If our most outspoken math and science professors (Jordan Ellenberg, Brian Greene), self-styled education experts (Alfie Kohn, Susan Engel), education reporters, and even literature professors (Cathy Davidson) are to be believed, our k12 schools are still mired in the 19th century, led by drill masters who force meaningless facts and meaninglessly abstract math and science concepts down students' throats, totally oblivious to the 21st century world all around them.
Our eager diagnosticians propose the same basic cures for this supposed illness: make classrooms more student centered (preferably student group-centered), and make the curriculum more concrete and relevant to students' lives. And our major newspapers--especially The New York Times--are equally eager to give them a forum.
In the latest collusion between armchair academia and the Fourth Estate, we hear from Sol Garfunkel, executive director of the Consortium for Mathematics and Its Applications, and David Mumford, an emeritus professor of mathematics at Brown. Writing in past Thursday's New York Time OP-Ed pages on How to Fix Our Math Education, they begin by diagnosing the illness. Our current math curriculum, they write, is "highly abstract," "'pure' math with no context," with its "mysterious variable x" and its emphasis on solving quadratic equations, understanding transformations and complex numbers. This, they write, is "simply not the best way to prepare a vast majority of high school students for life":
Of course professional mathematicians, physicists and engineers need to know all this, 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.In its place: "a math curriculum that focused on real-life problems" and that "will lead students to appreciate how a mathematical formula models and clarifies real-world situations--what they call a "contextual approach, in the style of all working scientists," where instead of x and y, you have, for example, E, m and c, as in Einstein's E=mc2.
Presumably Garfunkel and Mumford have never actually looked at the latest high school math texts, which contain such problems as this and this. While arguably not good examples of real world math, this stuff is hardly abstract and "pure." For truly real-world algebra you have to go back in time to the 1960's or before.
But Garfunkel and Mumford want to do more than just tinker with the curriculum; they want to stop teaching algebra, geometry and calculus, at least to most students:
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.In short:
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 practically between everyday problems and mathematical formulations (as when we decide whether it is better to buy or lease a new car).We've been here before: back in 1920, when the Committee on the Problem of Mathematics, headed by William Heard Kilpatrick, argued that algebra and geometry should be eliminated from most courses of study. As Diane Ravitch describes it in Left Back:
The Kilpatrick committee recommended that mathematics be tailored for four different groups: first, the "general readers," who needed only ordinary arithmetic in their everyday lives; second, students preparing for certain trades (e.g., plumbers or machinists), who needed a modest amount of mathematics, but certainly not algebra and geometry; third, the few students who wanted to become engineers who needed certain mathematical skills and knowledge for their jobs; and last, the "group of specializers," including students "who 'like' mathematics," for whom the existing program seemed about right, although the committee proposed "even for this group a far-reaching reorganization of practically all of secondary mathematics."This sounds an awful like the European system of vocational tracking which so many Americans rightly bemoan. Is this really what Garfunkel and Mumford want? Do they really want it determined in high school who is going to pursue physics and mathematics, or major in one of the many subjects for which college-level math is the prerequisite?
Equally questionable are Garfunkel and Mumford's closing assertions. First:
We 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.Perhaps Garfunkel and Mumford no longer see mathematics and science as worthwhile areas for American competition. Second:
It is through real-life applications that mathematics emerged in the past, has flourished for centuries and connects to our culture now.Here Garfunkel and Mumford aren't repeating history, but rewriting it. While mathematical guess and check procedures often emerge out of real-world application, in general, real-world mathematical application has lagged several hundred years behind pure mathematical theory. As irrelevant to today's non-mathematicians as today's mathematical advancements may appear to be, they may turn out in several centuries to be crucial to solving real-world problems in anything from cryptography to quantum computing to the generation of sustainable energy. Assuming, of course, that future scientists and engineers are still getting adequate training in basic high school math.