How & Why (Understanding Math)

“When we do our daily lessons, my son does great. Everything seems to click. But when he sees the same topic later, in a review or on a test, it’s like he’s never heard of it before. How can I help him pull math up from the dregs of lost memory?”

This is a common problem, and there’s no easy answer.

You see, it’s easy for humans to convince ourselves we understand something when someone else explains it. It seems to make sense, but it doesn’t stick in our minds.

If you think of times when you’ve tried to learn something new, you can probably remember the feeling—you thought you had it, but then when you tried to do it yourself, your mind went blank.

So how can we help our kids when they can’t remember what to do?

Explanations Are Easily Forgotten

One thing that can help is to NOT explain the lesson. Just start with a problem, and ask how your son would think about it. What would he try?

For example, if you are working on times-8 strategies, how would he try to figure out 6 × 8? What does he remember that would help him? Where would he start?

Then you can build on his answer.

If he figured it out, then can he think of another way to do it? There is always more than one way to do anything in math. So, if he solved it by counting 8’s, what’s another way? What if he wasn’t allowed to count? Could he figure it out using any math facts he knows?

Talking about how he reasons things through will help it stick in memory.

Posing His Own Problems

Or if he couldn’t figure it out, then let him name a problem he can do.

Perhaps 6 × 8 is beyond him, but he does know 6 × 2. Then work from there. If two 6s are 12, then how much would four 6s be? And if four of them are 24, then how many would double-4 of them be?

And then once he’s got that answer, can he think of another problem that will help to fix it in his mind? Maybe from knowing 6 × 8, can he figure out what 6 × 9 would be?

Or let him pose a problem for you to solve.

Maybe he gives you 16 × 8. How would you think about that? Talk about your reasoning. Perhaps you already know that 8 × 8 = 64, so 16 eights would be twice that much. Or you used some other way of thinking.

Going Deeper

Push the idea of multiplication beyond what the book has in mind.

• How about fractions? If he knows what 1 × 8 is, can he use that to figure out what 1/2 times 8 would be?

• Or −1 times 8?

• Or if he knows what 3 × 8 is, can he use that to figure out 300 × 8? Or something harder, like 33 × 8?

The idea is to start from where he is and push him to think as deeply as he can.

When we ask a student to listen to our explanation and follow our instructions, we are asking them to think our thoughts. But thinking someone else’s thoughts is boring.

What we want is to have kids who think their own thoughts about the topic at hand. Because thinking their own thoughts is fun and leads to more learning.