Saturday, October 1, 2011

Quantitative Literacy versus Mathematics

On August 25, Sol Garfunkel and David Mumford ignited a firestorm with their provocative piece in the New York Times on "How to Fix our Math Education.” I’d like to use this column to respond to one of their conclusions, the comment near the end of their article that, “In math, what we need is `quantitative literacy,’ …”

I’ve written many of my columns about Quantitative Literacy (QL), including as recently as this past January (Mathematics & Democracy + 10). I was one of the leaders in developing a QL program at Macalester, have served on the board of the National Numeracy Network, and continue to promote QL whenever and wherever I can. Yet I’m very bothered by the suggestion that QL is what we need in math.

This past winter, I visited Lehman College in New York to consult on the creation of a program in QL that is being developed by faculty from several disciplines. Their mathematics department was viewing this emerging course with some uneasiness. Would it replace their developmental courses in algebra? Were their students even ready for QL? In response to their concerns, I wrote:

A QL requirement should be independent of a mathematics requirement. If your students need algebra, QL should not replace that. In the other direction, algebra is not a substitute for QL. The mathematical and statistical skills needed for QL are basic. Algebra need not be a pre-requisite. What makes this college-level material is that these skills are applied and interpreted in messy, real-world situations, using quantitative approaches to aid analysis of complex social issues. In many respects, the natural home for QL is in the social sciences, but I believe that math and stat departments have an important role to play in keeping the mathematics of QL honest and encouraging quantitative thinking as one of the important tools for studying social issues.

This has been the guiding principle behind Macalester’s QL program. I am very proud of the strong inter-disciplinary nature of the QL program that we have created here, and I am suspicious of any program that claims to be QL but is taught exclusively by mathematicians. I also should add that Macalester has no mathematics requirement for graduation, but it does have a QL requirement. I heartily endorse this choice. I do not see a need for all students to study college-level mathematics, but I do see a need for improving their ability to apply quantitative reasoning.

This past summer, I had the chance to review a new textbook in QL that uses ratio and proportion as the unifying theme. The book presents a well-written course that can help students gain understanding of the power and uses of these basic mathematical tools. Many college students, some graduates of Macalester included, never achieve this level of understanding of ratio and proportion and would benefit from such a course. Yet I would hate to see this classified as a course in mathematics. It is not just that the mathematics is what should have been mastered in middle school. It is that the only reason this is a legitimate college-level course is that it transcends the concerns of the mathematics classroom.

While I feel strongly that we need to draw a clear distinction between mathematics and QL, I am not saying that mathematics should be taught without regard for the world beyond the classroom. All mathematics should be taught with the goal of promoting student ability to use these tools and ideas in ways that transcend the specific circumstances under which they have been learned. But we also need to recognize how very difficult it is to accomplish this. The research that I have seen suggests that the most effective means of reaching this goal is to lead students through an alternation of theory building and a variety of applications, combined with plentiful opportunities for personal experimentation and reflection. This goal is much more than quantitative literacy. It is the development of mathematical ability.

The Economist recently published an article that is directly relevant to August’s column, The Best Way to Learn. See “The Great Schools Revolution”, The Economist, Sept 14, 2011.