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February 11, 2013 3:33 PM Math Is Hard

By Daniel Luzer

Maybe students are learning the wrong math. Maybe the math is just too hard.

So argues By Andrew Hacker in a recent opinion piece in the New York Times. As he writes the current standard mathematics course sequence in American schools “prevents us from discovering and developing young talent. In the interest of maintaining rigor, we’re actually depleting our pool of brainpower.”

Well, maybe. Maybe or maintaining rigor is just hard.

Hacker’s idea is that making students take math for which they have no aptitude makes them hate school and give up early, thus depriving the country of potential artists or writers or pharmacists or something.

Students should still take mathematics, he argues, they just don’t necessarily need Algebra, Geometry, and Calculus.

Quantitative literacy clearly is useful in weighing all manner of public policies, from the Affordable Care Act, to the costs and benefits of environmental regulation, to the impact ofclimate change. Being able to detect and identify ideology at work behind the numbers is of obvious use. Ours is fast becoming a statistical age, which raises the bar for informed citizenship. What is needed is not textbook formulas but greater understanding of where various numbers come from, and what they actually convey.
[A new, better math might] teach students how the Consumer Price Index is computed, what is included and how each item in the index is weighted — and include discussion about which items should be included and what weights they should be given.

Well sure it might work, but such a system probably wouldn’t work very well. The trouble with this line of thinking is that computing something like the Consumer Price Index is actually a very difficult mathematical problem requiring mastery of, well, the standard mathematics course sequence in American schools. That’s why students take math, so they can do things with math.

It is true that one does not necessarily need a complete and sophisticated understanding of all branches of math in order to function as a responsible adult (I mean, I can’t calculate the CPI, or really even explain it without looking it up) but the real reason to study math concepts is to learn to think and solve problems, even if one doesn’t retain all of the material.

This plan to reform math in schools, he calls it “citizen statistics,” might sound practical. “It’s true that mathematics requires mental exertion. But there’s no evidence that being able to prove (x² + y²)² = (x² - y²)² + (2xy)² leads to more credible political opinions or social analysis,” he writes. That’s true, but having some understanding of how to prove that (x² + y²)² = (x² - y²)² + (2xy)² helps a great deal in terms of say, getting into college. And it probably always will.

This is not a new idea. We’ve actually seen this “citizen statistics” educational philosophy before. Throughout most of the 20th century high school education policy, based on a theory that people learn best when they choose their own subject matter based on their interests, resulted in practice in a situation where in America’s public schools the children of teachers and accountants learned polynomials and the children of laborers and factory workers learned to balance checkbooks.

The general principle under which Hacker seems to operate goes something like this: because many American students have trouble with standard math, math is preventing them from success. Therefore, the solution is to eliminate standard math. Well, no. If American students are having trouble because they don’t know math, maybe we need to improve the way we teach math.

Daniel Luzer is the news editor at Governing Magazine and former web editor of the Washington Monthly. Find him on Twitter: @Daniel_Luzer

Comments

  • Keith M Ellis on February 11, 2013 11:33 PM:

    This is a truism in general, but I think it's particularly the case that successful mathematics pedagogy is sensitive to variations in students' intellectual styles and strengths.

    Contemporary american math education is a one-size-fits-all hybrid of theoretical, technical/pragmatic, and historical approaches and arguably isn't very successful at any of these. More to the point, students are often much more temperamentally inclined to one of these approaches than the others and are much more successful (and happier) as students when their education is emphasized accordingly.

    Vocationally, at some level of preparation, one of these approaches becomes primary, regardless of a student's temperament. But high school students oughtn't be tracked so early into making choices between, say, being an economist and being an editor. So secondary math education needs to avoid precluding post-secondary/vocational opportunities for any given group of students while still achieving some level of competency. The one-size-fits-all approach fails at this because one size doesn't fit everyone and, for those it doesn't, creates an environment where they fail at math. Given that, the trick then is to tailor math pedagogy to a few different temperaments while not sacrificing the student's future opportunities for more vocationally necessary math competency.