Watching the kids progress in problem solving

One of my math goals for this year is to help the kids develop their problem solving abilities. It is a slow process (and also a hard to define process) but we seem to be moving in the right direction.

In the last two days I’ve had two really positive experiences watching each of the boys struggle through a problem. What was especially nice was that in both cases they didn’t know how to do the problem initially, but they stayed with it and were able to get themselves to the end.

The first example was with my older son. The problem was part of a NYT article about the Regents Algebra exam in NY. I don’t think he’s seen a problem like this one before:

The second example is from my younger son this morning. This problem from the 1994 AMC 8 gave him a little trouble initially, but he found his way through it when we talked about it later in the morning: