How quick they learn when the time is right

I realized this week that I hadn't reviewed division of fractions with Madison in a long time, and that I'd never taught her how to compute averages. We have been working our way through a sixth-grade assessment test that I gave her in January, working on the bits of math that she didn't remember or had never learned how to do.

Earlier this week, in 10 minutes, we did division of fractions.

Then, yesterday, in 10 minutes, we did averages.

The same thing happened this morning with Ella. She knows the multiplication tables, so today was the day to move on to multiple-digit multiplication (2 by 1). First I did some where there is no carrying (e.g., 22 x 3), then some where the tens answer has more than one digit (73 x 2) and then finally moved on to the need to carry the tens place (63 x 4).

She needed to be shown it once, and then did a dozen problems on her own, all of which she got exactly right.

I remember spending weeks in elementary school on things like these.

Don't get me wrong, I'm happy to spend the months it took Ella to learn the multiplication tables. But it's amazing how quickly they learn something new when they are rock-solid on what they need to know in order to learn it, and there is only one more little concept or strategy to employ to get the new skill. A lot of learning isn't like that; you have to learn two or three or even more concepts all at once in order to learn the new idea. We still do that kind of learning, with a lot being thrown at you all at once. But it's worthwhile remembering how pleasurable it is to do exactly-the-next-step learning. I'll try to do more of that with the girls.