To Include More Students, Don't Focus on Contests: Prepare for Mathematics!Author(s): Sarah-Marie BelcastroSource: The Mathematics Teacher, Vol. 97, No. 2 (FEBRUARY 2004), pp. 84-86Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/20871518 .

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Sarah-Marie Beicastro

Soundoff!

To Include More Students, Don't Focus on Contests:

Prepare for Mathematics!

Students perceive all

extra

curricular

mathematical

activity as related to or

leading to contests

IDON'T LIKE MATHEMATICS CONTESTS. I PARTICIPATED in some local contests in high school, was un aware of the existence of regional and national

contests, and avoided the Putnam in college. My general philosophical bent is toward cooperation rather than competition and toward mathematical enrichment rather than acceleration in the calculus stream. However, I also have nonemotional reasons for disliking contests, which I give in this article.

Additionally, I will relate efforts to diversify partici pation in contests to efforts to make extracurricular mathematics more welcoming to all students. Final

ly, inspired by the Hampshire College Summer Studies in Mathematics program (www.hcssim.org), I have some suggestions for more-inclusive high school mathematical activities.

The main purposes of mathematics contests are to encourage students to become involved in mathe

matics, especially in the long term, and to let them have fun with mathematics while they are learning a lot. However, I do not think that contests achieve those goals. Some students who participate in con tests become frustrated by mathematics in college because they view the field of mathematics as solv

ing problems rather than as building theories and because contest preparation does not equip them to succeed at theory building. So they become discour

aged or confused and leave mathematics. And

although many people think that contests are fun, many others do not. More important, many stu dents do not think that contest-preparation activi ties are fun. Yet, in many schools, students perceive

The views expressed in "SoundofFT reflect the views of the author and not necessarily those of the Editorial Panel of the Mathematics Teacher or the National Council of Teachers of Mathematics. Readers are en couraged to respond to this "Soundoff!" by sending typed and double-spaced letters to the Mathematics Teacher for possible publication in "Reader Reflec tions." "Soundoffs!" from readers are welcomed.

all extracurricular mathematical activity as related to or leading to contests.

I am not advocating that we do away with mathe matics contests, and I recognize that some students

enjoy competition or even thrive on it. Instead, I

suggest that we decentralize mathematics contests so that they are but one of many paths through which students can enter the mathematical com

munity and that we encourage highly competitive students to participate in and enjoy some noncom

petitive activities, as well. I do not believe (as some

people do) that competition is an inevitable part of the college-application and job-procurement process; we can focus instead on the appropriateness of the

college to the student and the student to the college, whence the grading is on "fit" rather than on num ber of achievements. Likewise, I agree with the sen timent that sometimes the pressure in competition comes more from parents than from the students themselves. (I have no solution for that problem, however.)

Recently, some members of the Mathematical Association of America (MAA) solicited suggestions on how to encourage students from underrepresent ed groups to participate in contests. The MAA spon sors the American Mathematics Contests (AMC)

(www.unl.edu/amc), which in turn determine the U.S. International Mathematical Olympiad (IMO) team members. Because of my longtime objections to contests, it had never occurred to me that anyone should (or would) worry about whether African

Americans, Latinos, Latinas, and females partici pate or succeed in them. My concern has always

Sarah-Marie Beicastro, smbelcas@cs.xu.edu, is a mathe

matician at Xavier University, Cincinnati, OH 45207 4441. In addition to living and breathing mathematics, she likes to think about (and do) dance, knitting, and fem inist philosophy of science.

Photograph by Thomas Hull; all rights reserved

84 MATHEMATICS TEACHER

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been that a variety of students should participate and succeed in mathematics in general. However, if the United States is going to enter the IMO (which it will do, no matter what my opinion of the contest

is), then it makes sense to think about working toward having a team that is representative of the

diversity that we have in the mathematical and

larger communities. The previously mentioned MAA solicitation indi

cated that females, African Americans, Latinos, and Latinas perform less well on contests than their white or Asian male counterparts. This state ment seems to imply that these underrepresented groups are less skilled in certain ways than their dominant-culture counterparts. So why might stu dents who have mathematical aptitude not develop their skills in ways that lead to success in contests?

They may not find contest preparation appealing for various reasons. Maybe the other students are not the folks they want to hang out with; maybe the kinds of problems done in preparing for contests do not interest them; maybe they do not like the pres sure of competition; maybe they do not want to be on a "team"; maybe scoring low on one contest has

discouraged them.

Many of these are reasons that I did not want to do contests myself... which reminds me of a much more general issue. Across the sciences, there has

long been concern about the representation and achievements of underrepresented groups at all lev els. Sometimes amelioration of these situations has occurred because cultural biases were uncovered; however, often a situation or atmosphere that is

unfriendly to everyone disproportionately affects some underrepresented groups. Making contests, or

mathematics in general, friendlier to everyone can

only improve participation by members of under

represented groups. My thoughts on how to excite students and encourage them to do mathematics

might also have the effect of interesting a broader cross section of students in contests.

The only way I know to draw nonparticipating students into mathematical activities is to make the contests compellingly interesting?and in fact so compelling that the draw of the mathematics overcomes all the social aspects that keep students

away from contest preparation. I do not claim that this type of activity will increase the participation of economically disadvantaged students. There's no

clear connection with college preparation or any other long-term benefit, and students who have to work or assist with child care outside school hours will not be convinced to reschedule their lives to fit in something that is merely interesting and not also useful.

Here is an approach to mathematical extra curricular activities that differs markedly from my

perception of contest preparation: Present mathe

matical situations; and challenge the students to find patterns, to make conjectures, and to find

examples. Then use their explorations as an avenue to teach proofs. Questions should be open-ended in their formulation (whether or not they actually have known solutions). Activities must then be

exploratory so that students can take many direc

tions, depending on their interests. The framework for the mathematical situations should be some what silly in some way (or otherwise inviting and

creative). Students should work in community rather than in isolation. Students should also have the option of deciding how they would like to work, since some students prefer to work alone, but they should still be together. Appropriate online mathe matical workbooks are available for students who are geographically isolated. Such material includes online courses available from the Michigan Math and Science Scholars Program (www.math.lsa .umich.edu/mmss) and new material posted regu

larly by the NRICH Mathematics Enrichment Club at www.nrich.maths.org.uk. This approach is

appealing, inclusive, and has low to no pressure. Students are more willing to work at the difficult task of learning if they can also enjoy themselves.

Furthermore, this approach still builds problem solving skills?these habits of mind, not memoriz

ing tricks to solve particular problems, are needed to engage with abstract mathematics.

I think a canonical (and quick!) example is Jim Tanton's Tootsie Roll activity. He breaks students into groups or puts them in a circle (depending on

the number of students) and hands some Tootsie Roll candies to each student. Then he gives an algo rithm for redistributing the candy?for example, one might pass half of one's candy to the person on

the right?and asks whether repeating this process

produces a stable state. Details can be found in Tanton (2001) and Iba and Tanton (2003). The world is rich in ideas for this kind of activity. Sources in clude College Mathematics Journal and Mathematics

Magazine (www.maa.org/pubs/journals.html), Math Horizons (www.mathcs.carleton.edu/math

Jiorizons), and Mudd Math Fun Facts (www.math .hmc.edu/funfacts).

The point is that if we take the focus away from contest preparation, then students will cease to

identify an interest in mathematics with an inter est in contests. Students who were very involved in contests have told me that they want to do more

theoretical mathematics and less contest work that contest mathematics is really fun but that

proofs are more fun. If contests become less central in high school mathematical culture, then those

who do not like pressure may find that the stakes are lower, because they can fail a contest and still be seen as good at mathematics. After working with

proofs and such, a student who has been discouraged

Students are

more willing to work at the difficult task of learning if they can

also enjoy themselves

Vol. 97, No. 2 ? February 2004 85

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Becoming better at

mathematics in general

should have the specific

effect of I improving

contest

performance

by one low contest score may become willing to try again. I am certainly not going to claim that contest

preparation is not necessary at the higher levels of contests. But to get people to excel, they have to be interested in doing the work that is necessary to excel. And I think the way to get them interested is

by doing mathematics that is fascinating, fun, and not related to contests.

Now, here's the funny thing. Doing mathematics that is not related to contests?mathematics that focuses on crafting proofs and understanding abstract structures rather than on finding answers to prob lems?seems to make people better contest partici pants. Of course, this statement is not my personal observation, because I do not work with contests. But anecdotal evidence suggests that doing explora tory mathematics seems to help contest skills. For

example, the director of the Hampshire College Summer Studies in Mathematics program told me that he had alumni on the U.S. IMO team in twenty two different years. It makes sense?becoming bet ter at mathematics in general should have the spe cific effect of improving contest performance.

So my suggestion for the contest crowd is to stop preparing students for contests. Do open-ended, exploratory activities with the students instead, and focus on understanding mathematical phenom

ena rather than on solving problems. Make mathe matical activities so enjoyable that the apt students cannot resist participating and learning. Draw them in so that when they start learning more about

proofs, they need to know why things work so much that they are willing to deal with the details. They will become skilled in mathematics, and then may be they will be willing to work on contests; or if they were already willing, they may begin to succeed.

REFERENCES Iba, Glenn, and James Tanton. "Candy Sharing." American Mathematical Monthly 110 (January 2003): 25-35.

Tanton, James. Solve This! Washington, D.C.: Mathe matical Association of America, 2001.

Thanks go to Thomas Hull, a fellow Hampshire College Summer Studies in Mathematics instructor, for helping me clarify my thoughts. This manu

script is loosely based on a talk that I gave at the 2003 Joint Mathematics Meetings in the MAA's ses sion on Encouraging Underrepresented Groups of Students in Math Contests. I also extend my thanks for the insights shared by the other speakers and the audience, all of which affected my writing of this article. Mr

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