In 2002, Paul Lockhart wrote an article about the state of mathematics education called A Mathematician’s Lament. Lockhart argues passionately that what children are typically taught is neither useful nor interesting. He believes children would get far more from emulating what mathematicians actually do, unstructured mathematical exploration and proofs. One of the problems, Lockhart acknowledges, is that many math teachers don’t understand or appreciate what he calls “real math,” leaving them unable to teach it. While I agree we need to improve our math teaching, and I agree that exposing many more children to “real math” is a good idea, I think Lockhart is at once too optimistic and too pessimistic.
Peter Gerdes, a graduate student in mathematical logic at Berkeley, critiques the over-optimism for me. While some children would greatly prefer “real math,” many students will be indifferent or downright hostile to it regardless. Why? Because math is difficult, much more difficult for some than others, and because there are serious social consequences associated with actual and relative mathematical skills.
But both Lockhart and Gerdes are too pessimistic in that they either deny or ignore the benefits from learning the math schools currently teach. Though more research should be done on evaluating the benefits, I will note that the math skills that are measured on standardized tests are highly predictive of later academic and labor market outcomes. There is even evidence that national economic productivity and growth is affected by the skills measured on such tests. These and other considerations lead me to believe that we could improve mathematics education a lot, even if we didn’t make any of the sort of changes Lockhart recommends.
Most importantly, what Lockhart recommends, and what we’re currently doing, are not mutually exclusive. In fact, though we will have to make tradeoffs, they are both necessary and (on some margins) complementary.
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