Thursday, January 28, 2016

Red Math, Blue Math, Old Math, New Math

It wasn't long after moving to the US before I found myself in a heated discussion about math teaching.

Not the perverse pride of "Oh, I was always hopeless at math", but a serious discussion about the best teaching methods in K-12.

As the conversation went on, though, I became more and more puzzled by the intensity that my partner brought to the discussion.  It seemed that he was less interested in talking about the different ways in which people learn, and what might be best in a mixed classroom; more alarmed that the correct, "traditional" way of teaching was being undermined by dangerous innovations promoted by impractical university professors.

Fast forward to today's polemics against "Common Core math" (see the meme above, and many like it which you can probably find in your Facebook feed).

Business Insider ran a nice article explaining what is going on above (which, honestly, is simply a representation on paper of how I and probably many people do mental subtraction, when making change for instance).    But I don't think that such explanations will do much to soothe some of the angry reactions that techniques like this seem to produce.

I felt I got some insight into why this might be from an unexpected source. I was reading the book American Grace by Robert Putnam and David Campbell. This is an exhaustive sociological and statistical analysis of the state of religion in America, full of graphs and tables. In Chapter 13 I learned that one of the most effective single questions that one can ask to identify whether a person has a generally "conservative" or "liberal" attitude to the world is this: Which is more important for a child to be taught: obedience or self-reliance?

Aha!  I wonder if, for some, following a classical pencil-and-paper arithmetic algorithm is the epitome of obedience.  Few children will be able to explain why the algorithm works.  For "liberal" education reformers, this is a deficiency; without understanding, algorithmic knowledge is brittle.  Perhaps for others, though, the question of understanding is moot; the cultural significance of arithmetic comes exactly from its being the paradigm case of "obedience", of following authoritative rules without question.

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