Math for the 21st Century


Just in case you missed it in the NY Times in late summer, David Mumford and Sol Garfunkel have sounded the latest call for a dramatic re-envisioning of secondary math education in America’s public schools. A similar movement in the mid and late 1990’s was quashed by the testing movement and math “purists”, but hopefully, as testing continues to lose its luster and energy, and  widespread alarm continues to grow about the state of our math education, Mumford and Garfunkel have taken up the torch. No computational slouches in their respective careers, Garfunkel is the executive director of the Consortium for Mathematics and Its Applications and Mumford an emeritus professor of advanced mathematics at Brown.

The nation’s on-going anxiety about math can be traced to the poor performance of American students on various international tests. All this worry, however, is based on the assumption that there is a single established body of mathematical skills that everyone needs to know to be prepared for 21st-century careers. That assumption is wrong, say Mumford and Garfunkel. Different sets of math skills are necessary for different career paths, yet American math education has failed to change to reflect that reality.

Today, most American high school students pass through a sequence of algebra, geometry, more algebra, and pre-calculus. Some make it to calculus. This pathway has now been adopted by the Common Core State Standards in more than 40 states, not to the authors liking. Such a highly abstract curriculum, say Mumford and Garfunkel, is simply not the best way to prepare the vast majority of high school students for productive work and civic lives. How often do most adults need to solve a quadratic equation, or need to know what constitutes a “group of transformations” or “complex numbers”? Professional mathematicians, physicists and engineers do need to know such things, but most citizens the authors argue would be better served by studying how mortgages are priced, how computers are programmed, and or how the statistical results of a medical trial are to be understood.

A math curriculum focused on real-life problems would still expose students to the abstract tools of mathematics, in particular the manipulation of unknown quantities. But there is a world of difference between teaching “pure” math, with no context, and teaching relevant problems that will lead students to appreciate how a mathematical formula models and clarifies real-world situations.

Imagine 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.

Traditionalists will object that the standard curriculum teaches valuable abstract reasoning, even if the specific skills acquired are not immediately useful in later life. This reminds one of the last generation’s traditionalists who argued that studying Latin helped students develop linguistic skills. Garfunkel and Mumford write that studying applied math, like learning living world languages, provides both useable knowledge and abstract skills.

In math, they pose, what we need is “quantitative literacy,” 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 between everyday problems and mathematical formulations (as when we decide whether it is better to buy or lease a new car).

Parents, state education boards and (reluctant) colleges deserve a choice, now,  say Mumford and Garfunkel. The traditional high school math sequence seems less and less the best and certainly not the only road to mathematical competence. The authors believe that the best way for the United States to compete globally is to strive for universal quantitative literacy: teaching topics that make sense to all students and can be used by them throughout their lives. It was through real-life applications that mathematics emerged in the past, has flourished for centuries and connects to our culture now.

(NY Times, Aug. 24, 2011)