## Saturday, December 25, 2010

(Math problems of the week: 2nd grade Investigations vs. Singapore Math)

Bky

I was thinking about these TERC problems again. Look at the instructions: "Solve each problem. Show your work." The point to take away is that in 2nd grade the TERC authors think of adding two one-digit numbers as a "problem" for which work needs to be shown. I would consider that a "fact" that one should know by automatic recall by now, and let's get on to more and more and more (for example, adding numbers close to 100 to other two- and three-digit numbers).  But the two problem sets are still related, because the TERC problem set is based (if I infer correctly) on the "making 10" strategy for learning the basic math facts that have to do with adding "large" one-digit numbers (9, 8, 7, 6). The Singapore problem set is for practicing the strategy of adding 98, for example, by adding 100 and subtracting 2.  What Singapore does very well is they explicitly teach these kinds of strategies. Eventually kids don't need a strategy any more for adding 9+7, they will recall that; but they will always need a strategy for adding 98 (even if they get to where they can do it quickly).  So this comparison of problems shows two things about TERC vs Singapore: (1) Singapore will get kids to automatic recall of simple things early on, and then move on to harder stuff; and (2) Singapore explicitly teaches kids strategies for computation (mental math, let's call 'em) and problem solving (think of the bar models and so on).   It seems a waste of time and energy to be still worry about how to "solve" 9+7 when you're in second grade. In first grade, however, that counts as a problem that needs to be solved ... until you just know it. What counts as a problem is like the horizon. The further you go, the more it recedes.

#### 1 comment:

kcab said...

I especially love the last bit of Bky's comment. The sense of problem-solving being work at one's skill horizon makes it very clear why it is so difficult to hit the right level of difficulty for a mathy child.