FOCUS February 2007

FOCUS is published by the Mathematical Association of America in January, February, FOCUS March, April, May/June, August/September, October, November, and December. Editor: Fernando Gouvêa, Colby College; Volume 27 Issue 2 [email protected] Managing Editor: Carol Baxter, MAA Inside [email protected]

Senior Writer: Harry Waldman, MAA hwald- 4 Ivars Peterson Named MAA Director of Publications for [email protected] Journals and Communications Please address advertising inquiries to: 4 Furstenburg and Smale Will Share the 2006-2007 Wolf Prize [email protected] President: Joseph Gallian 5 Bylaws Change on the Agenda for MAA Business Meeting at the San José MathFest First Vice-President: Carl Pomerance, Sec- ond Vice-President: Deanna Haunsperger, By Martha J. Siegel, MAA Secretary

Secretary: Martha J. Siegel, Associate 7 In FOCUS: The 2007 Joint Mathematics Meetings Secretary: James J. Tattersall, Treasurer: John W. Kenelly By Fernando Q. Gouvêa Executive Director: Tina H. Straley 8 JMM 2007: Report of the MAA Secretary By Martha J. Siegel, MAA Secretary FOCUS Editorial Board: Donald J. Albers; Robert Bradley; Joseph Gallian; Jacqueline 11 Undergraduates Win Awards in New Orleans Giles; Colm Mulcahy; Michael Orrison; Peter By Joe Gallian Renz; Sharon Cutler Ross; Annie Selden; Hortensia Soto-Johnson; Peter Stanek; Ravi 12 Undergraduate Students at the Joint Meetings Vakil. By Betty Mayfield Letters to the editor should be addressed to 13 The Undergraduate Poster Session 2007 Fernando Gouvêa, Colby College, Dept. of By Diana Thomas Mathematics, Waterville, ME 04901, or by email to [email protected]. 14 Prizes and Awards at the 2007 Joint Mathematics Meetings By Fernando Q. Gouvêa Subscription and membership questions should be directed to the MAA Customer 19 Photos from the New Orleans Joint Mathematics Meetings Service Center, 800-331-1622; e-mail: [email protected]; (301) 617-7800 (outside 23 Harry Lucas, Jr. is Inducted into the Icosahedron Society at the U.S. and Canada); fax: (301) 206-9789. MAA Joint Mathematics Meetings in New Orleans Headquarters: (202) 387-5200. 24 The MAA Goes To Middle School (and How You Can Too) Copyright © 2007 by the Mathematical By Steven R. Dunbar and Bonnie Leitch Association of America (Incorporated). Educational institutions may reproduce articles 27 In FOCUS: Curriculum Focal Points for their own use, but not for sale, provided Articles by Francis Fennell, Anthony Ralston, and Barbara Reynolds that the following citation is used: “Reprinted with permission of FOCUS, the newsletter 33 Call For Papers: Contributed Paper Session at MathFest 2007 of the Mathematical Association of America (Incorporated).” 37 Employment Opportunities Periodicals postage paid at Washington, DC and additional mailing offices. Postmaster: Send address changes to FOCUS, Mathematical Association of America, P.O. Box 90973, On the cover: Since the Joint Meetings began on the 12th day of Christmas, it was Washington, DC 20090-0973. only appropriate that mathematicians be greeted, in the lobby of the Sheraton, by a ISSN: 0731-2040; Printed in the United States New Orleans-style Santa and his alligators. of America.

FOCUS Deadlines May/June August/September October Editorial Copy March 9 June 9 Display Ads March 9 June 9 August 1 Employment Ads March 24 June 16 August 13 2 February 2007 FOCUS

MAA’s Math Gateway Now Online

M AA’s new NSF-supported digital library project, The Math Gateway, a pathway within the National Science Digital Library (NSDL) is now online at http://mathgate- way.maa.org.

The Math Gateway is the only mathematics pathway among the NSDL’s nine “pathway projects,” each of which has stewardship for a particular community of users. At Math Gateway you can simulta- neously search for online mathematics materials held by 17 partner collections, including all the components of MathDL, Math Forum, MathWorld, PlanetMath, the National Curve Bank, Demos With Positive Impact, iLumi- na Digital Library, causeweb. org, the Connected Curricu- lum Project, Virtual Labo- ratories in Probability and Statistics, the Mathematics Survey, the Ethnomathemat- ics Digital Library, and the NSDL Middle School Portal. The Gateway home page also features a Math in the News column, new each week. Soon a new Math in the News (MathDL) at http://mathdl.maa.org is one • Applied Math and Science Education column will appear each working day. of the original NSDL collections. Repository, with resources for two- year schools, at http://amser.org If you register at The Math Gateway, In addition to Math Gateway, other • your My Library section enables you NSDL pathway projects include: Teachers’ Domain at WGBH, with to collect particular resources and share • comPADRE, for physics, at http:// professional development for K–12 selected ones with a list of friends and compadre.org teachers, at http://teachersdomain. org colleagues. You may upload small files to • your Library, work on them collectively MatDL, for materials science, at http://matdl.org • NSDL Middle School Portal, the with those on your list, and discuss topics remaining public part of the Eisen- of common interest. • Engineering Pathway, at http://engi- hower National Clearinghouse, at neeringpathway.org http://msteacher.org The NSDL (see http://nsdl.org) is an • BiosciEdNet (BEN), for biology, at NSF-sponsored program that was begun http://www.biosciednet.org. • ChemEd Digital Library, being in 2000. Currently there are over 200 created by the Journal of Chemical individual projects supported by the • Shodor Foundation, for computa- Education. program, and the NSDL database has tional science, at http://shodor.org information on more than two million Lang Moore is the Director of the Math May/June August/September October online materials and services. MAA’s Gateway and the Executive Editor of Editorial Copy March 9 June 9 Mathematical Sciences Digital Library MathDL. He can be reached by email at Display Ads March 9 June 9 August 1 [email protected]. Employment Ads March 24 June 16 August 13 FOCUS February 2007

Ivars Peterson Named MAA Director of Publications for Journals and Communications

The MAA is pleased to announce it has and Chemistry from the University of To- selected Ivars Peterson as its new Direc- ronto. He is currently a writer at Science tor of Publications for Journals and Com- News and editor of Science News Online munications. Peterson will begin working and Science News for Kids. Peterson is with the Association at its Washington also a weekly mathematics columnist headquarters on Monday, March 5, 2007. for Science News Online and FOCUS In his position as Director, Peterson will Online, where his MathTrek column has be overseeing the MAA’s journals and been a perennial favorite. He is the author other periodicals, both in print and elec- of several books, including Mathematical tronic. He will also oversee the content Treks: From Surreal Numbers to Magic and resources available at the MAA’s Circles, published by the MAA. He pre- website. His other activities will entail viously worked as a high school science duties related to communications from and mathematics teacher. the MAA to its members, its sections, the public, and other constituencies. We are very pleased that Peterson will be joining the MAA and welcome him to the Peterson has an M.A. in Journalism from staff and the leadership team. the University of Missouri-Columbia, a B.Ed. in Education and a B.Sc. in Physics Ivars Peterson

Furstenberg and Smale Will Share the 2006–2007 Wolf Prize

The 2006–2007 Wolf Prize in Math- ematics will be shared by Harry Fur- stenberg of the Hebrew University of Jerusalem and Stephen Smale of the University of California at Berkeley. The prize, which has a total value of $100,000, is one of seven prizes given annually by the Wolf Foundation to recognize achievement in different areas of science and the arts. The prize will be formally awarded in Israel this May.

Furstenberg was honored “for his pro- found contributions to ergodic theory, probability, topological dynamics, analysis on symmetric spaces and homoge- neous flows.” Smale was honored for his “ground-breaking contributions that have played a fundamental role in shaping dif- Stephen Smale Harry Furstenberg ferential topology, dynamical systems, mathematical economics, and other subjects in mathematics.” More details, including a more complete description of the mathematical achievements of both men, can be found at the Wolf Foundation web site at http://www.wolffund.org.il.

February 2007 FOCUS

Bylaws Change on the Agenda for MAA Business Meeting at the San José MathFest By Martha J. Siegel, MAA Secretary

The MAA Board of Governors, at its Committee on Sections (see Article MOTION 2: meeting on January 4, 2007, passed the VI.7), the members of the Audit Com- following Bylaws changes to allow flex- mittee (see Article IX.3), and a current To change the current Article IX. 3: ibility in meeting government regulations journal editor or the chair of the Com- for organization audits. mittee on Publications. It shall be the The accounts of the Association shall function of this Committee to review be audited annually by a certified Currently, two members of the Associa- continually the policies and activities public accountant (the auditor). There tion are elected by the Board to serve on of the Association, to plan and organize shall be an Audit Committee, a sub- the Audit Committee for terms of four new activities, to formulate in broad committee of the Executive Commit- years. Members of the Audit Committee outline the programs of meetings and tee, consisting of two members each plus the Treasurer form the MAA’s Bud- of publications, to act on behalf of the elected by the Board in alternate get Committee, and all members of the Board on all financial matters as speci- even-numbered years for a term of Budget Committee are members of the fied in Article IX, and in general to four years. The Audit Committee shall Executive Committee and of the Board of consider all matters of importance or be responsible for selecting the auditor, Governors. These Bylaws changes allow interest to the Association. This Com- receiving the report of the auditor, and for the possibility that we appoint some- mittee shall prepare the agenda for making recommendations based on one with specific expertise in non-profit meetings of the Board and shall ana- the auditor’s report to the Executive accounting practices to serve on the Audit lyze the implications and aspects of all Committee. Committee. Such a person would not be matters which are to come before the a member of the Budget Committee, the Board for decision. It shall present to by changing the second sentence to: Executive Committee or the Board of the Board the viewpoints suggested by Governors. The expectation is that if this such analyses, as well as all such facts There shall be an Audit Committee is done, at most one such person would be as may seem pertinent or as may in any whose membership includes two mem- appointed to the Audit Committee. way facilitate the Board’s work. bers who are elected by the Board in alternate even-numbered years for a MOTION 1: by inserting the word ‘elected’ before term of four years. To change the current Article III, Section 3: the words ‘members of the Audit Com- mittee.’ As specified in the Bylaws, these changes There shall be an Executive Committee must be approved at the next MAA Busi- of the Board consisting of the Officers ness meeting, during MathFest, which of the Association, the chair of the will be held in San José, CA, on August 3–5, 2007.

Awesome Math in 2007

By Titu Andreescu

We’re going to do it again! About this time last year, I sent an e-mail to mathematics teachers and educators all around North America announcing a brand new program for middle and high-school students interested in spending part of their summer immersed in enriching mathematics. Despite starting from scratch, AwesomeMath had an extremely successful inaugural summer camp in 2006, with 101 students from seven countries participating.

The 2007 AwesomeMath Summer Program will be held on July 16–August 6, once again at the University of Texas at Dallas. We are assembling our faculty and staff and hope once again to have a successful summer. To find out more, visithttp://www. awesomemath.org, which also has information about our year-round training program and the free online journal Mathemati- cal Reflections.

Titu Andreescu is an Associate Professor in the Department of Science and Mathematics Education at the University of Texas at Dallas. He is a former director of the MAA’s AMC program and the author of many books.

5 FOCUS February 2007 Top n Reasons to “Experimental Mathematics in Action” in the Attend the PCUMC North Central Section’s Summer Seminar

By Alissa Crans The theme for this year’s Summer this area. His recent book, Experimental Seminar of the North Central Section of Mathematics in Action, will be the start- 0. A math conference designed the MAA is “Experimental Mathematics ing point for the seminar. Borwein will specifically for undergraduates! in Action: Insight through Computation.” “present a coherent variety of accessible The principal lecturer will be Jonathan examples of modern mathematics where 1. Free registration! Borwein of Dalhousie University. The intelligent computing plays a significant 2. Free lunch! event will be held at Carleton College in role and in so doing to highlight some of Northfield, MN, on July 16–20. the key algorithms and to teach some of 3. Talks for undergraduates by the key experimental approaches.” undergraduates. The program will focus on how comput- 4. Special sessions featuring talks ers have allowed us to “see” previously For more information, visit http://www. by freshmen and sophomores. unobservable mathematical phenomena, math.carleton.edu/comp_math/ or contact making mathematics much more of an ex- Steve Kennedy at skennedy@carleton. 5. Dynamic guest speakers, includ- perimental science than it has ever been. edu. ing Dylan Kohler from Electronic Jonathan Borwein is one of the leaders in Arts, Don Schmidt and Joshua Schpok from Dreamworks Animation and representatives from the NSA, MathFest 2007: Call for Student Papers Raytheon, RAND, and Northrop Grum- man. The deadline for receipt of applica- All presenters are expected to take full 6. Raffle prizes for participants, in- tions for student papers to be presented part in the meeting and attend activities cluding recent XBox and PS2 video at the 2007 MathFest in San José is sponsored for students on all three days game titles! Friday, June 15, 2007. Students may of the conference. Nomination forms and not apply for funding from both MAA more detailed information for the MAA 7. Math trivia contest. and PME. Every student paper session Student Paper Sessions will be available M room will be equipped with a standard at www.maa.org/students/undergrad/ by overhead projector, a computer projec- March 1, 2007. n – 3. Panel discussion about graduate tor, and two screens. Each student talk school. is 15 minutes in length. Pi Mu Epsilon Sessions n – 2. Panel discussion about career Pi Mu Epsilon student speakers must be opportunities. MAA Sessions nominated by their chapter advisors. Ap- n – 1. Homemade cookies! Students who wish to present at the plication forms for PME student speakers MAA Student Paper Sessions at Math- will be available by March 1, 2007 on n. A captive audience for sharing Fest 2007 in San Jose, California must the PME web site www.pme‑math.org undergraduate research projects, senior be sponsored by a faculty advisor famil- or can be obtained from PME Secre- theses, really cool problems from class, iar with the work to be presented. Some tary‑Treasurer, Dr. Leo Schneider leo@ and biographical or historical informa- funding to cover transportation costs jcu.edu. A PME student speaker who tion about mathematicians! (up to $600) for student presenters who attends all the Pi Mu Epsilon activities is are members of the MAA is available. eligible for transportation reimbursement The Pacific Coast Undergraduate Math- At most one student will be funded up to $600, and up to five speakers per ematics Conference will be held on from each institution and each REU. Chapter may be eligible for full or partial March 31, 2007 at Pepperdine University reimbursement. in Malibu, CA from 8 am to 4 pm. Infor- mation about the conference, including HRUMC XIV to be Held at Siena College registration details, can be found on the conference website at http://www.pcumc- The 14th annual Hudson River Under- or fourth year undergraduate mathemat- math.org. PCUMC is sponsored by Pep- graduate Mathematics Conference will ics majors. The keynote speaker for this perdine University, Loyola Marymount be held at Siena College in Loudonville, year will be Georgia Benkart, Professor University, and Lewis and Clark College New York on April 21, 2007. The con- of Mathematics at the Univeristy of and receives major funding from an NSF ference includes presentations on math- Wisconsin at Madison. For more infor- Grant DMS-0241090 through the MAA ematics by both faculty and students, mation, visit the conference website at Regional Undergraduate Mathematics and both are encouraged to participate. http://www.skidmore.edu/academics/mcs/ Conference program. Conference sessions are designed so pages/hrumc.htm. Those wishing to make that some presentations are accessible a presentation at the conference should to undergraduates in their first years of submit an abstract via the website by study, and others are accessible to third February 25th, 2007. February 2007 FOCUS In FOCUS: The 2007 Joint Mathematics Meetings

By Fernando Q. Gouvêa

The 2007 Joint Mathematics Meetings was mostly filled with were held in New Orleans on January 5 Louisiana State sup- to 8. Over 5,000 participants descended porters. On the night on the Big Easy for several days of of the game, the name mathematics in all its glorious variety, and logo of each team from Leonhard Euler to Pixar Animation, was projected onto the with stops in between for outer space, façade of the appropri- bar codes, all areas of mathematics and ate hotel, prompting mathematics education, music, and Gron- (unfulfilled!) dreams ingen. The exhibit hall started from the of seeing the MAA usual displays of books and software, but and AMS logos simi- also included jewelry, accessories, toys, larly displayed. ‘glass geometry,’ and booths promoting institutes, universities, journals, and Splitting the meet- even government agencies. The under- ing into two hotels graduate student poster session attracted generates interest- a huge crowd of bright students showing ing questions which off their research, and a huge crowd of I hope some of our adult mathematicians admiring it. Sur- more modeling-ori- rounding the meeting were many social ented readers might The Sheraton lobby as LSU Headquarters for the Sugar events, mini-courses, meetings of the want to consider. The Bowl. MAA Board of Governors and the AMS main talks were given th Council, and more committee meetings on the 5 floor of the heard suggested that most people were than most participants really wanted to Sheraton, and the exhibits were located rd not too impressed. Had the program- know about. on the 3 floor of the Marriott, with mers not expected a hotel that full, or are other events distributed throughout the mathematicians just picky? Analyses of New Orleans is still in many ways a surrounding floors. As a result, at any the situation would be welcome! city in distress, and the memory of the given moment there were lots of math- destruction following Hurricane Katrina ematicians either crossing Canal Street The articles that follow give a snapshot of was ever present. In an effort to offer (thankfully, not a very busy street) or the meeting and some of what happened some help, the meeting organized a sale on the escalators. Whoever calculated there. MAA Secretary Martha Siegel of t-shirts and a raffle with lots of very the maximum demand on the escalators reports on what was decided at the meet- nice prizes. The proceeds went to a lo- must have done a fairly good job, since ing of the Board of Governors and at the cal charity, the Second Harvest of New I only saw one broken escalator over the MAA Business Meeting. Diana Thomas Orleans Food Bank, and specifically to several days of the meeting. On the other writes about the student poster session, their BackPack Program, which provides hand, the throughput could have been and Joe Gallian (President of the Associa- food for children who otherwise might better. The escalators only just handled tion as of the end of the meeting) reports go hungry. I like this idea a lot, and hope the numbers at the peak moments, such as on two exceptional undergraduates who that the organizers will consider doing the just before and just after a popular talk. received prizes for their research. A report same in future meetings, since there are on prizes and awards given at the meeting no cities without social problems. Folks The Marriott featured an innovative and a large photo spread complete our can use the help, and the mathematical elevator system that generated some section on the JMM. community has the resources to offer it. discussion during the meeting. To call the elevator, one had to punch in the floor one The next national meeting of the MAA The meeting events were distributed was trying to reach. The device would is this summer in San José, and the next among two hotels, the Marriott and the then indicate which elevator would take Joint Mathematics Meetings will be Sheraton, which face each other across us there. Inside the elevator, there were next January in San Diego. We’ll see Canal Street, just next to the French no buttons to press except for door open/ you there. Quarter. Participants who arrived early close and emergency buttons. A panel on (for example, to attend the mini-courses, the inner door lighted up to indicate at Fernando Q. Gouvêa is Carter Professor as I did) got to experience a little bit of which floors it would be stopping. Surely of Mathematics at Colby College the excitement of the Sugar Bowl, since this system was intended to improve ef- and the editor of FOCUS. the Marriott was the official headquarters ficiency, and not just to render impossible of Notre Dame fans, while the Sheraton schoolboy pranks… but the comments I 7 FOCUS February 2007 JMM 2007: Report of the MAA Secretary

By Martha J. Siegel

It was a leap of faith that moved us to adhere to the plans to meet in New Orleans, as originally scheduled, long before Katrina. We were rewarded by having the all-time largest registration for the Joint Mathematics Meetings. I want to thank the MAA and AMS Meetings Staff, and MAA Associate Secretary, Jim Tattersall, for the success of these meetings. The Program Committee chose an outstanding list of invited speakers and all those who attended added substantially to the vibrant and friendly atmosphere. I note that more than 400 undergraduates attended this meeting. Thanks to the various MAA committees and individual faculty members who have contributed to this excellent undergraduate turnout demonstrating interest in and support for mathematics.

I will review briefly the matters discussed by the Board of Governors at its meeting on January 4 and mention one or two items of note from the MAA Business Meeting.

Our bottom line in 2005 was an operat- ing surplus of almost $600,000. As a result, we have added substantially to our Board meets in New Orleans. endowment. We cannot afford to rest on these laurels, though. Our endowment is Don Albers in bringing our publications issue of FOCUS, starting on page 18.) still far from what would be ideal for an to a larger market through agreements At these meetings we received the final association of our size. External funding with Cambridge and Amazon.com and reports of the working groups in three is likely to become more competitive, through the efforts of the book series important areas: Revenue, the American especially in the collegiate mathematics editors who keep excellent titles coming. Mathematics Competitions, and Pro- area, so we will continue to try to increase Although Don Albers has left the posi- fessional Development. The working revenue and control spending. The Car- tion of Associate Executive Director and groups on each of these areas, chaired by riage House is already being used for Director of Publications, Publications are Barbara Faires, Frank Farris, and Nancy meetings, and eventually we hope that it in good hands: Don continues to manage Hagelgans, presented reports to the Board will be a source of added revenue. Grand acquisitions from his base in California, and these will be posted on the website Opening ceremonies will be held in April. Elaine Pedreira is heading the Books pro- shortly after these meetings. I urge you More information will be available on the gram and Carol Baxter is acting Director to read them. Meanwhile, we are in the MAA web site. for Journals and Communications. midst of Cycle II with working groups in three new areas: Membership (chair: Carl The 2005 audit was very positive, reflect- As you may already know, Tina Straley Pomerance), Governance (chair: Carl ing the great improvement in Association and the Executive Committee, with Cowen), and Students (chair: Deanna finances and financial procedures in Board approval, have decided to spend Haunsperger). The Board voted to add recent years. The total income from some time revisiting our goals and Meetings, Sections, and STEM issues for publications in 2006 seems to be on strategic plans for the next five years, study in Cycle III to begin this spring. target. Much of this is due to the efforts ten years, and so on. (See the January of former Associate Executive Director

8 February 2007 FOCUS

The format of Board meetings has changed somewhat in that we have had breakout sessions to discuss strategic planning for part of the day. The Board itself suggested a more active role in the focus groups held last August and the implementation has made for some interesting discussions so far!

We have launched a new project with the American Institute of Physics (AIP), nominating Joe Gallian and Carl Pomer- ance as our Advisory Board to AIP. Visit http://www.aip.org/dbis/ to see what we’re up to. In addition, we have endorsed a film project on the Mathematical Olym- piad Program. President Joe Gallian and AMC Director Steve Dunbar are taking the lead on that.

The Euler Prize, endowed by funds contributed by Paul and Virginia Halmos, was given this year for the first time, in Pictured left to right are MAA staff members who worked on the meeting: Bryan celebration of the 300th anniversary of Lane, Bob Anastasio, Jim Tattersall, Becky Roemen, and Calluna Euving. Euler’s birth. The award winner is John them. Persons elected to office by has been a thoughtful, articulate, and Derbyshire for his book, Prime Obses- the Board of Governors, by the hard-working member of these two com- sion. The MAA study tour this summer general membership, or by the mittees and a true asset to the Executive will trace Euler’s life (1707-1783) from membership of a constituency Committee and the Board of Governors. Basel to St. Petersburg. This is the MAA within the Association may be We miss him and wish him well! Year of Euler, and celebrations included removed from office by a 3/4 vote a mini-course at the Joint Meetings and of the membership of the Board The Board approved the 2007 Budget and the release of two new books on Euler, of Governors, with or without the 2008 Dues. We are finishing the work complete with cake for the birthday boy. cause, if deemed to be in the best for the 2007 elections. The Nominating Three more books will come during the interest of the Association. The Committee for the 2007 Elections was year, and there will be many Euler-re- vote of the Board of Governors chaired by Ann Watkins. Wade Ellis, lated events at MathFest. I urge you take for removal from contractual Barbara Faires, Ron Graham, and Betsy advantage of the posters, the books, the positions is an authorization for Yanik served on the committee. We will courses, and the Study Tour highlight- the President or the Executive continue to use a mix of electronic and ing the mathematical contributions of Director to take the steps neces- paper ballots. We will be electing new Euler. sary for that removal. officers, including a new president, who will serve a year as President-Elect dur- An Ethics and Whistleblower Policy was The Board passed several other Bylaws ing 2008 and become president at the end recently adopted by the Board to comply changes that can be found online and of the 2009 Joint Meetings. with the requirements of the Sarbanes- elsewhere in FOCUS (see page 5). They Oxley Bill. At the Business Meeting, will be brought to a vote by the member- Daniel Velleman of Amherst College is an addition to the MAA Bylaws was ship at the Business Meeting in San Jose now the Editor of the American Math- formally approved. It provides a mecha- this summer. ematical Monthly and will serve a five- nism for removal from office in case of year term that began January 1, 2007. serious violations. Daniel Maki, member of the Audit and We again thank Bruce Palka for doing a Budget Committees, has taken a position splendid job as Editor of the Monthly and Addition to the MAA Bylaws, ap- with the NSF this year. He has resigned for his dedicated service as a member of proved at the MAA Business Meeting from these two committees and the Board the Board. Searches are now underway on January 8, 2007. has elected Richard Cleary of Bentley for new editors of the College Mathemat- College to serve for one year as his re- ics Journal and of Math Horizons. Article IV. 9. Persons appointed placement and then for a four-year term to positions within the Associa- to replace Jim Daniel, whose second and The Board approved a template for tion may be removed from of- final term ends this time next year. Dan Section bylaws. The Committee on Sec- fice by the entity that appointed

FOCUS February 2007 tions established a schedule The members of the MAA for periodic review of sec- Program Committee for Janu- tion bylaws and this should ary 2007 in New Orleans were streamline the process for the Frank Farris (chair), Jerome sections and the Board. Goldstein, Tom Moore, Mi- chael Neumann, Talmage I want to take this opportu- James Reid, V. Frederick nity to thank those governors Rickey, Don Saari, Carol whose term on the Board has Schumacher, James Tattersall expired: Tom Banchoff as a (ex off.), and Sylvia Wiegand. Former President; Jonathan The members of the Joint Borwein as Governor-at- AMS-MAA Program Com- Large for Canadians; and mittee for New Orleans 2007 Nathaniel Dean as Gover- were Frank Farris (MAA), nor-at-Large for Minority Gail D. Ratcliff (AMS), Don- Interests. We will miss the ald Saari (MAA), and Michael contributions of these three President Carl Cowen and Secretary Martha Siegel at the MAA Busi- Starbird (AMS) (Chair). active members, and look ness Meeting. forward to their continued It’s perhaps worth noting that involvement with the work January 6–9, 2010, San Francisco, CA Jim Tattersall’s term as As- of the Association. Governors-at-Large, August 5–7, 2010, Pittsburgh, PA sociate Secretary will end in February elected by the Board to begin a three- January 5–8, 2011, New Orleans, LA 2009, and that we are actively searching year term beginning after these Joint January 4–7, 2012, Boston, MA for a new Associate Secretary, who will Mathematics Meetings are: Camille January 9–12, 2013, San Diego, CA spend a year as Associate Secretary Elect McKayle, Governor-at-Large Represent- January 15–18, 2014, Baltimore, MD learning the ropes. See the MAA web site ing Minorities, replacing Nate Dean and August 5–8, 2015, Washington, DC for specifics and details. Andy Liu, Governor-at-Large Represent- ing Canadian Mathematicians, replacing The last of these is our Centennial Meet- We have lost several wonderful friends Jonathan Borwein. ing. The Co-Chairs of the Centennial of the MAA since MathFest. G. Bailey Celebration Committee, Deanna Haun- Price, who was President of the MAA in Those Section Governors who will serve sperger and Steve Kennedy, have some 1957 and 1958, died November 7. Paul on the Board until July, 2007 but for great plans! Halmos (1919-2006), a great friend of the whom this was the last Board meeting MAA, died in October, Leon Henkin died are: Doug Ensley (EPADEL), David I want to thank Tina Straley, Michael on November 1 at his home in Oakland, Kerr (Florida), Richard Wilders (Il- Pearson and the rest of the MAA staff. CA. and Don Kreider, former Treasurer linois), David Wright (Intermountain), They have been instrumental in making and President died suddenly at his home James Freeman (Iowa), Roger Waggoner the MAA a vibrant and intellectually ex- on December 7th. See the In Memoriam (Louisiana-Mississippi), David Carothers citing professional organization. I thank Section of Focus Online for more infor- (MD-DC-VA), Ruth Favro (Michigan), my assistant, Denise Raspa, whom most mation on these outstanding men. Dan Kemp (North Central), Art Benjamin of you know only by her electronic (Southern California-Nevada), and Eliza- name [email protected]. She has been Carl Cowen handed the gavel to our new beth Bator (Texas). The three years of a tremendous help to me. She and Cal- President, Joseph Gallian, at the MAA their terms have flown by! Most of these luna Euving at MAA have been working Business Meeting. This marked the end members are already actively enrolled diligently to simplify and streamline our of Carl’s two-year term as President. It as committee members. Join me also in operations. I thank them both for making has been a pleasure to serve under Carl. wishing a speedy and complete recovery my job so much easier. His quiet and steady leadership and his to our colleague, Jim Bruening, Governor interest in drawing a diverse group of of the Missouri Section. We look forward Of course, these meetings cannot take mathematicians into the governance of to seeing him in San Jose. place without the concerted effort and the MAA have made the MAA a stronger the considerable skill of many people. and more inclusive organization than The schedule of future meetings of the We acknowledge the staff in Washington, ever. I am sure I represent the entire lead- Association is: our Associate Secretary, Jim Tattersall, ership of the Association in thanking him and the volunteers who have served on for his service. We welcome President August 3–5, 2007, San Jose, CA the program committee and the local Joe Gallian with enthusiasm. January 6–9, 2008 San Diego, CA arrangements committee, as well as the July 31–August 2, 2008, Madison, WI many folks who have given papers and Martha Siegel teaches at Towson Col- January 7–10, 2009, Washington, DC run sessions. lege in Maryland and is Secretary of the August 6–8, 2009, Portland, OR Association.

10 February 2007 FOCUS Undergraduates Win Awards in New Orleans

By Joe Gallian

At the Joint Meetings in New Orleans Ana Caraiani won the Alice T. Scha- fer Prize given by the Association for Women in Mathematics for Excellence in Mathematics. Ana, a senior at Princeton, was cited for her research in number theory, her performance in her classes, and for being a winner of the Putnam Competition in both her freshman and sophomore years. One of her letters of support stated that she ranked among the top undergraduate mathematics majors that the author had seen in his fifty years at Princeton.

Ana’s number theory research focused on determining the structure of the mul- tiplicative semigroups of rational numbers having generators of the form (An + B)/(Cn + D) where n ≥ 0 for specific integer choices of A, B, C, D, with and Joe Gallian with Ana Caraiani and Daniel Kane at the Awards Ceremony. without adjoining 1/2 or other rational numbers as generators. The case (3n + 2)/(2n + 1) is known as the ‘weak 3x + 1’ problem.

In this case she answered a question raised by Jeff Lagarias and extended the methods of Applegate and Lagarias for completely describing the rationals in the desired semigroup for a general class that includes the case where the generators are of the form (5n +3)/(2n + 1), together with 1/2, thereby giving a complete answer to ‘weak 5x + 1’ problem. Ana is currently doing a senior thesis under the supervision of Andrew Wiles and intends to study mathematics in graduate school in the fall. The Schafer Prize: AWM President Barbara Keyfitz, Alyson Deines (honor- Daniel Kane, a senior at MIT, won the able mention), Yaim Cooper (runner-up) and Ana Caraiani (winner). AMS/MAA/SIAM Morgan Prize for Outstanding Research in Mathematics by ceedings of the American Mathematical Daniel is a three-time winner of the Put- an Undergraduate Student. The selection Society, the Journal of Number Theory, nam competition. He is currently doing committee wrote ‘At this early stage of and Integers: The Electronic Journal of research with Eric Demaine and will his mathematical career, Daniel has al- Combinatorial Number Theory. study mathematics in graduate school ready established a research record that this fall. would be the envy of many professional In one paper he proved an open con- mathematicians.’ jecture stated by a well-known number Joe Gallian is the President of the MAA. theorist. In another he improves a famous He teaches at the University of Min- He has eleven papers on diverse topics result that Erdös published in the Annals nesota-Duluth, where he also runs the that have been published or have been of Mathematics. In two others he answers world’s best summer research program accepted for publication in main stream questions posed by Ken Ono and Kiran for undergraduates. professional journals such as the Pro- Kedlaya. 11 FOCUS February 2007 Undergraduate Students at the Joint Meetings

By Betty Mayfield Almost five hundred undergraduate students — a new record — participated in the Joint Mathematics Meetings in New Or- leans. They were welcomed at a special reception on Friday night, where they munched on New Orleans King Cake and drank (non-alcoholic) hurricanes while chatting with other students. They attended invited and contributed talks, they hung out in the student hospitality suite, they enjoyed the MAA Student Lecture (“Mathematics: A Question of History,” given by Della Fenster of the University of Richmond), and they showed off their considerable mathematics skills. One hundred sixty-nine students displayed the results of their research projects at the Undergraduate Poster Session, and sixty-seven students from summer REUs gave talks about their work. Undergraduate students have become an important part of the Joint Meetings, accounting for almost 10% of the attendees. It is exciting to see the future of the profession in these talented and energetic students.

Betty Mayfield is the chair of the MAA Committee on Undergraduate Student Activities and Chapters.

(Non-alcoholic) Hurricanes He found the baby in the King Cake.

Students from Oakwood College. 12 February 2007 FOCUS The Undergraduate Poster Session 2007

By Diana Thomas Every year the number of posters entered in the Undergraduate Poster session at the Joint Mathematics Meet- ings increases tremendously. This year was no exception. There were a total of 175 poster submissions on topics rang- ing from the spread of fear to elliptic curves. Every student who presented a poster had an interesting account of their research experience and its consequent impact. I was able to talk to several students about their experience prior to the session and share a few of them with you here.

It is with pride that I note the dedica- tion and enthusiasm with which our mathematics community reaches out Student authors of the winning posters at the JMM 2007 Undergraduate Student to undergraduates in order to engage Poster Session. Photograph by Gordan Woodward of the University of Nebraska Lincoln. them in a research experience. Many undergraduate students are approached of his paper accepted only a week ago at the event on that day. Suzanne Len- in their individual classes by their pro- the Journal of Integer Sequences. Adam hart, Chair of the Committee on Under- fessors. Victor Camacho, a mathematics had responded to flyers at Truman State graduate Research, organized awards and major at Harvey Mudd College began his University advertising the STEP pro- the judging table on the day of the event. research project on a generalization of the gram. His consequent work with David Michael O’Leary from Towson State Burger’s Equation, a partial differential Garth from Truman State University University set up a new electronic scoring equation model describing turbulence in led to the publication and his poster at system, which reduced scoring time by an viscous fluids, after an interesting pro- the session. Each student I spoke to had hour. Members of the MAA Committee posal was provided by his professor John similar high impact stories and they were on Student Activities and Chapters spent Jacobson. He was very passionate about delighted to share their experiences with time assisting in organization of the ses- his research and is interested in continu- our mathematics community. sion on the day of the event. ing his work upon returning to Harvey Mudd. Other students are able to generate Management of the poster session was I would like to especially thank Margaret and focus research interest through REU handled by a large group of mathemati- Robinson from Mount Holyoke College (Research Experiences for Undergradu- cians, MAA and AMS staff, and student who came before the session started and ates) programs. Mathew Stamps attended volunteers. There were over 180 profes- stayed until the session was over, putting an REU at Valparaiso University that sional mathematicians who volunteered out many fires. In addition, Mario Mar- involved undergraduates in research on as judges for the poster session this year! telli from Claremont McKenna College a range of different topics. He discovered A large percentage of former judges re- who first organized and grew the session he really enjoyed pure mathematics. On turned this year and I thank them for their to the event it is today continues to assist returning to his home institution of Grand continued support of the session. Every me with organizational aspects and scor- Valley State University he asked his year Aparna Higgins from the University ing. Many more people were involved in advisor David Austin for an appropriate of Dayton recruits Project NExT fellows running the session smoothly and to all research topic. His work resulted in his to judge the session and we certainly of them we express our appreciation. We prize winning poster on Circle Packings could not run the judging portion without expect the session to continue to grow and Penrose Tilings. their involvement. and I look forward to seeing everyone in San Diego next year! One of the wonderful aspects of the As the poster session continues to grow, poster session is that it provides not Jim Tattersall (Associate Secretary of A list of all the prize winning posters, only the raw academic results of student the MAA), Michael Pearson (Director with advisors and institutions, can be research but also the personal excitement of Programs and Services), Hal Nesbitt found online at http://www.maa.org/stu- and electricity of student achievement. (MAA Program Coordinator), and Donna dents/undergrad/07winners.html. As I passed Adam Gouge’s poster on Salter (AMS Program Coordinator), Affinely Self-Generating Sets and Mor- continue to improve and streamline the Diana Thomas is an associate professor phisms, he proudly held up page proofs application process and coordination of at Montclair State University. 13 FOCUS February 2007 Prizes and Awards at the 2007 Joint Mathematics Meetings

By Fernando Q. Gouvêa

The Joint Mathematics Meetings bring together not only the MAA and the American Mathematical Society (AMS), but many other mathematical associations. The special session for prizes and awards, held on January 6, included many MAA prizes (several other MAA prizes are awarded at the summer MathFest, of course) and all of the annual prizes given by the AMS. In addition, prizes were awarded by the Association for Women in Mathematics (AWM), the Society for Industrial and Applied Mathematics (SIAM), and the Joint Policy Board for Mathematics (comprised of MAA, AMS, SIAM, and the American Statistical Associa- tion (ASA)).

This report lists all of the prizes awarded. For details about the prizes, including the official citations, brief biographies of the prize winners, and responses, visit the MAA awards site (use the “About the MAA” pull-down menu) or go directly to http://www. maa.org/Awards/JMM07.pdf. MAA Prizes and Awards

At the Joint Meetings, the MAA an- “the author or authors of an outstanding In addition, the MAA recognized the nounced its most prestigious award, the book about mathematics,” with emphasis winners of this year’s Haimo Awards, Gung and Hu Award for Distinguished on mathematical exposition. The Becken- given for distinguished college or uni- Service to Mathematics. A detailed ac- bach Prize is given for a “distinguished, versity teaching of mathematics, and count of the work and achievements of innovative book published by the MAA. awarded six Certificates of Meritorious the winner will appear in a future issue The award is not given on a regularly Service, presented for service at the na- of the American Mathematical Monthly. scheduled basis, but is given only when tional level or for service to a Section of Also announced are three important writ- a book appears that is judged to be truly the Association. ing prizes: the Euler and Beckenbach outstanding.” The Chauvenet Prize is book prizes and the Chauvenet Prize. The given “to the author of an outstanding Euler Prize, a new addition, was endowed expository article on a mathematical topic by Paul and Virginia Halmos and honors by a member of the Association.”

Deborah and Franklin Tepper Haimo Awards for Distinguished College or University Teaching of Mathematics

Jennifer Quinn Michael Starbird Gilbert Strang Association for Women in Mathematics University of Texas at Austin Massachusetts Institute of Technology

14 February 2007 FOCUS

Chauvenet Prize Beckenbach Book Prize

“The Gravity of Hades,” Mathematics Math through the Ages, Expanded Edition (MAA and Oxton House, 2004) Magazine, Vol. 75, No. 5, December 2002, pp. 335-350.

Fernando Q. Gouvêa and William P. Berlinghoff Andrew J. Simoson

Certificates of Meritorious Service Florida Section Kansas Section Michigan Section

Marilyn Repsher Sister Jo Ann Fellin Jerrold W. Grossman

Northeastern Section Rocky Mountain Section Texas Section

Donna Beers Janet Heine Barnett Stuart Anderson

15 FOCUS February 2007

Yueh-Gin Gung and Dr. Euler Book Prize JPBM Charles Y. Hu Prime Obsession: Bernhard Riemann Communications Award forDistinguished and the Greatest Unsolved Problem Award Service to Mathematics in Mathematics, (Joseph Henry Press, 2003).

Lee Lorch John Derbyshire Steven H. Strogatz

Association for Women in Mathematics Prizes AWM has two prizes that are awarded every year at the Joint Meetings. The Hay Award recognizes “outstanding achievements in any area of mathematics education, to be interpreted in the broadest possible sense.” The Schafer Prize is for an under- Frank and Brennie Morgan graduate woman who has shown excellence in mathematics; the criteria considered Prize for Outstanding include “the quality of the nominees’ performance in mathematics courses and special Research in Mathematics by programs, an exhibition of real interest in mathematics, the ability to do independent work, and, if applicable, performance in mathematical competitions.” an Undergraduate Student Alice T. Schafer Prize for Louise Hay Award for This prize is jointly awarded by Excellence in Mathematics by an Contributions to AMS, MAA, and SIAM. See page 10 for more information on the Undergraduate Woman Mathematics Education winner See page 10 for more information on the winner.

Daniel Kane Ana Caraiani Virginia McShane Warfield

16 February 2007 FOCUS

American Mathematical Society Prizes and Awards The AMS’s most prestigious prizes the Notices of the AMS or the Bulletin significant experimental component (this are the Leroy P. Steele Prizes, awarded of the AMS, the E. H. Moore Research is a new annual prize), the Satter Prize for every year at the Joint Mathematics Meet- Article Prize for an outstanding research an outstanding research contribution by a ings. There are three Steele Prizes: one article to have appeared in one of the woman, and the Veblen Prize in Geom- for mathematical exposition, one for a AMS primary research journals (this is etry. Finally, the Norbert Wiener Prize in seminal contribution to research, and one a new prize, to be awarded every three Applied Mathematics, given jointly with for lifetime achievement. In addition, the years), the Robbins Prize for a broadly SIAM, recognizes an outstanding contri- AMS awarded the Conant Prize for the accessible paper in algebra, combina- bution to applied mathematics. best expository paper published in either torics, or discrete mathematics with a

Leroy P. Steele Prize for E. H. Moore Research Article Prize Mathematical Exposition

David Mumford Ivan Shestakov and Ualbai Umirbaev

Leroy P. Steele Prize for Lifetime Achievement David P. Robbins Prize Henry McKean No picture available Leroy P. Steele Prize for Seminal Contribution to Research Karen Uhlenbeck No picture available Levi L. Conant Prize Jeffrey Weeks No picture available

Ruth Lyttle Satter Prize in Mathematics Claire Voisin No picture available Samuel P. Ferguson Thomas C. Hales

17 FOCUS February 2007

Norbert Wiener Prize in Oswald Veblen Prize in Geometry Applied Mathematics Peter Kronheimer and Tomasz Mrowka (AMS and SIAM) Craig Tracy and Harold Widom

Tomasz Mrowka and Peter Kronheimer

Winners of the Raffle to Benefit Craig Tracy Hurricane Katrina Survivors No picture of Harold Widom Mackichan Scientific Workplace (2 software prizes) available Barbara Jur M. M. Bogacz Four-Night stay at the San Diego Marriott during the 2008 JMM Oswald Veblen Prize Catherine Murphy in Geometry Dell Inspiron 1501 wireless notebook computer Peter Ozsváth and Zoltán Szabó Steve Hilbert Apple IPod with color video Carolyn Cuff MAA $300 Bookstore Credit Karen Bolinger AMS $300 Bookstore Credit Michael Barry New England Legal Seafood Lobster Bake Emily Moore TI-89 Titanium Graphing Calculator Deanna Caveny HP 30S Scientific Calculator (5 prizes) Michael Falk Max Tran Rich Neidinger Peter Ozsváth Andrew Shallue Kimberly Vincent No picture available for Bose Tri-port Acoustic Headphones Zoltán Szabó Fred J. Hickernell

18 February 2007 FOCUS New Orleans Joint Mathematics Meetings

The balloon arch, pre-collapse.

Just after and just before a popu- “The union must and shall be pre- lar talk: Escalators! served.” Joint Meetings Forever!

See: you’re in here! Don Albers shows Lee Stemkoski a brand-new copy of the January FOCUS.

No coffee, no theorems! The longest line, every morning, was at the Star- Chaos in what was later going to be the bucks. exhibit hall, January 3.

Bill Dunham signs books.

Fight Fiercely, Harvard! John Jones of Arizona State, Ed Dunne of AMS, Getting ready to cut the ribbon: on the left, MAA Secretary Martha Siegel, Fernando Gouvêa of Colby College, Executive Director Tina Straley, and President Carl Cowen; on the right, David Roberts of the University of AMS President Jim Arthurs, Executive Director John Ewing, and Secretary Minnesota Morris. Robert Daverman.

19 FOCUS February 2007

300 years old and still “the teacher of us all.” Bourbon Street at night.

Leon Harkleroad teaches his Minicourse on Math- ematics and Music. (Photo by Colm Mulcahy)

Hey, isn’t that MAA Development Manager Lisa Bill Dunham, Tina Straley, and Kolbe up there? Don Albers at the launch of The Genius of Euler.

Keith Devlin looks happy.

Loaded up and awaiting customers: the MAA booth before the ribbon-cutting.

At the undergraduate student poster session.

NExTers in feather boas! No getting in until it’s time: the crowd waits for the ribbon to be cut.

Much of the action at the A representative of Second JMM occurs in the many Harvest prepares to choose the winning raffle tickets. paper sessions. At the graduate student reception.

20 February 2007 FOCUS

Lisa Rezac and Graeme Fair- A collection of Eulerians: Lee Stemkos- weather at the MAA/Tensor grants ki, Erik Tou, and Rob Bradley. poster session. Want your own icosahedron? Hans Schepker’s Glass Geometry booth featured an isosahedral framework. More details at http://hansschepker. com.

MAA staffers show off their New Orleans t-shirts. Sales benefitted Second Harvest’s backpack program. Jan van Maanen gave an Is there a message for me? The mes- MAA Invited Address on sage boards were somewhat hidden on “The Bernoulli brothers in the 4th floor of the Marriott, but people the arena of the early calcu- still managed to find them. lus.”

At the MAA Special Session on “Entertaining with Math”. (Photo A collection of MAA editors: Art Benjamin of by Colm Mulcahy) Math Horizons, Lowell Beinecke of College Guess what’s in the Rampart Room? Mathematics Journal, Jenny Quinn of Math Horizons, Carol Baxter (the current boss), Fernando Gouvêa of FOCUS, Dan Velleman of the Monthly.

Speakers at the Euler mini-course. In back, Ed Sandifer, Janet Barnett, Steve Dunbar at the American Math- Rob Bradley. In front, Ron Calinger, ematics Competitions Booth. Jeff Suzuki, Stacy Langton, Larry Ron Calinger speaks on Euler’s life D’Angelo. at the MAA Short Course. 21 FOCUS February 2007

Scott Williams of the University of Data sets, homology, and bar codes Lee Lorch and Mrs. Scott Williams Buffalo, SUNY, gives the NAM Cox- come together in Robert Ghrist’s at the NAM Banquet. (Photo by Jac- Talbot Address. (Photo by Jaqueline talk at the AMS Current Events Bul- queline Giles) Giles) letin session.

It used to be all about books, but now software is just as important at the exhibits. AWM President Barbara Keyfitz The zome polyhedron from inside. (Pho- (left) and AWM Noether Lecturer to by Joe Gallian) Karen Vogtmann (right).

William Smith of the NExT directors. ASA presented the Serving beignets at the JPBM Communica- Hawkes Learning Systems tions Award. What have the Presi- booth. dents done to John Ewing?

Joe Dauben and Karen Parshall talk about being a historian of mathematics.

Michael Pearson, MAA Associate Ex- ecutive Director and Director of Programs Stacy Langton had one of Ed Sandifer signs copies and Services, shows the champion beards. of his new book while Bill Your turn now: MAA President Carl Cowen passes the gavel to MAA no respect for the Dunham looks on. President Joe Gallian. camera. 22 February 2007 FOCUS Harry Lucas, Jr. is Inducted into the Icosahedron Societyat the Joint Mathematics Meetings in New Orleans

By Lisa Kolbe

H arry Lucas, Jr., founder of the Educational Advancement Foundation, a philanthropic organization headquartered in Austin, Texas, was inducted into this prestigious society at the President’s Reception on Sunday, January 7, 2007 during the 90th national meeting of the Mathematical Association of America in New Orleans.

It is through Mr. Lucas’ incredible gener- osity that the Project NExT program has since 1999 supported six named Fellows known as the R.L. Moore Fellows. These Fellows are named for the renowned professor of mathematics at the University of Texas at Austin from 1920-1969, who promoted the study of more effective MAA President Carl Cowen congratulates Harry Lucas, Jr. (left) methods of learning and teaching. Mr. after his induction into the Icosahedron Society. Lucas was greatly influenced by the teaching methods of R.L. Moore and subsequently launched the Legacy of R.L. Moore Project, which promotes the Members of the Icosahedron Society study of effective methods of teaching and learning at all educational levels. Mr. Year 2003 Lucas’ support of named Fellows will Year 2000 Paul and Virginia Halmos increase to 8 in 2007. Henry L. Alder Mary P. Dolciani Halloran Foundation Edith Ross and Edward Brinn The Icosahedron Society was formed in Deborah Tepper Haimo Year 2006 2000 to recognize individuals, founda- Mary Alice and Marvin Schaefer Robert P. Balles tions, or corporations that have made sig- Tensor Foundation nificant contributions to the Association. Year 2001 Richard D. Anderson Donations of this type are extraordinary Akamai Foundation and make it possible for the MAA to con- ExxonMobil Foundation Year 2007 tinue to promote its mission: to advance Microsoft Corporation Harry Lucas, Jr. the mathematical sciences, especially at Andrew and Kaarina Sterrett the collegiate level. Year 2002 For further information about contrib- James W. Daniel and Ann Trump Daniel uting to the MAA or about The Icosa- hedron Society, contact Lisa R. Kolbe, Development Manager, at 202-293-1170 or [email protected]. Let’s Meet Again... I had forgotten how much fun the Joint Meetings can MathFest 2007 be when you aren’t interviewing for jobs! August 3–5, San Jose, CA JMM 2008 January 6–9, San Diego, CA —Darren Glass Gettysburg College

23 FOCUS February 2007 The MAA Goes To Middle School (and How You Can Too)

By Steven R. Dunbar and Bonnie Leitch Many MAA members participate in pre-college mathematics education: through the mathematical education of teachers, as teachers in the K–12 grades, by having children in K–12 grades, or perhaps by involvement with young learners through tutoring, math circles, or volunteering in schools. The MAA as an organization also engages K–12 mathematics education through its American Mathematics Competitions program.

For 22 consecutive years, the MAA has offered a stimulating and challenging mathematical contest program to middle schools. The contest, called the Ameri- can Mathematics Contest 8, or AMC 8 for short, is the younger sibling to the well-known high school mathematics contest the MAA has sponsored since 1950. Starting as the American Junior High School Mathematics Examina- tion, or AJHSME, in 1982, the contest Students taking the November 2006 AMC 8 at Affiliated Middle School to Jilin Uni- changed its name to the AMC 8 in 2000. versity, Changchun City, China, photo courtesy of Dr Xiaodi Wang. The change reflected the fact that many mathematical problem-solving skills problems and then the committee and the schools no longer called themselves ju- through friendly, fun competition. Of chair, acting as an editor, successively nior high schools, and also fit the contest course we hope that many of the students drafts, reviews, edits, and revises until a in an expanded array of contests: AMC taking the contests are challenged, and finished product is ready to send to the 8 for 8th grade and below, AMC 10 for maybe inspired, to learn mathematics middle and junior high schools registered 10th grade and below, AMC 12 for 12th they have not encountered before. The to take the contest. grade and below. contest also readies middle-school students for other contests, including Math- The contest takes place directly in class- Although the AMC 8 contest focuses Counts and the high school level AMC 10 rooms each year in November under the on students in the sixth, seventh, and and AMC 12. Many of the students who supervision of the local administering eighth grades, some accelerated fourth do well in the AMC contests find that teacher. The schools send their answer and fifth grade students also take part. they really enjoy mathematics so they sheets to the MAA’s American Math- The AMC 8 is a 25-question, 40-minute subsequently major in mathematics, or ematics Competitions offices on the multiple-choice contest with no penalty science and engineering. campus of the University of Nebraska- for guessing. A student’s score is the Lincoln for scoring and tabulation. About number of problems correctly solved. The AMC 8 contest is created by a com- three weeks later, each school receives a The AMC 8 questions cover the middle mittee of MAA members, like most math- detailed report on the scores along with school mathematics curriculum. These ematical productions from the MAA. The prizes for the high-scorers in the school. questions can include, but are not limited committee is a mixture of teachers with The AMC gives special recognition for to, everyday applications of mathematics, middle-school experience and college high scoring schools, the E. M. Sliffe percent, estimation, elementary prob- instructors with an interest in middle- awards for teachers with consistent high ability, counting, simple number theory, school mathematics education. All have team scores, medals and plaques for the reading and interpreting graphs, elemen- an interest in the great tradition of math- highest scores in each school, and special tary geometry, and spatial visualization. ematical problem setting and solving. plaques and awards for the highest scores No problem requires the use of algebra The committee chair solicits problems in each state. Since the AMC office tabu- or a calculator, although students may for the AMC 8 from a large group of lates all the scores, the overall statistics use calculators. interested MAA members each April, provide an insight about trends and what over a year in advance of the planned is happening mathematically in the minds The goal of the contest is to increase contest. A panel of reviewers rates the of middle-school students. interest in mathematics and to develop 24 February 2007 FOCUS

The AMC office has completely tabulated confound the measurement of what might and AE and CE is 11 units long. Triangle the results for the 2006 AMC 8, and be the hardest or easiest question in some ABD is congruent to triangle ECD. What we can glimpse the kinds of problems ranking of difficulty. is the length of BD?” that students found easy and hard this Measured by the percentage of students year. A total of over 147,000 students B took the contest in November 2006. choosing the correct answer, in 2006, E The participating students came from Problem 1 was the easiest question. D over 2200 schools. Over 68,000 female “Mindy made three purchases for $1.98, and over 76,000 male students took the $5.04 and $9.89. What was her total to contest. The participation numbers don’t the nearest dollar?” The choices were (A) A exactly match because some students do $10, (B) $15 (C) $16 (D) $17 and (E) C not mark the male/female bubble or the $18. 93.95% of the students answered mark is incomplete or unreadable. Last correctly with (D). The most popular Yet almost as many, 52.37%, got it cor- year, every state in the United States was wrong choice was (C) with 3.72%. rect. represented, as well as 6 Canadian prov- inces and 20 other countries. The largest The hardest problem on the 2006 test, at On the other hand, the committee may number of participants outside North least measured by the smallest percentage have been misjudged problem 7 in dif- America, about 7700, were in Taiwan. selecting the correct answer was Problem ficulty: “Circle X has a radius of π. Circle The average score overall was 10.14 out 24: “In the multiplication problem below, Y has a circumference of 8 π. Circle Z of a possible 25. A, B, C, and D are different digits. What has an area of 9 π. List the circles in order is A+B? from smallest to largest radius.” Only The committee arranges the 25 ques- 20.87% of the students got the correct tions with the easiest problems the first ABA ordering Z,X,Y and incorrect answer 5 or so, problems 6 through 10, a little x CD choice (A) X, Y, Z was too tempting with more challenging and so on until the CDCD 38.54% of the participants selecting it. last 5 problems are usually answered by only the best problem-solvers. The The choices were (A) 1 (B) 2 (C) 3 (D) Almost as hard as the hardest problem last 2 or 3 questions are designed to be 4 (E) 9. Only 15.39% chose the correct was problem 22, which had only 17.16% differentiators that are long enough or dif- answer (A), while 16.15% chose (B), choosing the correct answer. “Three ficult enough to isolate a relatively small 26.01% chose (C), 17.68% chose (D), different one-digit positive integers are number of perfect scores on the contest. 12.09% chose (E) and 12.55% omitted placed in the bottom row of cells. Num- The committee and the reviewers usually answering the question. bers in adjacent cells are added and the do a reasonably good job of constructing sum is placed in the cell above them. the “perfect” test, but any math educator In past years, problems involving geom- In the second row, continue the same who ever wrote a test knows students etry have often had lower percentages of process to obtain a number in the top never think in a predictable way. correct answers, but on the 2006 contest, cell. What is the difference between the this rule of thumb did not hold. Problem largest and smallest numbers possible in Measuring difficulty is not as obvious 6 “The letter T is formed by placing two the top cell?” as it might appear at first glance. The 2 x 4 inch rectangles next to each other contest is multiple-choice, and in the as shown. What is the perimeter of the T end we know the percentage of students in inches?” who chose the correct answer, but there is no way to know why they selected the right answer. Also, there is no penalty for + guessing, so relatively few questions are left unmarked. In typical adolescent style, some answer sheets are marked by pure guessing, even doodling, making designs + + and patterns with the array of answer bub- bles! Common or obvious mistakes are some of the answer choices provided on the contest, so some tempting distractors get marked. Perhaps the student’s logic Over half of the participants, 55.10%, Among the choices (A) 16, (B) 24 ( C) or problem-solving technique was cor- answered correctly with 20 inches. 25, (D) 26, and (E) 35, of course, (D) is rect, but a careless student mis-marked Problem 19, with its placement, should the correct choice. Could you explain the answer, or passed by a problem for have been a difficult problem: “Triangle why to a middle-school student? lack of a choice corresponding to the ABC is an isosceles triangle with AB = incorrectly worked answer. All of these BC. Point D is the midpoint of both BC A general trend to be drawn from this

25 FOCUS February 2007

Students taking the November 2005 AMC 8 at Bernardo Heights Middle School, San Diego, CA. These students are from mixed grades 6-8, drawn from classes in prealgebra, algebra, and geometry. Photo courtesy of Vickie Bakki, BHMS GATE Coordinator.

year’s contest is that participating middle school students in its area. Consider host- solutions and analyses of the problems school students do well with familiar ing the AMC 8 contest on your campus in on the contest. kinds of arithmetic and geometry prob- November. Start this September by acting lems. About half of the students have as a liaison between the American Math- If the opportunity to excite young stu- good facility with geometry problems, ematics Competition and middle schools dents mathematically while showcasing but comparisons using data about area in your area. The preliminary activities your institution interests you, contact the and length are still hard for students. This might be any combination of encouraging American Mathematics Competitions year the problems involving number logic students to take the contest to subsidizing office at [email protected] or 800-527- and puzzles presented the most difficul- the contest for students or schools that 3690. If you would like to do some of ties. Since the contest is created year by lack the resources, a comparatively in- your own statistical analysis or just learn year and reflects the interests and tastes expensive initiative, to providing middle more, check the AMC web pages by go- of the problem creators and editors, the school teachers and their students with ing to http://www.maa.org, then selecting analysis doesn’t have strict statistical va- tutoring opportunities with local college Programs, and finally American Math- lidity but it does suggest some tantalizing students or professors. ematics Competitions. If you would like insights into middle school mathematics to volunteer to write or review problems curricula. On the day during the week-long AMC for the AMC 8, the AMC 10 or the AMC 8 contest window in mid-November that 12, contact us at [email protected]. The Mathematical Association of Amer- is most convenient for your institution, ica is proposing that members become have a math field day. Students’ schools Steve Dunbar is the Director of the AMC more active in mentoring both high will provide transportation to and from Program. Bonnie Leitch is chair of the school and middle school students. The your campus and supervision. You will MAA’s AMC 8 Subcommittee. AMC 8 contest is a perfect opportunity be responsible for administering the con- for any college or university to become test, providing a tour of your institution actively involved with bright middle and after lunch directing a session with 26 February 2007 FOCUS In FOCUS: Curriculum Focal Points Articles by Francis Fennell, Anthony Ralston, and Barbara Reynolds As noted in our November issue, the National Council of Teachers of Mathematics (NCTM) recently released a document entitled Curriculum Focal Points. The document is available online at http://www.nctm.org/focalpoints/, where one can also find a lot more information and discussion, including questions and answers on the document. NCTM says the document extends the Council’s leadership of more than twenty-ﬁve years by describing an approach to curriculum development that focuses on areas of emphasis within each grade from prekindergarten through grade 8. Curriculum Focal Points, widely reported in the news media, was hailed by some as a retreat from NCTM’s previous positions. This misreading is addressed in each of the three articles that follow. We hope that they will shed some light on the goals and content of Curriculum Focal Points. The articles below are the opinions of the authors and do not reflect a position or stance of the MAA. NCTM’s Curriculum Focal Points By Francis (Skip) Fennell

The publication by the National Council of Teachers of Mathematics (NCTM) of Curriculum Focal Points for Prekinder- garten through Grade 8 Mathematics: A Quest for Coherence marks the Council’s next step in implementing the vision set forth in the Principles and Standards for School Mathematics (NCTM, 2000), with particular emphasis on curricular expectations.

The genesis of the Curriculum Focal Points, released on September 12, 2006, was a conference at the Park City Math- ematics Institute in 2004 organized by NCTM with the Association of State Supervisors of Mathematics (ASSM). It brought together mathematicians, supervisors of mathematics, and mathematics by NCTM and ASSM provides insights writers, who represented expertise in educators with the intent to examine the into where we appear to be headed in our mathematics and mathematics education K–12 mathematics standards of each of expectations for students’ mathematics as well as classroom experience from the states and how they were influenced learning. The report is an initial attempt pre-kindergarten through grade 8, was by Principles and Standards for School to examine across states the impact of reviewed and commented upon by some Mathematics. The expectation was that Principles and Standards for School 70 reviewers, including mathematicians, the consistency of the findings would Mathematics on curriculum reform, mathematics educators, and policymak- guide a discussion that could begin to discern how state educational agencies ers. After extensive further revisions, the lead to a meeting of the minds about approached the task of developing state publication was presented to the NCTM the important mathematics that should standards, and bring to light areas of Board of Directors, which on April 24, be taught at various grades. Instead, the commonality and difference. The find- 2006 approved it for publication. outcome was the discovery that there was ings from this endeavor laid a foundation little consistency between standards and for discussions about the future direction Curriculum focal points are important expectations or of what content fell in of local, state, and national mathematics mathematical topics for each grade level. what grade. Perhaps most troubling was curricula. From this were born the idea They are the related ideas, concepts, the consequent realization that this lack and concept of what became the Cur- skills, and procedures that form the foun- of consistency was inevitably detrimen- riculum Focal Points. dation for understanding, lasting learning, tal to the teaching and learning of K–12 and success in higher level mathematics, mathematics nationwide. Extensive, thoughtful, and at times beginning with algebra. NCTM views the intensely debated discussions among a Curriculum Focal Points as a framework An analysis of the conference findings group of nine writers generated the con- for developing mathematics curriculum resulted in the publication entitled “Stan- cept and early drafts of the Curriculum at the state and school district level. dards and Curriculum: A View from the Focal Points. The written draft of the The focal points are intended to frame Nation,” (NCTM, 2005). This joint report

27 FOCUS February 2007 discussions that will eventually inform new focal-points approach to curriculum — how multiplication is represented and the decisions of textbook publishers and development a ‘remarkable reversal’ for how properties, particularly the distribu- assessment developers, as well. NCTM. As stated in NCTM’s 1989 and tive property, are used when multiplying. 2000 Standards, conceptual understand- Students become fluent through their un- The Curriculum Focal Points address ing and problem solving are absolutely derstanding of how and why procedures curriculum, or what is taught, rather than fundamental to learning mathematics. work — with a focus on place value and instruction, or how it is taught. By design, The council has never promoted esti- properties of operations. there is no mention of instructional strate- mation ‘rather than precise answers.’ gies, instructional materials, technologi- Estimation is a critical component to The Purpose cal tools (e.g. the calculator), or manipu- the overall understanding and use of lative materials. This was the intent of the numbers.” Today’s mathematics curricula tend to be writers of the focal points — to provide a dominated by long lists of very specific publication that would foster discussion, A letter to the editor of the New York goals, standards, objectives, or learning dialogue, and decision-making relative to Times published on September 24, stated, expectations. By contrast, Curriculum the important mathematics for pre-kin- “What some refer to as basic skills (for Focal Points describes significant math- dergarten through grade 8. The ultimate example, multiplication facts, and flu- ematical concepts and skills for each goal would be for these suggestions, the ency with the addition, subtraction, multi- grade level. They are a way to organize focal points, to lead to the development plication and division of whole numbers) and connect critical mathematics top- of mathematics curriculum goals that are have always been a fundamental core of ics from grade to grade. Organizing a more cohesive from grade to grade and elementary school mathematics. Always. curriculum around the focal points can from school to school. Through its Con- But we want more. We want children provide students with a more coherent nections, the new publication also shows to understand the mathematics they are ever expanding body of mathematical additional ways in which the focal points learning and we want them to be able to knowledge. connect to Principles and Standards. solve problems, which is, in the long run, why we do mathematics.” Mathematics leaders should use the Cur- The Curriculum Focal Points provides riculum Focal Points to launch discus- an example, a critical foundation, for the The Curriculum Focal Points are in no sions about the next generation of cur- next generation of curricula and related way a reversal of the Council’s long- riculum standards, textbooks, and tests. assessments. Curriculum developers can standing position on teaching students Such dialogue, discussion, and debate are place Curriculum Focal Points and a lo- to learn critical foundational topics (e.g. critical and can lead to the development cal or state curriculum side by side when multiplication) with conceptual under- of new models for curriculum, instruc- refining their current curricula. Curricu- standing, and they are not a retreat from tion, materials, and assessments. Cur- lum developers can determine how much Principles and Standards for School riculum Focal Points for Prekindergarten time to devote to the focal points as the Mathematics. Rather, the Curriculum through Grade 8 Mathematics represents mathematical core for a particular grade Focal Points are the next step in imple- an important, initial step in advancing level, and then build other mathematics menting the Standards. The appendix in collaborative discussions about what topics around these important areas of Curriculum Focal Points directly links mathematics students should know and focus. the focal points to virtually all the expec- be able to do. tations in Principles and Standards. Media Coverage For More Information One of the questions asked most fre- The Curriculum Focal Points release was quently is about the standard algorithm Curriculum Focal Points for Prekinder- widely reported in the news media and and whether the Curriculum Focal Points garten through Grade 8 Mathematics is generated considerable discussion within expressly states that all students must available free of charge online. To down- the mathematics and education commu- learn the standard algorithm. The grade load the PDF version, visit http://www. nities. Some inaccurate coverage raised 2 focal point suggests efficient proce- nctm.org/focalpoints/downloads.asp. The questions among many who were asking dures, including the standard algorithm Curriculum Focal Points publication can “Is what the Wall Street Journal and New — including, not exclusively, access to be purchased through NCTM’s online York Times reported true? Is NCTM really the standard algorithm. Students should catalog at http://www.nctm.org/catalog, going back to basics?” use what they can do efficiently and ac- or by calling (800) 235-7566. curately. Most important, they should not In a letter sent to the Wall Street Journal use any algorithm until it is understood. Francis (Skip) Fennell is President of the and published on September 26, I wrote, National Council of Teachers of Math- “Contrary to the impression left in your Similarly, for grade 4 the quick recall of ematics and Professor of Education at article, learning the basics is certainly not multiplication facts and fluency with ef- McDaniel College in Westminster, MD. ‘new marching orders’ from the NCTM, ficient procedures, including the standard Fennell likes the number 7. It represents which has always considered the basic algorithm, is a focus. Again, and impor- the current number of grandchildren computation facts and related work with tantly, fluency emerges through deep un- and marathons completed. He hopes to operations to be important. Nor is the derstanding of the multiplication process expand one of these numbers to the very 28 nice number ten–within a few years. February 2007 FOCUS Focus on Focal Points: A Commentary on the NCTM Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics By Anthony Ralston In 1989 and 2000, the NCTM (National will be much less text to shoot at. The subtraction”) which appears 25 times Council of Teachers of Mathematics) Standards at 258 pages and PSSM at 402 — whereas “proficiency” appears only published two reports, Curriculum and pages were full of detail that could be once in the entire document, and that in Evaluation Standards for School Math- castigated by those so inclined. the introductory pages. Fluency is the ematics (hereafter the Standards) [1] kind of word that can be interpreted as and Principles and Standards for School Avoiding the trap of the Standards and mastery by those who want a back-to- Mathematics (hereafter PSSM) [2] on PSSM, the authors of CFP have obeyed basics approach to mathematics but as standards for school mathematics. The this rule admirably. Not counting the meaning only that students can deal with first of these, at least, was very important boilerplate at the front, CFP is 41 pages numbers flexibly and efficiently by those in influencing school mathematics cur- short. Of these, 20 pages are an Appendix who wish to avoid the “drill and kill” in- ricula, but both — although the second that relates the Focal Points to PSSM. struction of the past. Is this just a quibble? less so — have been rubbished by some Nicely color-coded for ease of use, this I think not. CFP says in three places mathematicians, mostly research math- Appendix may, indeed, be valuable to that “students should develop fluency ematicians, many of whom act — and curriculum developers but it is just what it with efficient procedures, including the write — as if NCTM were The Great claims to be: an appendix. The Appendix standard algorithm.” Clear enough, isn’t Satan of mathematics education. is followed by one page of references. it? When studying division, this surely Ten of the remaining pages are introduc- implies that the student should learn the But now with the publication under tory material explaining the motivation of standard algorithm for long division. review here there is (almost) universal CFP and explaining what Focal Points But not quite. When queried about this, praise from the most zealous of the tradi- are, how they should be used, and how NCTM responded that “including” means tional (as opposed to reform) Math War- they relate generally to PSSM. These do that the standard algorithm should be one riors (hereafter TMWs). “Traditional” is contain the most telling indication that of the available options, but that it need not actually a well-defined term in math NCTM’s approach has not changed: not, in fact, be taught to all students. education. Here, by “traditional” math warriors I mean those who generally “[CFP] assumes that the mathematical Throughout CFP the language has been support the back-to-basics approach ex- processes described in Principles and very carefully chosen so as not to upset emplified by the current California math Standards will be implemented in in- any of the most vocal traditionalists who standards. struction that requires students to discuss were so critical of the Standards and and validate their mathematical thinking; PSSM. (Full disclosure: I have been a The TMWs praise the new publication create and analyze a variety of represen- peripheral warrior in the Math Wars but even though the NCTM makes clear that tations that illuminate the connections hardly a neutral one. I am totally unsym- Curriculum Focal Points (hereafter CFP: within the mathematics; and apply the pathetic to the traditionalists whom, I available online at http://www.nctm.org/ mathematics that they are learning in believe, have utterly failed to grasp how focalpoints/, which also includes a ques- solving problems, judging claims, and mathematics education needs to adapt to tion-and-answer page and lots of other making decisions.” a world where calculators and computers information about CFP) builds on and are ubiquitous. But neither am I a fan of is closely tied to PSSM. Phrases such as The guts of CFP, however, are contained the so-called reform curricula that are “an end to the math wars” or “it’s about in 10 other pages, one each for the ten generally much too timid in proposing time” for this “role reversal” now roll off grades from Prekindergarten to Grade 8, changes in school mathematics.) the lips of prominent TMWs. How can each of which contains the focal points this be? If the NCTM was as hopeless for that grade. The C-word as it had been portrayed and if CFP only builds on previously denigrated NCTM A second rule is this: Wherever possible, Well, there I’ve done it by using just the publications, how can there now be such be ambiguous. Then just about everyone word the TMWs feel so strongly about, praise for its latest work? Read on! can interpret what you have written as namely “calculators.” It is particularly supporting his or her perspective. CFP noteworthy that the word “calculators(s)” Rules of Engagement abounds with language subject to what- appears nowhere — I repeat, nowhere ever interpretation the reader might wish — in CFP. (Well, not quite; “calculator” If you wish to produce a document on a to put on it. appears in four places in the Appendix controversial subject that will be praised but in each instance only as a reference or, at least, not damned by any side, the Take, for example, “fluency” (as in to PSSM.) How can this be at a time first rule is: Keep it short. If you do, there “fluency with multidigit addition and when whether or how much students use 29 FOCUS February 2007 calculators in elementary school arithme- Fuzzy Math side are the RMWs (reform math war- tic is one of the most, perhaps the most riors) whose leaders are mainly math controversial issue in elementary school The paeans of joy in the American press educators but with significant support mathematics education? The authors of (e.g., the Wall Street Journal [3], the New from parents and teachers. CFP would, I think, answer this ques- York Times [4], The New York Sun [5], The tion by pointing to the section in CFP on Washington Times [6], The Jewish World Indeed, viewed as the authors of CFP “How Should Curriculum Focal Points Review [7], and probably elsewhere also) state they intended, namely as an exten- Be Used” where they say all praised the retreat of NCTM from the sion of the Standards and PSSM, CFP “fuzzy math” of the Standards and PSSM. resolves none of the issues in the Math Its [CFP’s] presentations of the What is “fuzzy math?” It is, as I have Wars. Moreover, despite the response of focal points include neither sug- written elsewhere [8], “a fuzzy concept TMWs to CFP and the prior publication gestions for tools to use in teaching meaning whatever the critics of new of the Common Ground report [10], none nor recommendations for profes- [i.e., reform] curricula want it to mean of the really significant issues in the Math sional development in content or at a given time.” Sometimes it refers to Wars have been resolved nor can they be pedagogy. those [mythical] people who wish to fa- in any foreseeable future. vor inexact rather than exact answers. At Thus, we won’t discuss calculators other times it refers to anyone who favors Briefly stated, at the elementary school because we aren’t giving any “sugges- “constructivist math” [5] (whatever that level, these issues revolve around the tions for tools.” On the other hand there may be). question of whether arithmetic should are five references to those other tools, focus on attaining proficiency with the “pencil-and-paper.” The fact is that one In fact, the canard that NCTM ever fa- classical pencil-and-paper algorithms for just cannot speak or write persuasively vored fuzzy math, however you might the four arithmetic functions or whether about the elementary school mathematics define it, has never been true; it is, in- the elementary school curriculum should curriculum in the 21st century without deed, a lie which is repeated endlessly embrace the wide use of calculators in dealing with the issue of whether and, if without any evidence whatsoever in the teaching arithmetic to achieve sound un- so, when calculators should be used in hope that if you repeat a lie often enough, derstanding of arithmetic itself as well as teaching that curriculum. people will believe it. I know of no one to prepare students as well as possible for in NCTM or the math education com- the further study of mathematics. There CFP does, at least, pay lip service to the munity generally who has ever espoused are similar issues with respect to middle benefits of mental calculation, which is teaching children that exact answers are school and secondary school mathemat- mentioned four times. Three of these are not important and always to be desired, ics but most of the heat in the Math Wars in the context of estimating sums, differ- when they can be obtained with reason- has been focused on the elementary ences, products or quotients or calculating able effort. Nor does any math educator school curriculum. them mentally “depending on the context doubt that instant recall of the addition and the numbers involved,” making it and multiplication tables is necessary for These issues are nowhere near being re- clear that little more than knowledge of anyone studying arithmetic. solved. While we should all applaud any the addition and multiplication tables is attempt to achieve a debate more civilized expected here. (Am I wrong? Perhaps; At least, CFP, like the Standards and than at some times in the past, publica- but if so, this is another example of pur- PSSM before it, does stress the value of tions like the Common Ground report and poseful ambiguity.) The fourth instance being able to estimate, not as a way to now CFP merely fudge the important advocates the building of “facility with avoid calculating exact answers but rather issues. But resolution of the arguments mental computation” to do “addition and when an estimate is all that is required or in the Math Wars, not fudging, is crucial subtraction in special cases such as 2,500 to enable checking the reasonableness of to the future of American — but not just + 6,000 and 9,000 – 5,000”. While I ap- answers on a calculator. Indeed, any good American — school mathematics. My plaud any mention of mental arithmetic, contemporary elementary school math- own view is that the main controversies CFP essentially trivializes what students ematics curriculum must emphasize the in the Math Wars will not be definitively may accomplish in this domain. value of being able to estimate answers. settled for many years until, at least, the main protagonists have long since left The absence of even the word “calcula- The Math Wars the field of battle. In the meantime, it is tor” is the most important reason why important that those who feel strongly CFP has been so widely praised by Various comments about CFP ([3], [9]) about the reform mathematics agenda NCTM’s heretofore opponents. But the have expressed the belief or hope that fight for their beliefs with undiminished refusal even to discuss the crucial issue its publication would bring an end to the intensity and without propitiation of their of calculators means that anyone using Math Wars that for years now have roiled antagonists. CFP for curriculum development has the US math education scene. On one side no guidance whatever on how much or have been the TMWs, the most vocal The Real Issue how little use of calculators to build into of whom are research mathematicians, a curriculum. but which also include parents, business Sadly, however, despite my strong belief groups and some teachers. On the other in the need to reform American school 30 February 2007 FOCUS mathematics, neither the success nor fail- possibly contribute much to improve the ders091406.php3), 14 September 2006. ure of this reform will have much effect state of American school mathematics 8. Anthony Ralston, Research Math- on American mathematics education for education. ematicians and Mathematics Education: the foreseeable future. The real tragedy A Critique, Notices of the American of mathematics education in American References Mathematical Society, Vol. 51, 2004, p schools is the declining number of 408. first-class mathematics teachers (and 1. National Council of Teachers of 9. R. James Milgram as quoted in the growing number of uncredentialled Mathematics, Curriculum and Evalua- Education Week, 12 September 2006. teachers) in secondary schools and the tion Standards for School Mathematics, 10. Ball, D. L., Ferrini-Mundy, J., growing number of mathematics-averse NCTM, Reston, VA, 1989. Milgram, R. J., Schmid, W., Schaar, R., teachers in elementary schools. Nothing 2. National Council of Teachers of Reaching for Common Ground in K-12 in the No Child Left Behind Act (NCLB) Mathematics, Principles and Standards Mathematics Education, http://www.maa. will reverse this trend. Indeed, the op- for School Mathematics, NCTM, Reston, org/common-ground, also in Notices of posite is much more likely with NCLB VA, 2000. the AMS, Vol. 52, pp 1055-1058. (See already beginning to prove that act most 3. John Hechinger, New Report Urges also: A. Ralston, K-12 Mathematics destructive of good education ever passed Return to Basics in Teaching Math, Wall Education: How Much Common Ground by the United States Congress. Street Journal, 12 September 2006. Is There?, FOCUS, January, 2006, pp 4. Teaching Math, Singapore Style, 14-15.) This is not the place to discuss why teach- Editorial, The New York Times, 18 Sep- 11. Anthony Ralston, The Real Scan- ing, particularly mathematics teaching, is tember 2006. dal in American School Mathematics, failing to attract the best and the brightest 5. Andrew Wolf, Turnaround in the Education Week, 27 April 2005 (also: that we need in American schools (but Math Wars, The New York Sun, 15 Sep- http://www.doc.ic.ac.uk/~ar9/Teacher- see [11]). Nor is it the place to discuss tember 2006. Qual.html) the disaster that the testing regimen in 6. Phyllis Schafly, Parents Right, NCLB is wreaking on American schools. Experts Wrong, Washington Times, 27 Tony Ralston, who currently lives in Lon- But until the teaching profession does September 2006. don, is Professor Emeritus of Computer start to attract large numbers of the best 7. Debra J. Saunders, Fuzzy Memory Science and Mathematics at SUNY at and the brightest, a publication like on Fuzzy Math, The Jewish World Review Buffalo. He has been interested in math- CFP, whatever you think of it, cannot (http://jewishworldreview.com/0906/saun- ematics education for many years.

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31 FOCUS February 2007 What are the Curriculum Focal Points? … And Why Should We Care? By Barbara Reynolds

What are the Curriculum Focal Points riculum Focal Points would set minimal I began this reflection by asking why these for Prekindergarten through Grade 8 goals that would undermine the bold vi- Curriculum Focal Points should matter to Mathematics: A Quest for Coherence sion set by the Principles and Standards. me. Why should they matter to those of (National Council of Teachers of Math- Would the NCTM sell out to NCLB? us who teach undergraduate mathemat- ematics, 2006)? Why should they matter ics? After all, students coming into our to me? Why should they matter to the Instead what I see in the Curriculum Fo- undergraduate mathematics classrooms mathematics community? cal Points is a balanced set of guidelines are four or more years beyond Grade 8. that shows one way of developing a pre- What impact might these Curriculum In 2000 the NCTM released the Prin- kindergarten through grade 8 mathemat- Focal Points have on my own teaching ciples and Standards for School Math- ics curriculum, guidelines that give focus of undergraduate mathematics? ematics, a comprehensive document that to one or another area of the objectives set built on a bold vision that had been set by the Principles and Standards at each The Curriculum Focal Points could by An Agenda for Action (NCTM 1980) grade level, while illustrating ways of impact my own teaching in two ways: and expanded in a set of Curriculum making connections to the overall fabric First of all, if more schools adopt school and Evaluation Standards for School of mathematics throughout the entire pre- mathematics materials that implement the Mathematics (NCTM 1989). The Prin- kindergarten through grade 8 mathemat- vision of the Principles and Standards, ciples and Standards sets a challenging ics experience of school children. classroom teachers will need to have a comprehensive program, outlining goals deep and broad understanding of math- that are both broad and deep. Now just six The Curriculum Focal Points are not ematics. Classroom teachers will need an years later, the NCTM has presented us presented as a curriculum in and of understanding of mathematics that goes with Curriculum Focal Points. Does this themselves, nor are they presented as well beyond computational fluency and new document represent a change in di- a set of lesson plans. Rather they are that encompasses deeper mathematical rection, a strengthening of the guidelines presented as guidelines for developing reasoning and problem-solving skills. laid out in the Principles and Standards, an integrated pre-kindergarten through So we need to think about how to bet- or (as some might fear) a watering down grade 8 mathematics curriculum. These ter prepare pre-service teachers, and we of the content of the school mathematics Curriculum Focal Points illustrate one need to think about on-going professional curriculum? way of making explicit connections both development of in-service teachers. to topics that the child studied in the When it first came out, I studied the Prin- preceding years, and to content that will Secondly, if the calculus reform move- ciples and Standards rather thoroughly, be coming in subsequent years. ment of the 1980s taught us anything, and was excited by its comprehensive we must be aware that as school cur- vision. If students coming into college Curriculum developers and textbook riculum implements the bold vision ex- and university mathematics courses were writers could use these Curriculum Focal pressed in the Principles and Standards educated according to the goals outlined Points as an organizing outline — focal — something that will be facilitated by in the Principles and Standards, if they points, actually — to develop mathemat- the guidelines set out by the Curriculum came into college mathematics courses ics programs that will be integrated and Focal Points — we can expect that in with the depth and breadth of under- connected across grade levels. Classroom four to six years we will be seeing more standing proposed in the Principles and teachers would then be in a position students whose school mathematics Standards, wouldn’t our job as teachers to present mathematics at each grade programs implemented this bold vision of undergraduate mathematics be so level that implements the broad vision coming into our own undergraduate much easier! set by the Principles and Standards, and mathematics classes. Will we be ready builds coherently from year to year. The for such students? My fear as I began to read the Curricu- Curriculum Focal Points make it more lum Focal Points was that I would find likely that classroom teachers will have Barbara Reynolds, SDS, is professor of a simplified list of competencies, grade- well-designed materials that follow the Mathematics and Computer Science at level mastery objectives, and testable bold vision set by the Principles and Cardinal Stritch University in Milwau- outcomes — after all, this is the world Standards, and that allow them to de- kee, WI. She has a passion for teaching of No Child Left Behind (NCLB) — that velop problem solving, reasoning, and for understanding. might represent minimal goals for each critical thinking skills in their students grade level of the school mathematics without sacrificing computational skill curriculum. My fear was that the Cur- development.

32 February 2007 FOCUS Call For Papers Contributed Paper Session at MathFest 2007

The Mathematical Association of Contributed Paper Sessions This session will focus on innovative America will hold its eighty-fifth summer ways to incorporate emerging technolo- meeting, Friday, August 3, through Sun- Attracting and Retaining Students to gies into undergraduate mathematics in- day, August 5 in San Jose, California. Mathematics Programs via Outreach struction and invites papers that describe Friday morning implementations and/or assessments of The complete meetings program will ap- The migration away from the science, implementations of technologies that pear in the April 2007 issue of FOCUS. technology, engineering and mathematics were not originally designed or intended This announcement is designed to alert (STEM) fields starts in middle school and for educational purposes. Examples of participants about contributed paper continues until the undergraduate years. such technologies include but are not sessions and their deadlines. Please note We risk our nation’s leadership role in the limited to, iPods and other MP3 devices, that the days scheduled for these sessions high technology society we have devel- digital cameras, PDAs, Pocket PCs, or remains tentative. oped if the declining college enrollments GPS receivers. Speaker proposals should in STEM subjects remain unchecked. describe at least two of the following: The organizers listed below, solicit con- This session seeks to highlight innova- (1) how an emerging technology was tributed papers pertinent to their sessions. tive outreach programs from the higher implemented into mathematics instruc- Sessions generally limit presentations education institutes to stir interest in tion; (2) the effect of the technology on to ten or fifteen minutes. Each session mathematics as well as STEM fields and student learning and/or attitudes toward room will be equipped with a standard innovative programs to retain students in mathematics; (3) lessons learned in the overhead projector, an LCD projector mathematics programs. The presenters implementations; (4) assessment strate- (presenters must provide their own lap- may illustrate gies for emerging technologies. The ses- tops), and two screens. • Summer or year around programs sion is sponsored by the Committee on with middle schools Technologies in Mathematics Education Submission Procedures for Con- • Summer or year around programs for (CTiME). tributed Paper Proposals high schools • Bridge programs Lila F. Roberts To submit an abstract for MathFest 2007, • Retention programs in the higher edu- Georgia College & State University go to http://abstracts.maa.org. The instruc- cation for currently enrolled students Amy F. Kelley tions should be straightforward. You will It is hoped that presenters will include Georgia College & State University have the option to save a draft of your the impact of the programs measured abstract and return later to edit/complete by the statistical data. Current Issues in and submit it, or submit it immediately. Mathematics Education Once the abstract has been submitted, you Sangeeta Gad Friday afternoon will not be able to edit it later, but you University of Houston-Downtown This session invites papers dealing with will be able to log into the site at any time issues in mathematics education courses to preview your submitted abstract. The Mathematics of Sports and Games for pre-service and in-service teachers MAA will publish abstracts for the talks Friday morning at the elementary, middle school and in the contributed paper sessions. The world of sports provides numerous secondary levels. Topics of interest might applications that can enliven many math- include: new or nonstandard courses; An abstract should not be submitted to ematics courses, including but not lim- online courses or activities; community more than one session. Participants may ited to probability, statistics and discrete involvement variations such as service speak in at most two MAA contributed mathematics. Likewise, many examples learning or online tutoring; alignment paper sessions. If your paper cannot be exist in various games. The session is of courses to national or state standards; accommodated in the session for which seeking applications in board games, card interactions with local universities and/or it was submitted, unless you indicate games and quiz shows, among others. school districts; courses for master’s of otherwise, it will be automatically con- Papers that show a connection between arts in teaching programs; grants to sup- sidered for the general contributed paper mathematics and any of these fields are port mathematics education programs. session. In scheduling talks in the general welcome. In particular, we welcome reports on contributed paper session, preference evaluation and assessment of teacher will be given to authors who have not Howard Lewis Penn training programs. It is hoped that a wide had a paper accepted in another session. United States Naval Academy variety of presentations will provide Speakers will be limited to at most one E. Lee May, Salisbury University interest in topics related to mathematics presentation in any given session. Ab- education. stracts must reach the MAA by Tuesday, Emerging Technologies for May 22, 2007. Early submissions are Mathematics Teaching Carol Vobach encouraged. Friday afternoon University of Houston-Downtown 33 FOCUS February 2007

Nancy Leveille to integrate mathematics and biological Getting Students to Discuss and to University of Houston-Downtown content at the undergraduate level. This Write about Mathematics session is designed to highlight success- Saturday afternoon Innovative Ideas for Teaching Con- ful implementations of biomathemat- This session invites papers about assign- cepts in an Introductory Statistics ics courses or modules designed for ments and projects that require students Course students during their first two years of to communicate mathematics through Friday afternoon undergraduate study, efforts to recruit oral presentations, classroom discussions An ever-increasing number of college students into biomathematics courses, and writing. These assignments/projects students are taking introductory statistics involvement of these students in bio- can come from any area of mathematics courses, and the number of high school mathematics research, and assessment of including courses for mathematics or re- students taking Advanced Placement Sta- how these courses and activities impact lated majors, mathematics service courses tistics has been growing at a steady rate. the students. Topics may include issues or mathematics education courses. Each Many of these students have minimal related to the design of biomathematics presenter is encouraged to discuss how background in statistical concepts. courses, integration of biology into exist- the use of the assignment/project helped • What innovative ideas have been ing mathematics courses, collaborations students to improve their understanding found to enhance learning among these between mathematicians and biologists of mathematics, their communication of students? that have led to new courses, modules, or mathematics, and their attitude toward • Statistical software and hand-held tech- undergraduate research projects, collabo- mathematics. Of particular interest are nology can present graphical displays but rations between two-year and four-year innovative implementations of such how are they best utilized? institutions, effective use of technology assignments/projects including peer • Simulations can provide useful insights in introductory biomathematics courses, review of student writing or presenta- or they might be viewed as hands-on and assessment issues. We seek present- tions, using mathematical writing or activities that make the class “fun” but ers from two-year institutions, liberal arts presentations as part of service learning, do not broaden understanding. colleges, and universities of all sizes. We rubrics for assessing student writing and • Journal articles recommend using data encourage submissions from teams of presentations, using student writing or drawn from today’s newspaper but what mathematicians and biologists. The ses- oral presentations as part of program as- criteria should be used in selecting topical sion is sponsored by the MAA SIGMAA sessment, and programs to help students data for analysis? on Computational and Mathematical improve written and oral communication This session invites papers that highlight Biology. of mathematics. innovative ideas that have been effective as well as caveats resulting from Timothy D. Comar Murphy Waggoner, Simpson College those that produced less-than-glowing Benedictine University outcomes. All ideas, activities, and meth- Mathematics and the Arts ods should be immediately useful to one Graph Theory and Applications Saturday afternoon teaching Advanced Placement Statistics Saturday morning This session invites presentations of at a high school or to one teaching an in- This is a standard graph theory session. results on the connections between troductory statistics course at a two-year Graph theory provides mathematical mathematics and the arts: from geometry or four-year college or at a university. abstraction of situations that can model to origami to group theory on quilts, The session is sponsored by the MAA pairwise relations between objects. Some from perspective in paintings to patterns SIGMAA on Statistical Education. of the topics of interest are counting and plane tilings, from music to maps, problems, coloring problems, topological stitching to symmetries, tessellations Murray H. Siegel problems, distance in graphs, labeling, to textual analysis, weaving fabrics to Governor’s School for Science & Math- oriented graphs, algorithms, trees, as well fashioning words, dance to decorative ematics, Hartsville, South Carolina as applications to related fields. In the arts, theater and film to theorems and context of this theme, we solicit original fractals, beadwork to baskets to batiks Biomathematics in the contributions in all relevant areas of to Bessel functions, architecture to aca- First Two Years graph theory, including but not limited to: demic applications of the arts in algebra. Saturday morning graph coloring, route problems, covering We invite explorations of old and new Reports including BIO 2010: Transform- problems, optimization of network flows connections, from ancient Islamic tilings ing Undergraduate Education for Future and transportation, domination in graphs to contemporary folk arts to sculptures Research Biologists (National Research and digraphs, algebraic graph theory, of mathematical structures, as well as Council, 2003) and Math and BIO 2010: Ramsey theory, spectral graph theory, the use of new technologies to illustrate Linking Undergraduate Disciplines (L. and complexity. links between mathematics and the vari- A. Steen, ed., MAA, 2005) emphasize ous arts. Mathematical concepts inform that aspects of biological research are Ralucca Michelle Gera artistic presentation, while artistic pre- becoming more quantitative and that Naval Postgraduate School sentation can illuminate mathematics. there are needs to introduce life science Richard M. Low New technologies often provide new students to a greater array of mathemati- San Jose State University possibilities. Altogether, new approaches, cal and computational techniques and new tools, and new looks at old examples 34 February 2007 FOCUS provide new opportunities for working Student Research in course. This contributed papers session with and teaching mathematics, as well Industrial Mathematics presents ideas for developing and teach- as providing modes of outreach to the Sunday morning ing a history of mathematics course. We general public about the often under-ap- In recent years, several colleges and encourage discussion of courses aimed preciated place of mathematics in relation universities have started programs to give at all levels as well as general and topic to the arts, culture, and society. The ses- students the opportunity to do research on specific courses. This session is a follow sion is sponsored by the MAA SIGMAA problems in the mathematical sciences up to a session held at the JMM in 2004. on Mathematics and the Arts. coming from industry, government agen- The session is sponsored by the MAA cies, and businesses. In this session, we SIGMAA on the History of Mathemat- Douglas E. Norton invite faculty and students to describe ics. Villanova University their experiences with student industrial research at a variety of institutions. Spe- Joel Haack Fun and Innovative Teaching Tech- cifically, we invite presentations from University of Northern Iowa niques for an Abstract Algebra Class (1) faculty, describing what it is like to Amy Shell-Gellasch Saturday afternoon supervise student industrial research, Pacific Lutheran University Abstract algebra is, in many cases, one especially research done by teams of of the first “rigorous proofs” courses that students, and (2) students, describing how Advances in Recreational an undergraduate student will take. As industrial research programs changed Mathematics a result, students are sometimes intimi- their view of mathematics and affected Sunday afternoon dated by this course and find it difficult to their mathematical careers. (Please note There have been many recent advances make the transition from computational that student presentations on their actual in recreational mathematics. For the mathematics to abstract mathematics. research should instead be submitted to purposes of this session, the definition of This session will focus on fun and in- the contributed paper session on student recreational mathematics will be a broad novative ways of teaching some of the research). one. The primary guideline used to de- topics covered in an abstract algebra termine suitability of a paper will be the course. This session is a follow-up to our Bem Cayco, San Jose State University understandability of the mathematics. For very well-received session of the same Tim Hsu, San Jose State University example, if the mathematics in the paper title at MathFest. is commonly found in graduate programs, Challenges and Successful Strategies then it would probably be considered Sharon Clarke, Pepperdine University in Teaching a Numerical Analysis unacceptable. Novel applications as well Andrew Hetzel, Tennessee Tech Uni- Course as new approaches to old problems are versity Sunday morning welcome. Solutions using computers are Teaching a numerical analysis course is also welcome. Examples of use of the Teaching Calculus in High School: a challenge. Students taking numerical material in the undergraduate classroom Ideas that Work analysis usually have a variety of majors, are encouraged. Sunday morning backgrounds and levels of preparation Most mathematics majors now have the prior to the course. Moreover, students Paul R. Coe, Dominican University opportunity to take their introductory coming to the course have varying ex- Kristen Schemmerhorm calculus course while in high school. pectations and interests. Faced with these Dominican University SIGMAA TAHSM is committed to assist- challenges, the instructor seeks teaching ing teachers in making the mathematical strategies that motivate student learning, General Contributed Paper Sessions experiences of their students as chal- benefit all students attending the course, Friday, Saturday, and Sunday mornings lenging and exciting as possible. This and enrich student knowledge of both and afternoons session will serve as a forum in which to mathematics and computations. The ses- Papers may be presented on any math- share activities and approaches to teach- sion invites presentations on all aspects of ematically related topic. This session is ing calculus that work well with high teaching numerical analysis: challenges, designed for papers that do not fit into one school students. Of particular interest strategies, projects, demonstrations, in- of the other sessions. Papers that fit in into are projects and investigations, activi- novative techniques, and fun activities. one of the other sessions should be sent to ties, demonstrations, teaching strategies that organizer, not to this session. and techniques that bring the class and Olga Brezhneva the mathematics to life for the students. Miami University, Ohio Sarah J. Mabrouk The session is sponsored by the MAA Framingham State College SIGMAA on Teaching Advanced High Teaching a History of School Mathematics. Mathematics Course Sunday afternoon Dan Teague, North Carolina School of More and more college mathematics Science and Mathematics teachers with little or no background Susan Schwartz Wildstrom, Walt Whit- in the history of mathematics are being man High School asked to teach a history of mathematics 35 FOCUS February 2007

PDF 12/2006

Visiting Assistant Professor of Mathematics-Statistics Position available for Fall 2007. Emerson College Primary responsibilities include teaching a full range of undergraduate statistics courses, Boston, Massachusetts curriculum development, and consultation on faculty and student research projects. The standard teaching load is 12 contact hours per Mathematics semester. Additional duties include curriculum development and participation in the day-to- The School of Communication at Emerson College seeks to fill a full-time faculty day activities of the Department. A Ph.D. in position in Mathematics. Appointment may be a tenure-track Assistant Professor or a Statistics or closely related field at the time of Term (non-tenure track) faculty position depending on candidate qualifications and appointment is required. Full-time teaching preference. A PhD is preferred. Minimum qualifications include an advanced degree in experience and an ongoing program of scholarly activity is highly desirable. The successful Mathematics, Statistics, Mathematics Education or related discipline with a strong candidate will demonstrate commitment to background in mathematics and statistics. Ideal candidates will demonstrate a strong excellence in teaching and scholarship in an commitment to excellence in teaching introductory undergraduate mathematics and undergraduate setting that emphasizes the statistics courses and a commitment to a continued scholarly and professional growth. traditional liberal arts in the context of a Responsibilities include developing and teaching general education courses that satisfy comprehensive university. The most desirable the requirements of the College’s various majors. Because a full liberal arts candidates will have at least three years of full-time teaching experience and be engaged education is offered to undergraduates in majors including film/media studies; per- in an ongoing program of scholarly activity. forming arts; writing, literature, and publishing; journalism; marketing communication; Candidates should be proficient in one or organizational and political communication, and communication sciences and more of the statistical software packages in disorders, the College seeks candidates who can successfully bring Mathematics to widespread use, such as SAS, SPSS, or S-PLUS. students with these majors. This position is housed in the Department of Please visit www.rwu.edu for a full position Communication Sciences and Disorders. Appointment begins September 2007. description and to obtain submission requirements. Emerson College values campus multiculturalism as demonstrated by the diversity of its Roger Williams University is an Equal Opportunity faculty, staff, student body, and constantly evolving curriculum. The successful candidate Employer committed to inclusive excellence and must have the ability to work effectively with faculty, students, and staff from diverse encourages applications from underrepresented backgrounds. Members of historically under-represented groups are encouraged to populations. apply. Emerson College is an Equal Opportunity Employer that encourages diversity in its workplace.

Send a letter of application, curriculum vitae, selected reprints, information on teaching and research philosophy, experience and plans as well as three letters of recommendation to: Mathematics Search Committee Chair, c/o Dr. Daniel Kempler, Chair, Department of Communication Sciences and Disorders, School of Communication, Emerson College, 120 Boylston Street, Boston, MA 02116, 617-824-8302. Review of applications will begin on February 15, 2007 and continue until the position is filled.

visit our web site at www.emerson.edu Have You Moved?

The MAA makes it easy to change your address. Please inform the MAA Service Center Bringing Innovation to Communication and the Arts about your change of address by using the electronic combined membership list at MAA Online Discover a new crossword game with suffi- http://www.maa.org) or call (800) 331-1622, fax (301) 206-9789, 122006CC01_Emersoncient combinatorial email: [email protected], or possibilities tomaa intrigue a mathematician. mail to the MAA, PO Box 90973, Washington, DC 20090. Visit www.wildwords.us

36 February 2007 FOCUS

Employment Opportunities sibilities of the position and important KANSAS details on how to apply, see our position description at www.gvsu.edu/math/jobs. ALABAMA Washburn University html Review of applications will begin Mathematics and Statistics Faculty Posi- on February 9, 2007 and continue until the University of Alabama in Huntsville tions position is filled or the search is closed. The Department of Mathematical Sciences Washburn University’s Department of Recruitment for this position is subject to at the University of Alabama in Huntsville Mathematics and Statistics invites applica- the availability of funding. invites applications for a visiting position tions for a tenure-track Assistant Professor at the rank of Assistant Professor/Associ- and a full-time Lecturer beginning August Discover a new crossword game with ate Professor, beginning August 2007. A 2007. Requirements: Assistant Professor sufficient combinatorial possibilities to Ph.D. degree in mathematics or applied doctorate in mathematical sciences required intrigue a mathematician. Visit www. mathematics is required. Applicants must by time of appointment; Lecturer Master’s wildwords.us show evidence of excellent research po- degree in mathematics or related field; tential in an area that matches the interests must demonstrate strong teaching creden- PENNSYLVANIA of the department. Applicants must also tials and potential for scholarly activities; have a strong commitment to teaching and interest in directing undergraduate research Franklin & Marshall College show evidence of excellent teaching abil- projects essential as Washburn supports a FREE MATHEMATICS AND ART ity. Preference will be given to applicants very active chapter of national mathemat- WORKSHOP! Learn from experienced whose research area is partial differential ics honor society Kappa Mu Epsilon. Area instructors how to blend Math & Art in equations, mathematical modeling, or of specialization open with preference your classes at Viewpoints 2007, June mathematical biology. given to candidates interested in teaching 10-15, Franklin & Marshall College. The Applicants should send a curriculum vita broad range of undergraduate mathematics Viewpoints workshops are sponsored by with the AMS standard cover sheet and courses. Responsibilities: normally teach the National Science Foundation. Registra- three letters of recommendation (with at twelve credit hours per semester including tion, art supplies, meals, and lodging are all least one letter addressing teaching) to upper/lower division mathematics courses. free. Visit php.indiana.edu/~mathart/view- Chairman Send current vita, statement of teaching points, or contact Dr. Annalisa Crannell, Department of Mathematical Sciences philosophy, transcripts, names/addresses/ Dept. of Mathematics, Franklin & Marshall University of Alabama in Huntsville phone numbers of three references to: Dr. College, Lancaster, PA 17603, (717) 291- Huntsville, AL 35899. Kevin Charlwood, Chair of Search Com- 4222, [email protected] . For more information about the depart- mittee, Department of Mathematics and ment, visit our web site at http://www. Statistics, Washburn University, 1700 SW The Pennsylvania State University math.uah.edu. College Avenue, Topeka, KS 66621. Ap- at Harrisburg Review of applicants will begin March 1, plication review begins January 20, 2007 Faculty Positions in Mathematical Sci- 2007, and will continue until the position and continues until positions are filled. ences is filled. Women and minorities are encour- Washburn University is an EOE. www. The Pennsylvania State University at Har- aged to apply. The University of Alabama in washburn.edu risburg (PSH), School of Science SSET, Huntsville is an Affirmative Action, Equal Engineering and Technology (SSET) Opportunity Institution. MICHIGAN invites applications for multiple tenure track Assistant Professor positions in the INDIANA Grand Valley State University Mathematical Sciences for Fall 2007. All Grand Valley State University, an Affir- positions require a Ph.D. in Mathematics, Indiana University-Purdue University mative Action/Equal Opportunity Institu- Mathematics Education, or Statistics. Can- Indianapolis tion in Allendale, Michigan, is accepting didates with expertise in Statistics, Applied The IUPUI Department of Mathematical applications for the position of Postdoc- Mathematics, Operations Research, Math- Sciences invites applications for position toral Teaching Fellow in Mathematics, ematical Modeling, or Mathematics Educa- of Director of Mathematics Assistance with employment to begin in August 2007. tion will be given special consideration, but Center (MAC). The Director will oversee Candidates from groups underrepresented persons with other areas of specialization the entire operation of the MAC, leading in mathematics are especially encouraged will be considered. Successful candidates and managing the further development to apply. will teach a broad range of undergraduate of the MAC’s programs designed to sup- mathematics courses, including service port tutoring, mentoring and a variety of Required qualifications include a doctorate courses, for a growing department. Gradu- supplemental instruction for mathemat- in the Mathematical Sciences or Mathemat- ate students in Computer Science and Engi- ics coursework. Minimum qualifications ics Education by August 2007, completed neering will make up part of the population include a Master’s degree in Mathematics no earlier than May 2004; demonstrated of the higher-level courses. There are or related area with proven mathematics interest in teaching undergraduate math- regular opportunities for the Mathematical teaching experience of at least three years ematics or mathematics education; and Sciences Faculty to guide research projects at the college level. For more detailed commitment to continued scholarly and for graduate students in Computer Sci- information about this position and the professional growth. ence and Engineering. An active personal application process, see http://www.math. research agenda is required. All faculty iupui.edu/news/employment/. IUPUI is an For more information, including respon- members are expected to advise students EEO/AA Employer, M/F/D. 37 FOCUS February 2007 and to provide service to the College and to the University. Professional service to the community is encouraged. Information about the College and the Department can be found at www.hbg.psu.edu and at math. hbg.psu.edu.

PSH, with an enrollment of approximately 3,800 students, is a four-year undergraduate and graduate college in the Penn State University’s 24-campus system. SSET, one of the five academic schools within PSH, offers undergraduate and graduate degree programs in science, engineering, and engineering technology. PSH is located eight miles from the state capitol at Harrisburg. This unique metropolitan campus serves the citizens of south central Pennsylvania and is easily accessible via interstate routes from Philadelphia, Baltimore, Washington D.C. and New York. PSH offers students the opportunity to earn baccalaureate degrees in twenty-seven academic majors, seventeen master’s degree programs, and two doctoral degree programs.

Please send a letter of application, curriculum vitae (including teaching and research statements), and the names and addresses of at least three references to, Mathemat- ics Search Committee, c/o Mrs. Dorothy J. Guy, Manager of Human Resources, Penn State Capital College, P.O. Box FOCUS, 777 W. Harrisburg Pike, Middletown, PA 17057-4898. Review of applications will begin immediately and continue until the position is filled. The Pennsylvania State University is committed to affirmative action, equal opportunity, and the diversity of its workforce.

WEST VIRGINIA

Shepherd University The Department of Computer Science, Mathematics and Engineering at Shepherd University invites applications for a three year visiting position in the field of Ap- plied Mathematics starting from fall 2007. Teaching responsibilities include a variety of courses in Mathematics and Engineering. ic individual who can interact closely with herdstown, WV 25443. Please reference Ph.D. in Applied Mathematics, with back- students, engage in undergraduate research, position number in letter of application. ground and research interest in industrial is willing to be involved with public school AA/EOE. mathematics and engineering is preferred. mathematics programs, and can be an inspi- ration to students interested in mathematics. The department has recently approved an Salary is commensurate with experience. Industrial Mathematics majors and is in the Send letter of application, curriculum vi- process of designing a new degree program tae, transcripts, and at least three letters of in Engineering Science; both comprised of reference to Office of Human Resources, P. courses from Mathematics, Engineering O. Box 3210, Shepherd University, Shep- and Physics. We are looking for an energet-

38 February 2007 FOCUS

From the

® Mathematical Association of America The Great pip/e Debate Colin Adams & Thomas Garrity Hilariously funny-just right for the classroom, or as a gift! Colin Adams and Thomas Garrity settle once and for all the burning question that has plagued humankind from time immemorial: “Which is the better number, e or ppi?” In what could be the most important debate of the millennium, Williams College Professors Adams and Garrity use any means within their powers, legal or otherwise, to prove their point. Moderated by Edward Burger, our debaters challenge orthodoxy, brazenly flaunt convention and behave rather badly in their attempts to convince the audience of the absolutely ridiculous nature of their adversary's arguments. This event may have the historical significance of the Edict of Nantes, the Yalta conference, or the Kennedy-Nixon debates. Or perhaps not. But just in case, you don't want to miss it. The genesis of both numbers is explained and the entire debate lasts 40 minutes, just right for a high school or college class. Which number is the superior number? Which number deserves to be held in the highest regard? You may already have your strongly felt opinions but get ready to have them stood on their heads when you watch the Great pPi/e Debate! Catalog Code: PIE • DVD, 40 minutes, color, 2007 • ISBN: 978-0-88385-900-1 Price: $24.95 • MAA Member: $19.95 Order your copy today! 1.800.331.1622 • www.maa.org

Take a closer look at Governors State University

Mathematics Secondary Education Faculty

Governors State University invites applications for a full-time, tenure-track faculty position in mathematics secondary education at the assistant/associate professor level beginning August 2007. Our desired candidate will have the ability to work across disciplines. The successful candidate will teach courses at the upper-division level in a new BA in Mathematics with Secondary Education Sequence, serve as coordinator of the Mathematics Secondary Education sequence, teach mathematics education methods courses and mathematics content courses, provide leadership in developing and implementing the curricula, advise undergraduate teacher education students and supervise student teaching, supervise student research projects, and pursue scholarly activity. Qualifications: Ph.D. or Ed.D. in Mathematics or Mathematics Education is required. ABD will be considered; some contemporary secondary level teaching experience is required; secondary teaching certification in mathematics is required; graduate coursework in mathematics is required; A strong commitment to teaching and research is required; experience with NCTM standards and NCATE accreditation process is highly desirable. The review of applications will begin immediately and continue until the position is filled. To apply, qualified applicants should send a letter of application, curriculum vitae, a brief statement of research results and interests, statement of teaching philosophy, transcripts, and three professional letters of reference to: Mathematics Search Committee; c/o Mary Hellings; Division of Science, College of Arts and Sciences; Governors State University; 1 University Parkway, University Park, IL 60466.

AA/EOE

39 FOCUS February 2007

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