Miscellany

I did OK in math way back in high school, but I didn’t love it. I also recognized its basic uses in my later life, though I can’t say I’ve ever put to use (or even remember) what I learned in trigonometry. While few would argue with the importance of math for anyone wanting to be an engineer or an actuary, how necessary is it for the rest of us?

In a New York Times op-ed piece, “How to Fix Our Math Education,” Sol Garfunkel and David Mumford tackle the widespread anxiety in our country about the poor performance of American students on various international tests.

Garfunkel is the executive director of the Consortium for Mathematics and Its Applications, while Mumford is an emeritus professor of mathematics at Brown University.

They challenge the assumption that there is a set of mathematical skills that everyone needs to know to be prepared for 21st-century careers. Instead they argue that “different sets of math skills are useful for different careers, and our math education should be changed to reflect this fact.”

My older brother said to me many years ago, “I graduated from high school without being taught how to write a check.” Others can update that example, since many today don’t write checks.

Garfunkel and Mumford point out the “highly abstract” curriculum of American high schools today, which offer a sequence of algebra, geometry, more algebra, pre-calculus and calculus. Then they ask, “How often do most adults encounter a situation in which they need to solve a quadratic equation? Do they need to know what constitutes a ‘group of transformations’ or a ‘complex number’?”

No doubt learning about these is useful to professional mathematicians, engineers or physicists, but “most citizens,” write Garfunkel and Mumford, “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.”

The math curriculum they envision would still expose students to the abstract tools of mathematics but would focus on “relevant problems that lead students to appreciate how a mathematical formula models and clarifies real-world situations.”

They ask us to imagine replacing the sequence of algebra, geometry and calculus with a sequence of finance, data and basic engineering. They then offer an example of such an approach: “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.”

Garfunkel and Mumford call this approach a combination of “quantitative literacy,” which is “the ability to make quantitative connections whenever life requires (as when we are confronted with conflicting medical test results but need to decide whether to undergo a further procedure), and ‘mathematical modeling,’ the ability to move practically between everyday problems and mathematical formulations (as when we decide whether it is better to buy or lease a new car).”

Those fellow students of mine back in high school who protested, “Why do I need to study math?” had a point, even if they were mainly interested in not studying it at all. Much of education involves motivation, and making math relevant is a good motivator.