D A V I D.   C R U Z - U R I B E.  and   J U D I T H.  F.  M O R A N.

The following feature story appeared in the campus publication MOSAIC in January, 2000.

THOUGHTS ON THE MATH WARS

By Assistant Professor of Mathematics David Cruz-Uribe and Director of Trinity’s Math Center and Associate Professor of Quantitative Studies Judith F. Moran

Editor’s Note: On Nov. 18, 1999, The Washington Post published a full-page letter signed by 200 university mathematicians and physicists, including four Nobel laureates and two Fields medallists (the mathematical equivalent of the Nobel prize). The letter strongly criticized a recent Department of Education (DoE) report that identified 10 elementary and high school math curricula as either "exemplary" or "promising." The letter objected both to the content of the programs selected for endorsement by DoE’s panel of experts, and to the composition of the panel, which included few research mathematicians.

The recent letter in The Washington Post has brought the "math wars," which have been simmering for more than a decade, to a higher level, and have brought the extremes of the debate before the public. Within the mathematical community, hidden from the public, the reaction has been more mixed. While there is dismay at the divisive effect of the letter and the damage it has done to collaborative efforts of math researchers and math educators, there is also real sympathy for the feelings behind the original letter both within the Trinity College mathematics department and, we believe, among many other college and university math faculty.

Why do many mathematicians feel this way? Admittedly, many college and university mathematicians know little about primary and secondary school math curricula (unless our own children are having trouble in school). But every year we see the product of such curricula in our first-year classes. Anecdotes abound and possess a depressing sameness from school to school: students who cannot do simple arithmetic without a calculator, who find manipulating fractions a complete mystery, and who cannot do simple algebra. This does not describe a majority of our students, but neither are such students isolated exceptions.

Naturally, we want to know why students are so poorly prepared. Given the mutual distrust that sometimes exists between mathematicians and math educators, we are cautious in endorsing math reform movements. More anecdotal evidence reinforces our suspicions. For example, Connecticut State Board of Education guidelines recommend that teachers de-emphasize manipulating "fractions with unreasonable denominators like sevenths and ninths."Mathematicians do not regard such denominators as unreasonable. In fact, skills acquired from manipulating such fractions are essential to the acquisition of corresponding algebra skills.

But, despite our sympathy, we feel that The Washington Post letter has been polarizing and counterproductive. The letter ignored, and may damage, efforts by the American Mathematical Society and the Mathematical Association of America (representing university and college mathematicians) to provide constructive input into the revision of the National Council of Teachers of Mathematics Standards for elementary and high school math curricula. (The Standards lie at the base of much of the controversy in the math wars.)

After reflecting on the math wars, we believe that part of the problem comes from conflating two related but distinct problems. Mathematicians and scientists are primarily concerned with the well-being of their own disciplines. In particular, they want students who are prepared to take a rigorous calculus course as a prelude to more advanced courses. Though the teaching of calculus has evolved over the past two decades, both from the introduction of computer technology and from the pedagogical concerns of the calculus reform movement, the underpinnings of a rigorous calculus course remain the same: abstraction and algebraic manipulation. Mathematicians and scientists believe that every student entering college with the hope of studying math or science should have mastered these skills to the level necessary to take calculus.

On the other hand, math educators at the elementary and high school level are concerned not only with preparing students for college but also with the broader question of quantitative literacy: what should every person know about math, logic, statistics, and data analysis in order to be a functioning member of our technological society? Thus when math educators are accused of "dumbing down" the curriculum, and in turn mathematicians are accused of "elitism," it is because different problems, with different solutions, are being compared.

Once the two problems are distinguished, how should each be addressed? We have little experience at the high school level, but we can point to two initiatives at Trinity that are aimed, in part, at providing solutions to those very different problems. More than a decade ago Trinity established a quantitative literacy requirement for all students. The initiative came from the faculty as a whole, who believe that mathematical and writing proficiency are an integral part of a liberal arts education. The courses offered by Trinity's Math Center to help fulfill the quantitative literacy requirement supplement, but in no way replace, the more traditional mathematical courses, especially calculus, offered by the math department. Trinity's math department considers the training of future scientists and mathematicians one of its primary missions. This does not preclude, however, offering courses for students whose interests are in fields other than mathematics. A recent initiative in support of this aim has been the introduction of new courses, including a new calculus sequence, aimed at students who do not intend to become mathematicians or scientists.

Neither initiative is more than a small part of the solution. And for our part, we can only hope that the heat and acrimony generated by The Washington Post letter will dissipate and that mathematicians and math educators can resume their cautious dialogue with the aim of producing students who are both quantitatively literate and well prepared to pursue careers in math and science.