A recent opinion piece in the New York Times by Sol Garfunkel and David Mumford that what we really need is "quantitative literacy" among the general population, or the ability to make quantitative connections in the context of real life. They ask us to imagine replacing the traditional "sequence of algebra, geometry, and calculus with a sequence of finance, data, and basic engineering." In sum, they advocate the idea that the traditional "abstract" mathematics curriculum should be supplanted with a mathematics curriculum focused on "real-life problems." After all, most of us do not end up as a mathematician or physicist but in occupations that utilize basic applied math.

My wife taught high school chemistry in inner city Los Angeles for four years, spending two years as a Teach for America corps member. She would often tell me that some of her students did not even know how to use fractions properly, and that there was really no point in some of them learning high school chemistry because they likely would never use it in the jobs they would acquire after graduation. What they needed, rather, were basic math skills that would help them navigate the real-life problems that they would encounter in everyday life. On the one hand this fits well with the idea that quantitative literacy is critical for the general population. Yet it also raises the following question:

Why were some students in her high school chemistry classes unable to properly utilize fractions?

I don't have the answer to that question, but this does call to mind what Bill Gates has aptly pointed out: "I have never met the guy who doesn't know how to multiply who created software." I'm guessing that the guys Gates has met would also probably need to know how to use fractions.

I think that Garfunkel and Mumford have a point that perhaps we need to emphasize quantitative literacy in the general population. However, I'm not entirely clear on where traditional mathematics should end and where a curriculum focused on real life problems should begin and I think this give and take lies at the center of the debate. Certainly, at least up to a point, traditional mathematics education is critical. And just because the idea of quantitative literacy sounds appealing doesn't mean that implementing a new quantitative literacy curriculum would have the desired effect on our nation's mathematics performance.

Shouldn't We Emphasize Both Quantitative Literacy and Quantitative Excellence?

To their credit, the authors note that "The truth is that different sets of math skills are useful for different careers, and our math education should be changed to reflect this fact." So they acknowledge that people pursuing different careers will need different levels of math education. Quantitative literacy is likely important for the majority of the general population, but when it comes to national competitiveness, isn't it the quantitative excellence of the "smart fraction" that really will make the difference (see my article on this here)? We don't just need our future innovators in science, technology, engineering, and mathematics (STEM) to be literate, we need them to be outstanding.

That's why I think programs such as MATHCOUNTS are so critical. Not only does MATHCOUNTS focus on enhancing the mathematical skills of all students, but they also provide a program for the very best and brightest math students of our country. In essence, they emphasize both the development of quantitative literacy and quantitative excellence.

Garfunkel and Mumford began their article stressing that there is widespread alarm in America regarding the state of our math education. They note that this concern can be traced to America's performance on various international tests (such as PISA) when compared to other countries such as China, Japan, Korea, Singapore, and Finland.

I applaud the authors for their excellent article. I believe they have done a great service to us all by raising some intriguing points regarding math education that we should consider seriously.

On the other hand, I wonder if we have forgotten a very simple principle when it comes to competition as we attempt to propose novel solutions: If someone else is outperforming you, shouldn't you try to learn from them? How are China, Japan, Korea, Singapore, and Finland educating their students? I think it would be wise to consider that the solution to our problem might lie, at least in part, in first recognizing that the educational systems of other countries might have something important to teach us.

© 2011 by Jonathan Wai

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The image is by Dave Mosher from Flickr.