Yesterday’s Op-Ed piece in the New York Times, “How to Fix Our Math Education” is by two card-carrying mathematicians, Sol Garfunkel and David Mumford. To my surprise they argue that “different sets of math skills are useful for different careers, and *our math education should be changed to reflect this fact.*” (Italics mine) They propose that, as an example, we should be “replacing the sequence of algebra, geometry and calculus with a sequence of finance, data and basic engineering. In the finance course, students would learn the exponential function, use formulas in spreadsheets and study the budgets of people, companies and governments. In the data course, students would gather their own data sets and learn how, in fields as diverse as sports and medicine, larger samples give better estimates of averages. In the basic engineering course, students would learn the workings of engines, sound waves, TV signals and computers. Science and math were originally discovered together, and they are best learned together now.” At some point in the article they ask the rhetorical question “how often do most adults encounter a situation in which they need to solve a quadratic equation?”

My immediate reaction was “hogwash”, but upon further thought I can see some nuances in the argument. For example, the authors agree that “[o]f course professional mathematicians, physicists and engineers need to know all this “ (they mean algebra, geometry, complex variables, etc), “but most citizens would be better served by studying how mortgages are priced, how computers are programmed and how the statistical results of a medical trial are to be understood.”

Is this then, an argument for different math tracks? If it is, it presumes a career choice that must be made way before most kids know anything realistic about various careers. I know that many other countries (Europe, Asia) do in fact force the students to make this choice. In these countries, high stakes exams and course grades determine whether a student will be on the university path or on a non-academic one. Do we want to go that way? I can see arguments on both sides. My guess is that parents (i.e. voters) will not care as long as their kids get accepted into college.

As far as encountering a situation in which the average person needs to solve a quadratic equation, well…when does the average person encounter a situation in which s/he needs to do squats? Push-ups? We teach math the way we do because it exercises the logic part of the brain, just like squats and push-ups exercise the body. But is this argument valid?

I have yet to see a controlled experiment where the “logic IQ” of persons who “had” math is compared to that of those who did not have it. Personally, I believe that math does change pathways in your brain, towards some sort of more logical thinking (especially if you take a statistics course), but whether these pathways stay there without continuous exercise, I do not know.

Color me puzzled.

I also question when an adult encounters a situation in which s/he needs to know about phylum/kingdom/c;ass categories, about the dates of the 100 years war (or the participants), about King Lear, etc. I am always bothered by the ‘When will I use this stuff’ line of argument. It is ALL about problem-solving skills in my mind. The more ways that you can work your way through difficult ideas, the more likely it is that you can work your way through novel difficulties in whatever activity you engage in