mastery

On Tuesday, I had a whole grand plan for the day laid out. Both boys chose to start with math. 9 yo was in the throes of long division. He did a page, and then another, and then he asked me to give him any long division problem that I wanted, and then he made up his own problem and kept adding digits to the dividend until he could finish dividing without remainder.

He mastered long division and he could not wait to get more problems to prove his mastery.

Meanwhile 7 yo had a pre-multiplication unit. It mostly involved skip-counting, and he did page after page of math, probably 10 pages in all, till he was done with the unit. He understood the concept, and each page was another opportunity to apply it.

I thought math would be quick that day; instead it took over an hour. Both boys engaged in learning out of their own free will, and did not want to stop.

That same day a friend posted this post about unschooling math. I agree with some: kids will take lead in their learning, you will learn the math that you need to function, curiosity about math will go a long way. What I have a problem with is the blank assumption that math is hard, abstract and impenetrable subject, to which only people with a special aptitude take a liking. And the first thing that bugged me is the assertion that long division is useless.

People roll eyes at long division (and at fractions). They think nobody uses it. They also never memorized times table, so long division becomes tedious. Whenever I had any problem come up in kids' presence that required long division, I always grabbed a paper and did it out, the long way. They saw it, and even if they did not understand what I was doing, they saw that it is useful, and accessible. Oh, and I spent quite a few hours working with 9 yo on times table. We drilled it from Math Mammoth. I got flashcards and tested him. I hung up two multiplication tables. I asked questions which required multiplication. He does not know it super well (he HATES memorization), but he came around once he saw how useful it was to just know the product for 2- and 3-digit multiplication rather than work it out every time. Now that we hit long division, he saw that it is simply applying that multiplication and, voila, it works! Moreover, he can check himself by multiplying.

At dinner that night, out of the blue, 9 yo asked: "Is fifty divided by 6 equal to 8, remainder 2?"
"Yes."
"So to go on a five hundred mile trip, we need 8 hours and 20 minutes."

Before you think this is trivial, watch this: