Sol Garfunkel and David Mumford published an interesting op-ed in yesterday's The New York Times, entitled "How to Fix Our Math Education". They argue that there is no, "single established body of mathematical skills that everyone needs to know to be prepared for 21st-century careers." Rather, different skills find application in different careers, and "our math education should be changed to reflect this fact."
At its heart, Garfunkel and Mumford argue for a more practically-oriented approach to math education, "focused on real-life problems;" for example, "how mortgages are priced, how computers are programmed and how the statistical results of a medical trial are to be understood." In this manner, the quantitative component underlying practical problems in a variety of fields is made more apparent. This emphasis could perhaps more effectively demonstrate to budding math students the connections between math and other fields, such a science, sport, and everyday life. Garfunkel and Mumford call this ability to recognize connections, "Quantitative literacy."
Garfunkel and Mumford make a good point, in that most people will not need to know how to use the quadratic equation, except perhaps to help their 9th grader with homework. And practical math could well make math as a subject more tolerable to the large section of students who growing up found it so much Sanskrit.
Yet for all the perceived benefits of an emphasis on the practical, I wonder where we would be without a healthy dose of the abstract as well. If math was simply useful, what would we fuss about anymore? English perhaps, what with all that grammar and vocabulary. In all seriousness though, would we better off? Would practical math instruction attract talented youngsters to math and engineering fields, for which politicians and education specialists continually advocate?
Garfunkel and Mumford make the point that math should be taught in conjunction with other subjects, especially science and engineering. This makes good sense to me. Too often it seems, people are turned off to careers in such fields solely because of bad experiences with abstract, high school math.
But for all that, I still wonder if something important would be lost if we abandoned the abstract side of mathematics. Would we be doing a disservice to the most talented students by denying them the challenge of higher-level math at a young age? My experience as a friend of several math-oriented folks suggest that you often don't need to teach practical math to the math-savvy; they can already interpret graphs, figure out tip, balance a check-book, and calculate mile-splits in their head.
Yet for those who struggle with math, it is not simply the degree of abstraction that gets them. Often, these folks simply have a hard time using their skills; cashiers who forget how to do basic arithmetic while on the job, or job candidates who forget how to perform a simple percentage problem (cough, cough, me...) might all be well served by a more practical grounding of math. The extra practice and emphasis upon the useful could take a poor math student and make him or her a fair, good, or even great math student.
To adopt this approach for everyone, however, seems inappropriate. Just as some athletes can naturally trainer at a higher intensity than others, some students seem to have an easier time with advanced math than others. That's not to say that slow-starters won't someday reach the elite level. It simply describes what I observed while growing up, which was that some people took to math far more easily than others. These folks probably would not benefit from a practical approach to math. But the vast majority in the same classroom might.
That seems to me to be the most pressing dilemma in the matter.
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