Alfie Kohn, the education critic, in a book about education, devoted a chapter on the downsides of teaching math in the traditional manner. Here’s an excerpt:
“The teacher begins by demonstrating the right way to do a problem, then assigns umpteen examples of the same problem (except with different numbers), the idea being for students to imitate the method they were shown, with the teacher correcting their efforts as necessary.”
Yes, traditional math can be done poorly, it’s no lie. But that doesn’t mean that it is always done poorly. Good textbooks and good teachers scaffold problems so that they increase in difficulty and are variants of the original worked example. Students are expected to stretch and move beyond, using reasoning based on the original structure.
“It’s a pretty sharp contrast, between math defined principally in terms of skills and math defined principally in terms of understanding. But if we are persuaded by a constructivist account of learning, even the latter isn’t enough. When traditionalists insist that it’s most important for kids to “know their math facts,” we might respond not only by challenging those priorities but by asking what is meant by know. The key question is whether understanding is passively absorbed or actively constructed. In the latter case, math actually becomes a creative activity.”
In Alfie Kohn’s world (and in the world of others who think similarly) there is a dichotomy between procedures and understanding. And even then, “understanding” must come via constructivism. In his world, there are no “aha” moments when being directly instructed. Homework problems do not entail any discovery, in his view.
I could go on, but you get the message. He wrote this in 1999, but the thoughts contained in his epistle to the masses have become scripture and are taken up by the likes of Jo Boaler and others. Be aware of it. If you teach a class in an ed school make it an exercise for students to describe “what’s wrong with Alfie’s picture”. And if they don’t know, then enlighten them.
But chances are that if you’re reading this and you teach in an ed school, you’re probably wondering why I’m bothered so much by what Alfie has to say.