In a recent article about math education that ballyhoos the “latest approach” in how to teach math, this statement was made:

“If the teachers are telling students how to solve a problem, and then that problem isn’t exactly what’s on the test, it creates this disequilibrium for a student,” said Beverly Velloff, the math and science curriculum coordinator for the University City School District.

There is nothing new about the so-called breakthrough ideas the article discusses. Moreover, this quote is representative of how traditionally taught math is mischaracterized. The notion is that students are taught by rote, given a set of problems that are all exactly alike, and thus leaves them flummoxed when presented with a problem that is even slightly different. Such a caricature may be true for traditionally taught math done poorly, but it makes no allowance for it being done well.

Looking at an example from algebra:…

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