I attended the NCTM regional meeting in Phoenix. Here are some notes.
A Brief History of Math Education
NCTM President Matt Larson talked about the history of the math wars, which as it turns out started in the early 1800’s. A previous version of his presentation can be found on his page on the NCTM site. If you want to know how we got to the current conflict around the Common Core, this is a great place to start, as the slides are abundantly footnoted.
For 200 years, memorized procedural fluency and conceptual understanding have been duking it out… there is not much new under the sun. Well, except for one thing: Matt ends his talk with a bunch of reasonable strategies for this round, strategies that might help prevent yet another swing of the pendulum. His key point may be that we should make clear that procedural fluency and conceptual understanding are not in conflict with each other. Quite the opposite: you can’t really have one without the other. We want fluency, but we want more. (I have been saying this for a long time: see for example the cheerfully titled Nothing Works. Also, as long as I’m talking about myself, I should go further back, and mention my own involvement in math war skirmishes: my reply to a vitriolic attack on my work, and a discussion about geoboards.)
Matt gave examples of how to talk to parents about these issues. He shows how the traditional multiplication algorithm includes much misleading language: when we say “carry the 2”, we’re really talking about 20 (or 200, etc. When we say “add a zero” what are we saying?) He then shows the “box method” (aka “area model”, etc.), which reveals the underlying mathematics (place value, the distributive law). Apparently, parents’ response is “Oh! I get it!” He then explains that we’re trying to have 4th graders “get it” when they’re in 4th grade, not in 30 years when their children are in 4th grade. He also tells the story of the perfect job for someone who is expert at arithmetic computation. Come in, do calculations on paper, go home, get a big salary. Of course, in our technological age, such jobs no longer exist.
I have just one bone to pick with Matt: in this presentation, he talks about the importance of assessment, done well, without explicitly denouncing the standardized test mania that has been so destructive to math education. This in spite of having pointed out, in this very talk, that much opposition to the Common Core stems from people who confuse the standards with the high stakes tests. I hope that NCTM will become more visible in the movement against those tests, as the organization has been unconscionably quiet on that front.
PS: Before the talk, Matt somehow recognized me, and told me that the NCTM team that will be working on “coherence and focus” for grades 9-12 will be looking at my paper on the strengths and weaknesses of the Common Core standards for those grades. Good news! If you haven’t read it yet, check it out!
More Phoenix notes in my next post.