Teaching Time Savers: Some Advice on Giving Advice Michael E

Claremont Colleges Scholarship @ Claremont

All HMC Faculty Publications and Research HMC Faculty Scholarship

12-1-2006 Teaching Time Savers: Some Advice on Giving Advice Michael E. Orrison Jr. Harvey Mudd College

Recommended Citation Orrison, Michael. "Imagine Math Day: Encouraging Secondary School Students and Teachers to Engage in Authentic Mathematical Discovery." MAA FOCUS 26.6 (2006): 24-27.

This Article is brought to you for free and open access by the HMC Faculty Scholarship at Scholarship @ Claremont. It has been accepted for inclusion in All HMC Faculty Publications and Research by an authorized administrator of Scholarship @ Claremont. For more information, please contact [email protected]. FOCUS December 2006

FOCUS is published by the Mathematical Association of America in January, February, FOCUS March, April, May/June, August/September, October, November, and December. Volume 26 Issue 9 Editor: Fernando Gouvêa, Colby College; [email protected] Inside Managing Editor: Carol Baxter, MAA; 4 2007 Haimo Award Winners to Speak at the January Joint Meetings [email protected] By Colin Adams Senior Writer: Harry Waldman, MAA; [email protected] 6 Archives of American Mathematics Spotlight: The School Mathematics Please address advertising inquiries to: Study Group Records [email protected] By Kristy Sorensen President: Carl C. Cowen 8 MAA Names Arthur Benjamin—Mathematical Wizard, Writer First Vice-President: Carl Pomerance, and Editor—Pólya Lecturer Second Vice-President: Deanna Haunsperger, By Harry Waldman Secretary: Martha J. Siegel, Associate Secretary: James J. Tattersall, Treasurer: 9 The Fourth Blackwell-Tapia Conference John W. Kenelly By Joe Gallian Executive Director: Tina H. Straley 9 Math Horizons: Time for a New Editor FOCUS Editorial Board: Robert Bradley; By Steve Kennedy Joseph A. Gallian; Jacqueline Giles; Colm Mulcahy; Michael Orrison; Peter Renz; Sha- 10 Geometry If not, why not? If so, what? ron Cutler Ross; Annie A. Selden; Hortensia Soto-Johnson; Peter Stanek; Ravi Vakil. By P.N. Ruane Letters to the editor should be addressed to 13 MAA is Offered Unique Opportunity to Buy Golden Icosahedron Fernando Gouvêa, Colby College, Dept. of By Harry Waldman Mathematics, Waterville, ME 04901, or by email to [email protected]. 13 Summer Mathematics Program for Women at Carleton College Subscription and membership questions By Deanna Haunsperger should be directed to the MAA Customer Service Center, 800-331-1622; e-mail: 14 Perception and Research: Mathematics, Gender, and the SAT [email protected]; (301) 617-7800 (outside By Cathy Kessel U.S. and Canada); fax: (301) 206-9789. MAA Headquarters: (202) 387-5200. 16 Teaching Time Savers: Some Advice on Giving Advice By Michael E. Orrison Copyright © 2005 by the Mathematical Association of America (Incorporated). 18 What I Learned at the MAA Digital Library Workshop Educational institutions may reproduce articles By Gizem Karaali for their own use, but not for sale, provided that the following citation is used: “Reprinted 21 Legendary Mathematician and Former MAA President G. Baley Price with permission of FOCUS, the newsletter Dies at 101 of the Mathematical Association of America By Harry Waldman (Incorporated).” 22 AAAS Meeting in San Francisco Will Feature Periodicals postage paid at Washington, DC and additional mailing offices.Postmaster: Send Interdisciplinary Mathematics Program address changes to FOCUS, Mathematical By Edward Aboufadel Association of America, P.O. Box 90973, Washington, DC 20090-0973. 23 A Mathematician’s View of the AAAS Annual Meeting By David L. Finn ISSN: 0731-2040; Printed in the United States of America. 25 Writing as an Effective Teaching and Assessment Tool By Anna Davis 31 Employment Opportunities On the cover: The golden icosahedron on the cover was offered for sale to the MAA. See page 13 for the full story. Photograph provided by Sebastian Thewes.

December 2006 FOCUS

Birth Announcement: It’s a SIGMAA!

We are proud to announce the arrival tional opportunities among undergradu- Joint Meetings, including an MAA panel, of a new Special Interest Group of the ates and undergraduate faculty in the an MAA CUPM subcommitee discus- Mathematical Association of America, fields of mathematical and computational sion and an MAA minicourse, as well as on Mathematical and Computational biology. This necessarily includes inter- AMS & SIAM events. BIO SIGMAA is Biology, henceforth to be known as BIO action with all concerned departmental the official sponsor of a three-part MAA SIGMAA. This SIGMAA was officially structures (i.e. mathematics, computer session on Integrating Mathematics and born at MathFest in August 2006, after science, biology, and other related de- Biology in Undergraduate Education, to the usual nine month gestation period. partments) and also institutions and be held on Friday, January 5, 2007, from organizations that feed into, and from, 8:00 am to 10:55 am, Sunday, January 7, The BIO SIGMAA charter begins: the undergraduate programs. 2007, 4:15 pm to 6:10 pm, and Monday, January 8, 2007, 8:40 am to 10:35 am. The focus of BIO SIGMAA is on the The first BIO SIGMAA Business Meet- pedagogy of mathematical and computa- ing and Reception will take place on Questions regarding membership in BIO tional biology at the undergraduate level. Saturday, January 6, 2007, from 5:45 SIGMAA or the goals and activities of This includes the support of curriculum pm to 7:00 pm, at the Joint Mathematics BIO SIGMAA, should be directed to development, faculty development, and Meeting in New Orleans. the BIO SIGMAA Chair, Eric Marland undergraduate research in those fields. at [email protected]. The BIO The purpose of BIO SIGMAA is to sup- Dozens of talks and other interesting ses- SIGMAA web site is at http://www.maa. port those activities that will enhance the sions relating to mathematical and com- org/SIGMAA/biosigmaa. exchange of ideas and access to educa- putational biology are scheduled for the

MAA Study Tour to Celebrate Euler’s 300th

By Lisa Kolbe

T o help commemorate Leonhard In four full days in Berlin, we will not Euler’s 300th birthday, the MAA Math- only visit the Berlin Academy where ematical Study Tour for 2007 will be an Euler worked, but also learn about math- Euler tour, visiting his birthplace, Basel, ematics in the time of Weierstrass at the and the two cities in which he spent his University of Berlin (now the Humboldt working life, St. Petersburg and Berlin. University). In addition, we will meet The Study Tour will happen on July 1- with mathematicians in Berlin today, to 14, 2007. There will be five full days in discuss common issues in mathematics St. Petersburg, with tours of the places education, and be able to enjoy a musi- where Euler lived and worked and the cal performance at one of Berlin’s many cemetery where he is buried. We will musical venues. visit the Academy of Sciences to see their archive of Euler letters and manuscripts The tour leaders will be Victor J. Katz, and meet with Russian mathematicians Professor Emeritus of Mathematics, at the St. Petersburg Mathematical So- University of the District of Columbia, as well as that of other mathematicians, ciety and with teachers who work with and Phyllis Katz, founding Executive can help inspire and motivate mathemat- talented youth. Director (retired) of Hands On Science ics learning. In addition, participants with Outreach, Inc. In each city, Phyllis Katz expertise in any area related to the tour In two days in Basel, we will visit the will provide interested participants with are encouraged to contact Victor Katz church where Euler’s father was pastor ways to use the tour experience in teach- personally to discuss the possibility of and hear about how work is proceeding ing. She will help you formulate plans sharing their knowledge with the other on the massive collection of Euler’s col- to use your photographs and other infor- tour members. lected works. There will also be visits to mation to assist students in developing sites associated with Johann Bernoulli, projects involving mathematics history. See http://www.maa.org/ euler_trip/ for Euler’s teacher at the University of Ba- She will also provide suggestions on how full details, itinerary and registration. sel. visits to museums can supplement formal The number of travelers for this tour is

teaching, and on how Euler’s biography, limited to 35. FOCUS December 2006

2007 Haimo Award Winners to Speak at the January Joint Meetings By Colin Adams

The Deborah and Franklin Tepper the co-editor of the MAA’s undergraduate His expository work and his workshops Haimo Award for Distinguished College magazine, Math Horizons, she has writ- have touched many more students either or University Teaching of Mathematics ten a variety of expository and research directly or through the teachers who have recognizes excellence at the national articles. Her MAA book, Proofs that learned from him. level in the teaching of mathematics. Really Count: the Art of Combinatorial The 2007 winners are Michael Starbird Proof, co-authored with Arthur Benja- Mike’s teaching excellence is document- from the University of Texas at Austin, min, has been described (by Persi Di- ed by about a dozen teaching awards, Jennifer Quinn of the Association for aconis) as a blend of the talents of Martin including the Excellence Award from Women in Mathematics, and W. Gilbert Gardner and Houdini: “It gives magical the Eyes of Texas (twice), the Dad’s Strang of the Massachusetts Institute of ‘aha’ proofs that are real mathematics but Association Centennial Teaching Fellow- Technology. As happens every year, the accessible to everyone.” Not surprisingly, ship, the President’s Associates Teaching winners have been invited to speak on it won the MAA’s Beckenbach Book Excellence Award, the Jean Holloway “the secrets of their success” at the Joint Prize in 2006. Award for Teaching Excellence, the Chad Mathematics Meetings, to be held in New Oliver Plan II Teaching Award, the Friar Orleans on January 5–8. This special ses- The excellence of Jenny’s teaching has Society Centennial Teaching Fellowship, sion will be held on Sunday, January 7, been recognized in other ways as well. In awarded to only one of the 2,700 faculty from 2:30–4:00 pm. 2001, she received the Southern Califor- at UT per year, and the Minnie Stevens nia MAA Distinguished Teaching Award. Piper Professorship, awarded to ten fac- Jennifer Quinn In Fall 2005, she was the recipient of the ulty in any field per year at any college Sterling Prize from Occidental College, or university in the state of Texas. Jennifer Quinn has a contagious enthusi- awarded to only one professor at the asm that draws students to mathematics. College per year, based on professional Mike is also in great demand as a speaker The joy she takes in all things mathemati- achievement, excellence in teaching and and workshop leader. Since he stepped cal is reflected in her classes, her presen- service to the college. down as Associate Dean at the University tations, her publications, her videos and of Texas in 2000, he has delivered over her on-line materials. Jenny’s presentation at the Joint Meetings 50 invited addresses in a wide spectrum is entitled “My Practice of Mathemat- of venues. He has presented workshops When Jenny was at Occidental College, ics.” She will explore the way in which for a variety of programs, including the she created many popular and innova- “teaching, learning, experimentation, MAA’s Project NExT, PREP, and PMET tive courses. Working with members inquiry, action, and reflection are hope- programs, MER, and the NSF Chautaqua of the physics department and funded lessly intertwined” in her practice of program. by an NSF grant, she helped develop a mathematics as a college professor, and combined year-long course in calculus discuss several significant questions In 2001, with Edward Burger, he co- and mechanics. She also developed a about what and how we teach. authored a “Math for Non-Majors” course on “Mathematics as a Liberal Art” textbook, The Heart of Mathematics: An which included computer discussions, Michael Starbird Invitation to Effective Thinking. It was writing assignments, and other means to awarded the Robert W. Hamilton Book draw technophobes into the course. One Michael Starbird has as his goal to Award in 2002, and it has been adopted project that grew out of her History of help his students unleash the creativity at over 200 colleges and universities. The Mathematics course was a math game within them. He doesn’t just teach them expository mathematics book Coinci- show called “The Number Years.” It was mathematics. He teaches them how to dences, Chaos, and All That Math Jazz: a huge hit at the winter Joint Mathematics discover and appreciate mathematics for Making Light of Weighty Ideas, also co- Meetings in 2000. themselves. authored with Edward Burger, appeared in 2005, and has already received a lot of Jenny has been invited to give talks on Mike has impacted dramatic numbers of attention. As Ian Stewart said, it is, “in- mathematics to wide and varied audi- students. In addition to the thousands of formative, intelligent, and refreshingly ences, from middle school students to students he has taught at the University of irreverent. A roller-coaster ride along the senior citizens. Her ability to give suc- Texas over his 32 years there, his teach- frontiers of today’s mathematics.” cessful talks over such a wide range is ing videos, which appear in the Great remarkable. She has also made her mark Courses series offered by the Teaching At the Joint Meetings, Mike will speak as a writer and editor: in addition to being Company, have reached countless others. on “Teaching the Joy of Thought.” In

December 2006 FOCUS

Michael Starbird Jennifer Quinn W. Gilbert Strang the light of B. F. Skinner’s dictum that In the 1980s, Gil began to think about Gil Strang will unfortunately be unable to “Education is what survives when what how mathematics was taught to engi- attend the Joint Meetings in New Orleans. has been learned has been forgotten,” neers. Recognizing the impact of com- He has agreed to give his Haimo talk in Mike will explore what students will puters, he believed that students would the 2008 Joint Meetings in San Diego. retain from our courses when, twenty be better served by a deep understanding His title will be “Linear Algebra: A years later, they have forgotten the math- of the mathematical methods underlying Happy Chance to Teach Mathematics.” ematics, and argue that we should guide numerical methods. In 1986, he published students to discover the joy of thinking. Introduction to Applied Mathematics, a The Haimo Distinguished Teaching textbook for a course on that material. Award is awarded to up to three re- W. Gilbert Strang MIT’s Graduate Student Council rec- cipients each year, who are typically ognized his work on that course with a from amongst the past winners of the W. Gilbert Strang has influenced a tre- teaching award in 2003. sectional teaching awards. If you know mendous number of students, both at his someone who you think is deserving, home institution of MIT and around the In 2001, MIT began implementing a pro- please nominate them for their section world. His approach to teaching linear gram of “Open Courseware” which made teaching award. algebra and mathematics for engineers course materials and lectures available has changed the way we all approach online for any students who wish to view Colin Adams is Professor of Mathematics these subjects. them. From among the over 500 courses at Williams College, in Williamstown, now available , Gil’s linear algebra course MA. He is currently the chair of the In 1970, Gil began teaching the linear ranks first among math courses and 16th Haimo Awards Committee. algebra course at MIT. He realized the among all courses available. Calculus is subject was not simply for mathemat- the second most popular math course fol- ics majors and so he included a variety lowed by Gil’s “Mathematical Methods of engineering applications. Students for Engineers” and “Wavelets and Filter loved his lecturing style and appreciated Banks” in the third and fourth slot. the material he included. Enrollments Have You Moved? steadily grew. In 1976, Gil published In 1977, Gil received the MAA’s The MAA makes it easy to change Linear Algebra and its Applications, his Chauvenet Prize for an article that ap- your address. Please inform the MAA textbook based on that course. This book peared in the Bulletin of the American sparked a revolution in the way linear Mathematical Society. In 2006, he was Service Center about your change of algebra was taught and has influenced a the recipient of the MAA Northeastern address by using the electronic com- multitude of books that have come out Section Teaching Award. In addition, Gil bined membership list at MAA On- since then. Rather than utilizing a theo- is a prolific researcher and has supervised line http://www.maa.org) or call (800) rem-proof format, the book was written 20 PhD dissertations and five Master’s 331-1622, fax (301) 206-9789, email: in a conversational tone and included students. [email protected], or mail to the many practical applications. In 1993, he MAA, PO Box 90973, Washington, published a successor, Introduction to DC 20090. Linear Algebra.

FOCUS December 2006 Archives of American Mathematics Spotlight: The School Mathematics Study Group Records

By Kristy Sorensen

One of the most comprehensive and distinctive collections at the Archives of American Mathematics is the School Mathematics Study Group Records. In order to make this collection more accessible to our researchers, the archivist has recently completed a project to transfer the ninety-five linear feet of files and publications from hanging file folders in filing cabinets into archival boxes. During the process of re-housing these materials, staff also enhanced the inventory by adding more detail to the existing folder list.

Under the direction of Edward G. Begle (1914-1978), the School Mathematics Study Group (SMSG) created and imple- mented a primary and secondary school curriculum between 1958 and 1977 that A worksheet from Mathematics for the Elementary School: Book 1, was widely known as the “new math.” Student’s Text, Unit 52 by the School Mathematics Study Group, 1965. The SMSG Records at the Archives of From the School Mathematics Study Group Records, Archives of American Mathematics document the his- American Mathematics, Center for American History, The University tory of the writing, implementation, and of Texas at Austin. evaluation of the SMSG curriculum. The records consist largely of the director’s files, and include correspondence, meeting agendas and minutes, grant proposals, a separate concern. The inventory to the are in the process of hiring a new archi- financial records, newsletters, drafts of New Mathematical Library Records is vist for the collections. Until then, all publications, tests, and training films. The available online at: http://www.lib.utexas. inquiries can be directed to cahref@uts. collection also includes a comprehensive edu/taro/utcah/00387/cah-00387.html. cc.utexas.edu. collection of SMSG textbooks and other publications as well as the records and The Archives of American Mathematics publications of the National Longitu- is located at the Research and Collections dinal Study of Mathematical Abilities Division of the Center for American His- (NLSMA). The inventory to the School tory on the University of Texas at Austin Mathematics Study Group Records is campus. The Archives web page is at available online at:http://www.lib.utexas. http://www.cah.utexas.edu/collectioncom- edu/taro/utcah/00284/cah-00284.html. ponents/math.html.

The SMSG Records are closely related Kristy Sorensen served as the Archivist to the New Mathematical Library Re- at the Archives of American Mathematics cords, another collection at the Archives at the Center for American History until of American Mathematics. The New November, when she accepted a new po- Mathematical Library was originally a sition as archivist and records manager publishing arm of the SMSG project, be- for the Austin Presbyterian Theological fore it was taken over by the Mathemati- Seminary in Austin, Texas. The Archives cal Association of America and became

December 2006 FOCUS

Letter from E.J. McShane to Edward Begle, 22 November 1961. The “New Math” movement drew widespread praise as well as extensive criticism. In this 1961 letter, E.J. McShane, a professor of mathematics at the University of Vir- ginia and a former president of both the AMS and MAA, writes to Edward Begle about criticisms of the SMSG program from physicists, as told to McShane by Joe Weyl (son of Hermann Weyl). The letter highlights the ongoing conflict in the classroom between pure and applied mathematics. From the School Mathematics Study Group Records, Archives of American Mathematics, Center for American History, The University of Texas at Austin.

FOCUS December 2006

MAA Names Arthur Benjamin — Mathematical Wizard, Writer, and Editor — A Pólya Lecturer

By Harry Waldman George Pólya, renowned teacher and 1989, he has taught at Harvey Mudd writer, embodied the high quality of College, where he is Professor of Math- exposition that the MAA seeks to en- ematics and past Chair. In 2000, he courage. To further this goal, the MAA received the MAA’s Haimo Award for created a George Pólya Lectureship in Distinguished Teaching. 1991. This year’s Pólya Lecturer—the 16th such named—is Arthur Benjamin. Benjamin’s research interests include game theory and combinatorics, with a Each Section of the MAA is entitled to a special fondness for Fibonacci numbers. Pólya Lecture for a Section meeting ap- Many of these ideas appear in his book proximately once every five years. (co-authored with Jennifer Quinn), Proofs That Really Count: The Art of Combina- Arthur Benjamin, 45, earned his B.S. torial Proof, which the MAA published. in Applied Mathematics from Carnegie In 2006, Benjamin’s book received the Mellon and his Ph.D. in Mathematical MAA’s Beckenbach Book Prize. Sciences from Johns Hopkins. Since Knowles Science Teaching Foundation Offers Fellowships for Research topic: A three-week summer program for Statistical Mechanics graduate students Future Teachers undergraduate students Education Theme: mathematics researchers In the United States, approximately Knowledge for Teaching undergraduate faculty half of all secondary teachers leave the Mathematics secondary school teachers math education researchers teaching profession within five years. Research on issues of recruitment, reten- tion and induction of secondary science IAS/Park City Mathematics Institute (PCMI) and mathematics teachers indicates that July 1 – 21, 2007 among key challenges facing beginning Park City, Utah teachers are a sense of professional isola- Organizers: Scott Sheffield, Courant Institute; Thomas Spencer, tion and a lack of support and mentoring. Institute for Advanced Study. The Knowles Science Teaching Foun- Graduate Summer School Lecturers: David Brydges, University of dation (KSFT) has created a Teaching British Columbia; Alice Guionnet, Ecole Normale Supérieure de Lyon; Fellowship program to meet these needs Richard Kenyon, University of British Columbia; Gregory Lawler, University of Chicago; Yuval Peres, Microsoft Research and University by encouraging future school science of California Berkeley; Wendelin Werner, Université Paris-Sud. and mathematics teachers as they earn a Clay Senior Scholars in Residence: Andrei Okounkov, Princeton teaching credential and through the early University; Srinivasa Varadhan, Courant Institute. years of their career. Other Organizers: Secondary School Teachers Program: Gail Burrill, Michigan State University; Carol Hattan, Vancouver, WA; James King, KSTF Teaching Fellows are young University of Washington. Undergraduate Summer School: Aaron men and women who have received a Bertram, University of Utah. Undergraduate Faculty Program: William bachelor’s or advanced degree in science, Barker, Bowdoin College. engineering or mathematics and are committed to teaching high school science Applications: www.ias.edu/parkcity and/or mathematics in U.S. schools. The Deadline: February 15, 2007 fellowship supports them professionally IAS/Park City Mathematics Institute Institute for Advanced Study, Princeton, NJ 08540 and financially for up to five years as Financial Support Available they go through a teacher preparation program and then begin their teaching careers. Applications for the next round of fellowships are due January 16, 2007. For more information, visit http://www. kstf.org/teaching_fellowships/. December 2006 FOCUS

The Fourth Blackwell-Tapia Conference

By Joe Gallian

More than 150 people attended the fourth in a series of biannual confer- ences honoring David Blackwell and Richard Tapia held at the University of Minnesota’s Institute for Mathematics on November 3–4, 2006. The conference featured sixteen invited talks, two panels and thirty-four posters.

The goal of the conference was to continue the work of Blackwell and Tapia of inspiring under-represented groups Discussions during break. Seated from left to right: Shirley Mal- to pursue careers in the mathemati- com, Bill Vélez, Farrah Chandler, Da- cal sciences. To this end, it showcased vid Manderscheid. research done by African-Americans, Native Americans and Latinos/Latinas and provided opportunities for network- ing. The highlight of the meeting was the closing address on dynamical queueing systems by William Massey of Princeton University, who was awarded the 2006 Blackwell-Tapia prize at the meeting for his outstanding research achievements and for his work towards increasing diversity in the mathematical sciences.

The closing banquet address was given by Tony Chan of the National Science Standing from left to right: Gerardo Chow- Foundation. See http://www.maa.org/ ell, Chehrzad Shakiban, Abba Gumel, Kar- news/052406blackwell.html for the news en Rios-Soto, David Murillo, Carlos Cas- release about the 2006 Blackwell-Tapia Richard Tapia tillo-Chavez. Prize.

Math Horizons: Time for a New Editor

By Steve Kennedy

The MAA is searching for a new Search Committee about the applicant’s Editor for Math Horizons, the MAA writing, editing, and organizational skills. student magazine. The ideal candidate Joint applications from prospective will have a wide-ranging interest in editorial teams are welcome. Review mathematics, as well as its culture, of applications will begin on March 15, history, institutions and people. She 2007 with appointment as Editor-elect to or he will also need to be an excel- commence on March 15, 2007. The five- lent expositor, a painstaking editor, year editorial term runs January 1, 2009 and a careful manager. An application through December 31, 2013. Some sup- consists of a curriculum vitae, a letter port, largely in the form of release time, is of interest outlining a vision for Math available. Send inquiries and applications Horizons, and the names and contact to Steve Kennedy, Department of Math- information of three references willing ematics, Carleton College, Northfield, and able to answer questions from the MN 55057 ([email protected]).

FOCUS December 2006 Geometry If not, why not? If so, what?

By P.N. Ruane

It’s common knowledge that geometry with geometric figures is by movement equivalent to a translation or another is the Cinderella of contemporary math- (dissection, pattern formation and creat- rotation. ematics curricula; but restoring it to its ing compound shapes using triangles, rightful place is no easy matter. For a squares etc). Then there are activities Thus far, primary school geometry will start, there is no clear consensus con- such as ‘shape postbox’, in which squares have provided an informal, investiga- cerning the best approach to geometry are put in square holes, triangles in trian- tional introduction to transformation at school and early undergraduate levels. gular holes, rhombus in the rhombic slot geometry with the important notion of And school geometry falls between two and so on. In how many ways will the invariance making its first appearance. stools, because it constitutes neither a square fit its slot? Which triangles fit their Alongside this, work on area, length, an- coherent coverage of Euclid nor a mean- outlines in one way only? Later on, this gle will have taken place – not to mention ingful introduction to transformation activity can be followed by paper-fold- the general development of spatial aware- geometry. Consequently, those wishing ing exercises that lead to definition of 2d ness and knowledge of 3d shape etc. to incorporate the subject into their shape by symmetry properties: university programmes have to take into Moving on from isometries, there are account the very poor levels of geometric • A square has sides and four lines of many practical ways of introducing knowledge of the students. symmetry. enlargement, shear and other transforma- • A quadrilateral with two diagonal tions. For instance, children draw a sim- Then there are impediments of a ‘politi- lines of symmetry is a rhombus. ple shape on 1cm2 paper and then transfer cal’ sort, such as that mentioned by Bres- • Rectangles are quadrilateral whose it to a variety of other grids (e.g., 4cm2 soud [1], who says that ‘No one wants to two lines of symmetry bisect its paper, a 1cm x 2 cm rectangular grid or relinquish several variable calculus, dif- sides. even any topologically equivalent grid). ferential equations, linear algebra, or the • Circles have infinitely many lines of The degree to which the results are ana- department’s bridge course to make way symmetry, etc. lysed obviously depends on the abilities for geometry.’ In the UK, mathematical • Rectangles and rhombi are ‘sym- of the children but, in the later primary education is more widely political since, metrically dual’. years, pupils can investigate changes in at school level, important aspects of perimeter, area, angle etc, and students curriculum development are partly deter- Work on tessellation raises various ques- can explore many interesting ideas of nu- mined by government agencies. tions, such as which 2d figures tessellate? merical and algebraic interest. Questions Which of the movements slide, turn, flip of invariance again emerge, and much of There is some irony, however, in the fact are required in order to tessellate with the above work can be coordinatised. that, by re-interpreting existing syllabi, a particular shape? And the fact that all it is possible to provide a coherent treat- triangles and all quadrilaterals will tes- Secondary ment of geometry from early primary sellate indicates that their angle sums are school to first year university level, and 1800 and 3600 respectively. There may be continuation of previous that treatment could be very much Klein- practical/investigative work, but it will ian. So, by way of illustration, I delineate Tessellation with, say, a rectangular sten- lead to more formal analysis and alge- such a development, beginning with a cil, and perhaps the shape of an animal braic representation of transformations range of 2d topics that are compatible cut from its interior, can be an artistic (coordinates, matrices and vectors). with the material specified in the section activity but, for primary pupils, it will Building upon a practical introduction on ‘Shape and Space’, which is part of reveal important connections between to similarity, early concepts on trigo- the UK national framework for primary the three basic isometries: nometry will emerge. Relationships be- mathematics. tween the isometries can be formalised • Two successive slides (translations) and they can be applied to a variety of Primary are equivalent to another single slide situations. For example, by applying (translation) suitable translations to the curve y = x2, From the age of 5 years and upwards, • Two successive flips (reflections) methods for solving general quadratics the emphasis is physical movement and in parallel sides of the stencil are can be explored (motivating the method description of position. Use of spatial equivalent to a translation. If the flips of completing the square). prepositions (inside, next to, between, are made in perpendicular sides, the etc) and directional language (left, effect is a rotation of 1800 Speaking of transformation geometry, far right etc) is encouraged, whilst work • A combination of rotations may be too many texts and school maths syllabi

10 December 2006 FOCUS take it only as far as introducing the trans- which can be done at any level, from tion course on geometry, which should formations themselves, possibly going late primary school onwards. Beginning build well-founded approaches to school as far as matrix representation and some with creation of circle patterns, it can geometry. Naturally, this would be Klein- vector geometry. Consequently, students proceed to more structured activities ian geometry, based upon the book like often see this as a rather pointless activity like constructing triangles with given that by Brannen, Esplen and Gray [3]. because they are rarely shown how trans- side-lengths, bisecting angles, drawing To my mind, this is the best introductory formations can be used to derive many of perpendiculars and so on. Subsequent book ever written on introductory univer- the theorems seen in Euclid. I give a few work at high school and first-year uni- sity geometry, with that by John Silvester instances of what can be done: versity, could be based upon the chapter [4] being on almost equal terms (it is on ‘Geometrical Constructions’ from less accessible in terms of self-tuition). • Rotational proofs for angle proper- Courant and Robbins [2]. This contains From such sources, many marvellous ties of triangles and quadrilaterals. a fascinating range of topics, such as: results emerge by means of a fascinating • Relating the Kleinian definition for construction of fields, square root extrac- range of powerful algebraic methods. In congruence of triangles with that of tion, constructible numbers, Apollonius’ the first of the above books, readers are Euclid (SSS, SAS etc). problem, polygon construction and the introduced to the notions of Euclidean • Reflectional proof of Pons Asino- unsolvability of the three classic Greek congruence, affine congruence, projec- rum. problems etc. tive congruence and certain versions of • Proof of the Pythagorean theorem non-Euclidean geometry (hyperbolic, using translations and rotations. Early university years spherical and inversive). Not only are • Rotational proof of the fact that equal students introduced to a wide range of al- chords subtend equal angles at the Seeking further evidence in support of gebraic methods, but they will encounter circumference. Bressoud’s comments, I conducted a brief a most pleasing combination of process • Angle properties of cyclic quadrilat- informal survey to detect the extent to and product. erals. which geometry is actually included in undergraduate mathematics. Specifically, Having laid such good foundations, we Later work (for high school or sixth form) I went online and examined undergradu- may be inclined to return to the theme could, for instance, include proof of the ate mathematics courses in nine universi- of ruler and compass constructions, theorems Ceva and Menelaus within ties (randomly chosen). Three of these and what better means than by the book the context of affine invariance, or ho- were in the USA, three in the UK and Ruler and the Round by Kazarinoff [5]. mothetic derivations of the nine-point three in Australia. Not one of the nine of- It begins by explaining the ground rules circle etc. fered a meaningful foundation course on for ruler and compass constructions geometry, although a few included some leading to some historical discussion This is not to say that all the theorems of geometry amongst a whole range optional the problems of angle trisection, cube Euclid concerning plane geometry should subjects. However, when geometry did duplication and squaring the circle etc. be directly derived via transformations, begin to appear, it was in the form of 3rd The book then places the notion of only a judicious selection in fact, because or 4th year specialist courses in subjects constructible geometric objects in the there is still scope for inclusion of syn- like differential geometry, introductions context of analytic geometry, thereby thetic and algebraic methods, as can be to algebraic topology or algebraic geom- providing algebraic classification of illustrated by a the following sequence: etry etc. For example, I have just received constructible numbers. The concept of for review what seems to be an excellent fields of real numbers then emerges as • Pythagorean theorem suggested by book on Desarguesian projective geom- a source of roots of algebraic equations. motivational, practical activities. etry. This is intended for use with 3rd or The second part treats non-constructible • Proved by transformational meth- 4th year maths majors who are expected to regular polygons and introduces the al- ods. be familiar with a significant range of algebra associated with them. This begins • Explore variations of the Pythago- gebraic ideas, such as finite fields, group with consideration of irreducibility and rean theorem (is it true for rectan- theory and linear algebra. But the only factorisation, unique factorisation of gles placed on each of the sides of reference to prior geometric knowledge quadratic integers, finite dimensional a right-angled triangle? What about is a vague requirement for some previous vector spaces, algebraic fields and non- semi-circles? Etc). work on coordinate geometry. What, I constructible regular polygons. • Devise a coordinate proof of a 3d ask, can be achieved in such courses version of the Pythagorean theo- when they are effectively the first time Such approaches to geometry would rem. students will have studied anything that motivate the introduction of a wide range • Investigate the Pythagorean theorem is specifically geometric? of algebraic ideas, which could be syn- as special case of cosine rule. thesised by subsequent (or simultaneous) • Pythagorean triples. I suggest that all undergraduate math- courses on algebra. Moreover, they form ematics courses include a strong founda- a springboard for subsequent ventures But there is also opportunity for work into many other aspects of mathemat- with ruler and compass constructions,

11 FOCUS December 2006

ics (differential geometry, geometry of Director of Publications for Journals curves, algebraic geometry etc). and Communications References Mathematical Association of America [1] Launchings from the CUPM Curricu- Washington, DC lum Guide: Geometry in the Mathematics The Mathematical Association of Ameri- staff, national and sectional officers, com- Major. David M. Bressoud, August, 2006. ca seeks a highly qualified person for the mittees and editors, and others in strategic Online at http://www.maa.org/columns/ position of Director of Publications for planning and program development. launchings/launchings_08_06.html. Journals and Communications. The pri- [2] What Is Mathematics?: An Elementary mary responsibilities of the position are The mission of the MAA is to advance Approach to Ideas and Methods, Richard to oversee journals and other periodicals the mathematical sciences. The MAA, Courant and Herbert Robbins,revised by and content and resources on the MAA with nearly 30,000 members, is the larg- Ian Stewart, Oxford 1996. website. In addition, the Director will est association in the world with a focus perform other duties related to communi- on mathematics accessible at the under- [3] Geometry, by David A. Brannen, cations of the MAA to our members, the graduate level. Membership includes Mattew F. Esplen, Jeremy J. Gray, Cam- public, and other specific constituencies. college and university faculty and stu- bridge 1999. Requirements for the candidate include dents, high school teachers, individuals editorial experience, writing articles for from business, industry, and government, [4] Geometry Ancient and Modern, by journals, periodicals, and the web, and and others who enjoy mathematics. The John R. Silvester, Oxford 2001. experience with creating web content. Director will be responsible for ensuring An advanced degree in mathematics or a that publications encompass the interests [5] The Ruler and the Round, by Nicholas related field in the sciences, engineering, of all major constituencies of the MAA, D. Kazarinoff, Dover 2003. or computer sciences is desirable but not embrace all areas of mathematics, and are required. The candidate should have a easily available to all of our members and Assistant/Associate/Full Professor strong interest in writing and publication, the larger community who are interested Mathematics Education & Mathematics and express a vision for MAA publica- in mathematics, especially for expository tions in print and online. mathematics and materials for faculty Hunter College of the City University of New and students. York invites applicants for an open rank The Director will oversee publication of tenure-track faculty position for a joint appointment in the Department of Curriculum the Association’s three journals, three Applications will be accepted and re- and Teaching for the School of Education and magazines (two online), the Association’s viewed as received, with a preference the Department of Mathematics and Statistics newsmagazine, a variety of columns to those received by January 1, 2007. in the School of Arts and Sciences, effective Fall 2007. and articles, the MAA’s Mathematical The position is located at the national Sciences Digital Library (MathDL) and headquarters of the MAA in Washing- Applicants should have an earned doctorate in the new Math Gateway site. In addition, ton, DC. math education, mathematics or a related field and a strong research agenda in mathe- the Director will oversee mathematical matics education. Responsibilities include: and professional resources on the MAA Candidates should send a resume and teaching undergraduate and graduate mathe- website and will work with members letter of interest to: matics education course, advising and super- vising students in the field, and serving on and staff to develop content for new department school and university commit- resources to serve our members and the Ms. Calluna Euving, Chief of Staff tees. The College places a high priority on public. The Director will be responsible Mathematical Association of America research and teaching experience with an for communications of the MAA such as 1529 18th Street, NW expectation that candidates will also be active in the profession. reports, news articles, and public aware- Washington, DC 20036 ness pieces. Send a letter of application, curriculum vitae and three current letters of reference to: Joint Applications may be submitted electroni- Math/Math Education Search, Dept. of The Director will oversee a staff of three cally to [email protected]. References Curriculum and Teaching, School of located in the headquarters office and will be requested after review of applica- Education, Hunter College, 695 Park numerous editors and editorial boards. tions. Applications from individuals from Avenue, Room 1023 West, New York, NY 10021 or email: [email protected] Duties include administration of the underrepresented groups are encouraged. department and grant management. The Additional information about the MAA Director will report to the Executive Di- and its programs and services may be rector and will be a key member of the found on MAA’s website: www.maa. MAA’s staff leadership team. S/he will org. AA/EOE. work closely with other members of the EEO/AA/ADA/IRCA employer

     December 2006 FOCUS MAA Is Offered Opportunity to Buy a Unique Golden Logo By Harry Waldman A rare 40 ounce gold box, in the shape of the MAA’s logo — the icosahedron — was offered for sale to the MAA… at 200,000 pounds. The offer came this past summer from Sebastian Thewes, a fine arts consultant with Strathgarry House, in Killiecrankie, Pitlochry, Scotland.

This 17th or 18th century piece of Islamic art had been part of the treasury of Tipu Sultan, who died at the hands of the Brit- ish in India at the Battle of Seringapatam, in May 1799. The victors then claimed possession of this and other valuables of the vanquished army of Tipu.

Each of the sides of the golden box is in- In May 2005, the gold icosahedron had Unfortunately, while the MAA finds the scribed with Arabic numerals in the form been offered for sale by Sotheby’s, in work of art appealing, its purchase price in use in Mughal India. The numbers are London, as part of its “Exotica — East is out of reach — even if it were not sub- 11, 20, 21, 31, 41, 51, 61, 71, 81, 91, 101, meets West 1500-1900” auction. An ject to the 20% buyer’s premium applied 201, 301, 401, 501, 601, 701, 801, 901, observer noted that the box “exudes an to objects bought at auction! and 202. Research, however, has failed aura of royaly and mysticism.” Nonethe- to offer clues as to the meaning of these less, it failed to attract any buyers at the © Photograph Sebastian Thewes. All inscriptions. (Perhaps some of MAA time. One reason for this, according to rights reserved. member can offer a conjecture.) Thewes, is that the box was “somewhat beyond the contemplation of the ordinary collector.” Summer Mathematics Program for Women at Carleton College

By Deanna Haunsperger The mathematics department of Car- supervision of female faculty who are ter. The mathematical part of the program leton College is pleased to announce that active in research and renowned for their is balanced with weekend events includ- NSF has renewed the funding for our teaching. In past summers we have had ing canoeing, hiking, picnics, and tubing. month-long summer mathematics pro- the following instructors: Judy Kennedy Past participants (through program evalu- gram for eighteen mathematically-talent- (Topological Dynamical Systems), Laura ations and the list server set up for their ed first- and second-year undergraduate Chihara (Algebraic Coding Theory), correspondence) report increased facility women. By introducing them to new and Margie Hale (Fuzzy Logic), Rhonda with mathematics, bolstered self-confi- exciting areas of mathematics that they Hatcher (Game Theory), Katherine dence, and new or renewed excitement would not see in a standard undergraduate Crowley (Morse Theory) and others. This toward mathematics. curriculum, and by honing their skills in summer’s courses will be offered by Eri- writing, speaking and doing mathematics, ca Flapan of Pomona College (Knots and If you have first- or second-year women the program leaders endeavor to excite Chemistry) and Karen Brucks of the Uni- students whom you think would benefit these women on to advanced degrees in versity of Wisconsin-Milwaukee (Low from a demanding, invigorating month- the mathematical sciences, and, more Dimensional Dynamical Systems). long exposure to mathematics next importantly, to increase each woman’s summer (June 17 July 15), please refer confidence in her own abilities and con- Besides the coursework, participants take them to our web page at http://www.math. nect them all into a supportive network part in a variety of mathematical events: carleton.edu/smp or have them contact to carry them through their undergraduate panel discussions on graduate schools Deanna Haunsperger at Department of and graduate education. and careers, colloquia on a variety of Mathematics, Carleton College, North- topics, recreational problem-solving, and field, MN 55057 (dhaunspe@carleton. At the heart of the program are two visits from at least one REU organizer edu). The deadline for applications is demanding, intense courses under the and the organizer of the Budapest Semes- February 23, 2007.

13 FOCUS December 2006

Perception and Research: Mathematics, Gender, and the SAT

By Cathy Kessel Camilla Benbow is the vice-chair of In 1980, Camilla Benbow and Julian did not discuss other social and environ- the National Mathematics Advisory Panel Stanley published an article in Science mental factors that might affect seventh and has been recently appointed to the entitled “Sex Differences in Math- and eighth graders. National Science Board, which oversees ematical Ability: Fact or Artifact?” They the National Science Foundation. Since reported large gender differences in At the time, their article was criticized 1980, the work of Benbow and her col- “mathematical reasoning ability.” Their for the way in which the sample was colleagues has received attention in the evidence was scores on the mathematics lected, its measure of “mathematical rea- media (“Do males have a math gene?,” SAT taken by seventh and eighth graders soning ability” (the SAT), and the way in Newsweek, 1980; “Academy of P.C. Sci- as part of a talent search for a program which the results were interpreted. Susan ences,” New York Times, 2006) and in at Johns Hopkins University. In a sample Chipman, then at the National Institute popular books (Brain Sex: The Real Dif- of about 10,000, collected between 1972 of Education, wrote, “The most serious ference Between Men and Women, 1991; and 1979, the distribution of boys’ scores problem with the report by Benbow and Boys and Girls Learn Differently!, 2001), differed greatly from the distribution of Stanley is the underlying presumption and recently on various web sites. This girls’ scores. For example, 1,817 boys that the concept of mathematical ability research is often perceived to support the and 675 girls scored above 500. In their as defined by the SAT is theoretically view that humans have two extremely dif- conclusion, Benbow and Stanley explic- defensible.” The mathematicians Alice ferent patterns of cognition and behavior, itly favored (their word) “the hypothesis Schafer and Mary Gray also questioned and that these are explained by male and that sex differences in achievement in the use of the SAT as a measure of math- female brain differences. and attitude towards mathematics result ematical ability, and moreover, noted that from superior male mathematical abil- environmental and cultural factors could At the same time, criticisms and findings ity… [which] is probably an expression not be lightly set aside. that conflict with the work of Benbow of a combination of both endogenous and and her colleagues have received little exogenous variables,” thus including the In 1983, Benbow and Stanley published notice, in the media and even in academic possibility of social and environmental another article in Science entitled “Sex writing. In this article, I describe some of factors. Benbow and Stanley had not Differences in Mathematical Reasoning those criticisms and findings, and their found differences in formal education Ability: More Facts” They reported that relevance for current studies. for students in a 1976 talent search, but in talent searches in 1980, 1981, and SAT-M Scores of Seventh- and Eighth-Grade Students in Talent Searches Year N N scoring 700 or above M/F Ratio Scores ≥ 700 Total M F M F Hopkins 1972–1979a 9,927 5,674 4,253 – – – 1980-1982b 39,820 19,883 19,937 113 9 12.6 1984-1991b 243,428 122,185 121,063 622 106 5.7 1997c – – – – – 4 2005d – – – – – 3 Nationwide 1980-1982a ~24,000e – – 147 11 13 1983f 121 12 10 1980-1983g – – – 268 23 12 Duke 1981-1983h 39,754 19,157 20,597 32 3 10.7 1984-1986 73,278 35,424 37,854 54 6 9.0 1987-1989 92,268 44,642 47,626 94 6 15.7 1990-1992 103,097 50,231 52,866 91 33 2.8 1981-1992 308,397 149,454 158,943 271 48 5.6 14 December 2006 FOCUS

1982, about 13 boys to every 1 girl scored degree level careers in engineering, The Association for Women in Math- above 700. The numbers were very small mathematics, computer science, or ematics has expressed concern about (see table). In 1986, Camilla Benbow physical sciences (EMS) was limited to Camilla Benbow’s presence on the Na- and Robert Benbow wrote that, based individuals who had ability (as measured tional Mathematics Advisory Panel — see on talent search results, “it is quite clear by high school mathematics test scores) http://www.thepetitionsite.com/takeaction/ that there are very large sex differences in the top few centiles…. This belief 474037752?ltl=1162163842. in mathematical reasoning ability” and was so well accepted that no empirical that extensive studies conducted over a analysis testing this assumption has yet Sources for the Data on Page 14 14-year period had failed to show an “ex- been published.” Weinberger analyzed clusively environmental explanation.” longitudinal data from 1972 and 1980 a Calculated from C. Benbow and R. high school seniors. In this sample, less Benbow, “Biological Correlates of High Between 1988 and 2000, the 13-to-1 than one-third of college-educated white Mathematical Reasoning Ability,” in ratio was reported in journal articles by men working in EMS occupations had Progress in Brain Research (Vol. 61), Benbow and her colleagues (Behavioral high school SAT-M scores above 650 and ed. G. De Vries et al. (Amsterdam: and Brain Science, 1988; Current Direc- more than one-third had SAT-M scores Elsevier, 1984), p. 472. tions in Psychological Science, 1992; below 550. Psychological Scientist, 2000). In 2000, b L. E. Brody, L. B. Barnett, and C. J. Lubinski, Benbow, and Morelock gave Use of the SAT as a measure of math- Mills, “Gender Differences Among the 13 to 1 ratio in the International ematical ability has also been questioned Talented Adolescents: Research Studies Handbook of Giftedness and Talent and recently on theoretical grounds. Gender by SMPY and CTY at Johns Hopkins,” said, “Comparable ratios have been Differences in Mathematics, a recent in Competence and Responsibility: replicated across the U.S. in a number compendium of psychological research The Third European Conference of the of talent searches (Benbow & Stanley, on mathematics and gender, concludes European Council for High Ability, ed. 1996), as well as in other cultures [no that mathematical reasoning is only K. A. Heller and E. A. Hany (Seattle: reference given].” vaguely defined in most testing orga- Hogrefe & Huber, 1994), p. . nizations that produce measures of this However, in 1997, Stanley reported that construct. It notes that “Specifications c J. Stanley, Letter to the editor, Johns the ratio had fallen to 4 to 1. Earlier stud- for the contents of such tests are often Hopkins Magazine, September, 1997, ies, published in 1994, of talent searches based more on historical precedent than http://www.jhu.edu/~jhumag/0997web/ letters.html. at Johns Hopkins and Duke University on theoretical work defining which cogni-

had also reported different, smaller ratios tive processes are crucial components of d obtained from larger samples (see table). mathematical and spatial reasoning and L. E. Brody and C. J. Mills, “Tal- In 2005, Hopkins researchers reported which are not.” ent Search Research: What Have We this ratio as 3 to 1. Learned?,” High Ability Studies, Vol. 16, Year N N scoring 700 or above M/F Ratio No. 1 (2005), 97–111. Scores ≥ 700 Since the 1980s, Benbow and her col- Beyond Bias and Barriers, a new report leagues have repeatedly reported on e from the National Academies, notes the longitudinal studies of talent search C. Benbow and J. Stanley, “15:1 Cer- change from 13-to-1 to 3-to-1 and says, participants identified in the 1970s and tainly Isn’t ‘Catching Up’!,” Psycho- “This difference can obviously not be early 1980s. Conclusions based on this logical Reports (1983), p. 656 report a explained by biological factors and sug- sample about “mathematically facile men different ratio and an overall sample size gests that social and cultural changes in and women,” “intellectually precocious of 23,736.

the education of men and women have youths,” or “correlates of high math- f influenced test scores.” This echoes ematical reasoning ability” are subject to Calculated from Benbow and Benbow, Schafer and Gray’s earlier criticism that the limitations of the sample. Moreover, 1984 and C. Benbow “Sex Differences environmental and cultural factors could such conclusions need to be considered in Mathematics,” Behavioral and Brain not be set aside. Whatever the reason for in light of related studies, as is customary Sciences, Vol. 11 (1988), p. 172.

the change in ratios, it seems unscientific in empirical work. g to reiterate the 13-to-1 ratio, without C. Benbow “Sex Differences in Math- explanation, when other studies consis- Cathy Kessel works as a mathemat- ematics,” Behavioral and Brain Sciences, tently report conflicting findings. ics education consultant in Berkeley, Vol. 11 (1988), p. 172.

California. She is president-elect of the h A second major criticism from 1980 Association for Women in Mathematics. All Duke statistics from D. Goldstein was that the SAT may not be a good Portions of this article appeared in the and V. Stocking, “TIP Studies of Gender measure of mathematical ability. Recent Newsletter of the Association for Women Differences in Talented Adolescents,” work provides some empirical evidence in Mathematics. This article has benefited in Competence and Responsibility: that it is not. The economist Catherine from discussions with members of the The Third European Conference of the Weinberger writes, “It was previously AWM but represents only the views of European Council for High Ability, ed. widely believed that entry into bachelor’s the author. K. A. Heller and E. A. Hany (Seattle: Hogrefe & Huber, 1994). 15 FOCUS December 2006

Teaching Time Savers Some Advice on Giving Advice

By Michael E. Orrison There are always a lot of questions that suggestions for how to be successful in construct, if the advice were coming from need to be answered at the beginning of a the course. The whole process started former students of the course instead of course. When are office hours? What are well enough with advice that I thought me. After all, as far as my students were the grading policies? How many exams was pretty straightforward: start your concerned, the comments of former stu- will there be? Will late homework be homework early, make sure to read the dents would come with built in weight accepted? We have all seen the answers book, and don’t hesitate to ask questions and legitimacy. Moreover, if I were able to these sorts of questions form the bulk in class. to gather advice from former students, of a standard course syllabus, and most then I would almost certainly be able to of us feel an obligation (and rightly so) It didn’t take long, though, for the process pass on great tips that I would have never to provide such information. to become bogged down. Aside from a thought of myself. handful of generic bits of advice (like A few years ago, it occurred to me that starting homework early), I began to So I gave the class my generic list at the there was a particularly helpful question wonder if the advice I might give would beginning of the course, but on the last that my students could have been asking be too specific. Did it simply reflect who day of class I asked them, “What advice me all along. That question might go I was when I was a student? Would the do you have for future students of this something like, “As the instructor, what majority of my students find it helpful? course?” The results were amazing. The advice do you have for someone who Moreover, I was the instructor, not some bits of advice were genuinely sincere and wants to be successful in this course?” trusted roommate who had recently taken reflective, and although each of my origi- It is no secret that I want all of my stu- the course. Would my students really nal suggestions appeared somewhere in dents to succeed in my courses, so why believe me? Would I have believed the the collection, there were indeed some wouldn’t I want to share such advice? instructor when I was a student? great additional suggestions or phrasings that I would not have (and could not have) So, in preparing for a course I was about I then realized that the entire list would be come up with on my own. to teach, I decided to create a list of much more effective, and much easier to Nowadays, I ask all of my classes to Found Math provide advice for future students, and I make sure to share what I feel are the most important tips with those future students. I am confident that it is working because of the large number of my students that are, for example, actually starting their homework early, reading the book, and asking questions in class. Of course, not only do these activities help my students be successful in my course, but they also end up saving me time as well!

Time spent: 15-30 minutes to read, filter, and type up selected student advice.

Time saved: 30-60 minutes to create and type up your own advice, and an estimated 2-10 hours per course associated with the consequences of students not following that advice.

See the next page for a sample of the results of this process when applied to “Math 55”, a Discrete Mathematics Portion of a poster of “division facts” on sale at a teaching supply store in course at Harvey Mudd College. Indiana. (Thanks to Carl Cowen)

16 December 2006 FOCUS

Advice from Former Students for Math 55 Terence Tao to Receive Math 55, Harvey Mudd College 2006 SASTRA Prof. Michael Orrison Ramanujan Prize

• Read everything! On top of the Fields Medal and a McArthur Fellowship (see our November • Read the book! It is essential. issue), Terence Tao will also recieve the 2006 SASTRA Ramanujan Prize. This • He’s not kidding — read the book, and don’t skim. It’s an awesome book. annual prize, valued at $10,000, was launched in 2005 to recognize outstand- • Do the reading right after class and look at the homework problems. A lot of ing contributions to areas of mathematics time the problems need to sit for a couple of days before you see the solu- influenced by Srinivasa Ramanujan. The tion. age limit for the prize has been set at 32 because Ramanujan achieved so much in • You can’t do homework for this class last minute. his brief life of 32 years. The prize will be awarded at the International Conference • Start homework early! Don’t wait until the night before. Some problems on Number Theory and Combinatorics, require a lot of thinking. to be held on December 19-22, at SAS- • Look at the homework assignments a couple of days in advance and let the TRA University in Kumbakonam, India, problems sink in. Discrete is easier if you’ve been thinking about the prob- Ramanujan’s hometown. lems before you actually attempt them. RAMAPO COLLEGE OF NEW JERSEY Ramapo College of New Jersey is located in the • Do the special problems early in the semester. beautiful foothills of the Ramapo Valley Mountains, approximately 25 miles northwest of New York City. • Always have people you can talk to about discrete. ASSISTANT • I’ve found that working through all of the problems on your own is es- PROFESSOR OF sential for really understanding the material. However, once you finish the MATHEMATICS problems, or if you can’t, go talk to your classmates. You will find far more Tenure Track Position - Fall 2007 errors working with them than on your own, and learning how to talk and DESCRIPTION: Responsibilities include teaching communicate math ideas clearly helps you learn the ideas and is a great side a wide range of undergraduate mathematics benefit from this course. courses, and the teaching and development of General Education mathematics courses. REQUIREMENTS: Ph.D. in Pure or Applied Math- • Don’t hesitate to ask Prof. O. for help on your assignments if you need it. ematics by September 1, 2007, is required. Col- He won’t chase you away. lege teaching experience preferred. Faculty members are expected to maintain • Take advantage of rewrites. active participation in research, scholarship, college governance, service, academic advisement and professional development activities. • LaTeX is very nice, but it may not be for you. Don’t feel pressured into using All applications must be completed online at: it. http://www.ramapojobs.com. Attach vita, cover letter, statement of teaching philosophy, research interests and a list of three references • Learn the definitions. to your completed application. Since its beginning, Ramapo College has had an intercultural/ international mission. Please tell us how your • Going to every single class will make your life much easier. background, interest and experience can con- tribute to this mission, as well as to the specific • This course has a lot of material that comes up again later in the semester, position for which you are applying. so it’s important to get the concepts early on. Review of applications will begin immediately and continue until the position is filled. Position offers excellent state benefits. To request accommoda- • Understand the big picture and how everything is related. tions, call (201) 684-7734. Supportive materials in non-electronic format can be sent to Dr. Giovanni Viglino, Search Committee Chair. Copyright © 2005-2006 Michael Orrison

Teaching Time Savers are articles designed to share easy-to-implement activities for Att: Dept 42, 505 Ramapo Valley Road streamlining the day-to-day tasks of faculty members everywhere. If you would like Mahwah, NJ 07430 to share your favorite time savers with the readers of FOCUS, then send a separate “New Jersey’s Public Liberal Arts College” [email protected] email description of each activity to Michael Orrison at . Make Ramapo College is a member of the Council of Public Liberal sure to include a comment on “time spent” and “time saved” for each activity, and to Arts Colleges (COPLAC), a national alliance of leading liberal arts colleges in the public sector. EEO/AFFIRMATIVE ACTION. include pictures and/or figures if at all possible.

POSNER ADVERTISING FINAL APPROVAL: INITIAL & DATE JOB NO: R 4670-0906-093 Art Director AE Client Proofreader Production DATE: 9/28/06 CLIENT: Ramapo College ARTIST: jg/Ruth SIZE: 2-5/16 x 5-13/16 PAGE: 1 PUB: FOCUS REV: 2 INSERT DATE: DEC 2006 ALL 5 ARE REQUIRED FOR FINAL RELEASE FOCUS December 2006 What I Learned at the MAA Digital Library Workshop By Gizem Karaali I have to admit that I am a regular (vir- and its uses in the classroom, (There is ing forward to the chance to participate in tual) surfer, and sometimes this habit of also a cool “On this day…” feature from the first workshop ever to use the MAA mine takes me places. This is the story of which I learned that I am writing these Carriage House Conference Center. This one of those places, and involves color- notes precisely 163 years after Sir Wil- small building next to the MAA Head- ful personalities, great catered food, and liam Rowan Hamilton discovered the quarters in Washington, DC had been a tremendously ambitious project in the quaternions!) under construction for the last year, with making. the aid of a sizeable donation from Paul MAA Reviews: The online continuation and Virginia Halmos. (During the week Toward the end of July 2006, an item of the Telegraphic Reviews that used of our workshop, Halmos passed away, appeared briefly on the MAA website. to be in the American Mathematical leaving a sad mathematical community This was the call for participants for the Monthly. The site has information on behind him.) MAA Digital Library Workshop. Curious more than 2200 books and new books are surfers like me clicked on it to find the constantly being added to the database; Then came October, and it was time for description of this workshop, which was why not check out the MAA Reviews the workshop. Teaching on the West to be held over the course of a weekend before you decide which textbook to use Coast cost me the Friday dinner and the in October 2006 in Washington, DC. The for your next algebra course or what book official introductions, but the Saturday announcement included a cryptic sen- to recommend for your curious niece? morning, during breakfast, I had the tence of the form “The primary aims of chance to meet some of the participants the workshop are to provide an overview Classroom Capsules: An online data- and Lang Moore, one of the organizers. of the two MAA digital libraries and of base collecting together the wealth of I was certainly glad, after hours of flying the National Science Digital Library, and short classroom resources available in the and staying in my hotel room, to finally to prepare participants to offer a short various MAA print publications. More get some fresh fruit and water and caf- workshop on these digital libraries at than 10,000 such pieces have appeared feine. Then we started. MAA Section meetings.” in the MAA journals, and the process of selecting materials, classifying them ap- The program was quite intense, and the I had spent (possibly more than) enough propriately, and making them available organizers had planned for many short time on the MAA website before, so I did online is still ongoing. sessions. We first began with MathDL. have an idea of what the Mathematical I felt at ease because I, of course, knew Sciences Digital Library (MathDL) was. A sixth component is in the works, everything! However, as expected, I But for those who have more important containing all the MAA prize-winning still had so much to learn! For instance things to do instead of mindlessly surfing articles. It should appear very soon. I had no idea that MathDL had been in the Internet, I should perhaps summarize: preparation ever since 2000, and that in MathDL is an online resource published So I knew more or less what the MathDL the beginning it was a joint venture with by the MAA and accessible via MAA is. (As it turned out I knew less, rather Math Forum. I also did not know how Online, the official website of the Math- than more; that is to come later in the the tech boom (or more significantly, the ematical Association of America. It cur- story.) But I had no idea what this Na- following bust) influenced the develop- rently has five components, which are: tional Science Digital Library was. So ment of MathDL. There were some quite I looked it up online; I confess, I went interesting and juicy stories told and The Journal of Online Mathematics ahead and googled it. I was feeling lucky many only left to our imagination… All and its Applications (JOMA): An on- and I was not wrong, I got myself on ended well of course, with the MathDL line scholarly journal focusing on online the NSDL site, which was, according moving under the umbrella of the MAA learning materials, (JOMA is rigorously to itself, “the Nation’s online library for in 2003. peer-reviewed and mainly publishes education and research in Science, Tech- articles which make significant use of nology, Engineering, and Mathematics.” Next we started discussing the Math online tools and the World Wide Web in That sounded fascinating and certainly Gateway, and after a handsome lunch, we general as the publication medium) appetizing, but I had other things to do continued in the afternoon. Simply put, and so I left it at that. I just shot an ap- Math Gateway is the mathematics portal Digital Classroom Resources (DCR): plication for the workshop to see what of the National Science Digital Library; it A free library of online resources for would come out of it. aims to “bring together collections with use in the classroom, (All items on DCR significant mathematical content and have been peer reviewed and classroom When I received an invitation to the services of particular importance to the tested) workshop I was very happy. I expected delivery and use of mathematics on the that I would learn a lot about the digital Web.” MathDL is one of these collec- Convergence: An online magazine libraries. I was also hoping that I would tions, but Math Gateway has several other focusing on the history of mathematics meet interesting people, and I was look- partners. Among these are Eric Weiss-

18 December 2006 FOCUS tein’s MathWorld, the well-established topic of our choice. My partner was Ge- were represented in the workshop), and online homework system WeBWorK, rard Kiernan of Manhattanville College, we even had international participation. National Curve Bank, College Board NY. We chose the Fundamental Theorem On top of everything, walking from the AP Central, and one of the oldest math of Calculus and began our search. Since hotel to the workshop and back, I had the resources online, the Math Forum, now both Kiernan and I have strong opinions chance to witness autumn with all her housed at Drexel University. The focus about how one should teach, some of glory. Those of us on the West Coast do of the Math Gateway is on undergraduate the items we found on the databases we not often (if ever) get to see the beauty level mathematics education. used received more criticism from us of the change of seasons. I felt lucky to than enthusiastic support and interest. have this scenery along with the wonder- The last item on the agenda for the day Nevertheless both of us could see how ful workshop. I flew home with a cold, was the National Science Digital Library these tools we were learning to use would but also with the contagious enthusiasm (NSDL). In some sense, throughout the come in handy in our career. of the idealism underlying this huge day we were looking consecutively at project. larger and larger scale projects; the NSDL On Sunday morning, we discussed the is the largest of them all. MathDL is one nature of our introductory workshops at Gizem Karaali is Assistant Professor of big catalogue of resources, the Math our own local MAA section meetings. We Mathematics at Pomona College. Gateway is a catalogue of catalogues, were once again reminded about our part each of which is like MathDL, and the of the deal. Now, it was our turn and we NSDL is a catalogue of catalogues of would be asked to go back to our local catalogues. mathematics communities and spread the word! So coming soon to a sectional NSDL is a project of the National Sci- meeting near you is your very own MAA ence Foundation. It initially began as Digital Library workshop! Keep your a platform intended to publicize NSF- eyes open and be on the lookout for funded research projects and their results, that friendly person who will tell you Tom Marley Wins Distin- which in itself is a solid, respectable goal. all about these digital libraries and then Sometimes, though, scientists and policy- some more. (You will even get hands-on guished Teaching Award makers get carried away in their dreams. experience playing with the tools dur- from Nebraska-S.E. South In this case, too, somehow people started ing the workshop!) But of course if you Dakota Section dreaming on and things got out of hand are like those of us who prefer instant (in a good way!). NSDL was eventually gratification, you can always go ahead transformed into this incredibly idealistic and check out these web resources on project of creating the ultimate online your own. Note that the MAA Reviews science library for the nation and the and the Classroom Capsules components world. of MathDL require you to enter in your MAA member number (this is the num- Still in its development stage, the NSDL ber you will find in the upper left corner already offers its audience (K-12 teach- of the mailing address on your FOCUS ers, librarians, university faculty, and magazine) and password. Non-members others who are looking to find scientific can purchase access by buying a $25/year and mathematical content from reliable subscription. The other tools are all freely online resources) material from over available, though Convergence requires 1.5 million individual records. The end (free) registration. goal of NSDL seems to be becoming the virtual equivalent of the Library of Me? I enjoyed the whole package. I Congress. The collections of the latter learned a lot about what I can find on hold more than 130 million items, and the web and where to look for it. I also so NSDL has a long way to go, but those learned that catered food can be delicious, of us who love Google (or plug in your and that there are some very friendly East Tom Marley favorite search engine here), but still hate Coasters who nonetheless love to tease University of Nebraska-Lincoln it when a search yields hundreds of thou- us West Coasters. I met many wonderful sands of results which we then need to people, two of whom are my colleagues wade through to get what we really want, from the Southern California region. The will be fine with waiting a while. fact that we represent different parts of the educational spectrum made our con- At various points during the workshop, versations more stimulating. There were we were told to pair up and try our hands people who came from all over the coun- at searching for resources to teach some try (approximately 20 of the 29 sections

19 FOCUS December 2006 MAA Textbooks The Mathematical Association of America has a great selection for you to choose from! Choose from some of these great texts:

Game Theory Cryptanalysis/ Transition to Topology Logic Combinatorics Advanced Mathematics

Statistics Analysis History Business Math Modeling

Check out our selection online at: www.maa.org or request a catalog by calling: 1.800.331.1622

To request an examination copy of one of our books, please send your request on departmental letterhead to: The Mathematical Association of America, Examination copy, P.O. Box 91112, Washington, DC 20090-1112. Include the name of your course, the estimated class size and the adoption decision date. We will send the book along with an invoice payable in 30 days.You may keep the book free for desk use by returning the invoice along with certification that you have ordered the book for your course. Otherwise, you may either pay for the book, or return it for full ® credit.

20 December 2006 FOCUS Legendary Mathematician and Former MAA President G. Baley Price Dies at 101

By Harry Waldman Former MAA President G. Baley Price, ment of the “New Math” nationally and who died on November 7, was a legend- in the purchase of the first computer at ary mathematician. A gentle, soft-spoken KU in 1956, an IBM 650, which was the man, Price was known for his keen mind granddaddy of today’s desktop models. and his recognition in the 1950s that Price was named the first E. B. Stouffer technology would be a major influence Distinguished Professor of Mathematics in how we learn and how we teach. He at KU in 1974, and retired in 1975. and his late wife, Cora, were devoted professors and mentors. G. Baley Price served as president of the MAA in 1957–1958. In 1970, “Wherever he looked,” said University Price received the MAA’s Award for of Kansas Chancellor Robert Hemenway, Distinguished Service to Mathematics, “G. Baley Price saw potential.” Long af- which recognized him for his part in ter his retirement from the University of establishing Mathematical Reviews, the Kansas, Price remained deeply connected NSF Summer Institutes for Mathemat- to mathematics and to his university. He ics Teachers Program, and the School was always generous in support of his Mathematics Study Group. pattern of conceiving, organizing, and former university. finding funding for and implementing An article by Steve Carlson on the occa- new ideas, programs and opportunities Price began his mathematical career at sion of the celebration of Price’s 100th at the local and national level. During KU in 1937, five years after earning his birthday appeared in the May/June 2005 “retirement,” Price completed two math- PhD from Harvard University. In 1943 issue FOCUS. It included photographs ematical monographs. He also turned he served with the U.S. Army’s 8th Air and more details about his life and his interest to documenting the history Force Operational Research Section in achievements. of mathematics, publishing a history of England. His duties included improv- the KU Department of Mathematics in ing the accuracy of bomber pilots and Price was involved in many national addition to articles on the contribution anti-artillery interception over Britain. and international activities, earned of mathematics to the World War II effort Price was instrumental in the develop- many grants and awards, and showed a and related topics.

In Memoriam

Leon A. Henkin (1921–2006) died on In 1990, Henkin received the first Yueh- Zalman Rubinstein (1933–2006) of November 1 at his home in Oakland, Gin Gung and Dr. Charles Y. Hu Distin- the University of Haifa passed away CA. Born in Brooklyn, NY, Henkin did guished Service to Mathematics Award unexpectedly on Septemeber 7, 2006. his doctoral work in Princeton under the from the MAA. The citation, which Born in Warsaw on June 14, 1933, he direction of Alonzo Church, receiving appeared in the January 1990 issue of completed his PhD under Mishael Zedek his PhD in 1947. He worked in logic, the American Mathematical Monthly, at the University of Maryland in 1962. but during World War II he did quite a focused on Henkin’s contribution to He taught at Clark University for several lot of applied work for the war effort, mathematics education and to increasing years before moving to the University including a stint at Los Alamos. He went opportunities for women and minorities of Haifa in 1972. Rubinstein’s area of to the University of Southern California in mathematics. Henkin appeared unex- research was complex analysis, with a in 1949, then moved to the University of pectedly on the cover of the December special interest in the zeros of real and California at Berkeley in 1953, staying 2005 issue of FOCUS, when Kristy complex polynomials; he wrote over 30 there until his retirement. In addition to Sorensen of the Archives for American papers on this subject. Rubinstein was his mathematical work and his teaching, Mathematics asked for help in identifying President of the Israel Mathematical Henkin made a mark with his work to- the mathematician appearing in a series Union in 1974–76. He had been a mem- wards increasing the number of women of photographs. Kristy’s report on the ber of the MAA since 1963. and minorities in mathematics. He started responses she received appeared in the this work in the 1960s, and he was still at March 2006 issue. Henkin was a member it until recently. of MAA for 49 years.

21 FOCUS December 2006 AAAS Meeting in San Francisco Will Feature Interdisciplinary Mathematics Program

By Edward Aboufadel

The 2007 Annual Meeting of the Amer- ments; New Approaches to the Develop- have been symposia on subjects such ican Association for the Advancement of ment of the U.S. Computing Work Force; as the changing nature of mathematical Science will be February 15–19, in San and Internet Searching in 2017. proof, models for how insects fly, and Francisco, CA. This year’s program fea- mathematical oncology. tures many outstanding expository talks The above symposia are only a few of the by prominent mathematicians. The theme 200 or so AAAS program offerings in the The 2008 meeting will be February 14- of the meeting is “Science and Technolo- physical, life, social, and biological sci- 18, 2008, in Boston. The Steering Com- gy for Sustainable Well-Being,”and many ences. For further details about the 2007 mittee for Section A seeks organizers of the symposia sponsored by Section A AAAS program, see the October 20, 2006 and speakers who can present substantial (Mathematics) are interdisciplinary ses- issue of Science, or visit http://www.aaas. new material in an accessible manner to sions that fit this theme. See the list on meeting.org and look under “Program a large scientific audience. All are invited this page for topics and organizers. and Events.” to attend the Section A Committee business meeting in San Francisco on Friday, Other symposia that will be of interest AAAS annual meetings are the show- February 16, 2007, at 7:45 PM, where to the mathematical community include: cases of American science, and they we will brainstorm ideas for symposia. Decision-Making Under Uncertainty: encourage participation by mathemati- In addition, I invite you to send me, The Challenge of Sustainable Well-Be- cians and mathematics educators. (AAAS and encourage your colleagues to send ing; Climate Change: Treatment of acknowledges the generous contributions me, proposals for future AAAS annual Uncertainty in Assessment and Decision- of AMS for travel support and SIAM meetings. Making; Numbers and Nerves: Affect for support of media awareness.) The and Meaning in Risk Information; Math- AAAS Program Committee is genuinely Edward Aboufadel is the Secretary of ematics and America’s Future: A Call to interested in offering symposia on pure Section A of the AAAS. He can be reached Action; Examining TIMSS Teaching and and applied mathematical topics of cur- at [email protected]. Learning Through Videos and Assess- rent interest, and in previous years there

Symposia Sponsored by Section A at the 2007 AAAS Meeting

The Science and Modeling of Hurricanes Organized by Clint Dawson

New Vistas in the Mathematics of Ecology and Evolution Organized by Simon Levin

Prime Numbers: New Developments on Ancient Problems Organized by Dan Goldston

New Mathematical Methods in the Visual Arts Organized by Dan Rockmore

Are We a Democracy? Vote Counting in the United States Organized by Stephanie Singer

How Should Elementary Mathematics Be Taught? Organized by Cathy Kessel

Controversies in Forest Fire Suppression and Management Organized by John Braun

Blockbuster Science: Math & Science Behind Movies & Entertainment Organized by Tony Chan

22 December 2006 FOCUS A Mathematician’s View of the AAAS Annual Meeting By David L. Finn

In February 2006, I had the opportunity Krantz’s description of the status of the las Fallaci and Cheryl Heuton, mathemat- to attend the Annual AAAS meeting in St. Poincaré Conjecture as unclear. Tom ics advisors Gary Lorden, Tony Chan Louis. AAAS is the American Associa- Hales described the status of the Flyspeck and others, and actor David Krumholtz. tion for the Advancement of Science; it Project, which deals with how to check After describing the show and explaining describes itself as “an international non- the correctness of computer proofs and how it tries to display mathematics in a profit organization dedicated to advanc- reflects the unsatisfactory status of his positive light, the symposium focused on ing science around the world by serving proof of Kepler’s Conjecture. He was the connections between the show and as an educator, leader, spokesperson and asked about how computers are used in high school education. Questions from professional association.” This includes theoretical mathematics as opposed to the audience covered the spectrum, from the mathematical sciences, though mem- scientific investigations. Many of the questions to David Krumholtz about his bership in AAAS by mathematicians is questions were from scientists curious mathematical background and how he low (less than 1,000) compared to the about current mathematical practice. tries to portray mathematics to ques- memberships of AMS (about 31,000), They were especially interested in how tions about NUMB3RS and high school MAA (about 27,000), and SIAM (about mathematical progress seems to be more mathematics education. There were 10,000). similar to scientific progress and in some also questions about the mathematics areas of mathematics is becoming more involved in the show and about how the The 2006 annual meeting included like a research program in science. As mathematical themes are chosen. I en- some interesting mathematics. Each a mathematician who is aware of some joyed hearing David Krumholtz remark annual meeting has a theme; in 2006, it of the particulars in these proofs, it was that he used to hate mathematics but that was “Grand Challenges and Great Op- great to hear the experts explaining them he now likes it, because it makes sense portunities.” The mathematical part of to non-mathematicians. I feel I learned when it is explained passionately and the meeting included several symposia more of the big picture than I ever would with enthusiasm in a way that highlights spread over two days: “Paradise Lost: at a mathematics conference. practical and commonplace applica- The Changing Nature of Mathematical tions. He made particular reference to an Proof,” “Million Dollar Mathematics: The symposium on NUMB3RS drew a early episode which connected Fibonacci Challenge Problems in the 21st Century,” large audience, partly due to the schedul- numbers to flowers and nature. This illus- “How Insects Fly,” “Astrodynamics, ing (late afternoon) and partly due to the tration helped him to understand higher Space Missions and Chaos,” “Tsunamis: presence of producers and writers Nicho- mathematics. Their Hydrodynamics and Impact on People,”NUMB3RS and the Challenge of Changing Public Perception of Math- ematics,” and “Arches: Gateways from    Science to Culture.”       The mathematical symposia were well   attended. To give a flavor of the symposia              and the level of interest in mathemat-            ics at the meeting, let me describe the                  symposium on “Paradise Lost” and the    questions asked by the audience. The             symposium started with a description by         Keith Devlin on what is usually meant by                           a proof, then moved towards the modern               research programs and how they differ             from the classical view of proof. Michael             Aschbacher described the classifica-           tion of finite simple groups, currently        estimated at more than 10,000 pages in   500 journals by over 100 authors. It may                  well be that there are some gaps in the         proof. One serious gap has been filled  (see http://www.ams.org/notices/200407/ fea-aschbacher.pdf), but are there others?  Further interest was generated by Steven

23                FOCUS December 2006

All in all, the meeting was very interesting. Joining AAAS was a worthwhile ad- venture. As a member, besides a cheaper Can your new Calculus students registration fee at the meeting, you get the weekly magazine/journal Science. answer this question? Science contains research articles and news on science, science policy, and science education. At the moment, one will y This figure shows the not find much explicit mathematics in graph of a polynomial Science, but many applications of math- function g. Which of the ematics and some items on mathematics y = g(x) education do appear in Science. For in- following could define stance, several news items on President g(x)? Bush’s National Mathematics Advisory O x 3 Panel appeared this year. A. g(x) = x – 4 B. g(x) = x3 – 4x At the meeting, I talked to Ed Aboufadel, C. g(x) = -x3 + 4x the new secretary of Section A (mathe- D. g(x) = x4 – 4x2 matics) of AAAS. Ed has been a member E. g(x) = -x4 + 4 x2 of AAAS for almost twenty years. His reason for joining AAAS is that he has ® “broader interests in science other than The CLEP Precalculus exam just mathematics.” His involvement in AAAS has given him ideas for classes will help you measure the (in particular, a statistical literacy class “calculus readiness” of your students. for non-majors) and at least one research paper. His 1996 article in the Monthly, “A x mathematician catches a baseball,” was Computer delivered; immediate score reporting motivated by an article by two psycholo- x 90 minutes in length; approximately 50 questions gists that appeared in Science. x Integrated online graphing calculator x Test specifications reflect current texts and curriculum, Ed and I talked about how mathematics is under-represented in AAAS. The including: program in St. Louis seemed dominated - Algebraic expressions, equations and inequalities by the life sciences, which just reflects - Functions: concepts, properties, and operations that AAAS itself is dominated by the life - Representations of functions: symbolic, graphical, and tabular sciences. Ed said that Section A “needs - Analytic geometry more mathematical involvement and - Trigonometry and its applications more ambassadors for math.” He argued - Functions as models that “if mathematics does not have a loud voice, it does not a have a voice” in AAAS and science in general. For more information, visit www.collegeboard.com/clep/precalculus From my experiences at the meeting and as a fairly new a member, I would encourage more mathematicians to join AAAS, especially if they are interested in applications of mathematics to science and in science and science policy in general.

David L. Finn is Associate Professor Mathematics at the Rose-Hulman Insti- tute of Technology. He is also the editor of the newsletter of the Indiana Section of the MAA, where this article first appeared.

24 December 2006 FOCUS

Writing as an Effective Teaching and Assessment Tool

By Anna Davis As teachers of mathematics we con- In light of these observations, I started The three students were shocked and tinually face two questions. How do we assigning essay questions in my upper discouraged by the magnitude of their best foster learning? How do we assess division mathematics courses. One as- errors, and I was shocked by my inability the learning that has taken place? The signment turned out to be particularly to get the concept across to a very bright following two (mostly real) stories may meaningful to me and to the class as a group of people. We had to start over. I cast some light on these questions. whole. The topic in question was es- had to find new ways of explaining the tablishing a one-to-one correspondence concept, while they had to put their previ- Story 1: Bob, a student in my calculus between a given set and the set of natural ous misconceptions aside and work with class, says that he had not really un- numbers to demonstrate that the given set me on overcoming their difficulties. After derstood the geometric meaning of the is countable. Based on regular homework some one-on-one discussions and new derivative until he had to explain it to assignments I felt that we were making drafts, all three of them submitted new a friend. good progress. Then came the paper… — error-free — papers which, I hope, were indicative of their new and better Story 2: John, a student in my college For their essay, I asked my students to understanding. algebra class, gets an A on a quiz deal- find a listener with no mathematical back- ing with sketching solutions to systems ground and explain to that person how we The one outstanding essay was written of inequalities. When John comes in to can measure the size of an infinite set by by Sam Belk who is studying to be a pick up his quiz, he excitedly tells me comparing it to the set of numbers 1, 2, high school mathematics teacher. He how all of a sudden he started getting 3, … Students were instructed to avoid chose to explain countable infinity to his right answers after someone showed technical jargon and symbols. Students mother. Asking her to imagine an infinity him how each graph can be interpreted were asked to submit their explanations of souls in heaven, he asked what would as “a big fish coming over the x-axis to and their listener’s reactions in writing. happen when one more person died: swallow the little fish…” Apparently, would heaven become bigger? Her first someone had shown him some trick that Some amazing misconceptions surfaced. answer was yes, but his essay explained seems to work, but offers absolutely no For example, a student who had suc- how he had conveyed to her the notion of insight into the meaning of solutions, cessfully written up a proof of the fact one-to-one correspondence as a way of systems or inequalities. John is thrilled that a countable union of countable sets measuring size, and led her to conclude with his grade, but I am left to ponder is countable claimed in her paper that if that the new heaven was in fact no larger how I single-handedly gave someone an there were countably many people there than the first. A for interpreting graphs as fish. would be uncountably many phones, because one person might have more This assignment combined learning- The first story has to do with effective than one phone, which would violate the through-speaking with assessment- learning, the second, with effective as- one-to-one correspondence requirement. through-writing. Those students who sessment, but the two share a trait. It was Another student, who readily told me that made no conceptual errors came to the use of language, not mathematical sets Z and N have the same cardinality, understand the topic better by having to symbols, that aided learning in the first claimed in his paper that if there were explain it to someone else. Those students case and helped identify problems in the countably many juice bottles in an infinite who had major misconceptions saw them second case. The episode described in line, adding an extra bottle at the front exposed through their writing. Having the Story 2 is a rare experience, but some of the line would increase the size of the students speak and write about mathemat- less staggering versions of it are quite set by one. ics revealed problems that might have common. Just let an average student otherwise stayed hidden. spend a few minutes in your office talking Overall, three out of eight papers con- to you about your subject and you will tained major blunders, four papers were Anna Davis received her Ph.D. from the quickly observe a high level of discom- acceptable and one paper was outstand- University of Kentucky in 2002 and is fort with vocabulary and ideas. Sooner ing. These results indicated to me that I now assistant professor of mathemat- or later a phrase will slip out that will had completely failed to reach over one ics at Ohio Dominican University. Her offer you an insight into the nature of the third of my class. What was even more research area is geometric topology. She student’s misconceptions. This is what I frightening was that every one of the now incorporates “concept essays” into call “mathematical self-incrimination.” three students who failed to grasp the all of her courses, starting with Calculus Students try to fall back on symbols be- concept was earning an A or a B in the I. She would like to thank Sam Belk for cause they are not comfortable speaking course. his outstanding essay and for agreeing mathematics. to allow her to use it in this.

25 FOCUS December 2006

Letter to the Editor   In the Nov 2006 (vol 26, issue 8) of    Focus, on page 14, appears an illustration of the theorem “The 3 medians of any triangle are concurrent”, but the diagram does not show medians, which are lines   from the vertices to the midpoints of the     opposite sides.                                             On page 16, in “Removal from Office”,             Martha Siegel describes a proposal to           comply with the Sarbanes-Oxley Act, a                        law to protect Whistle Blowers. However,               the proposal removes all protection from           whistle blowers. I am curious why the                  MAA needs to remove all protection from whistle blowers.

Mike Brenner MITRE Corporation                             The picture on page 14 came from the papers of Alfred Schild, so we cannot be sure why it is drawn as it is. There is more than one triangle in the picture, however, and in the case of the lighter triangle the  lines do seem to be medians. Perhaps one of our readers can take a guess at what  Binary Clock The Binary Clock, so simple, yet no one figures Schild was up to. out what it is until you explain how to read binary code. Then they are amazed at what a great clock  this is and how easy it is to tell the time. As to the proposed bylaws change, note Tix Clock Perfect for the techie, nerd and ham. The clock that a Whistle Blower Protection Policy includes a dimmer switch and real binary as well The Tix Clock is perfect for the nerd in training, those was passed by the Board of Governors a as BCD. Comes with instructions on how to read that are learning math or those that like functional piece of artwork in the house or shack. The clock year ago; it can be found at http://www. the clock. For more details or to purchase, visit www.realnerds.com has 4 fields like the 4 digits of a digital clock. The maa.org/Aboutmaa/whistleblowerpolicy. time is the NUMBER of lights per field, allowing html. However, it is possible that as a re- millions of patterns while still making the clock simple to read. Available in Silver or Black. sult of the complaints of a whistle blower Binary Clock someone will be found guilty of some kind of wrongdoing. The proposed change addresses that situation, providing a means by which someone who has been found guilty can be removed from office.

Found Math

“With the new school year looming, I was increasingly worried I would never reach my goal. My daughter had already started on fractions and decimals, which were still as incomprehensible to me as Poincaré’s conjecture. I discussed my dis- tress with Shah, but she said doing the same problem multiple times was essential to mastering the material. I accept that this unshakable attachment to drills and repetition may be why the Japanese are better at math than Americans. But it may also be why the Japanese invented ritual seppuku.”

Emily Yoffe attempts to use the Kumon method to learn enough mathematics to help her daughter in school. From Salon’s “Human Guinea Pig” column, online at http://www.slate.com/id/2152480.

26 December 2006 FOCUS

Treat your students with these great books from the Mathematical Association of America

!aha! A Two-volume Collection • aha! Insight and aha! Gotcha Martin Gardner aha! Gotcha and aha! Insight are here combined as a single volume. The aha! books, as they are referred to by fans of the author Martin Gardner, contain 144 wonderful puzzles from the reigning king of recreational mathematics. In this combined volume, you will find puzzles ranging over geometry, logic, probability, statistics, number, time, combinatorics, and word play. Gardner calls these puzzles aha! problems. He explains that aha! problems "seem difficult, and indeed are difficult if you go about trying to solve them in traditional ways. But if you can free your mind from standard problem solving techniques, you may be receptive to an aha! reaction that leads immediately to a solution. Don't be discouraged if, at first, you have difficulty with these problems. Try your best to solve each one before you read the answer. After a while you will begin to catch the spirit of offbeat , nonlinear thinking, and you may be surprised to find your aha! ability improving."

Spectrum • Catalog Code: AHA • 380 pp., Hardbound, 2006 ISBN 10: 0-88385-551-8 • ISBN 13: 978-0-088385-551-5 List: $47.50 • MAA Member: $37.95

The Edge of the Universe Celebrating Ten Years of Math Horizons Deanna Haunsperger and Stephen Kennedy, Editors

Beautifully printed with 24 pages of full-color images. A must for all math clubs. Math Horizons celebrates the people and ideas that are mathematics. Containing the editors' selection from the first ten years of the magazine's existence, this volume features exquisite expositions of mathematics accessible at the level of an undergraduate or advanced high school student. Broad and appealing, the coverage also includes fiction with mathematical themes; literary, theatrical, and cinematic criticism; humor; history; and social history. Mathematics is shown as a human endeavor through biographies and interviews of mathematicians and users of mathematics including artists, writers, and scientists. The puzzles, games, and activities throughout make it a valuable resource for student math clubs. Spectrum • Catalog Code: BOMH • 320 pp., Hardbound, 2006 • ISBN 10: 0-88385-555-0 • ISBN 13: 978-0-88385-555-3 List: $57.50 • MAA Member: $45.95

First Steps for Math Olympians Using the American Mathematics Competitions J. Douglas Faires “Within each chapter, three well-chosen examples illustrate a variety of problem-solving strategies and applications of concepts. The examples are followed by ten exercises, graduated in difficulty so that nearly every student reader will be able to solve at least one problem easily and nearly every reader will struggle with at least one. The thoughtful choice of examples and exercises is one of the book's strengths, providing a wealth of opportunity for students to become experienced problem solvers within a remarkably small number of pages.” -David Wells, Penn State University A major aspect of mathematical training and its benefit to society is the ability to use logic to solve problems. This book considers the basic ideas behind the solutions to the majority of these problems, and presents examples and exercises from past exams to illustrate the concepts. Anyone taking the AMC exams or helping students prepare for them will find many useful ideas here. But people generally interested in logical problem solving should also find the problems and their solutions interesting. Problem Books • Catalog Code: PSC • 320 pp., Hardbound, 2006 ISBN 10: 0-88385-824-X • ISBN 13: 978-088385-824-0 • List: $46.50 • MAA Member: $36.95 Order your copies today! 1.800.331.1622 • www.maa.org ®

27 FOCUS December 2006

Employment Opportunities Avenue, Little Rock, Arkansas 72204, E-mail: Science beginning August 2007. A doctorate in [email protected]. mathematics or mathematics education at the time of appointment is required. Demonstrated ARIZONA The University of Arkansas at Little Rock is an excellence in teaching is essential. Preference affirmative action, equal opportunity employer will be given to candidates with experience in The University of Arizona and actively seeks the candidacy of minorities teaching elementary, middle grades, or high The Mathematics Department at the University and women. Under Arkansas law, all applications school mathematics, and mathematics courses of Arizona invites applications for tenure-track are subject to disclosure. for K-8 pre-service teachers. Duties include positions at the Assistant, Associate or Full teaching 12-13 hours per semester to include Professor levels, to begin Fall of 2007. By the CALIFORNIA mathematics and mathematics education courses time of appointment, candidates are expected for the elementary, middle grades, and secondary to have a PhD and an excellent research record California State University, Fresno mathematics education programs and engag- or potential, as well as a strong commitment to The Department of Mathematics at the California ing in service and scholarly activities. Salary teaching. State University, Fresno, invites applications is commensurate with qualifications. Further for four tenure-track assistant professor posi- information appears at http://www.ngcsu. There will also be Post-doc positions and/or tions beginning August of 2007. All areas of edu/adminsrv/hr/facultypositions.htm. Visiting positions available. mathematical expertise will be considered for two of the positions. One position however is Review of applications begins January 31, 2007, Please refer to the “Employment” portion of reserved for mathematical analysis and another and continues until the position(s) is filled. All our website at http://math.arizona.edu for ad- for Mathematics Education. A Ph.D. (or ABD) applicants should send a letter of application, ditional information, application procedures in mathematics is a requirement. Exceptional CV, unofficial transcripts of all undergraduate and deadlines. faculty at a higher rank may be considered. For and graduate credit, a statement of teaching more information consult the web site http:// philosophy, and three letters of recommenda- Arkansas www.csufresno.edu/aps/vacancy/sm.html For tion that include telephone numbers and e-mail full consideration, all application materials must addresses of references to: University of Arkansas at Little Rock be received by 1/15/2007. Chair Department of Human Resources The University of Arkansas at Little Rock DISTRICT OF COLUMBIA ATTN: Mathematics Education Position invites applications for the position of Chair in North Georgia College & State University the Department of Mathematics and Statistics. American University Dahlonega, GA 30597 Successful candidates should have a Ph.D. in Tenure-track Assistant Professor in Mathemat- mathematics or a related field with experience ics, American University, beginning Fall 2007. MARYLAND commensurate with the rank of a tenured profes- PhD required. American University is an AA/ sor. The Chair position is a 12-month appoint- EEO employer, committed to a diverse faculty, United States Naval Academy ment. Rank and salary will be commensurate staff, and student body. Minority and women Mathematics Department with qualifications. candidates are encouraged to apply. For posi- The USNA Mathematics Department anticipates tion information and application instructions, at least one tenure-track position (subject to Requirements include; outstanding research see math.american.edu/positions, or contact the approval and funding) at the Assistant Profes- credentials and teaching experience, a record Department of Mathematics and Statistics at sor level to start in August 2007. See web site of university and professional service, effective (202) 885-3120. http://www.usna.edu/MathDept/website/Hire. leadership, communication and administrative htm for full information. Tel: 410-293-6701; skills. Applicants must be strongly committed GEORGIA Fax: 410-293-6707; Email: [email protected]. The to lead the faculty in shaping, improving, and United States Naval Academy is an Affirmative developing the department’s initiatives in teach- Georgia College & State University Action/Equal Employment Opportunity Em- ing, grant-funded research, interdisciplinary The Department of Mathematics at Georgia Col- ployer and provides reasonable accommodations research and service. The Department consists lege & State University invites applications for a to applicants with disabilities. of twenty-three full time faculty members. The tenure-track position in mathematics and a tenure faculty currently has interactions with other track position in mathematics education, at the MICHIGAN university departments and research centers, rank of Assistant Professor. A terminal degree is with regional governmental organizations, with required for each position. Excellence in teach- Northern Michigan University private research and development organizations, ing, scholarly activity, and service are require- Mathematics and with local schools. In addition to B.A. and ments for promotion and tenure. Employment POSITION TYPE: Tenure Earning, Assistant B.S. degrees, the Department offers an M.S. will begin August 1, 2007. GCSU is Georgia’s Professor (2 positions) DEPARTMENT: Math- degree in Applied Mathematics and participates Public Liberal Arts University, with a strong ematics and Computer Science DESCRIPTION/ in the Applied Science Ph.D. program. For commitment to student-centered education in a REQUIREMENTS: Visit HigherEdJobs.Com, more information about the university and our residential setting. For more information about or call (906) 227-2020 ANNUAL SALARY: department visit, http://www.ualr.edu/mathdept/ these positions and application instructions, Competitive APPLICATION DEADLINE: about_us.html. see http://www.gcsu.edu/facultyjobs. Review Screening will begin January 3, 2007, and of applications will begin November 27, 2006. continue until the positions are filled. NMU is Letters of application for job #175 should in- GCSU is an Equal Opportunity/Affirmative an AA/EOE clude a curriculum vita and names with contact Action institution. information for at least three references. Review NEW HAMPSHIRE of applications will begin November 15, 2006 North Georgia College and will continue until a successful candidate is & State University Dartmouth College selected. Send applications to: Dr. Hassan Elsal- Applications are invited for one or more ten- John Wesley Young loukh, Chairperson, Search Committee, Depart- ure-track mathematics education positions in Research Instructorship ment of Mathematics and Statistics, University the Department of Mathematics and Computer The John Wesley Young Instructorship is a Arkansas at Little Rock, 2801 South University 28 December 2006 FOCUS postdoctoral, two- to three-year appointment ter of application, curriculum vitae, and a brief The successful candidate will be expected to de- intended for promising Ph.D. graduates with statement of research results and interests, and velop an ongoing professional/research agenda, strong interests in both research and teach- arrange for four letters of reference, at least one support outreach programs in cooperation with ing and whose research interests overlap a of which specifically addresses teaching, to be departmental colleagues and the School of Edu- department member’s. Current research areas sent to Annette Luce, Recruiting Secretary, De- cation, and support a new master’s program in include applied mathematics, combinatorics, partment of Mathematics, Dartmouth College, mathematics education. Further responsibilities geometry, logic, non-commutative geometry, 6188 Kemeny Hall, Hanover, New Hampshire include teaching responsibilities in an under- number theory, operator algebras, probability, 03755-3551. Applications received by December graduate liberal arts and sciences program. set theory and topology. Instructors teach four 15, 2006 will receive first consideration. ten-week courses distributed over three terms, To receive full consideration, all materials must though one of these terms in residence may be Dartmouth College is committed to diversity and be received by January 12, 2007. A complete free of teaching. The assignments normally strongly encourages applications from women application consists of a resume, three letters include introductory, advanced undergraduate, and minorities. Inquiries about the progress of of recommendation, a statement of research and graduate courses. Instructors usually teach the selection process may be directed to Dana and professional plans, a statement of teaching at least one course in their own specialty. This Williams, Recruiting Chair. philosophy, and a graduate transcript. Both appointment is for 26 months with a monthly teaching abilities and research abilities should salary of $4650.00, and a possible 12 month OHIO be addressed in the letters of recommendation. renewal. Salary includes two-month research Please include an e-mail address in your cor- stipend for Instructors in residence during two Miami University Middletown Campus respondence. of the three summer months. To be eligible for Assistant Professor in Mathematics a 2007-2009 Instructorship, candidate must be Miami University Middletown invites appli- Send applications to: Dr. Robert Gorton, Chair able to complete all requirements for the Ph.D. cations for a tenure-track assistant professor of the Mathematics Education Search Commit- degree before September, 2007. Applications position in mathematics beginning Fall 2007. tee, Department of Mathematics, University may be obtained at http://www.math.dartmouth. Requires a doctorate by date of appointment of Dayton, Dayton, OH 45469-2316. Contact edu/recruiting/. Or, submit a letter of application, in a mathematical science or mathematics the search committee at Robert.Gorton@notes. curriculum vitae, graduate school transcript, education; strong credentials or demonstrated udayton.edu. For further information, see http:// thesis abstract, statement of research plans and potential for high quality teaching. The ability www.udayton.edu/~mathdept. interests, and at least three, preferably four, let- and willingness to teach mathematics service ters of recommendation to Annette Luce, Depart- courses for education and/or computer science The University of Dayton is a private comment of Mathematics, Dartmouth College, 6188 majors is desired. Miami University Middletown prehensive Catholic university founded by Kemeny Hall, Hanover, New Hampshire 03755- is primarily a teaching campus with courses at the Society of Mary in 1850. It has more than 3551. At least one referee should comment on the first and second year levels; however, there 6000 undergraduate and 3000 graduate students. applicant’s teaching ability; at least two referees will be opportunities to teach in the area of spe- The Department of Mathematics offers bac- should write about applicant’s research ability. cialty. Service and scholarly activity required calaureate degrees in mathematics and applied Applications received by January 5, 2007 receive at appropriate levels. Salary is competitive, mathematical economics, and master’s degrees first consideration; applications will be accepted excellent benefits package (visit www.muohio. in applied mathematics, financial mathematics, until position is filled. Dartmouth College is edu/benefits for more details). Our university and mathematics education. The University of committed to diversity and strongly encourages values campus diversity; we particularly encour- Dayton is an Equal Opportunity/Affirmative Ac- applications from women and minorities. age members of historically underrepresented tion employer. Women, minorities, individuals groups to apply. Send letter of application, AMS with disabilities, and veterans are encouraged Dartmouth College cover sheet, curriculum vitae, description of cur- to apply. The University of Dayton is firmly The Department of Mathematics anticipates a rent research, statement of teaching philosophy, committed to the principle of diversity. tenure-track opening with initial appointment in and three letters of recommendation (at least one the 2007-2008 academic year. In extraordinary should address teaching) to: Mathematics Search OKLAHOMA cases, an appointment at a higher rank is pos- Committee, Miami University Middletown, sible. Preference given to candidates working 4200 East University Boulevard, Middletown, The University of Oklahoma in discrete or combinatorial mathematics with Ohio 45042. Electronic submissions may be sent Department of Mathematics connections to existing research interests in to [email protected]. Screening Applications are invited for one or more full- the department including discrete probability, begins December 11, 2006 and continue until time, tenure-track position(s) in mathematics graph theory, algebraic combinatorics, combi- position is filled. Miami University is an affirma- beginning 16 August 2007. The position(s) natorial number theory and discrete geometry. tive action, equal opportunity employer. is initially budgeted at the assistant professor Candidates for the position must also be com- For information regarding campus crime and level, but an appointment at the associate pro- mitted to outstanding teaching and interaction safety, visit www.muohio.edu/righttoknow. fessor level may be possible for an exceptional with students at all levels of undergraduate and candidate with qualifications and experience graduate study. University of Dayton appropriate to that rank. Normal duties consist Applications are invited for a tenure track of teaching two courses per semester, conduct- To create an atmosphere supportive of research, position in the Department of Mathematics at ing research, and rendering service to the De- Dartmouth offers new faculty members grants the assistant professor level starting in August partment, University, and profession at a level for research-related expenses, a quarter of sab- 2007. The position focuses on mathematics appropriate to the faculty member’s experience. batical leave for each three academic years in education. The position(s) requires an earned doctorate and residence and flexible scheduling of teaching research interests that are compatible with those responsibilities. The teaching responsibility in Candidates must have a Ph.D. in mathematics of the existing faculty; preference will be given mathematics is three courses spread over three education with a master’s degree in mathematics to applicants with potential or demonstrated of four ten-week terms. or a Ph.D. in mathematics. Candidates must have excellence in research and prior successful a commitment to teaching, advisement, cur- undergraduate teaching experience. Salary and Applications may be obtained at http://www. riculum development, and research supervision benefits are competitive. For full consideration, math.dartmouth.edu/recruiting/. Or, send a let- at both the undergraduate and graduate levels. applicants should send a completed AMS cover

29 FOCUS December 2006 sheet, curriculum vitae, a description of current Candidates must have a Ph.D. in mathemat- to Dr. J. Robert Buchanan, Staff Search Com- and planned research, and have three letters of ics or a related field, a strong commitment mittee/FOC1206, Department of Mathematics, recommendation (at least one of which must to undergraduate teaching using technology Millersville University, P.O. Box 1002, Millers- address the applicant’s teaching experience and in the classroom, and evidence of continuing ville, PA 17551-0302. Full consideration will proficiency) sent to: professional development. We are looking for be given to applications received by 1/19/2007. an excellent teacher flexible enough to offer An EO/AA Institution. E-mail applications will Search Committee courses ranging from quantitative literacy to not be accepted. Department of Mathematics undergraduate research. Preference will be given The University of Oklahoma to candidates able to teach courses in abstract Millersville University 601 Elm, PHSC 423 algebra, geometry, and philosophy of math- Full-time, tenure-track assistant professorship Norman, OK 73019-0315 ematics. Additional information on the college, to begin August 2007. Area of expertise in the department, and its facilities is available at MATHEMATICS EDUCATION. The depart- Phone: 405-325-6711 http://www.juniata.edu. ment, consisting of 20 faculty members and FAX: 405-325-7484 approximately 220 undergraduate majors, E-mail: [email protected] Please send a letter of application, vita, evidence offers B.A. and B.S. degrees in mathematics of teaching abilities, graduate transcripts, and and B.S.Ed. and M.Ed. degrees in mathematics Screening of applications will begin on De- three letters of reference to: Gail Leiby Ulrich, education. Duties include an annual 24-hour cember 15, 2006 and will continue until the Director of Human Resources, Juniata College, teaching load, including mathematics courses position(s) is filled. 1700 Moore Street, Box MT, Huntingdon, PA for pre-service elementary and secondary teach- 16652. No electronic submissions will be accept- ers and a variety of undergraduate mathematics The University of Oklahoma is an Equal ed. Review of applications will begin December service courses, scholarly activity, student Opportunity/Affirmative Action Employer. 15, 2006. Preliminary interviews will take place advisement, curriculum development in math- Women and Minorities are Encouraged to at the Joint Mathematics Meetings in January. ematics education at both the undergraduate Apply. Informal inquiries can be directed to John and graduate levels and committee work. This Bukowski, Chair, Department of Mathematics, position may include supervision of secondary PENNSYLVANIA [email protected]. It is the policy of the student teachers. Doctorate (or completion by College to conduct background checks. time of reappointment to the second year) in Albright College mathematics education or in mathematics with Mathematics Juniata College will take positive steps to a specialization in mathematics education is re- The Department of Mathematics invites applica- enhance the ethnic and gender diversity on quired, including broad training in mathematics tions for a tenure-track position beginning fall its campus. The College commits itself to this with at least 24 hours of graduate level courses 2007. The applicant should have a doctorate (by policy not only because of legal obligations, but in pure or applied mathematics. Must exhibit August 2007) in mathematics and evidence of because it believes that such practices are basic evidence of strong commitment to excellence a strong commitment to teaching at a small lib- to human dignity. in teaching and continued scholarly activity, and eral arts institution where students expect close have familiarity with current directions in math- contact with their professors. Duties include AA/EOE ematics education, including technology. Must teaching three course per semester normally, complete a successful interview and teaching scholarship (undergraduate research highly Millersville University demonstration. Evidence of teaching effective- valued), and service to the department and Col- Full-time, tenure-track assistant professorship ness is a primary consideration. Preference will lege. Subject line: Mathematics Search. Full to begin August 2007, in a department of 20 be given to candidates with experience teaching consideration will be given to all completed ap- faculty and approximately 250 majors in math- both 7-12 and college-level mathematics. Sal- plications received by December 1 and continue ematics and mathematics education. Required: ary/benefits are competitive. Send application until position is filled. Send letter of application, Ph.D. (or completion by date of appointment) letter, vita, copies of undergraduate and gradu- CV, evidence of teaching effectiveness, sample in mathematics with expertise in geometry or ate transcripts and three letters of reference (at syllabi, scholarship sample and plan, statement topology. Must exhibit evidence of strong com- least two of which attest to recent teaching of teaching philosophy, graduate transcripts and mitment to excellence in teaching and continued effectiveness) to Dr. Janet A. White, Search arrange for 3 letters of recommendation to the scholarly activity; must be prepared to teach a Committee/ FOC1206, Department of Math- Office of Human Resources, Albright College, broad spectrum of undergraduate mathematics ematics, Millersville University of Pennsylvania, P.O. Box 15234, Reading, PA, 19612-5234 or courses and to teach undergraduate geometry as P.O. Box 1002, Millersville, PA 17551-0302. to [email protected] (PDF preferred) with the it relates to the preparation of secondary school Completed application must be received by subject line Mathematics Search. Additional teachers. Must complete a successful interview January 10, 2007 to assure full consideration. information is available at www.albright.edu. and teaching demonstration. Duties include an An EO/AA Institution. E-mail applications will Albright is an Affirmative Action/ Equal Op- annual 24-hour teaching load, scholarly activity, not be accepted. portunity Employer committed to diversity student advisement, curriculum development within its community. Women and minorities and committee work. Millersville University TEXAS are encouraged to apply. is a selective, comprehensive, state university of 8000 students located in historic Lancaster The University of Texas at Tyler Juniata College County, PA within convenient traveling distance The University of Texas at Tyler invites applica- Assistant Professor of Mathematics to Baltimore, Philadelphia, New York, and the tions for the position of Chair of the Department Juniata College, a highly ranked, national liberal Atlantic Ocean beaches. Additional information of Mathematics to begin fall 2007. The univer- arts college of 1,400 students located in the on the university and the department can be sity seeks a candidate who will energetically lead scenic Allegheny mountains of central Penn- found at www.millersville.edu. Send application the department in continuing to build excellent sylvania, invites applications for a position as a letter that addresses the position requirements, undergraduate and graduate programs and who tenure-track assistant professor in Mathematics vita, copies of undergraduate and graduate tran- will mentor faculty in teaching, research, and to begin August 2007. scripts and three letters of reference (at least two service. of which attest to recent teaching effectiveness)

30 December 2006 FOCUS

The successful candidate will have a Ph.D. in Departmental Website: http://math.uttyler.edu national publications for its “applications-ori- mathematics; an outstanding record of teach- ented” approach. Faculty are judged primarily ing and research commensurate with a tenured Review of applications will begin December on excellence in teaching. MSOE graduates are faculty appointment; effective leadership, 1 and continue until the position is filled. UT in high demand as evidenced by our strong job administrative, and interpersonal skills; and the Tyler is an Equal Opportunity & Affirmative placement rate. ability to lead the faculty in obtaining external Action employer. funding. The review of candidates will begin immediately WISCONSIN and continue until the position is filled. To apply, Located 90 miles east of Dallas in the beautiful please submit a detailed resume, evidence of piney woods of East Texas, The University of Milwaukee School of Engineering teaching excellence and three professional ref- Texas at Tyler has an enrollment of about 6000 Mathematics Faculty Position erences to: Dr. Karl David, Chair, Mathematics students. The Department of Mathematics of- The Milwaukee School of Engineering invites Department, Milwaukee School of Engineering, fers degrees at the undergraduate and master’s applications for one and possibly two full-time 1025 N. Broadway, Milwaukee, WI 53202-3109. levels. For more information, visit http://www. mathematics faculty positions starting in the fall The information can also be faxed to (414) 277- uttyler.edu. of 2007. The person selected should be able to 7462. Please visit us at www.msoe.edu. teach any of the standard courses in an under- Please submit a letter of application, curriculum graduate mathematics curriculum and possibly a MSOE is an Equal Opportunity Employer. vitae, a brief description of research plans, state- course in graduate level engineering mathemat- ment of teaching philosophy, and names of at ics. MSOE offers degrees in engineering, engi- least four references to neering technology, technical communication, business, construction management and nursing. Dr. Dick Mitchell Candidates should possess an appropriate doc- Department of Mathematics toral degree and related experience. Salary and The University of Texas at Tyler rank will be commensurate with experience. 3900 University, Blvd. Tyler, Texas 75799. MSOE is located in the heart of downtown Milwaukee and has been recognized in several

                                                                                                                                                                                                



               31 FOCUS December 2006

The Mathematical Association of America Periodicals Postage paid at 1529 Eighteenth St., NW Washington, DC and Washington, DC 20036 additional mailing offices