of the University, Youngstown, OH Clarion, PA Canadian Society for History and Phi• OKLAHOMA-ARKANSAS - April 4-5, EASTERN PA & DELAWARE - April 17, losophy of Mathematics, Memorial Uni• 1997, University of Central Oklahoma, 1997, Ursinus College, Collegeville, PA versity, St. John's, Newfoundland. Edmond, OK - November I, 1997, University of Penn• - March 27-28, 1998, University of Ar• Featured speaker: Ruediger Thiele sylvania, Philadelphia, PA kansas-Little Rock, AR (Leipzig). Contact Glen Van Brummelen, INDIANA - October 18,1997, Wabash Col• - Spring 1999, Southern Nazarene Univer• Secretary/Treasurer; (403) 465-3500; lege, Crawfordsville, IN sity, Bethany OK fax: (403) 465-3534; e-mail: - March 20-21, 1998, Ball State Univer• PACIFIC NORTHWEST - June 19-21, 1997, [email protected] sity, Muncie, IN Western Washington University, INTERMOUNTAIN - April 10-12, 1997, Bellingham, WA Utah State University, Logan, UT ROCKY MOUNTAIN - April 11-12, 1997, IOWA -April 11-12,1997, Iowa State Uni• Metro State College and Univ of Colo• versity, Ames, IA rado-Denver,CO HAVE YOU KANSAS - March 14-15, 1997, Pittsburg SOUTHEASTERN - March 13-14, 1998, State University, Pittsburg, KS College of Charleston, SC LOUISIANA-MISSISSIPPI - March 6-7, SOUTHERN CALIFORNIA - October 4, MOVED?? 1998, University of New Orleans, LA 1997, Claremont McKenna College, MD-DC-VA-ApriI18-19, 1997, William & Claremont, CA Mary, Williamsburg, VA MAA makes it easy to SOUTHWESTERN - April 4-5, 1997, New METRO. NEWYORK-May 3,1997, Mercy Mexico State University, Grants, NM change your address Please inform the MAA about yourchangeof address by MAA NATIONAL ELECTIONS ARE AROUND THE CORNER using the electronic com• bined membership list at Your vote counts towards MAA Onlinewww.maa.org or call 1-800-331- the future of the 1622, fax; (301) 206-9789, email mathematical profession! [email protected] or mail to MAA, Check your mailbox. Your ballot P.O. Box90973, Washington, will arrive in April. D.C.20036.

23 ! The new TI-83! The singular solution for a multi-function world.

One calculator x V, to hall(lIe algebra o ., through calculus. '-.....li-- . '!7~ -i.n Another fol' finance. I .n i:. 1.33 -.211 And a comput.er program to 1.6OS .S711 )1:1 .0""27 perform statistical computations. V:-.15517M1 Whoa. Wouldn't it be extraordinary Math. Gmph-7i!I!/f' :>p/il Sf'I"('{!/1 ulloU'.~ one calcuhlt.or ('Quid meet so if lJml 10 Iran' III(' yl"llpll many diverse needs, and Wid scrol/ille lubll' still be easy to usc? si HI IIi/(! !WOllsl Y Well, now one docs just that. Presenting the Tl~83 Graphing Calculator. Statistics. Disploy 111(; revolutionary r('S/lII.~ oj IIlJlXJlIlI'sis /I'.~ls {jmpilical/y '1'1 -83 handles a host. of functions mllIIlUIiI(')·iclIl/y. for a variety of co!lcge subjects. Por Cuit"lIiall'r01uiril'IiC(, instance, the TI-8-3 allows your students to i /11"1'1'0/.\. differentiate graphs with a variety of line styles, analyze data set.s of up t.o "'''''48 . 00 -1%"'1 4.90 999 elements, and solve for different variables interactively. Plus, 1h e TI-8!J PV'9000 .. PM T =·2~ • . 00 handles inferenr iaI statistics and the most popular financial functions lI'il h FV=0.ae case. Because it's based on the popular 1'1-82, there's 110 learning wive either-. P' V·l2. 00 C/ Y=12.00 In fact, the tWO can be used side-by-side in class. The affordable, portable PMT: BEGrH

1'1-83. !n a multi-function world, there simply is no equal. Finance. Fi 110 IIcilli j!lIIcliom; include Time-Vaiw>-oj-Molley, H!sl! j1(JII".~, rr lid ~TEXAS 1111/0"/ i.:ml iOIl. INSTRUMENTS For more information about the Tl-&1, ealll-800-TI-CAfu.:S (U.S. and Canmla), scnd c-mail to: ti-Ctlrtls@/ioo))/orvisit us or l the Internet at hl/p.//u'",//" lI.cuII/leak