Claremont Colleges Scholarship @ Claremont

All HMC Faculty Publications and Research HMC Faculty Scholarship

8-1-2006 Teaching Time Savers: Style Points Michael E. Orrison Jr. Harvey Mudd College

Recommended Citation Orrison, Michael. "Teaching Time Savers: Style Points." FOCUS, 26.6 (August/September 2006): 24.

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

FOCUS is published by the Mathematical Association of America in January, February, FOCUS March, April, May/June, August/September, October, November, and December. Volume 26 Issue 6 Editor: Fernando Gouvêa, Colby College; [email protected] 4 USAMO Winners Fêted in Washington, D.C. By Harry Waldman and Fernando Q. Gouvêa Managing Editor: Carol Baxter, MAA [email protected] 6 Association for Women in Mathematics Announces Michler Prize Senior Writer: Harry Waldman, MAA hwald- 7 Is the Poincaré Conjecture Proved at Last? [email protected] By Fernando Q. Gouvêa Please address advertising inquiries to: Re- 8 University of Mississippi Graduates Record Number of African-American becca Hall [email protected] PhDs President: Carl C. Cowen By Tristan Denley President-Elect: Joseph Gallian 10 Oral History and the Archives of American Mathematics By Kristy Sorensen First Vice-President: Carl Pomerance Second Vice-President: Deanna Haunsperger, 12 Making the Most of Your Sabbatical Secretary: Martha J. Siegel, Associate By Jennifer R. Galovich, Charles R. Hampton, William A. Marion and Secretary: James J. Tattersall, Treasurer: Thomas Q. Sibley John W. Kenelly 14 Some Advice for Graduating PhDs Executive Director: Tina H. Straley By Felix Lazebnik and Keith E. Mellinger Associate Executive Director and Director of Publications: Donald J. Albers 16 NUMB3RS: Positive and Negative FOCUS Editorial Board: Rob Bradley; J. 18 Letters to the Editor Kevin Colligan; Sharon Cutler Ross; Joe 20 2006 Award Winners for Distinguished Teaching Gallian; Jackie Giles; Maeve McCarthy; Colm Mulcahy; Peter Renz; Annie Selden; 22 How to Help Your Students Get the Most Out of the MCM and ICM Hortensia Soto-Johnson; Ravi Vakil. By Holly Zullo, Mark Parker, and Kelly Cline Letters to the editor should be addressed to 24 Teaching Time Savers: Style Points Fernando Gouvêa, Colby College, Dept. of By Michael E. Orrison Mathematics, Waterville, ME 04901, or by email to [email protected]. 25 What I Learned...From Teaching With Technology By Meighan Dillon Subscription and membership questions should be directed to the MAA Customer 26 The Open Source Revolution Service Center, 800-331-1622; e-mail: By Jeff Suzuki [email protected]; (301) 617-7800 (outside U.S. and Canada); fax: (301) 206-9789. MAA 28 Advertise! Headquarters: (202) 387-5200. By Richard Ehrenborg Copyright © 2006 by the Mathematical 30 AP Calculus: Friend or Foe? Association of America (Incorporated). By Susan Schwartz Wildstrom Educational institutions may reproduce articles for their own use, but not for sale, provided 31 In Memoriam that the following citation is used: “Reprinted with permission of FOCUS, the newsletter 32 Measuring the Perception of Leadership of the Mathematical Association of America By Randall J. Covill (Incorporated).” 34 College Algebra Redesign at Louisiana State University Periodicals postage paid at Washington, DC and By Lawrence Smolinsky, Phoebe Rouse, George Cochran, Jimmie Lawson additional mailing offices.Postmaster: Send address changes to FOCUS, Mathematical 36 The National Mathematics Advisory Panel Association of America, P.O. Box 90973, By Fernando Q. Gouvêa and Victor Katz Washington, DC 20090-0973. On the cover: The 2006 USA team at the International Mathematical Olympiad, ISSN: 0731-2040; Printed in the United States Ljubljana Slovenia, July 17, 2007: Alex Saltman, Deputy Leader; Ryan Ko, Silver of America. Medal, Allendale, NJ; Zuming Feng, Leader; Zachary Abel, Silver Medal, Dallas TX; Yi Sun, Silver Medal, Saratoga, CA; Steve Dunbar, MAA Director of American Mathematics Competitions; Alex Zhai, Silver Medal, Champaign, IL;, Arnav Tripathy, Gold Medal, Chaepl Hill NC; Zeb Brady, Gold Medal, Van Nuys, CA.  August/September 2006 FOCUS

U.S. Team Comes in 5th at 2006 IMO

By Harry Waldman and Fernando Q. Gouvêa

At the 2006 International Mathemati- cal Olympiad, held Ljubljana, Slovenia, nearly 500 young mathematicians com- peted in solving problems posed in a test administered on July 12 and July 13. The USA team came in 5th among the 90 participating countries. Top honors went to the People’s Republic of China (214 points), followed by Russia (174), Korea (170), and Germany (157). Iran and Moldova placed among the top ten teams.

Overall, the IMO awarded 42 gold med- als, 87 silver and 124 bronze medals. The top three individual contestants tied for first place with 42 points, the maximum possible score. They were Zhiyu Liu of China, Iurie Boreico of Moldova, and Alexander Magazinov of Russia. One of the testing rooms during the competition. Photograph by George Csicsery. The USA team has consistently finished in the top five for the last seven IMOs. The six members of the USA team got 152 points overall, receiving 2 gold and 4 silver medals. The team members and their results were:

• Zachary Abel, a graduate of Green- hill School in Dallas, TX received a silver medal. • Zarathustra Brady, who attends Magnolia Science Academy in Van Nuys, CA, received a gold medal. • Ryan Ko, who graduated from Philips Exeter Academy in Exeter NH and is from Allendale, NJ, received a silver medal. • Yi Sun, who graduated from Harker School in Saratoga, CA, The US team waiting for the opening ceremonies to begin. Photograph won a silver medal. by George Csicsery. • Arnav Tripathy, who graduated from East Chapel Hill High School competitions. The competition poses six The US team members are selected for in Chapel Hill, NC, won a gold math questions to be solved, three very their high scores in the various stages of medal. challenging problems each day in a 4.5 the competitions organized by MAA’s hour session. American Mathematics Competitions • Alex Zhai, who attends University program, including the USAMO (for Laboratory High School in Cham- The MAA is the main sponsor of the USA which see page 4). More details on paign, IL, won a silver medal. team at the IMO. Additional contribu- this year’s IMO are available at http:// tions come from 23 organizations and imo2006.dmfa.si. The 2006 IMO was the 47th in the an- companies in the mathematical sciences. nual series of international mathematical  FOCUS August/September 2006 USAMO Winners Fêted in Washington, D.C.

By Harry Waldman

The 35th U.S.A. Mathematical Olym- Winners received the USAMO Medal, The highlight of the evening came when piad Awards Ceremonies took place in named in honor of Gerhard C. Arenstorff, the Akamai Foundation Scholarships Washington, DC on Sunday and Monday, twice a winner of the USAMO and a were presented to the 1st place win- May 21 and 22. This event honored the member of the first USA team in the In- ner, Brian Lawrence, 2nd place winner, twelve top winners of the annual USA ternational Mathematical Olympiad. Alex Zhai, and 3rd place winner, Yufei Mathematical Olympiad (USAMO), the Zhao, by Wendy Ravech, Director of the premier high-school level mathemati- After dinner, Brian Lawrence received Akamai Foundation. These scholarships cal problem solving competition in the the Samuel L. Greitzer/Murray S. Klam- are in the amounts of $20,000, $15,000, United States. kin Award for his superior achievement and $10,000, respectively. By awarding in the Olympiad exam. Dr. James Carl- these scholarships, the Akamai Founda- The two day celebration began with son, President of the Clay Mathematics tion hopes to encourage these and other a Sponsors’ Reception at the MAA Institute, designated Brian Lawrence as students to continue their pursuit of math- Headquarters, at 1529 18th. St. N.W. the eighth CMI Mathematics Olympiad ematics education. Representatives of the sponsoring orga- Scholar as Brian best fulfilled the prize’s nizations of the American Mathematics criteria of elegance, beauty, imagination, The road to the USAMO began with the Competitions along with members of the and depth of insight. American Mathematics Contest 10 (AMC MAA Executive Committee greeted the 10) and American Mathematics Contest winners and their families. On Monday The Robert P. Balles Distinguished Math- 12 (AMC 12) exams. In February, about morning, the winners toured the Crypto- ematics Student Award, given to each 240,000 students from over 4,000 schools logic Museum at the National Security of the twelve winners, is a prize given participated in these contests. The AMC Agency and enjoyed a talk on classical to the winners in an effort to recognize 10 and AMC 12 have 25 questions from cryptography from one of the on-site and reward their high achievement in the high school mathematics curriculum mathematicians. the world of mathematics competitions. to be answered in a timed 75 minute Robert P. Balles is a life long student of format. The problems range from easy to The 2006 USAMO winners were Yakov mathematics, former community college quite challenging. The top 5% of scorers Berchenko-Kogan of Raleigh, North instructor of mathematics, and retired on the AMC 12 and the top 1% of scorers Carolina; Sherry Gong of San Juan, businessman who established this gener- on the AMC 10 are then invited to take Puerto Rico; Yi Han of Pittsburgh, ous prize in 2005. the American Invitational Mathematics Pennsylvania; Taehyeon Ryan Ko of Al- Exam (AIME). lendale, New Jersey; Brian Lawrence of Kensington, Maryland; Tedrick Leung of Winnetka, California; Richard Mc- Cutchen of Silver Spring, Maryland; Peng Shi of Toronto, Canada, Yi Sun of San Jose, California; Arnav Tripathy of Chapel Hill, North Carolina; Alex Zhai, of Champaign, Illinois; and Yufei Zhao of Toronto, Canada.

Dr. John Marburger, III, Director of the Office of Science and Technology Policy in the Executive Office of the President, hosted the celebratory reception and din- ner in the Diplomatic Reception Rooms of the U.S. Department of State. The formal awards ceremony, presided over by MAA President Carl C. Cowen, took place in the Dean Acheson Auditorium of the State Department where Dr. Fan Chung Graham, Akamai Professor in In- ternet mathematics at UC San Diego gave 35th USA Mathematical Olympiad Winners the USAMO address, “Graph Theory in From left to right: Brian Lawrence, Arnav Tripathy, Sherry Gong, Yi Sun, Tedrick the Information Age.” Leung, Yi Han, Alex Zhai, Richard McCutchen, Yakov Berchenko-Kogan, Peng Shi, Taehyeon Ryan Ko, Yufei Zhao

 August/September 2006 FOCUS

Dr. Fan Chung Graham giving the Melanie E. Wood (USAMO winner in President Carl Cowen with 1st place Olympiad address titled “Graph 1998 and 1999) with Sherry Gong. winner and Clay Mathematics Insti- Theory in the Information Age.” tute Olympiad Scholar winner Brian Lawrence.

Three big checks from Akamai. Photograph by Bill Rundell. Tina Straley speaks. Photograph by Bill Rundell.

The AIME is a challenging 15 question solutions are available on the web by solving, proof-writing and deeper in- contest spanning 3 hours. The difficulty choosing “Students” on the MAA home struction on algebra, geometry, number of the questions ranges from equivalent page (http://www.maa.org) and following theory, combinatorics, probability, and to the most difficult on the AMC 12 to the links. The twelve winners and other trigonometry in preparation for solving extremely difficult. In March, nearly young students who took the Olympiad Olympiad-style problems. The summer 12,000 students took the AIME. Based exam are invited to the Mathematical program was funded in part with a grant on a combination of scores from these Olympiad Summer Program (MOSP) for from the Akamai Foundation. two contests, 430 students were invited advanced training for the International to take the USA Mathematical Olympiad Mathematical Olympiad (IMO). The final US team for the IMO was (USAMO) exam which was held on April selected from among the 12 winners 18 and 19. The 2006 Mathematical Olympiad Sum- at the MOSP. Each year since 1974, a mer Program was held on the campus small team of exceptionally talented The USAMO is a 6 question proof-essay of the University of Nebraska-Lincoln high school students has represented the contest, taking 9 hours over two days. from June 11 to July 1 with 54 students United States at the IMO. See page 3 for The problems on the USAMO would be and 14 instructors and graders in at- news on the US team’s performance at challenging even to professional math- tendance. The students received a mix the IMO. ematicians. This year’s USAMO and of training on mathematical problem

 FOCUS August/September 2006

Association for Women in Mathematics Announces Michler Prize

The Association for Women in Math- the editor also remembers her indignant ematics (AWM) has announced that Ger- refusal to review a book that she felt was hard Michler of Essen, Germany donated unworthy of the attention. $1 million to Cornell University to estab- lish a prize in the memory of his daughter, At the time of her death, Ruth was 33 Ruth Michler, who was tragically killed years old; she had recently been pro- in November, 2000 while riding her bi- moted to Associate Professor and was cycle. The prize will be administered by spending the year as a Visiting Scholar AWM and will be known as the Ruth I. at Northeastern University on an NSF Michler Memorial Prize of the Associa- POWRE grant. She was struck and killed tion for Women in Mathematics. by a construction vehicle, while wait- ing to cross a busy intersection near the The AWM press release described Ruth Northeastern campus. The prize in her as “a constant source of energy, per- memory will enable other mid-career sistence, and talent.” She was born in women to follow Ruth’s example and Ithaca, NY, while her father was a visiting more deeply pursue their own mathemati- mathematician at Cornell. She studied in cal research. Ruth Michler Oxford and did her graduate work at the University of California at Berkeley. She The prize will be awarded annually by months at Cornell to pursue a research taught briefly at Queen’s University in the AWM to a recently promoted female or book project. The application deadline Canada, and then went to the University associate professor of mathematics (or for the first prize is November 1. For of North Texas at Denton. Longtime read- equivalent) working at a university other details about the Michler Prize and the ers of FOCUS Online may remember her than Cornell. The prize is intended to applications process, see http:// www. two reviews for our Read This! column; allow the winner to spend four to six awm-math.org/michlerprize.html.

Your smarts belong at Epic! We're hiring smart and innovative people for all kinds of positions and we’ll train you.

Apply at www. systems.com

 August/September 2006 FOCUS Is the Poincaré Conjecture Proved At Last? By Fernando Q. Gouvêa

The Poincaré Conjecture, one of the to be homeomorphic to S3. While very and must survive the examination of the Clay Mathematics Institute’s million-dol- plausible, this conjecture turned out to be mathematical community for at least a lar Millennium Problems, may be settled extraordinarily difficult to prove. two-year period. So far, Perelman shows at last. In 2002 and 2003, Grigori Perel- no indication of any intention to publish man of the Steklov Institute in St. Peters- Analogues of the conjecture in dimension his papers. Perelman’s preprints are fairly burg posted several papers to an online five and higher were proved in the 1960s sketchy and would probably not be pub- preprint archive in which he claimed to by Smale, Stallings, and Wallace. The lishable as they stand. The two exegeses have proved Thurston’s Geometrization four-dimensional version took twenty by Kleiner and Lott and by Cao and Zhu Conjecture, which is known to imply more years, being proved by Freed- are immensely longer than the Perelman’s Poincaré. Specialists have been read- man in the 1980s. It now seems that the original papers, and both claim to contain ing his papers and developing his ideas original three-dimensional conjecture has the full details of the proof, leaving an since then. Two recent papers, published finally been settled. Perelman’s methods interesting knot for the Clay Institute to almost simultaneously, have claimed are based on ideas of Richard Hamilton disentangle. a complete proof based on Perelman’s on the “Ricci flow” and on William ideas. One is “Notes on Perelman’s Pa- Thurston’s high-powered “Geometriza- In addition to the CMI site noted above, pers,” by Bruce Kleiner and John Lott tion Conjecture,” which provides a very one should check the site maintained by (posted to the ArXiv preprint server on general description of all closed three- Kleiner and Lott, http://www.math.lsa. May 25, 2006); the other is “A Complete manifolds with finite fundamental group. umich.edu/~lott/ricciflow/perelman. Proof of the Poincaré and Geometriza- Thurston’s conjecture contains the Poin- html, which contains links to many other tion Conjectures—Application of the caré Conjecture as a special case. It is the online materials related to the work of Hamilton-Perelman Theory of the Ricci Geometrization Conjecture that seems to Perelman. See also the news story pub- Flow,” by Huai-Dong Cao and Xi-Ping have been proved, therefore settling also lished in the Wall Street Journal on July Zhu (published in the June 2006 issue of the Poincaré Conjecture. 21, 2006 (page A9). Details on all the the Asian Journal of Mathematics). Millennium Problems can be found in Interest in the conjecture was height- Keith Devlin’s The Millennium Problems To understand the conjecture, start with ened by the fact that in 2000 the Clay and in the recent official publication from the three-sphere S3, i.e., the set of points Mathematics Institute made it one of its the American Mathematical Society and 4 (x1, x2, x3, x4) in R satisfying the equation seven Millennium Problems, offering one the Clay Institute, The Millennium Prize 2 2 2 2 x1 + x2 + x3 + x4 = 1. This is perhaps million dollars for its solution. One can Problems, ed. by J. Carlson, A. Jaffe the simplest compact three-manifold. read more about the conjecture and the and A. Wiles. Devlin’s account of the One way in which it is simple is the fact Millennium Problems at the CMI web conjecture is aimed at the general public, that any loop embedded in it can be con- site at http://www.claymath.org/millen- while the article by Milnor in the official tinuously deformed to a point. Poincaré nium/Poincare_Conjecture/. volume is more technical (but still quite conjectured, early in the 20th century, readable). The Asian Journal of Math- that this property in fact characterizes the Curiously, it is unclear whether Perel- ematics is at http://www.ims.cuhk.edu. three-sphere, that is, that any other com- man will win the prize. The rules for the hk/~ajm/ and the ArXiv preprint server pact three-dimensional manifold with the Millennium Prizes specify that the work is http://arxiv.org. loop contracting property would have must be published in a refereed journal

Found Pedagogy

“If we can start them thinking about science early, and taking the right courses early, then science is not dif- ficult — it’s exciting. I see this as a marvelous beginning of an effort not only to educate, but to prepare a work force.”

(State Senator Pete Knudson of Utah, on the state’s plans to organize science camps for teenagers, one of which is AWE+SUM, which stands for “Attend Westminster, Explore Science, Use Math.” See http://goed. utah.gov/science/.)

 FOCUS August/September 2006 University of Mississippi Graduates Record Number of African-American PhDs

By Tristan Denley

Readers of FOCUS may have seen the national headline news from the Department of Mathematics at the University of Mississippi. At our spring commencement, UM broke the national record among American colleges and uni- versities for producing the most African- American PhD graduates in mathematics at one commencement. On Saturday, May 13, the University awarded doctoral degrees to Joe Anderson of Rosedale, Mississippi, Carla Cotwright of Los An- geles, Bryan Williams of Missouri City, Texas, and Adrian Wilson of Jackson, Mississippi.

The milestone warranted making head- lines across the country, and it did, in media outlets statewide, as well as some regional spots and a couple of national New PhD graduates Carla Cotwright, Bryan Williams, and Adrian Wilson with hits. But in many of my conversations math department chair Tristan Denley. since the announcement, colleagues, friends and others have expressed puzzle- ment as to why this accomplishment was ican doctorates in mathematics overall.” students, the mathematics department’s newsworthy at all. Even a columnist from Furthermore, Cole said, “with continued innovative external and internal financial a prominent publication that covers issues faculty efforts to provide deserving programs, the research faculty’s outreach of diversity was surprised: Don’t students students with financial assistance and to minority students, the administration’s graduate with PhDs every year — even challenging learning experiences, as well leadership to coordinate these efforts and in mathematics? as a commitment to sustain a nourishing Chancellor Robert Khayat’s passion for campus environment for minority stu- diversifying the campus. “These four will In fact, the figures show that the number dents, the University of Mississippi can be role models to other people, both black of minority doctoral graduates in math- become the nation’s leader in producing and white, and we will see I hope an addi- ematics is much smaller than expected. African-American mathematicians.” tional interest among students to come to The 2005 American Mathematical Soci- this university or to other universities to ety survey, for example, reported 1,116 In the context of the exuberance sur- pursue math and science as their careers”, new doctoral graduates. But only 14 of rounding the announcement, I am re- said Chancellor Robert Khayat. those graduates were African-American. minded of the years of quiet work by In fact, the figures are similar for students many that brought us to this level of In the mathematics department, work to- of any minority race. In light of these success. Dedicated people across the ward this goal began almost six years ago figures, the impact of UM’s four recent University and at all levels of the ad- under the leadership of Professor Gerard graduates comes into clearer focus. ministration support our commitment to Buskes, my predecessor as chair. He was increase the number of minorities com- the driving force behind an application Don Cole, UM’s associate professor of pleting doctoral degrees. Such a desire for GAANN (Graduate Assistance in mathematics and assistant to the chancel- reflects this institution’s commitment Areas of National Need) funding from lor for multicultural affairs, said, “What to inclusiveness, mirroring a sustain- the Department of Education. In his pro- happened on May 13 in Oxford was an ing minority undergraduate population, posal, Buskes pointed to a large pool of historic milestone, unprecedented in the a committed faculty and a supportive talented minority students in this region United States, with only the University of administrative structure. In particular, and concluded that they had the potential Maryland coming close, in 2000. Indeed this year’s achievement is a result of the to become interested in the beauty of only a few of the nation’s larger institu- Graduate School’s aggressive recruit- mathematics. “I thought at the time that tions have produced more African-Amer- ment and retention programs for minority if I were to be able to successfully recruit,

 August/September 2006 FOCUS train and graduate from this talented of the Graduate School staff and profes- allowed them to blossom into promising pool, then I would be able to make some sors in the mathematics department, I felt young mathematicians. All four already contribution to a slow transformation that while the PhD in mathematics is a have teaching positions, or are deciding from Mississippi as a largely agricultural difficult program, it was something that I between offers for the fall. state to Mississippi as a technology-based could be confident and successful in pur- economy,” Buskes said. “That the success suing.” Cotwright completed a bachelor’s Indeed, this is not the end of their story or would be as strong as it now turns out to degree in mathematics at California State our story, but another beginning for both. be is beyond my wildest dreams, and I University at Long Beach and holds An important impact of these four gradu- am proud of each of these students now Master’s degrees in mathematics from ates is that others like them are following receiving their PhDs,” Buskes said. both UM and Southern University/A&M the same path here at the University of College in Baton Rouge, LA. The larger Mississippi. This summer, we have three The resources that GAANN funding number of students interested in research more minority students completing PhD provided and the students that it enabled has provided opportunities to intensify requirements. And the older students are us to recruit had a transforming effect the department’s research activities, and encouraging those coming behind them not only on those students but also on the additional funding has allowed to follow in their footsteps on the road to our program. When I became chair, 12 graduate students to attend national and doctoral research. And to cap it all off, I months later, there were fresh graduate international workshops and conferences was recently notified that a new GAANN students, many of whom were minor- as never before. I have rarely attended a grant proposal has been approved. ity and/or female, who had entered the conference without coming away hungry program focused on trying to obtain the to work on a problem that I saw there, In the words of now Dr. Adrian Wilson, highest academic degree possible. They or simply catching the excitement of the “I am certain this milestone will serve dramatically increased the size our PhD new areas that other researchers have be- as an incredible catalyst in the African- program at a single stroke. This change gun to explore. All of this was true of our American community to increase the in perspective was hugely important. students too. As they saw others stand and interest in mathematics. It is my dream Up until that time, students often began share the results that they had found, they that one day an accomplishment of this graduate work with their eyes set no began to come together as a community caliber won’t be looked at as a University further than a master’s degree. They who wanted that for themselves. graduating four African American Math- saw graduate mathematics as a ticket to ematicians, but rather four American a teaching job at a junior college. Here However, in the end, we all know that mathematicians.” was a chance to raise their dreams. graduate research is not really a team sport. An enormous amount of the credit Tristan Denley is chair of the Depart- “I was pleasantly surprised that the goes to these graduates’ faculty advis- ment of Mathematics at the University academic atmosphere greatly outweighed ers James Reid, Haidong Wu and Alan of Mississippi. He holds a PhD from the any concerns that I had about the univer- Paterson. Their careful and dedicated University of Cambridge, U.K. sity,” Cotwright said. “With the support work one-on-one with these students

Slocum Puzzle Collection at the New Site for Lilly Library Mathematics Jobs

Jerry Slocum, who has been collecting engineer and a former vice president of and studying puzzles for over fifty years, Hughes Aircraft,” who is also “the author A new web site that collects employ- has announced that he will donate his of 10 books on the history of puzzles, ment ads of interest to mathematicians collection of 30,000 puzzles and 4,000 including a recently published account has been created in Switzerland. Located books about puzzles to the Lilly Library of the sudoku-like 15 Puzzle.” (We beg at http://www.math-jobs.com/, it allows at Indiana University. The library opened to differ about the supposed similarity searches by country and by type of job its new Slocum Puzzle Room on August 3. between the 15 Puzzle and Sudoku!) and also includes links to articles with tips About 400 puzzles are on display, most of The book, which is co-authored with for those looking for a job. One of them, them mechanical puzzles such as Chinese Dic Sonneveld, will be distributed by for example, links to an article about Rings and Rubik’s Cube. Visitors to the MAA. A review appeared in July in the “How to get from a poor country into a library will be able to test their wits by our online book review column; see the rich country (as a Mathematician or other attempting to solve the puzzles. main MAA Reviews site or go to http:// Quant).” As usual, applicants get access www.maa.org/reviews/15puzzle.html. For to job listings for free, but employers An article on the exhibit, including more on the Lilly Library, see http://www. have to pay to have their ads listed. The photos of several puzzles, appeared in indiana.edu/~liblilly/ site belongs to Luchsinger Mathematics, the July 25, 2006 issue of the New York with headquarters in Zurich. Times. It describes Slocum as “a retired

 FOCUS August/September 2006

Oral History and the Archives of American Mathematics

By Kristy Sorensen

Oral history interviews can be some of the most revealing and detailed resources for archival research. A good interview can provide a researcher with a uniquely rich documentation of an individual life and a moment in history.

The Archives of American Mathemat- ics at the Center for American History actively collects oral history material and makes it available to our patrons. We have audiocassettes and videotapes containing interviews with a wide vari- ety of mathematicians and mathematical educators. In many cases we also have full-text transcriptions of the interviews as well as supporting biographical mate- rial, making the oral histories an even more valuable resource.

Conducting high-quality interviews is a skill that can be mastered by anyone, and you may find that undertaking an interview with a friend or colleague is as rewarding an experience for you as it is for them. (http://www.cyndislist.com/oral.htm): An Mathematical Association of America As in many topics, the Internet has a extensive collection of oral history links great number of sources that can help Records, Committees Section – if it is available online, it is probably (Leon Henkin interview): guide you in conducting an oral history listed here. http://www.lib.utexas.edu/taro/ interview. Some particularly helpful web- utcah/00476/cah-00476.html sites include: If you are interested in conducting an oral history interview, or if you would like NCTM Oral History Project Re- Archival Leaflet Series, “Doing Oral to use our existing oral histories in your cords: History,” by L. Dale Patterson, Archivist, research, please contact the archivist at http://www.lib.utexas.edu/taro/ The General Commission on Archives the information below. utcah/00319/cah-00319.html and History of the United Methodist Church (http://www.gcah.org/oral.html): Online inventories for collections in the Albert W. Tucker Papers: This site provides an overview of best Archives of American Mathematics that http://www.lib.utexas.edu/taro/ practices as well as a list of concrete tips contain oral history material include: utcah/00301/cah-00301.html that will make the interview process go more smoothly. R. H. Bing Interviews: The Archives of American Mathematics http://www.lib.utexas.edu/taro/ is located at the Research and Collections “One Minute Guide to Oral History,” utcah/00306/cah-00306.html by Carole Hicke, The Bancroft Library division of the Center for American His- tory on the University of Texas at Austin Regional Oral History Office, UC Berke- Melvin Henriksen Oral History http://bancroft.berkeley.edu/ROHO/ campus. Persons interested in conducting ley ( Collection: resources/1minute.html): The name says research or donating materials or who http://www.lib.utexas.edu/taro/ have general questions about the Ar- it all! This is a nice concise guide on the utcah/00496/cah-00496.html basics of oral history creation. chives of American Mathematics should contact the archivist, Kristy Sorensen, at R. L. Moore Legacy Collection: [email protected] Cyndi’s List of Genealogy Sites on the , or by phone http://www.lib.utexas.edu/taro/ at (512) 495-4539. Internet, Oral History and Interviews utcah/00310/cah-00310.html

10 August/September 2006 FOCUS

11 FOCUS August/September 2006 Making the Most of Your Sabbatical

By Jennifer R. Galovich, Charles R. Hampton, William A. Marion and Thomas Q. Sibley

Sabbatical! No students banging project, know how to make it hap- down your door, no grading, no pen, and can accomplish your objec- lectures to prepare, no committees, tives in the time available. (This is no campus politics, no whining, and yet another reason to choose two you get paid (sort of). What’s not semesters.) If you are going away, to love? Together the authors rep- you will need a letter of support or resent a total of twelve successful invitation from the host institution; sabbaticals, but that success is not if you are engaged in a writing proj- automatic. Here are some pointers ect, you may need a letter from your from our collective experience: editor or publisher. Your institution may also require letter(s) of support Advance Planning — Nuts and from colleagues regarding the value Bolts of your project and your prepared- ness for it, as well as a letter from Most places won’t just let you walk your department chair. out the door every seventh year. There is probably some kind of Ideally, your sabbatical project has application process. Find out what its roots in some idea(s) you’ve it is. Make sure that you know all already begun to ponder. What ad- the details regarding deadlines, pro- ditional preparation will you need cedures and criteria, as well as the in order to accomplish your project? less tangible institutional traditions If you are changing fields, you may and standard practices. (Ask senior need to audit a course, do some colleagues about this if you are not additional reading and writing, or sure.) Keep all these factors in mind attend a professional meeting or as you put together your proposal, workshop in the new area. If you and don’t hesitate to consult if any are writing a text, you will want to part of the process is unclear. Once have a prospectus and some initial you have determined that you Cartoon by John Johnson chapters already in the works. If you are in fact eligible (check your faculty are picking up an old project, set aside handbook), have decided on one vs. two courses in theoretical computer science time to review (and find) your old notes semesters (we recommend two — see and pursuing those items listed in the and papers. Your proposal should have below), and have some idea what you “future directions for research” chapter enough detail to be compelling, but it would like to accomplish, we recommend of the dissertation. Whatever you choose, should not be voluminous. that you consult with your department without daily deadlines to spur you on, chair. You will need her support, and this you will need the project to call you. Keep your audience in mind as you write. is when you can find out if your project And institutional agendas can change, At smaller institutions, the members or timing will need tweaking in order to sometimes without warning. Ultimately, of the committee reviewing proposals be aligned with some departmental or what’s good for you is good for the may come from a variety of disciplines. institutional need of which you are not institution, but it can be helpful in the You may need to explain (briefly) how aware. application process to understand how to research in mathematics differs from make those connections explicit. research in, say, biology or English Institutions will (quite reasonably) be literature. Finally, as with any writing disposed toward supporting projects that Not all institutions are able to fund all project, follow the guidelines and run benefit the institution. That said, it is criti- applicants, so the process may be quite your proposal by a disinterested third cal to choose a project that you are aching competitive. Your written proposal is party before you send it off. to tackle. The authors have engaged in your chance to make your case — why projects such as writing a text, developing is this project good for you, why is it Though you may not need to put it in your a bioinformatics curriculum, monitoring good for the institution/department, and proposal explicitly, we recommend that and analyzing gerrymandering and redis- why should anyone believe you can do you have a backup plan, in case you find tricting after the 1990 census, studying of it? You will need to provide convincing a counterexample in your first week, or the philosophy of mathematics, auditing evidence that you are serious about your the project turns out to be more like Mt.

12 August/September 2006 FOCUS

Everest than Mt. Shasta. (Or, as happened sabbatical renewed and refreshed — hard Making it Work to one of us, someone publishes your idea to do when you are surrounded by the before you were finished thinking about same old same old. Going away means Academics typically work too hard, with it. The lemonade from those lemons was not only taking advantage of new op- grading and class preparation regularly a series of ultimately successful under- portunities but also being able to decline spilling into the evenings and weekends. graduate research projects.) the old ones. And you may have access Sabbaticals are an opportunity to inter- to books, journals and software that are rupt that cycle and make a clean break Go Away not easily available at your home institu- from the distractions of campus politics tion, not to mention the interactions with and requests from colleagues to help with The authors are unanimous in their advice many colleagues who will share and spur chores. Find a new rhythm that fits your to take full year sabbaticals and go away your interests. project, and doesn’t wear you out. Work from your home institution if at all pos- on your project regularly, but don’t feel sible. One of us has even taken several You probably have some ideas about guilty about taking time off if that’s what sabbaticals abroad. We know that going what kind of place would work best for you need. Galovich and Sibley have a away can be difficult — in most institu- your project — perhaps you have some rule that you can’t bring work home from tions, you will take a significant pay cut specific places in mind. You may be the office. for a full year sabbatical compared to a drawn by the opportunity to work with semester sabbatical, and if you go away a particular person or research group, or In any case, whether or not you go away, as well, the financial challenges are mag- perhaps the institution supports a special don’t isolate yourself. Make time to enjoy nified. Sometimes this can be addressed project such as the IMA at the University your surroundings (whatever they are), by advance planning — some host in- of Minnesota, MSRI at UC Berkeley, or exercise, and take advantage of seren- stitutions may be willing to hire you (or the MBI at Ohio State University. How- dipitous opportunities, such as travel, your spouse/partner) on a part-time basis. ever, it is worth discovering (perhaps auditing a class or working on a side (However, be warned that even part-time through colleagues) the nature of the project that you stumble on. If you are employment will dilute your energy for work climate at your host institution. If going to a new place, e-mail the chamber your project, unless it is directly related.) you are expecting to do a lot of collabora- of commerce, get a city map, check out Or your project may be just what some tion and everyone is a Lone Ranger, you the local newspaper (e.g., on-line). You funding agency is looking for and you could be sadly disappointed. Depending could also resurrect old interests — get can apply for a grant. (Don’t forget the on your project, a non-academic institu- that clarinet out of the attic and join a Fulbright folks for sabbaticals abroad.) tion may appeal to you, but in our expe- community orchestra or other music or We also note that there are significant rience, corporations and laboratories are drama group. Or you could take on a tax advantages (a sabbatical qualifies as a not tuned in to the rhythms of academic new interest, such as getting involved in job away from home), and recommend a life. In particular, you may be expected to a community service project. pre-sabbatical consultation with a profes- be more immediately available than your sional and/or purchase of one of the tax institution’s application process permits. Whatever you do and wherever you do it, guides for college teachers, such as the In any case, if you choose a non-aca- refresh, renew, learn and enjoy! one published by Academic Information demic setting, be sure that your mutual Service, Inc. expectations about what you will do and Jennifer Galovich is Associate Professor when you will do it are in sync. of Mathematics at St. John’s University Other challenges are presented by family (MN); Charles Hampton is Johnson Pro- circumstances. These vary so much that Wherever you go, make a connection fessor of Mathematics at The College it is hard to give advice. However, we do with someone there, by e-mail, shared of Wooster; Bill Marion is Professor report that the same factors that make it acquaintance, or just introduce yourself of Mathematics and Computer Science work for you can also make it work for at a meeting. Find out what the host at Valparaiso University; Tom Sibley is your family. Finding housing and decid- institution’s procedures are, and what Professor of Mathematics at St. John’s ing what to do with your own house can they will be able to offer you. In our University (MN). Hampton, Marion and be a bit nerve-racking, but on both fronts experience, most institutions are quite Sibley are also former department chairs. we recommend faculty bulletin boards, welcoming, though less accommodating The authors served on a MAA Project the always helpful secretary to the Dean the more you ask for. Visiting scholar NExT panel at the San Antonio Joint or Provost, and http://www.craigslist.org. status, parking permits and access to li- Mathematics Meetings. This article is a Of course, taking your children out of braries are easy (though parking may not compilation of their remarks. school and placing them in a new school be free). An office (even shared), phone, environment can make for a difficult tran- computer and secretarial services are a sition, but is potentially a very enriching bit harder, but most places are willing if experience for them. these are available at all. In general, we have found that it is fairly easy to wrangle However, the advantages of going away an invitation someplace as long as you are many: Ideally, you return from your don’t want any money.

13 FOCUS August/September 2006

Some Advice for Graduating PhD Students

By Felix Lazebnik and Keith E. Mellinger

You may feel pressure to publish early in can hurt your research, primarily by What to tell a graduating PhD student your career. With that in mind, the fol- taking time and energy, and by stirring in mathematics? One thing we learned is lowing advice might be easier to say than negative emotions. This is especially that everybody has a different answer to do. Try to work only on those problems true if you are an ambitious teacher. Be this question. There are many different which you really like. It will make you aware of this. You may like both research pressures placed upon new mathemati- happier. The consequences are obvious. and teaching, but only a few of us can do cians. In what follows, we will assume both things really well simultaneously. that a graduating student answers the Similarly, you may have mixed feelings Fortunately, there exists this wonderful question “To be or not to be?” as “To about the role of teaching in your career. time of year called summer. be.” Unfortunately, this does not resolve Teaching can help you to become a better all the problems. Everyone’s experience, scholar. This is true even if you teach only Finally, to quote the renowned Joe Gal- circumstances and difficulties are so very undergraduate courses. Think about what lian, find your niche in the profession. special, right? you teach from different perspectives Whatever you decide, there is something and you will find many related questions important and valuable you can do. Think Your situation is not that special. Many crying for answers. Like “what if instead about the mission of your institution and new or budding Doctors-of-Philosophy of that assumption, I use an alternate as- follow your instinct. have had similar problems of their own, sumption?” “Can this be generalized?” the same ambitions, aspirations and “How and why did this notion/theorem Those are probably our most important doubts. Life for the young and talented appear?” “Why does this boring theo- points to share. But here are a few other is not easier than for, well, just about rem/exercise appear in just about every things to think about. anybody else. Relax and stop blaming text? Why should I teach it?” In other the circumstances. It is up to you to words, teaching can help you with your Get on publishing that dissertation right make choices. Remember Woody Allen: research. Listen to your students. They away. At the end of your thesis you may “The only thing standing between me can ask good questions. It is certainly think that what you did was minor. “OK, and greatness is me.” In what follows, possible that an innocent question asked it was sufficient for the degree, but who we assume that you have sorted personal by a student in class could lead you to a really needs it? Probably many people problems like finding a partner, dealing new research problem. could do the same thing if they decided to with parents, or owning a dog. What is work on it.” Nonsense. It is hard to judge left is research and teaching. the value of your work at this time. It’s Your situation is not that spe- very likely that, in ten or fifteen years, You may have mixed feelings about re- you will read what you published and be search. Make up your mind about this, cial. Many new or budding surprised with how nontrivial the logic at least for the first six years. Do not Doctors-of-Philosophy have and the arguments are! You will feel question this decision every month and had similar problems of their much better about the work. And no one be ready to face the consequences. The own, the same ambitions, can predict how your published word demography of institutions where people will echo in the future. And it is harm- can do good research has changed. The aspirations and doubts. Life less. Try to publish your PhD thesis. You internet, email, and low rate telephone for the young and talented is might even start putting your thesis into services, ameliorate the problems caused not easier than for, well, just article form before graduation. This will by the absence of a good library, limited about anybody else. Relax help you to hit the ground running after resources for travel, and lack of a col- graduation. Your PhD thesis is your first league in the next room who can under- and stop blaming the circum- class ticket to publication at this point in stand your math. If you decide you will stances. your life. Don’t let it go. be doing research, it is clear what to do: read, think, call, email, go to conferences Take advantage of every speaking op- to meet others, many of whom are in the portunity you can get towards the end of same position as you, and collaborate. If Teaching often helps relieve the frustra- your time in graduate school. You will, you do not have travel funds, pay your tions of research, and the emotions you undoubtedly, be expected to give talks. own way. Share driving and hotels with get from it can help you to resume your If nothing else, you will be expected to others. This way you can attend more research program. Don’t buy in to the speak to a diverse group while being meetings. Consider it as an investment in myth that success in one area (teaching interviewed for a job. You don’t want your future. And again, read, read, read. or research) implies failure in the other. this to be a new experience. Along the Nevertheless, it is possible that teaching same lines, learn how to write well.

14 August/September 2006 FOCUS

Mathematicians have a bad reputation less fulfilling than you expected. Reality your colleagues about the last article you for their writing skills. Don’t be one of check! Your first year out of graduate read in FOCUS or the Notices of the AMS, those guys. Give details eloquently and school will be difficult. You’ll probably or even in a newspaper. It is not always understand that good writing comes with be teaching much more than what you are easy to be a good professor. We need each practice. used to, and your schedule will change other; it is easier to jog with other people dramatically. Be ready. running next to you. There is a difference between state schools and private schools. For instance, Document your teaching material, even if There are many activities which are when interviewing, you might discover it is in imperfect form. How many times essential for the survival of our profes- that publicly supported schools often do you think you’ll be teaching first se- sion, but often do not bring you much offer lower starting salaries, but better mester calculus? Answer: a lot. So make credit. For example, refereeing, review- opportunities for salary increases over notes, write good quizzes and exams, ing, translating, editing the writing of a the years. Find information on faculty and make nice handouts. Anything you colleague, talking at length to students, salaries. Remember to look not just at do now will make your life easier down posting a useful document on the web, starting salaries, but also what associate the road. etc. Do not be afraid to be generous with professors are earning. Also, ask ques- time spent on such things. Many people tions about benefits. Ask around. See how There will be many activities begging for do notice and will be grateful. It helps much people are paying for things like your time, more than you can do in a 24- to feel that you belong to something health insurance. Many public schools hour day. And most of them will be sen- important, like the Eternal Order of have very good insurance plans that beat sible worthwhile things to do. Learn when Mathematicians. Welcome aboard. the private schools. to say “Yes” and when to say “No.” You need to find your niche. If undergraduate The authors are thankful to Peter Haskell Meet as many people as you can. Net- research is your thing, then say yes to the for inviting Keith Mellinger to Virginia work. Go to conferences. Introduce opportunities that will help you to grow Tech in the fall of 2005 to speak to the yourself. Ask questions. Talk to people. in that direction. If research is not your graduate students about some of the Assuming you make a good impression, thing, agree to be on a university com- issues mentioned here. In addition, we the more people you meet the better off mittee, or to teach a new course. Do say thank Professor Haskell for carefully you’ll be. This requires no further expla- “yes.” But also learn when saying “no” reading the article and making several nation. Some mathematicians are quiet, is the better answer. valuable suggestions. In particular, we aloof people. Try not to be, especially are grateful to him for mentioning an when you’re fresh on the market. editorial by John Ewing (Some Advice Reality Check! Your first for Young Mathematicians, Notices of the A 12 hour teaching load and a high AMS, v. 45, no. 11, Dec. 1998, p. 1452) research expectation are not very com- year out of graduate where some similar suggestions to young patible. Many faculty teach 12 hours (or school will be difficult. mathematicians were made. 4 courses) per semester and very much enjoy it. But be a little cautious of such a teaching load coupled with an expecta- tion of three or more scholarly publica- Apply for grants, but do not make it an tions per year. initial priority. Grants help us to achieve some goals in both research and teaching. Have You Moved? Keep all your options open and apply But they are neither a necessary nor suf- for different kinds of jobs. This might be ficient condition for measuring one’s suc- easier to say than to do. But you never cess in the discipline. Your administration The MAA makes it easy to change know what’s going to happen out there in values them. Unfortunately, many people your address. Please inform the MAA the job market. Post-doc opportunities are often equate receiving them with the no- Service Center about your change of more plentiful these days (especially for tion that you are “good” or “valuable” address by using the electronic com- U.S. citizens), so don’t rule such things (a separate issue entirely). But we can bined membership list at MAA On- out thinking that you have no chance. guarantee you that you will never receive line http://www.maa.org) or call (800) You could have the pleasure of learning a grant if you do not apply. So keep an 331-1622, fax (301) 206-9789, email: a whole new area of mathematics while eye out and apply when you can. [email protected], or mail to the having a very low teaching load your MAA, PO Box 90973, Washington, first few years out of graduate school. Exhibit good “mathematical citizenship.” DC 20090. Such experiences have far-reaching Have lunch with colleagues, discuss what consequences. new math you learned while preparing for today’s class or what difficulties you had. Don’t be surprised if your first year of full Share and ask for interesting problems. time teaching seems more difficult and Share clever student responses. Inform

15 FOCUS August/September 2006

NUMB3RS: Positive and Negative

The May/June issue of FOCUS includ- TV standards and romance and sensitiv- great content. A show about a talented ed the article “Complex NUMB3RS,” by ity are emphasized in many scenes. The basketball player would likewise show Sarah J. Greenwald, in which the author emotional consequences of violence are some balls being put through some hoops. expressed her doubts as to the pedagogi- also portrayed in nearly every episode, However, although Charlie sometimes cal value of the well-known television as are the consequences of greed, over- shows off, he works hard at what he does, show. We received many letters respond- weening ambition, and gambling. I could is nearly always shown struggling with ing to the article, several of which we give dozens of examples of morality tales mathematical problems, and often makes collect here. within episodes — I’ve read and reread mistakes. Many times he is redirected the scripts of all of them. to the correct path by his father, Larry the physicist, or Amita. The episode Thank you, Prof. Greenwald 2. Amita’s relationship with Charlie is “Convergence” shows some of his ma- touching and innocent. She was a student jor professional work being disproved, I am delighted to see that there are at least of his, and we know that while they had and how he eventually patches it up; did a few people in the mathematics com- that relationship they had no other. In an Greenwald see this? munity who are not running around and early episode he tells his father (who’d crying “they like us! they like us!” just like to marry off his sons) that he can’t 4. “Little attempt is made to show how because someone decided to make a TV date Amita because she is his student. mathematicians actually think and math- program featuring a young, curly-haired, Then she finishes her PhD (pretty good ematics is often presented as consisting socially adept, handsome, fiendishly role-model that). Their first “date” ends entirely of formulas rather than concepts clever mathematician who hardly ever up with them talking mathematics and and logical connections between them.” seems to actually sit down and work on then being introspective about that fact; This is exactly not true and I could show his mathematics. And he solves crimes the reason Charlie even suggests a date is you dozens of scripts where the role of too. If anything, Prof. Greenwald was that his affection for her is kindled by his logic and concepts is emphasized over too generous. explicit admiration of some mathematical mere formulas. In fact, that’s one of the advice she offers him: this is as clear as themes of the show. Yes, there are equa- Outis Niemand day if you watch the episode. If any tele- tions that are written without much ex- Dystopia College vision character ever respected a member planation: that’s where my blog comes in. of the opposite sex as a person and not The show is not about teaching math, it’s as a sexual object, it is Charlie. He and about the usefulness of math. It is a fact Complex, perhaps, but good Amita never embrace or kiss until Amita that many shows have Charlie “dropping nevertheless smooches Charlie (to his surprise) when names” of various arcane and technical he suggests that Amita renew ties with sounding results. This is a valid criticism I write about the math behind NUMB3RS her family in India. This occurs in a very of the show, and something I and other on my blog, at http://www.atsweb.neu. positive show about Amita’s affection for consultants have been trying to change. edu/math/cp/blog/. I am also a consultant her family and sympathy for her fellow And I can tell you that people at NUM- to the show. From both standpoints, I’d Tamils. In any case, Amita, having com- B3RS are aware of this problem. like to take exception to the “review” pleted her thesis in combinatorics and of the show by Sarah Greenwald in the electing to write another in cosmology, is 5. “Research studies have shown that ste- May/June FOCUS. I will deal with her certainly free to contemplate a different reotypical representations of mathemati- major points one by one. relationship with Charlie. The issue of cians can actually discourage students Amita’s career and its independence from from pursuing more mathematics.” Well, 1. “The violence and sexual innuendos on Charlie has been the subject of some very research studies in education, I am sorry the show make any classroom use more interesting shows recently, which raise to say, have “shown” all sorts of things. complex.” Well, yes, more complex is exactly the issues of career and relation- Education is not a scientific field, and the true — certainly for kids in elementary ship that are deep and difficult. They have definitions of terms like “stereotypical” school. The fact is, NUMB3RS is far yet to be resolved on the show. and “discourage” are hardly precise. less violent than most crime shows on I’ve also read (and commented on) a fair TV, and many of the issues it raises are 3. “Charlie often fits the stereotype of the amount of nonsense in the Mathematics exactly the ones that high schools are gifted mathematician who readily finds Teacher. Kids who like some activity, be trying to deal with every day: sexual the right answer.” Well, he is a gifted it a sport or game or subject, want to be harassment, stalking, rape, and general mathematician: that’s what the show like the people they identify as excelling physical violence. The show comes down is about. To say that gifted people fit a in it. If you like basketball, you want to very firmly on the law-and-order side on stereotype that they employ their gifts be like Shaq; if you’re into soccer you these issues. The sex is quite tame by successfully is hardly a statement with want to be like Mia Hamm; if you bike,

16 August/September 2006 FOCUS you’re inspired by Lance, not someone ties as a mathematics teaching tool. As a things” such as tests and other stressful who rides, uh… the way you do. How- math educator for more than 16 years and and enforced practices are too often in- ever, Greenwald misses the whole point a district math curriculum administrator, vasive and detrimental to learning and to of Amita as a role model: she is a woman I disagree with her assessment that the learners), I question the very idea of using who likes math, is good at it, and isn’t program could discourage students from worksheets in the school curriculum to ashamed to admit it. She didn’t feel she pursuing more mathematics. supplement the TV program NUMB3RS. had to drop out of the top algebra class, or It seems to me that the main beauty of a take AB instead of BC calculus: she’s not Educators in my district have been us- program like NUMB3RS is that it’s non- afraid of challenges. Similarly, Charlie ing the NUMB3RS activities since they invasive; people can simply watch and shows that it’s OK to learn and read and launched last September as part of the enjoy the program, while simultaneously know things. He’s not big and pushy and “We All Use Math Every Day” initia- observing and appreciating the math (or fearless: he’s sympathetic, compassion- tive by CBS and Texas Instruments, in anything else) that it imparts, on perhaps ate, committed to the life of the mind, association with the National Council of a subconscious level. An interesting pro- and he abhors violence. Are these bad Teachers of Mathematics (NCTM). The gram all by itself without “obligation” role models? overwhelming response is that students is the kind of thing that is lacking in so not only enjoy watching the show, but many other educational situations, and 6. Greenwald goes on to question the also are more enthusiastic about learn- perhaps well enough should, at least in usefulness of the TI-NCTM website con- ing math because they see it being used some settings, be left alone. taining exercises linked to NUMB3RS. in “real life” situations and not just in a I have gone to this site many times and textbook. I’m sure that many students enjoy and have referred readers of my blog to it benefit from the worksheets, but for when appropriate. The site is very un- The classroom activities are extremely others it could spoil the fun and the even, as Greenwald says, and also pretty beneficial because they translate the math positive feelings. In grade school, hav- low-level. Since I have been explaining concepts from the show into hands-on ing to write an essay every September the math of the NUMB3RS show since problems that students can solve them- on “How I Spent My Summer Vacation” way before this site appeared, I assumed selves. Some of the activities follow the can spoil that summer vacation. I’m not that I could work with NCTM; however, show plots and others explore related saying we should completely “lose” the they have refused to respond either to concepts. The activities are aligned to NUMB3RS worksheets; I’m just saying calls or e-mails. This is rather strange state and national curriculum standards, that they should be used sensitively and since we have the same goals. In any and they are an excellent tool for teach- with care. case, the shortcomings of the TI-NCTM ing concepts and discussing how math website are hardly a reason to criticize impacts students’ lives outside of the Marion D. Cohen the show itself. classroom. University of Pennsylvania

7. Greenwald also creates a straw man Greenwald is correct that educators when she suggests that the CBS NUM- should use discretion in bringing tools B3RS website is implying that the math- into the classroom. 28,000 educators Sarah Greenwald ematics community endorses the show as and supporters around the nation have Responds: a “good tool for teaching students.” No decided the We All Use Math Every Day one is saying anything like this. NUM- program is worth signing up for. Based on B3RS doesn’t teach any math and doesn’t my district’s experience, I encourage all I am pleased that the article has re- intend to. Its goal is to show that “we all math educators to sign up at http://www. ceived so many responses. Fictional use math everyday” and that there are cbs.com/numb3rs to receive a teacher kit entertainment shows should not be people who are good at math and love and learn more about the activities for held to a role-model standard; instead, doing it. I would say that it achieves these themselves. that it is our responsibility as educa- ends quite admirably. Does anyone object tors to be proactive and carefully con- to that as a modest first step? Nancy L. Foote sider how to address the complexi- Math Curriculum Specialist ties that arise from popular culture Mark Bridger Higley, AZ explorations. How we should handle Northeastern University the topics of violence, sexuality, ge- nius stereotype, mental illness, etc.? The show, yes, but perhaps not the It works for us worksheets I hope that the deep thinking necessary to effectively use popular culture in Sarah Greenwald’s article “Complex Concerning Sarah Greenwald’s “Com- the classroom will continue to evolve. NUMB3RS” in the May issue discusses plex NUMB3RS?”: As a former home- the potential issues with using the TV schooling parent (who home-schooled show and associated classroom activi- largely because I felt that “school-type

17 FOCUS August/September 2006

Letters to the Editor look at a similar webpage hosted by our department http://www. cs.utep.edu/DeptCS/HowToGetARec.pdf. Our webpage also has More Sudoku detailed explanations of some of the requirements. By com- bining the best features of different websites, FOCUS readers I enjoyed the recent article “The Sudoku Epidemic,” and I will be able to come up with their own “Recommendation for must say that I have also been caught up in the craze. I espe- Recommendations.” cially liked the puzzle using the letters of logarithm. I enclose an alternative sudoku puzzle using the same letters. I was also Vladik Kreinovich, University of Texas at El Paso able to incorporate another mathematical term into the puzzle. [See puzzle on this page. The solution is on page 37] One More Commandment

Kory Boughton, University of Wisconsin Whitewater Yankee catcher Yogi Berra once appeared on a postgame radio interview and received as an honorarium a check for $50 writ- Puzzle ten as “Pay to Bearer.” He replied “After all these years in the league, you’d think they’d know how to spell my name.” L G Well, after 30-plus years in the MAA, may I offer as the 0-th I O T A G Commandment: “Thou shalt check the names of thy authors carefully in thy galleys.” H O I Bruce Reznick, University of Illinois at Urbana-Champaign

R M I Mea culpa, mea culpa, mea maxima culpa. Our apologies.

L M H And An Axiom

G I R I enjoyed reading the “Ten Commandments for Mathematicians” in the May/June issue of FOCUS. I wouldn’t add another com- mandment, but perhaps would suggest an axiom: “Division by G zero is the immaculate exception.”

T Keith Ferland, Plymouth State University

T H L R A G Successful ways to get students to math talks?

Do readers of FOCUS have any innovative methods for encour- Things I Learned at an MAA Section Meeting aging undergraduates to attend departmental colloquia? Our talks are aimed at upper-division mathematics and computer Here are some opinions that I heard at the Spring Meeting of the science majors (we offer degrees in both), yet even with out- Northeast Section of the MAA that may interest your readers: standing speakers and attractive topics we’re lucky to get one or two students at each talk. “You have an inalienable right to be interested in and enjoy mathematics.” — from a college Dean. For various reasons we have been reluctant to offer some credit hours for attending colloquia, as we do for our Putnam problem- “A Geek is someone with strong and possibly uncommon or solving sessions, or to require majors to write short summaries of unique interests. A Dork is someone lacking in social skills. some talks, as has been tried but with limited success elsewhere. Geeks and Dorks are not the same. It is far better to be a Geek Any suggestions that have worked? than a Dork.” — from college students. Peter Ross, Santa Clara University Randall Covill On Richard Cohen on Algebra More Recommendations on Recommendations It is very aggravating to listen to Dumbbells tell the world that Many thanks for the article in May/June 2006 FOCUS about they have lived a full life and found no use for algebra. (See the Harvey Mudd College-based webpage that helps students Short Takes in our May/June 2006 issue, page 22.) What they provide their professor with all the information necessary for a really mean is that they are too stupid to see the uses of algebra recommendation letter. FOCUS readers may also want to also which abound on every side.

18 STT-10_4.8125x9.75 11/22/05 4:36 PM Page 1 August/September 2006 FOCUS

Surveys will show that nine out of ten rocket scientists could not hold their jobs without algebra. But these writers are NATIONAL SECURITY AGENCY obviously not rocket scientists. NSA So, if the question is “Algebra?”, the answer should be “Please! Please! Pleeease!!”

Those who say that algebra does not teach us anything about ourselves should be asked: “What is there about you that anyone would want to know? Especially if you can’t or won’t master algebra?” Algebra, and the mathematics that de- rives from it, tells us a great deal about the world we live in, as any scientist will affirm. Any university professor can tell you that he has a class load of foreign students who came here to learn what we (and the West generally) has to offer: Science, Engineering, and, above all, Mathematics. I doubt that anyone would come here to learn what algebra’s critics have to offer. They can find plenty ofthat at home. Even the Third World has plenty of their kind of wisdom. James P. Coughlin, Towson University Put Your Math Richard Cohen caught off-base

When Richard Cohen’s Washington Post Intelligence to Work dig at algebra instruction appeared in the When you join NSA, you join a highly talented group of San Jose Mercury News on February 16, I wrote a brief letter to the editor which Mathematicians who deduce structure where it is not the paper then published the next day. apparent, find patterns in seemingly random sets, and Perhaps the readers of FOCUS would create order out of chaos. They apply Number Theory, enjoy it too: Group Theory, Finite Field Theory, Linear Algebra, Writer Shows Why He Flunked Algebra Probability Theory, Mathematical Statistics, Combinatorics, and more to a world of challenges. They exchange ideas Richard Cohen is a good writer, but his reasoning needs attention. He says, and work with some of the finest minds and most “Writing is the highest form of reasoning. powerful computers in the country. And you can too, Algebra is not.” In his writing, he then when you put your math intelligence to somehow blames algebra for the dismal lack of geographic knowledge exhibited work at NSA. by a student named Shelly who is a whiz at math. I can understand why he perhaps had trouble organizing his thoughts in NSA: Securing Tomorrow Today algebra class.

For more information and to apply online, Les Lange, Capitola, CA visit our Web site. www.NSA.gov/Careers WHERE INTELLIGENCE GOES TO WORK

U.S. citizenship is required. NSA is an equal opportunity employer. All applicants for employment are considered without regard to race, color, religion, sex, national origin, age, marital status, handicap, sexual orientation, or status as a parent.

19 FOCUS August/September 2006 2006 Award Winners for Distinguished Teaching

Pacific Northwest

Iowa

James Morrow University of Washington

Catherine Miller Northern California, University of Northern Iowa Nevada, Hawaii

Intermountain

Rocky Mountain

Tatiana Shubin San Jose State University Oklahoma-Arkansas

Tyler Jarvis Southern California- Brigham Young University Nevada

Barbara Moskal Colorado School of Mines

Southwestern Linda Braddy East Central University

Asuman Aksoy Claremont McKenna College

Texas

Irene Bloom Arizona State University

Stuart Anderson Texas A & M University

20 August/September 2006 FOCUS 2006 Award Winners for Distinguished Teaching

Northeastern

Wisconsin Michigan

Seaway

W. Gilbert Strang Massachusetts Institute of Robert Calcaterra Technology University of Wisconsin, Timothy Carroll Platteville Eastern Michigan University Morris Orzech Queen’s University, Ontario

Ohio Allegheny Mountain

New Jersey

Thomas Price University of Akron James Sellers Pennsylvania State University

Kentucky Indiana Southeastern

Bonnie Gold Monmouth University

Other Section Award Winners: Daniel Maki William M. Priestley (No picture supplied) J. Austin French Indiana University Sewanee Georgetown College The University of the South Eastern Pennsylvania-Delaware J. Patrick Brewer Louisiana-Mississippi Florida Lebanon Valley College

Maryland-DC-Virginia David Kung St. Mary’s College of Maryland

Missouri Timothy Ray Richard DeVault Southeast Missouri State University Northwestern State University Lubomir Markov of Louisiana Barry University 21 FOCUS August/September 2006

How to Help Your Students Get the Most Out the MCM and ICM

By Holly Zullo, Mark Parker, and Kelly Cline

Each February the Consortium for Mathematics and Its Applications (CO- MAP) coordinates the Mathematical Contest in Modeling (MCM) and the Interdisciplinary Contest in Modeling (ICM). Students from around the world compete at their home institutions in teams of three, working on an open- ended applied mathematics problem. The problems are big, messy, and not at all like a homework problem; instead, they resemble an applied research problem. Past problems have included estimat- ing the global effects of a large meteor impacting Antarctica, studying dinosaur hunting strategies, and developing meth- ods for detecting submarines in the ocean. In other words, the students spend 96 hours working on a problem that is unlike anything they have ever seen before. Steffan Francischetti, Kyle Nixon, and Ben Dunham: Carroll College’s 2006 Out- Most students have great fun with the standing MCM Team at Work. contest and learn a lot of math. Best of all, it can be a really inspiring experience. The contest gives them a chance to test The pre-contest practice sessions are task, and how to resolve the conflicts that themselves against a genuinely difficult particularly helpful in arming our stu- will inevitably arise. Last year we invited problem with no faculty training wheels dents with the skills they need in order a faculty member from Communications to help when they get stuck, giving them to make sure that this contest is a fabu- to meet with our students and work with a taste of what it is like to use mathemat- lous learning experience instead of an them on small group communication ics in a real-world situation. The model- overwhelming disaster. Teams need to skills. We found that during the contest ing contest has become one of the high be formed early and meet regularly for weekend students were much more aware points of the year for our department, practice. We try to form our teams in of the need for communication, and they luring more students to pursue majors early November and get practice sessions were actively practicing the skills they and minors in mathematics. going immediately. We generally have had been taught. five meetings, each one lasting about However, if you want this to happen, you two hours. But what should we do with One dangerous pitfall that many teams can’t just sign up a few bright students our ten hours of practice time? First we face is that when a disagreement comes and throw them in the deep end, hoping need to recognize what skills are needed up, they vote, two students on one side, that things will turn out well 96 hours for this contest. We break these skills one student on the other, the majority later. Your students will be much more into three categories: communication, rules and the thoughts of the third student successful if you can provide support problem solving, and writing. are ignored. Several times we have seen by helping them form teams, running a team member frozen out who then feels practice sessions prior to the contest, Communication disenfranchised and left out. Instead, and then making sure they have what students need to be told right from the they need during the contest. We provide Although students may have experience beginning that voting is off the table, each team with a room of their own on working on group projects, it is likely and that all decisions need to be made campus (an NP-hard task considering that that there is nothing in their backgrounds by consensus or not at all. If there’s a the contest runs through both a Friday that has come close to preparing them 2–1 split then they need to sit down and and a Monday). We make sure that they to work with two other people on one talk things through, and the two need to have computers and internet access. We project for 96 straight hours. They need listen very carefully to the thoughts of even provide food, munchies, and caf- to learn how to be sure that everyone’s their teammate, to understand where he feine to help fuel them through those ideas receive proper consideration, how or she is coming from, and to figure out late nights. to keep everyone busy with a valuable what they are not seeing.

22 August/September 2006 FOCUS

It’s also important to remind the students their solution process. Although they are to spend time listening very carefully to able to solve the problem in about five all of their teammates. The most talk- minutes, most have trouble completing ative person usually ends up being the the writing in the allotted 30 minutes. team leader, and more quiet students are They learn a lot about how to write as ignored. However, being talkative has a team, but even more importantly, they little to do with intelligence, and some learn how long it takes to write about very smart people are quiet and perhaps even a small amount of work. We always shy. Students need to listen, to make are given the details about how much encourage students to begin writing sure that everyone is participating, and coal the tipple can hold, how much time almost immediately during the contest, if someone on their team isn’t speaking it takes to the load the tipple, how much and to cease all work shortly after the up, they should specifically ask for their the trains can hold, and the relevant costs halfway point and devote all their energy teammate’s opinion. involved. to writing up their results.

Problem Solving The students must determine the number The MCM provides a great opportunity of crews to have on duty to load the tipple for students to challenge their skills in MCM problems are big, and the students and the average monthly costs. Last year, mathematics, teamwork, and mathemati- need help managing problems of this after 30 minutes of brainstorming and cal writing. They will get the most out magnitude. They need to learn a mod- work, our students developed initial mod- of this opportunity if they have some eling process where they take a large els that assumed all days were equivalent preparation and advance practice with problem, make simplifying assumptions and that the three train arrivals were de- their teams. In the end, whatever their to develop an initial model, and then relax terministic and evenly spaced throughout rankings are, we want the students to feel assumptions to develop more realistic the work day. Next, the teams planned satisfied with the work they did during models as time permits. to incorporate some form of probability the weekend, and to come away more ex- distribution into their models and account cited about the power of mathematics. We use about half of each practice session for the non-homogeneity of the work to have our teams carefully look at past days. This exercise of creating a mini- For more information on the MCM/ICM, problems. Our standard exercise has been mal model seemed to help the students see http://www.comap.org. For more to hand out a problem from a previous quickly get started during the contest. information about the MCM/ICM at year and have each team read the problem Carroll College and our preparation, see Writing statement carefully, brainstorm ideas, and http://www.carroll.edu/~mparker/mcm. then outline their solution strategy. This html. can be very useful, because it gives the The end result of this contest is a writ- students a sense of what to expect, as well ten paper that is submitted for judging. Holly Zullo, Mark Parker, and Kelly as a little practice in how to get started. Students tend to greatly underestimate the Cline teach at Carroll College in Helena, However, these sessions often result in time necessary to prepare this paper, and Montana and have been involved in the a laundry list of minutiae that could be they sometimes flounder when it comes Modeling Contest for the past eleven important to the problem, without settling to writing as a group. Often a team will years. on any particular starting point. do some really good mathematics, but not put nearly enough time into writing the paper, resulting in something barely The COMAP Undergraduate To avoid this trap, we now send students Modeling Contests off with a problem and a goal of finding coherent. Also, the writing should be as a very simple model for the situation. collaborative as possible, and every team member should read and try to improve Rather than wandering around all the he Mathematical Contest in Mod- possible complications of a problem, we every word in the paper. A team that di- T vides up the sections of the paper and then eling (MCM) challenges teams of stu- want them to focus on the bare minimum dents to clarify, analyze, and propose details and simplifying assumptions. blindly combines them together at the end will rarely turn in a lucid document. solutions to open-ended problems. The Once they have a very simple model, contest attracts diverse students and fac- they can decide what complicating factor ulty advisors from over 500 institutions would be added next. It is not easy to convince the students to set aside enough time for the writing part around the world. of the contest. We can talk at them all we Last year, we gave students the Coal The Interdisciplinary Contest in Tipple Problem (MCM Problem B, want about writing, but in the end they have to experience it first-hand to get the Modeling (ICM) is an extension of 1993). In this problem, students are asked the Mathematical Contest in Modeling to analyze the operation of a coal tipple point. To provide them this experience, we give the students a simple optimiza- (MCM) designed to develop and ad- which is used to load coal trains. Three vance interdisciplinary problem-solving trains arrive stochastically throughout tion problem from first-semester calcu- lus, and we ask them to solve the problem skills as well as competence in written each day, with a high capacity train ar- communication riving on Thursdays, and the students and write a paragraph or two describing 23 FOCUS August/September 2006 Teaching Time Savers: Style Points

By Michael E. Orrison

When I began as an assistant profes- As a bonus, I was also saving about two meeting a few years ago, many of my sor, I had a pretty good sense of how minutes per exam. With sixty or so stu- colleagues decided to make Style Points much time it would take for me to prepare dents in my two sections of the class, the a part of their exams too. Most of my for each class. After a few conversations savings quickly added up. advanced students have therefore already with my new colleagues, I even had a been thinking about their mathematical good sense of how much time I should I now use Style Points for all of my writing style for several semesters. This, devote to tasks like office hours and com- classes, but I occasionally vary the setup. of course, gives me even more time to mittee work. Somewhere in the middle of For example, in my advanced courses, enjoy reading what they write in my grading my first exam, though, it became my students can no longer gain Style course! painfully clear that I had underestimated Points — they can only lose them. I the amount of time I would need to grade should point out, however, that it has Time spent: about 5 minutes in one class exams! been several semesters since any of my period to explain how Style Points can be advanced students has actually lost any gained (or lost) on your exams. It was (and still is) important to me that Style Points. This used to surprise me. my students felt my exams were fair, Then I remembered that, after sharing Time saved: about 2 minutes, on average, both in how they were written and in the idea of Style Points at a department for every exam you grade. how they were graded. I tried to create exams that gave students ample opportu- nity to demonstrate their mastery of the course material, and I genuinely looked forward to reading their responses. By the end of that first semester, however, I felt certain that I was spending too much time and energy simply trying to navigate each exam. For example, I was having a hard time deciding what was or was not scratch work.

The next semester, as an experiment in my multivariable calculus course, I re- served five of the 100 points on the first exam for what I called “Style Points.” I told the students that I expected almost everyone to receive all five points. I also told them that if I had to reread a solution several times to find a train of thought, or if a solution was illegible, ambiguous, or incoherent, it would affect their Style Points, and that they should therefore give some thought to how they presented their work.

The result was dramatic. Without much work on my part, most solutions on the exam seemed to have a beginning, middle, and end. In fact, most solutions Teaching Time Savers are articles designed to share easy-to-implement activi- actually seemed to flow (more or less) ties for streamlining the day-to-day tasks of faculty members everywhere. If you with direction and purpose. This helped would like to share your favorite time savers with the readers of FOCUS, then me give more honest and focused feed- send a separate email description of each activity to Michael Orrison at orrison@ back. In addition, the mere presence of hmc.edu. Make sure to include a comment on “time spent” and “time saved” for Style Points led to lively and worthwhile each activity, and to include pictures and/or figures if at all possible. discussions about the importance of good writing, regardless of one’s field of study.

24 August/September 2006 FOCUS What I Learned from… Teaching with Technology By Meighan Dillon

When I went to work at a college folks went all out technically, they used It was no surprise that the students appre- that used scientific calculators in its core overhead projectors. They never talked ciated internet access in class to a fault. mathematics curriculum in 1992, I bit about electronic gadgetry to facilitate the Maybe it was so exasperating because I the bullet and learned my way around presentation of mathematical ideas. They was the one supplying them with elec- the little machine. I did not particularly did talk a great deal about mathematics. tronic dope. like teaching with the calculator, but For their own onerous calculations, they thought it better to lead rather than fol- used software, in private, with profi- Have I abandoned technology in teach- low in the effort, lest someone force ciency and abandon. ing? That would be neither possible nor me, blind, down an unfortunate path. desirable. The TI-89 is still required in Towards that end, I became a technol- Teaching there was at once ludicrous and all our precalculus and calculus courses; ogy leader in the department. Five years revelatory. It seemed absurd to teach dif- I use it happily but sparingly. The now- after starting at the college, I was at the ferential equations without an easy way elderly big-screen computers in our class- vanguard of the effort to integrate the to show slope fields in class, for instance. rooms get a regular workout in my hands TI-89, a calculator with symbol ma- As I struggled to learn new mathematics for demonstrations in class. Animated nipulation capability, into our curriculum. myself in courses and seminars, though, and interactive graphics that depict de- I felt my own engagement reenergize my rivatives, intersecting cylinders, and the Using the TI-89 was a big change, but teaching. I started thinking I had spent Frenet basis moving along a space curve, students and faculty adjusted. In the too much time fussing with toys and not for example, have become invaluable to meantime, I embarked on an ambitious enough time growing mathematically. me over the years. program of professional development My enthusiasm for the integrated class- that went way beyond calculator tech- room project waned. My evolving opinion is that technology niques. I learned web page design and should occupy a small but important built up a collection of devices for class- Enthusiasm waxed anew when I returned place in teaching and learning mathemat- room demonstrations. I made slide shows to my home institution and saw my new ics. The details of its role should depend with PowerPoint, exploiting its animation classroom: a modern computer with a on the students and instructors using it. capabilities. I used web sites in class two flatscreen monitor for each student, a Technology as an aid to learning math- or three days some weeks. Smart Board for me. Tables and chairs ematics is ineffective with students who were arranged to foster interaction among are reluctant to acquire basic computa- My enthusiasm for technology in teach- students and a fluid shift of their atten- tional skills. They lack the firepower for ing escalated beyond an approach into a tion from the Smart Board, to print, to precise mathematical thinking required to pair of grant proposals. The first project software, to the blackboard, to the TI-89. interpret calculations done by machine. was a plan to overhaul calculus and dif- After a few weeks of teaching this way, Instructors loathe to familiarize them- ferential equations emphasizing project I went to a conference and reported with selves with technology as an aid to teach- work and deemphasizing calculations. It proselytizing zeal about interactive learn- ing should be encouraged to overcome was funded at the state level. The second ing, access to the best of what’s out there, their aversion, if only because it is better project was a plan to retrofit a classroom students putting their hands on applets to make an informed decision. I doubt that would put computers in the students’ under my gimlet gaze. that the impact of technology on learn- hands. It was funded at the federal level. ing is so dramatic as to warrant forcing Thus was born the Integrated Classroom Sometime in the middle of the next year, the issue, though, especially with faculty for a Blended Approach to Course De- I unplugged the computers. The students members who are engaged mathemati- livery. quickly realized they had to pounce on cally. The same could be said of students the plugs the first time my back was who dislike using calculators. Is there a The year of the grant proposal was also turned so they could still check email and sound pedagogical reason to press the use the year I spent at a research depart- surf the web in class. Next, I unplugged of calculators on these students? I doubt ment at an engineering institute of some the cables connecting monitors to CPUs. it. Make them aware of what technology renown. In the small, underfunded col- The more intrepid students developed can do, but let them study mathematics lege, we had classrooms equipped with proficiency working plugs and pins be- while they have the chance. large-screen computers and web access hind my back, and still managed to surf for demonstrations. In the big-time en- the web in class. That semester ended, Meighan Dillon’s web page at http://math. gineering institute, they had classroom and I bolted the door to my room and the spsu.edu/dillon/nsf.htm links to most of hook-ups for laptops that no one seemed blended approach, tired of vying with the the electronic materials she uses in her to use. The effect was almost comically machines for control of the students’ at- classes. low-tech. Visiting speakers with laptop tention, and with the students for control presentations were anomalous. When of the machines.

25 FOCUS August/September 2006 The Open Source Revolution

By Jeff Suzuki

Computer Algebra Systems (CAS) and Dynamic Geometry Software (DGS) are powerful methods of investigating mathe- matics, but institutional licenses for Mathematica or Geometer’s Sketchpad can be quite expensive. Graphing calculators with CAS and DGS software exist, at a cost of a few hundred dollars. Does this mean CAS/DGS will only exacerbate the gap between rich and poor institutions? Not at all: those on more modest and realistic budgets can turn to open source software.

“Open source software” is software whose code is freely avail- able for anyone who wants to examine and modify it. For the computer gurus this means that if they find a bug in the program, they can fix it; if they decide the program needs additional features, they can add them. Periodically, these changes are collected and a new version of the software is released. Figure 2 Graphs in Maxima

The main implication for non-programmers is that open source software is free, since there is no reasonable way of apportion- ing profits among the programmers. Unlike “free” or “student” versions of proprietary software, there is no functional differ- ence between versions. For mathematicians, the open source model has another advantage: proprietary software is a black box that delivers answers with no means of verifying their validity. Open source CASs have their source code available for examination.

Do you “get what you pay for?” In some cases, yes. But in many cases, open source software is as good (or better!) than proprietary equivalents. For example Open Office includes word processing, spreadsheet, presentation, and drawing software that rival (and in some cases, surpass) their commercial equivalents. Mozilla and Firefox, popular web browsers, are open source, Figure 3: 3D Graph as is the Linux operating system. Those who work on open source software do so because they enjoy it, and not because Maxima of the monetary rewards; in that sense, being an open source programmer is a lot like being a teacher! Open source CAS include CoCoA, done by a group at the University of Genoa; Eigenmath, a limited but easy-to-use system for algebraic operations; and Maxima, a general purpose CAS. Maxima was one of the first CAS being developed in the 1960s at MIT under the name Macsyma; it has been open source since 1998. Some examples of Maxima in action are shown in Figure 1.

While Maxima does not display math as cleanly as the current version of Mathematica, in terms of functionality and ease of use, it rivals its proprietary competitors. The main limitation of Maxima is that while it can graph several functions on the same graph (and its 3D graphing capability is excellent and allows “point and drag” manipulation of the graph to view it from dif- Figure 1: Maxima Commands ferent perspectives), it does not seem possible to display more than one graph simultaneously. In fact, if you have it display a

26 August/September 2006 FOCUS graph, execution of a sequence of statements pauses until the More information about the ideals and implementation of the graph window is closed (Figure 2 and Figure 3). open source movement, including the the GNU general public license that applies to many open source packages and links to GeoGebra many of them, can be found at the GNU web site.

Open source DGS includes C.a.R. (“compass and ruler,” the Jeff Suzuki ( [email protected] ) is an Associate Professor English version of Z.u.L), KSEG, and GeoGebra, my own fa- of Mathematics at Brooklyn College. His interests include the vorite. GeoGebra was developed by Markus Hohenwarter and history of mathematics, integrating technology into the cur- Yves Kreis, and is hosted at the University of Salzburg. It is riculum, and songwriting. available in several languages (including German and Austrian). Like Maxima, it is comparable to its proprietary competitors.

GeoGebra has a built-in Cartesian coordinate system, and ac- cepts both geometric commands (drawing a line through two Web Addresses: given points) and algebraic ones (drawing a curve with a given equation). Among its more interesting features is the ability to Open Office: http://www.openoffice.org draw tangent lines to algebraic and even transcendental curves at given points (Figure 4). You can also export your dynamic Mozilla: http://www.mozilla.org geometry construction as an interactive java applet to embed Firefox: http://www.firefox.com/ in a web page (See figure 5). Linux: http://www.linux.org CoCoA: http://cocoa.dima.unige.it Eigenmath: http://eigenmath.sourceforge.net Maxima: http://maxima.sourceforge.net C.a.R.: http://www.z-u-l.de KSEG: http://www.mit.edu/~ibaran/kseg.html GeoGebra: http://www.geogebra.at

GNU: http://www.gnu.org

Figure 4: Constructing an Advanced Locus

Mathematical Imagery at the AMS

The American Mathematical Society has created a Mathemati- cal Imagery web site, located at http://www.ams.org/mathim- agery/. “The connection between mathematics and art goes back thousands of years,” it says. “Mathematicians and artists continue to create stunning works in all media and to explore the visualization of mathematics — origami, computer-gener- ated landscapes, tesselations, fractals, anamorphic art, and Figure 5: Interactive Web Page more.” The site includes a large collection of images that can be viewed and even sent to friends as e-postcards. It also includes links to galleries, other web pages, and articles about art and mathematics.

27 FOCUS August/September 2006 Advertise! Two consecutive Fibonacci numbers are the worst case scenario for Euclid’s algorithm. Consecutive Fibonacci numbers also By Richard Ehrenborg appear when counting spirals on pineapples and pine cones. What do These days it is not enough to teach interesting courses. We also cicadas have to attract students to take our courses. Even more so, we have know to attract and retain students in the sciences and in mathematics. about prime I have been teaching a junior level course called Applicable numbers? Algebra at the University of Kentucky. The course begins with elementary number theory in order to cover topics in- Assume that the cicadas appear every n years. A preda- cluding RSA, primality testing and factoring large integers. tor that appears every k years, where k is a divisor of n, The course then continues to discuss polynomials in order to can happily eat away. Hence the fewer divisors the period introduce finite fields and turn the attention to error correct- n has, the more likely the cicada population will survive. ing codes, such as BCH codes. The course focus is on the Prime numbers provide the minimum. See the article by applications and how the mathematics supports them. The Meredith Greer in the February 2006 issue of FOCUS. course aims to make mathematics appealing to the students. The goal is twofold: First, to encourage students to major in Fermat mathematics; second, to attract students from other majors, thought such as computer science, to double major in mathematics. 4294967297 How does one get the word out to potential students? Ad- was vertise! Inspired by the NSA advertising campaign to hire prime. mathematicians, I made a collection of posters. I handed them He out to interested students and posted them around campus. was wrong.

Here are the posters and some short explanations and refer- 2 5 2 1 ences. The number in question is + Euler showed that 641 is a prime factor. There is a nice way to do this using the fact that Shuffle a deck of cards 641 = 27 x 5 + 1 = 54 + 24. eight times. Do it perfectly each time. How did Then you are back to the where you started. twin primes Nice card trick. 824633702441 Why does it work? and If you are curious, take 824633702443 CS 340/Math 340 improve Spring 2006 your Pentium chip? The perfect shuffles mentioned here are out-shuffles, that is, the top card stays on the top. For a deck with an even number n In the computation of Brun’s constant, Tom Nicely dis- of cards, label the positions 0 through n–1. Now a perfect out- covered that the Pentium chip could not divide. See shuffle brings the card in position x to position 2x (mod n–1). the nice article byBarry Cipra in What’s Happening in So what we need to verify is that 28 is congruent to 1 (mod 51). the Mathematical Sciences 1995–1996, pages 38–47.

How do Why pineapples is relate the inequality 2 to the ln((lcm1,, 2 …,) n –n ≤ n() ln()n greatest for n at least 100 common divisor? worth If you are curious… $1,000,000?

28 August/September 2006 FOCUS

This inequality is equivalent to the Riemann Hypothesis, something that we all should care about. How do you send How are pictures an old Greek, from Mars a French lawyer and over a Swiss man noisy channels involved in and still you sending get your credit card number a clear picture over to give the internet? to CNN? Fermat’s little theorem and Euler’s theorem are the basis of The answer to both of these questions is error correcting codes. RSA, the first public key crypto system. Euclid also belongs It is amazing that your CD-player can lose 2.5 mm of track since his algorithm allows us to find the decoding exponent and you will not hear the difference. Also note that NASA put from the encoding exponent and the secret factorization. high resolution cameras on the two Mars rovers in order to make both scientific observations and good PR for themselves. Your friend (?) claims that 34034065601122854197959819122215174693 The is a prime number. NEW How do you engineering prove her/him MATH: wrong? error correcting codes and Primality testing is important when you need primes for your public key cryptography. own RSA crypto system. These topics are what we mathematicians should be teaching What is the probability our computer science and engineering students. that two people in this room have the same There are three people. birthday? On each person we put either What does this a blue or red hat. have to do Each person can see with the color of the hats of the other two. factoring At the same time they have to guess LARGE numbers? the color of their own hats. If any of them is wrong, they lose. For a year with P days and about persons, the probability is If at least one of them is right they win about ln()4 P fifty-fifty. This fact is used to show that the $1,000,000. 1/2 Pollard Rho factoring method will factor a number N in O(P What is their best strategy? ) ≤ O (N1/2) steps, where P is the smallest prime factor of N.

This hat problem is related to Hamming codes, the first known How come class of error correcting codes. See Mira Bernstein’s article in the your cat November 2001 issue of FOCUS or the article by Joe Buhler, “Hat can scratch Tricks,” in the Fall 2002 issue of The Mathematical Intelligencer. your favorite CD Fun and interesting advertising is one way to attract more stu- and dents to our classes. Finally, recall what Oscar Wilde wrote in still The Portrait of Dorian Gray: There is only one thing in the world it worse than being talked about, and that is not being talked about. sounds great? Richard Ehrenborg is Royster Research Professor at Uni- versity of Kentucky. He can be reached at [email protected].

29 FOCUS August/September 2006 AP Calculus: Friend or Foe?

By Susan Schwartz Wildstrom

It is often argued that there is a “rush taught. Later, when a clever student offers In some textbooks, complex numbers are to calculus” in the school curriculum. an unusual approach the most common taught before simplification of radicals. Students, teachers, and everyone else teacher reaction is to say “No! That is Current algebra (1 and 2) textbooks no act as if learning calculus was the goal not the way I taught it.” While teachers longer contain an important theorem of school mathematics. Along the way, should be wary of “dumb-luck” methods that appeared in every algebra text- other things might be neglected, leaving of getting an answer, they should also book when I started my career in 1969: students without a good foundation for examine them carefully enough to assess ab =a ⋅ b if and only if a, b ≥ 0. future courses. Is AP Calculus a friend if they are in fact valid. And, if the alter- Are we surprised, then, that students or a foe? natives are valid, teachers should strive who learn about complex numbers be- to understand how the alternate processes fore simplifying radicals give us bizarre It is not the rush to calculus that has work and even try to incorporate them as negative or complex valued answers for weakened the preparation our students a part of their future teaching. problems that should be straightforward? have for doing advanced (never mind Several years ago, two colleagues who advanced, any) mathematics. Rather, this Since the mid-1980s, I have argued for were teaching Algebra 2 in my school is the result of the weaker preparation of math specialists in every elementary came and asked me why a student teachers who serve our elementary school school. No school would be without a couldn’t claim that 36 = – 6 by argu- students and the dilution of the cur- reading specialist, why not a math spe- ing as follows: riculum of the other high school courses cialist too? Some of the services that this (algebra, geometry, precalculus). The person could provide include information 1989 standards emphasize relevance, use about multiple methods for teaching a of real-world data, data collection, data concept, remediation for students who analysis, and technology (replacing drill are having difficulty mastering a concept, My answer to them was to state the and practice). Pursuing these goals has enrichment for students who are ready theorem about the values having to be taken a lot of class time away from the for extensions of grade-level concepts, non-negative, but when we looked at the teaching of solid mathematical processes teacher encouragement, support and in- book we were using as a textbook, it was including algebraic operations and equa- service training. nowhere to be found. I pulled out an older tion solving. (1960s or earlier) text and, naturally, Then there is our actual high school cur- there it was. Alas, these days students Let’s start with elementary school. If stu- riculum. Its organization seems to waste getting teaching certification for grades dents could complete elementary school a lot of time teaching mathematics as just 7–12 may have had a topology course with a mastery of the basic operations for so many individual isolated processes, (not part of my math major in 1969), but whole numbers, decimals, and fractions, unrelated one to another. Students end may not realize that if then their middle and high school experi- up wasting a lot of their effort learning and only if a, b ≥ 0. ences could be more productive. these concepts in isolation. When stu- dents actually do see the connections of All students now seem to have the I believe that children arrive in school processes to one another, they are able technology — a graphing calculator is as eager learners. We can encourage or to learn more quickly and easily because a standard requirement for most high discourage them by our attitudes and their understanding of earlier concepts school classes — but they seldom un- enthusiasms. The classroom teacher is can be brought to the new ones. derstand how to use it judiciously. They a major force influencing how and what will turn it on to compute 9 x 5 yet they these students learn. If the teacher con- Students (sometimes) learn, for example, will return from the AP exam and ask veys the impression that math is hard, to factor quadratic polynomials. They me how they were supposed to find the we should not be surprised that students learn to solve quadratic equations us- point of intersection of f(x) = 3x2 + 2 and internalize that attitude as well. (If the big ing the quadratic formula. They learn g(x) = cos x . person can’t do something, how could to graph quadratic functions on their little old me do it?) calculators. It is surprising how many of A friend and colleague of mine, who also them do not realize that setting a factor taught calculus for many years, used to I fear that many elementary school teach- to zero and solving produces the same wonder why we taught calculus concepts ers have not been required to take enough value that the quadratic formula does and in algebra 1 and 2. (Our school system mathematics to actually understand clear- that that very value is the x-coordinate of has units on functions in the algebra ly how the mathematics works. They may the point where the graph is crossing the course; they seem to leave the kids more have taken methods courses in which just x-axis. Does this make sense? bewildered about functions when they one way to do a particular operation is are done than when they started. These

30 August/September 2006 FOCUS units include the notions of increasing, are likely to be well-served. If the course taking AP Calculus? Probably not. But, as decreasing, and continuous functions; we offer in high school (which is likely to I try to do, we should be looking at these they also discuss maxima, minima, meet five days a week for forty-five min- people carefully early in the year, and if end-behavior, etc). If we were using the utes a class and for 36 weeks — I suspect we see that they are too poorly prepared time we spend on those ideas to teach that “block scheduling” is another fad to succeed even with the extra algebraic polynomial operations, factoring, solving that will eventually be cycled back out support that we offer in the course, we equations, deeper understanding of these of schools) involves filling in the algebra should try to have them take a course that ideas and how they actually connect to and geometry gaps that are left by what I is more likely to help them build up the one another, I believe the time would view as an inadequate curriculum, and if needed strength. In my school (and many be better spent. In calculus we teach the course takes the time to explain not others, I believe) we offer a non-AP, non- these concepts (increasing, decreasing, just how to get answers but what we are rigorous, “Calculus with Applications” continuity, end behavior, maximum and doing and why it works, then the students class that helps students learn “how” to minimum values) again, and I am not will arrive in math departments at univer- take derivatives and such while spending convinced that the students grasp them sities ready for more advanced work. an even greater amount of time building more quickly because of the earlier ex- the algebraic and trigonometric skills posure. Maturity matters more. The AP test does seem to do a fairly good and understanding that is lacking. These job of detecting whether the test takers students can enroll in Calculus 1 at their I don’t like having to stop in the middle have some understanding of what calcu- colleges with stronger basics and an in- of a calculus lesson to teach factoriza- lus is about or not. Thus, students who troductory sense of the major concepts of tion of quadratic functions, why setting score 4 and 5 seem to be demonstrating calculus. They can, if they will, use this a factor equal to zero produces a root, a readiness for college mathematics. I am computational knowledge of limits, de- and so many other topics that I always not sure whether a 3 should still qualify a rivatives and integrals to help them take considered basic ideas of elementary student to advance to a second semester the time to learn more about the concepts algebra. I believe my calculus students course without additional proof of com- that underlie these processes, and they too would have a far easier time learning petency (perhaps the new MAPLE/MAA should be able to be successful in future the difficult calculus notions if we didn’t placement materials could serve that mathematics courses. have the mid-topic distraction of having function), and I am certain that scores be- to review an algebraic step that is needed low 3 give evidence that a student should Susan Wildstrom is the MAA Gover- to complete a process. plan to retake calculus to build the depth nor-at-Large representing High School of understanding that isn’t yet there. Teachers. This article is based on a pre- I do believe that those students who sur- sentation given at a Joint Mathematics vive calculus in our high school classes Should we be discouraging students from Meetings special session entitled “AP Calculus: Friend or Foe?”

In Memoriam Karen Dee Michalowicz (1942-2006)

By Victor Katz

Karen Dee Michalowicz died on July high school teachers of mathematics, chapter on “History in support of diverse 17, 2006 at the age of 63. She was a na- who produced such a large amount of educational requirements — opportuni- tionally recognized mathematics teacher material for teaching mathematics us- ties for change”. Over the years, she had at the Langley School in McLean, Vir- ing history that the MAA was forced to amassed a huge collection of mathemat- ginia, having received the Presidential publish it as a CD. In 1998, she was also ics texts from the nineteenth century and Award for Mathematics Teaching in invited to participate in the study group earlier, a collection whose contents she 1994. Karen was especially interested on History in Mathematics Education, enthusiastically shared with students in the use of history in the teaching of organized by the International Commis- and colleagues in many presentations at mathematics. In that role, she co-directed sion on Mathematical Instruction. After national and international meetings. She the NSF-sponsored, MAA administered an intensive week of discussions, the will be greatly missed by her numerous grant program, Historical Modules for group ultimately co-authored the ICMI friends and colleagues in the MAA, the the Teaching and Learning of Mathemat- Study, History in Mathematics Educa- WME, the NCTM, and the Benjamin ics, beginning in 1998. That program tion, which appeared in 2000. Karen Banneker Association, among others. involved about twenty-five college and was in charge of the group writing the

31 FOCUS August/September 2006 MAA is Seeking a Associate Director for Student Activities

The Mathematical Association of prehensive collection of web-based government, and others who appreciate America (MAA) seeks an Associ- resources for students, and work with mathematics. ate Director to oversee a wide range other MAA staff and member volun- of activities for both undergraduate teers to build an MAA student website Applications will be accepted and re- and graduate students and to develop that will be the primary web destination viewed as received, but it is expected new initiatives to advance the MAA for students of mathematics at the un- that the position will begin July 1, 2007, in the area of student services and dergraduate and graduate levels. though a January 2007 start date will be programs. considered. The position is located at The Associate Director for Student the national headquarters of the MAA The Associate Director will provide Activities will report to the Director of in Washington, DC. Salary will be both programmatic and administrative Programs and Services. The success- based upon the candidate’s credentials supervision to ongoing activities, such ful candidate will have an advanced or current salary for a reassignment as the MAA Student Chapter Program, degree in one of the mathematical sci- position. The MAA offers a generous undergraduate student paper/poster ences, and experience working with benefits package. sessions and poster sessions and work- students both in and outside of the shops for graduate students at national classroom through math clubs and/or Candidates should send a resume and meetings. Working with the Committee mentoring undergraduate research. letter of interest to: on Undergraduate Student Activities Experience using on-line instruction or and Chapters and the Committee on development of web content is a plus. Ms. Calluna Euving Graduate Students, the Associate Di- Though this is a continuing position, Chief of Staff rector will seek to identify successful we welcome applications from faculty Mathematical Association of America programs currently in place in MAA’s members who wish to take a leave of 1529 18th Street, NW Sections that are suitable for expan- absence from their current position. Washington, DC 20036 sion, and develop new programs such as establishing a national network for The mission of the MAA is to advance Applications may be submitted elec- student chapters. the mathematical sciences. The MAA, tronically to [email protected]. Refer- with almost 30,000 members, is the ences will be requested after review of The Associate Director will oversee ex- largest professional association with a applications. Applications from indi- ternally-funded programs for students focus on mathematics that is accessible viduals from underrepresented groups and will develop proposals to continue at the undergraduate level. Membership are encouraged. Additional information existing programs and to establish new includes college and university faculty about the MAA and its programs and programs. The Associate Director will and students, high school teachers, in- services may be found on MAA’s web- lead MAA efforts to develop a com- dividuals from business, industry and site: http://www.maa.org. AA/EOE. Measuring The Perception of Leadership

By Randall J. Covill Euclidean distance between rankings can Note that although the leadership attri- be calculated and the SIAM algorithm bute scores themselves are subjective, What does mathematics have to do for efficiently finding the median of a calculation of the sums of distances with leadership? Quite a lot, in the sense set of multi-dimensional data points can between scores is not subjective. The that mathematics can be used to mea- be used to identify the median or central calculations are based on very basic vec- sure public perceptions of the presence member of a group of leaders. tor and Euclidean distance calculations. of leadership attributes. I was recently What was the value of measuring lead- reminded of this while reading a book I tried this with the following data set: ership attributes in this fashion? In my on leadership attributes and an article in opinion, such measurements demonstrate the SIAM Journal on Optimization about 1 ,2, 3, 4, 5 that public perceptions of leadership can efficiently finding the median or centroid 1, 2, 2, 2, 5 be quantified, ranked, and used by the of a set of multi-dimensional data. 2, 1 ,3, 4, 5 public to identify extreme and centrist 5, 4, 3, 2, 1 leaders. According to the book on leadership, 5, 4, 4, 4, 1 common leadership attributes include Randall Covill’s life has truly been a respect for others, a willingness to re- I found that the median was the leader journey, not a destination. His academic ciprocate, shared experiences, trust, and with attribute rankings 1, 2 ,3, 4, 5 and background includes degrees in computer mutual fun. It occurred to me that mem- the smallest possible sums of distances science, finance and business, law and as bers of a group can be ranked in terms to other data points is 16.1. soon as he finishes his current studies a of the extent to which they are perceived masters degree in quality assurance and as displaying leadership attributes. The regulatory affairs. 32 August/September 2006 FOCUS

Travel to the land of the Ancient MAYA On the MAA’s 5th MATHEMATICAL STUDY TOUR December 26, 2006–January 2, 2007

Full details, itinerary, and application, CONTACT INFORMATION are available on MAA Online Lisa Kolbe (www.maa.org). Development Manager, MAA [email protected] COST $2,310 per participant 202-293-1170 COST SAVING OPTION Share a room with another participant and pay $2,160

Cost does not include airfare. Number of travelers is limited to 30. The Mathematical Association of America 1529 18th Street NW Washington DC 20036 www.maa.org

33 FOCUS August/September 2006 College Algebra Redesign at Louisiana State University

By Lawrence Smolinsky, Phoebe Rouse, George Cochran, Jimmie Lawson

LSU is restructuring its precalculus and other introductory by the Pew Charitable Trusts. We often consulted the PCR mathematics courses with a variety of changes in delivery. In alumni schools, particularly the University of Alabama and the this article we consider one aspect of this new structure, which University of Idaho. gave us an opportunity for a large scale comparison involving 2500 students using three delivery systems. As part of our transition away from the old system, we offered College Algebra in three formats in the fall of 2005: the tradi- Part of the motivation for restructuring these courses was to tional format, a 175 student large-lecture format with computer direct resources to the place where they were most appropriate. support, and the R2R format. The latter two formats both used Redesigning College Algebra is one part of a larger plan. Other MyMathLab software and required both computer homework introductory courses have also changed; the graduate program and computer quizzes and testing for all assessments. Exact was expanded; the tenure-track faculty expanded; additional answers were required for the computer assessments. In the opportunities for undergraduate research were created; and traditional format, sections were administered in the same man- a new partnership was formed with an LSU interdisciplinary ner as they have been for the last twenty-five years. Individual institute, the Center for Computation and Technology. teachers wrote (with the guidance of the course coordinator) and graded with partial credit, each of the assessments. Stu- Each course change required effective ways to use technology dents met with their teacher for three class periods. Graduate and a reconsideration of the division of labor and the use of students, some of whom had experience teaching the course in our resources. For College Algebra, we had a few instructors previous semesters, taught these sections. The enrollment (after whom we consider star teachers of pre-calculus — popular with the initial add/drop period) was 743 students. In the large lecture students and believed to be very effective — but not enough of format, students met with their teacher for three class periods these teachers to cover the large enrollment of our introductory and had computer assignments. Sections were initially capped courses. These exceptional teachers can do an effective job in at 175 students each. Students had required computer-based large classes of up to 200 students, but we believe that large homework, quizzes, and tests. The star college-algebra instruc- classes are not appropriate for graduate students to teach and tors taught these sections. The enrollment was 841 students. In so we looked for alternatives. the R2R format, students met for one period with their teacher in a classroom initially capped at 44 students. They were also required to spend a minimum of 2 flexible hours each week in the LSU Math Lab. A 200-point, common, group-graded final exam was given to all the students at the conclusion of the course. Since students had taken different sorts of exams all semester, some students were going to be at a disadvantage on the final. The final exam was in the traditional style, i.e., hand written with partial credit.

Prior to 2004, College Algebra was taught in high-school style classes of approximately 44 students each. Classes were taught by instructors who were non-tenured teaching faculty with master’s degrees or by graduate students. The department is now moving toward a computer-based system that requires more of the individual student but offers extensive support. The state, the university, and the students have made a one-time invest- ment of over 1.1 million dollars in a large teaching laboratory (the LSU Math Lab) to supplement the new system. Tutors are available in the lab 60 or more hours per week to answer any questions students have on an individual basis. The new system Man plans, God laughs. When the second week of classes was is part of a US Department of Education FISPE funded program to begin, Hurricane Katrina struck. Many LSU students were call the Roadmap to Redesign (R2R), which (for mathematics) directly affected. Many of the students’ families lost their homes. involves universities, colleges, and community colleges in a Some temporarily moved into the dorms with their children. project of pre-calculus redesign. The predecessor to R2R was When College Algebra students were surveyed at the end of the the Program in Course Redesign (PCR), which was sponsored semester as to whether they were directly affected by Katrina,

34 August/September 2006 FOCUS

half answered “yes,” and many in especially large handwrit- Table III shows the comparison of the median of the final ing. Classes were disrupted, but the R2R sections were most exam medians for all sections of the course taught by instruc- affected. The university used the R2R lab as a registration center tors compared to the median of the final exam medians for all to register 3000 visiting students from New Orleans schools. sections of the course taught by TAs in the fall of 2001-4 using The R2R students were moved to another temporary facility the traditional approach and in the fall of 2005 using the R2R or worked on their own in other campus labs. This disruption approach. It appears that the final exam success of the students occurred at the beginning of the semester, when many needed is less sensitive to the experience level of the teacher in R2R guidance with the software and the complex scheduling the method than it is in the traditional sections. course relies upon to function properly. The lab was also closed for several days surrounding Hurricane Rita and again when the Four instructors with recent experience in the traditional format New Orleans Saints games were held on campus. taught in the R2R format in the fall of 2005. We can compare SET scores for these instructors on the question “Overall, Data was examined for a variety of factors, but comparison the instructor was an effective teacher,” to measure student was partly limited by the previously available historical data. satisfaction across the two methods. The SET questionnaire Final exam medians in the 3 delivery systems were compared was not written to compare delivery the two methods, but is a as a measure of learning outcomes. Within the R2R system, we questionnaire from the college concerning student’s opinion of examined results to determine whether final grades were cor- the teacher and his or her methods. We examined results in the related to participation. Final exam medians of sections taught R2R sections in fall 2005 verses the results in the traditional by star instructors were compared to final exam medians of format from falls 2002-2004. The results are in Table IV. It sections taught by graduate students to check the sensitivity of appears that there is at most a small difference between the learning outcomes to the experience of the teacher in both the evaluation averages of the R2R sections and the traditional traditional and R2R methods. And finally, student responses sections. While SET do not measure students satisfaction with were gathered from Student Evaluations of Teaching (SET) R2R, a separate survey was administered. Students were asked and compared across the two delivery systems. if they would recommend this format to their friends and 59% answered “yes.” The results of the common final exam are given in Table I. One surprise was the success of the large lecture model. Its A comparison of the section GPA with the final exam median success may require the star instructors, or it may be due to in Table I makes it apparent that the R2R sections were graded the fact that these students were required to spend more time more harshly than the traditional sections. The difference is the doing college algebra, i.e., three periods in class and monitored grading on the 75% of the grade that was not necessarily based computer homework. The R2R model did well in comparison on the final: The R2R students were graded on getting the right to the traditional model. PCR alumni schools have warned us answer and the traditional students were graded with partial that it takes several years for students to acclimate to the new credit. Students greatest complaint is that the lack are partial demands of participation. credit impacts their grade. Adjustment of the grading scale is a point of controversy among the faculty. The success of the system for those who participate is shown in Table II. To receive a participation grade of 100% students had The R2R redesigned model will continue to develop in future to attend the 50 minute focus group and spend 2 hours in the lab semesters, and we will continue to assess the results. A few each week. Note that 86% of the students who participated at technical adjustments and additions are already planned for least 90% of the required time earned a grade of A, B, or C. This the fall semester of 2006. We also plan to follow the students’ is a strong indication that students who participate in the R2R progress in subsequent courses in a variety of subject areas model are likely to be successful with a reasonable amount of beyond mathematics. Overall, we are quite pleased with the effort. We did not compare ABC rates across the three methods success of this redesign and plan to implement this model in because of the grading discrepancy. other precalculus courses in the near future.

35 FOCUS August/September 2006 The National Mathematics Advisory Panel — An Update

By Fernando Q. Gouvêa The May/June issue of FOCUS in- Jim Simmons of Renaissance Technolo- author of three research articles published cluded a report about the creation, by gies, and Hung-Hsi Wu of Berkeley. A in the 1980s in which she argued that Presidential order, of a National Math- full list of members can be found online at there are “intrinsic gender differences ematics Advisory Panel, intended to the NMP web site, at http://www.ed.gov/ that favor males at the highest levels of advise the President and his Secretary of about/bdscomm/list/mathpanel/. mathematics.” Benbow told the press she Education about the results of research stands by her results, but pointed out that in mathematics education and how they The first meeting of the panel happened they represent only one small portion of might be used to improve the teaching of on May 22 and the second was on June a long research career. mathematics in American schools. Since 28 and 29. Transcripts of the meetings are then, the members of the NMP have been posted online; the Department of Educa- Most of the panelists have argued that appointed and its first meetings have tion also offers interested members of these are over-reactions. Deborah Ball occurred. the public an opportunity to subscribe to was quoted arguing that the AWM’s email updates about the panel’s work. objections are misguided, saying that Larry Faulkner, president of the Houston “having people snipe at the panelists does Endowment and President Emeritus of Controversy is already swirling around not help things.” Tom Loveless, a senior the University of Texas at Austin, will be the panel’s work. Almost immediately scholar at the Brookings Institution who chairing the panel. The vice-chair will be after the appointment of the panelists, is also a member of the panel, argued Camilla Benbow, Dean of Education and critics objected that the panel was that in fact the panel represents “an op- Human Development, Vanderbilt Uni- weighted towards critics of the NCTM portunity to cut through a lot of the noise versity, Peabody College. Other mem- and its Principles and Standards for surrounding math.” bers likely to be known to our readers School Mathematics. Also noted was include Deborah Ball of the University the fact that only one K–12 teacher is on The NMP is expected to submit an in- of Michigan, Francis Fennell (president the panel. The Association of Women terim report by January 31, 2007. of NCTM), Liping Ma of the Carnegie in Mathematics objected to the panel’s Foundation, Wilfried Schmid of Harvard, vice-chair, Camilla Benbow, who is the The National Mathematics Advisory Panel — Commentary

By Victor Katz The first meeting of the National ing Mathcounts teams, Jim Simons, a the ex-officio members of the panel Mathematics Advisory Panel took place 1976 winner of the AMS Veblen Prize from the White House and the Depart- on May 22 at the National Academy of in Geometry who is now the president of ment of Education, the goal of the panel Sciences building in Washington, DC. Renaissance Technologies Corporation, is to examine the research literature on The panel has seventeen members and is a very successful investment firm using the teaching of mathematics, determine chaired by Larry Faulkner, President of mathematical strategies, five professors which studies are “rigorous” and “scien- the Houston Endowment and President of psychology or human development, tifically-based” rather than “anecdotal,” Emeritus of the University of Texas at three educational consultants, and a suggest possible avenues for additional Austin. Some of the panelists should former California elementary school research, and craft recommendations that be familiar to members of the MAA, principal whose school saw great gains will “inform the future.” Of course, the including Deborah Ball of the University in standardized test scores in reading criteria for determining whether or not a of Michigan, Liping Ma of the Carnegie and mathematics under her leadership. study is “rigorous” were not specified. Foundation, Francis “Skip” Fennell, the It is surprising, perhaps, that Professor Nevertheless, the NMP is charged with President of the NCTM, and two research Wu is the only member of the MAA on investigating studies in at least the fol- mathematicians, Wilfried Schmid of Har- the panel. And, although most of the lowing five areas: vard and Hung-Hsi Wu of the University panelists have made contributions toward of California, Berkeley, who have been mathematics education in their profes- (1) the critical skills and skill progres- vocal critics of recent reforms in math- sional lives, it is also curious that the sions for students to acquire competence ematics education. Other panelists are panel failed to include even one expert in algebra and readiness for higher levels Vern Williams, a middle school math- elementary teacher of mathematics. of mathematics; ematics teacher from Fairfax, Virginia who was a 1994 Sliffe award winner As was made abundantly clear in the (2) the role and appropriate design of and has had great success in develop- opening public meeting by several of standards and assessment in promoting mathematical competence;

36 August/September 2006 FOCUS

(3) the process by which students of (See the review on MAA Reviews.) In- ness should be evaluated systematically. various abilities and backgrounds learn terestingly, Professors Ball and Wu were Such efforts should be coordinated, con- mathematics; members of the CML and authors of its tinual, and cumulative. final report. Among the CML’s recom- (4) instructional practices, programs, and mendations were: These recommendations, and others, materials that are effective for improving were fleshed out with numerous examples mathematics learning; and (1) All students should become math- drawn from educational research studies. ematically proficient. That is, they should These studies include details on what (5) the training, selection, placement, and possess conceptual understanding, skill children know about numbers by the time professional development of teachers of in carrying out procedures accurately they arrive in pre-K and the implications mathematics in order to enhance students’ and appropriately, the ability to formu- for mathematics instruction and details on learning of mathematics. late and solve mathematical problems, the processes by which students acquire the capacity for logical thought, and the mathematical proficiency with whole The panel members spent some time at habitual inclination to see mathematics as numbers, rational numbers, and integers, their meeting discussing the meaning of sensible, useful, and worthwhile. as well as beginning algebra, geometry, these five categories, and it was clear measurement, and probability and statis- that there is a great diversity of opinion (2) Instruction should not be based on ex- tics. The committee noted, however, that among the group. Numerous questions treme positions that students learn solely there were many unanswered questions for study were brought up, ranging from by internalizing what a teacher or book about mathematics learning that remained “what do we mean by algebra?” to “is says or solely by inventing mathematics to be answered by further studies. pattern recognition in the early grades on their own. an important pre-algebraic skill?”; from How the recommendations of the NMP “what is the relationship of teacher (3) Schools should support, as a central will differ from those of the CML remain Praxis scores to their students’ achieve- part of teacher’s work, engagement in to be seen. ment?” to “what is the evidence for the sustained efforts to improve their math- effectiveness of particular commercial ematics instruction. This support requires Victor Katz is a well-known historian of textbooks?”; from “is ability grouping the provision of time and resources. mathematics, author of several books constructive or destructive?” to “how and articles, including the well-known can we keep mathematics teachers in the (4) Efforts to improve students’ math- survey A History of Mathematics. He teaching profession?”. ematics learning should be informed by has long been interested in mathematics scientific evidence, and their effective- education. The NMP is planning to divide itself initially into four sub-panels, who will Solution to Sudoku Puzzle from page 18 separately deal with items 1, 3, 4, and 5 in the list above. They may schedule public hearings and invite testimony from concerned individuals or organizations. L O G A R I T H M But in any case they will be interested in hearing from mathematics educators at I H M L O T R A G various levels. To find out more informa- tion about the panel and to contact it, go to http://www.ed.gov/about/bdscomm/list/ R T A G H M O I L mathpanel/index.html.

It should be noted that a similar commit- H R T O A L G M I tee with a similar charge, the Committee on Mathematics Learning (CML), was A L I R M G H O T established in 1998 by the National Research Council at the request of the National Science Foundation and the G M O I T H L R A U.S. Department of Education. Three years later, that committee produced its M A R T G O I L H report: Adding It Up: Helping Children Learn Mathematics (Washington: Na- tional Academy Press), a 454-page book O G L H I A M T R containing numerous serious recom- mendations for mathematics education, based on a multitude of research results. T I H M L R A G O

37 FOCUS August/September 2006 MAA is Seeking a Director of Publications for Journals and Communications

The Mathematical Association of on the MAA website and will develop of all major constituencies of the MAA, America seeks a highly qualified person content for new resources to serve our embrace all areas of mathematics, and are for the position of Director of Publica- members and the public. The Director easily available to all of our members and tions for Journals and Communications. will be responsible for communications the larger community who are interested The primary responsibilities of the posi- of the MAA such as reports, news ar- in mathematics, especially for expository tion are to oversee journals and other ticles, and public awareness pieces. mathematics and materials for faculty periodicals and content and resources and students. on the MAA website. In addition, the The Director will oversee a staff of three Director will perform other duties related located in the headquarters office and Applications will be accepted and re- to communications of the MAA to our numerous editors and editorial boards. viewed as received, but it is expected that members, the public, and other specific Duties include administration of the the position will begin between January constituencies. department and grant proposal develop- 1, 2007 and July 2007. The position is ment and management. The Director located at the national headquarters of the A candidate should have a PhD in the reports to the Executive Director and is MAA in Washington, DC. mathematical sciences. Requirements a key member of the MAA’s staff leader- include editorial experience, writing ship team. S/he will work closely with Candidates should send a resume and articles for journals, periodicals, and other members of the staff, national and letter of interest to: the web, and experience with creating sectional officers, committees and edi- web content. The candidate should be tors, and others in strategic planning and Ms. Calluna Euving familiar with the MAA, have a strong program development. Chief of Staff interest in writing and publication, and Mathematical Association of America express a vision for MAA publications The mission of the MAA is to advance 1529 18th Street, NW in print and online. the mathematical sciences. The MAA, Washington, DC 20036 with nearly 30,000 members, is the larg- The Director oversees publication of est association in the world with a focus Applications may be submitted electroni- the Association’s three journals, three on mathematics accessible at the under- cally to [email protected]. References magazines (two online), the Association’s graduate level. Membership includes will be requested after review of applica- newsmagazine, a variety of columns and college and university faculty and stu- tions. Applications from individuals from articles, the MAA Mathematical Sciences dents, high school teachers, individuals underrepresented groups are encouraged. Digital Library (MathDL) and the new from business, industry, and government, Additional information about the MAA MAA Gateway site to other digital librar- and others who enjoy mathematics. and its programs and services may be ies. In addition, the Director will oversee found on MAA’s website: http://www. mathematical and professional resources The Director is responsible for ensuring maa.org. AA/EOE. that publications encompass the interests Found Math Deadlines for FOCUS are Changing Ah, so this was the little genius? In order to make sure FOCUS goes out on time, we need to move the deadlines for editorial copy slightly earlier than they have been. We are increasing the lead Gauss made a bow, as he had been taught. time from six weeks before publication to eight weeks before, so that the deadline He knew that there would soon be no for the issue for month n will be the first week of month n - 2 (mod 12). We may more dukes. Then absolute rulers would be able to squeeze in news items received after the deadline, but longer pieces only exist in books, and the idea that one should be delivered before the dates indicated. Please note, in addition, that the would stand before such a person, bow, October and April issues are meetings issues and therefore do not include any and await his all-powerful word would editorial material. seem so strange as to be a fairy tale. FOCUS Deadlines Count up something, said the duke. October November December (Gauss meets the Duke of Brunswick, Editorial Copy September 1 October 1 in Daniel Kehlman’s short story “The Display Ads August 20 September 24 October 27 Mathematician,” published in The Paris Employment Ads August 13 September 10 October 10 Review 177, Summer 2006.)

38 August/September 2006 FOCUS

October November December Editorial Copy September 1 October 1 Display Ads August 20 September 24 October 27 Employment Ads August 13 September 10 October 10

39 FOCUS August/September 2006

Getting Mixed ? Keep Up with a Graduate Certificate in Radar Signal Processing

Four 10-week Courses Cover: The new Graduate Certificate in Radar Signal Processing will be • Fundamental principles of radar functionality, taught by leading experts in the field at the Norbert Wiener Center architecture, and performance for Harmonic Analysis and Applications in the College of Computer, • Modern mathematical methods of signal and Mathematical, and Physical Sciences. The program is designed for image processing technologists, scientists, and mathematical engineers who want to • Detection theory, pulse compression, waveform stay attuned to the latest developments in Radar Signal Processing. design, clutter phenomenology and processing • Target tracking and filtering For more information: Apply online today! Single Point of Contact (SPOC) Classes start in August Highlights: Office of Professional Studies •12 credit graduate certificate 877.989.SPOC (7762) • Can be completed in only 12 months 301.314.3572 • Credits may be applied toward a Masters in Mathematics of Advanced Industrial Technology

www.professionalstudies.umd.edu

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

40