Learning Strategies

It’s hard to know where to begin. What’s wrong with the video “Math Education: An Inconvenient Truth, ” which is primarily an attack on TERC’s Investigations in Number, Data, and Space and other standards-based curricula? Well, let me count the ways.

On second thought, I don’t want to count them, because I’ll be here all day. Let me just mention a few:

1. Narrator M.J. McDermott complains that Investigations teaches kids to “reason through problems.” As I say, it’s hard to know where to begin. Surely this is a good thing. Surely reasoning through problems is the primary goal of school mathematics learning.


2. The video’s first example is finding 26 × 31. It goes on to show an “inappropriate” way of reasoning that TERC promotes. Quoting verbatim:

   I know that 26 × 31 = (20 × 31) + (5 × 31) + (1 × 31).
   So how do I find 20 × 31?
   Well, I know 10 × 31 is 310, and I can figure out from mental math that 20 × 31 is twice this, and I can figure out that that’s 620.
   Now I need to find 5 × 31, and I can figure out that 5 × 31 is half of this [points to the 310], so I can figure out from mental math that that’s 155.
   So I add that to the 620 and I get 775 so far.
   So now all I need is one more. I know 1 × 31 is 31, and now I just add the 775 here, and I get 806.

   McDermott correctly calls this method “inefficient,” but surely it demonstrates much more understanding than the standard magical algorithm, and surely the skills involved will have far more payoff in doing algebra.


3. Ah, next we get to long division — a current favorite in my precalculus class, since we’re doing long division of polynomials in order to factor them. (And later we’ll be doing long division of polynomials in order to find asymptotes.) Many of my students find that their memory of long division with numbers help them with algebra, but more of them find that the work with algebra finally lets them make sense of the traditional algorithm with numbers. Anyway, back to the video. The sample problem is 133 ÷ 6, and — no surprise — McDermott objects to TERC’s avoidance of the traditional algorithm. TERC’s “less efficient” method eventually results in the sentence 6 × 22 + 1 = 133, which is exactly the right form for doing algebra and number theory in high school. But McDermott sarcastically quotes the teaching guide for another series she attacks, Everyday Math, because it concludes that it is “counterproductive to invest many hours of precious class time” to memorizing traditional algorithm for long division. “The mathematical payoff is not worth the cost,” correctly observes Everyday Math.


4. McDermott laments the lack of math skills among many college students. I’ve lamented that too, but surely it’s not because of TERC and the like. Most of these college students went through traditional math programs!

In any case, it is easier to supplement a reform math curriculum with traditional practice than it is to supplement a traditional curriculum with innovative activities. Both can be done. I could keep going here, but I think I’ll stop there.

Labels: math, teaching and learning, Weston