Multiplication - My goodness, my kids are so different

I'm teaching Ella the multiplication tables, and I can't believe what a difference it is from teaching Madison hers. I thought it was worth outlining.

It's fascinating to observe the difference in their approach to memorization, for instance. Madison memorizes something almost instantly -- IF it makes conceptual sense and is either words expressing whole thoughts, or set to music. She memorizes poetry almost effortlessly, and can practically quote passages from books she's read a few times. Memorizing her lines for drama took almost no effort.

But putting the answers to the equations for the multiplication tables, boy was that a struggle for her. She was her own worst enemy about it. I had to try method after method before we finally finished those tables.

In contrast, Ella seems to be decent but not startling at her ability to memorize poems and songs, but has picked up the memorization of the multiplication tables so fast she almost takes my breath away.

I didn't start either of them out memorizing until they both had a conceptual grasp of what multiplication is. They learned this approximately the same way, "4 rows of 3 block" or "7 groups of 5 M&Ms." Ella, now, thinks of it as "Four 3's" or "Seven 5's" and often says the equations that way.

Then, once they had the method, I set them about memorizing the tables, which Ella has just started. And they both use approximately the same method for that, too. I ask Ella what is 7 x 3. Well, she has memorized 7 x 2, so she counts up 7 from 14. Madison did about the same thing, I recall.

However, Ella has now realized that memorizing the numbers in the skip counting sequence makes it much, much easier. Madison was never one for skip counting, she prefered the more conceptual method, and regarded the skip counts (which we didn't focus on so much) as just one more memorization issue. But Ella, well, I had her derive the answers for the 4-times table yesterday by using the Math-U-See blocks and writing down the equations and answers on little note cards. And then, she simply proceeded (at a suggestion of mine) to memorize, in not even 10 minutes, the skip counting sequence of 4, 8, 12... up to 40. All day yesterday, at completely her own initiative, every so often she'd come out with "4, 8, 12, 16..." So now she has a method that is even EASIER for her, and if I ask her 4 x 6 she'll either know it because she knows 4 x 5 and that the next one, which is 24, must be 4 x 6, or she'll just use her fingers and count up the sequence of skip counting. This morning (she's been sleeping with us the last few days, the Nancy Drews have "freaked her out,") she snuggled over to me and the first thing she said was a triumphant whisper in my ear, "4, 8, 12, 16..."

If it is this easy, I'll thank my lucky stars.

Later on in the process, by the way, the fact of not knowing the answer would get in Madison's way terribly, because she takes a trip down the road of what the implications are of the fact that she doesn't know it, and ruminates about THAT, instead of putting her energy to solving it. So, I'd ask her:

What's 4 x 6?

She'd realize that she had forgotten the answer. And to my dramatic little girl, this became akin to disaster. I could almost hear the internal dialogue:

"What's 4 x 6? Okay, let's give this the fraction of a second of thought that this usually requires. Oh no! I don't know it! I can't believe I don't know this! I knew it the other day. Come on, Madison. You're blowing it, here! You SHOULD know this, Madison. You're supposed to be good at math, this is a big deal that you don't know 4 x 6. How are you going to do real math if you don't know 4 x 6? Maybe you're not as smart as you thought."

Whereas, I have this feeling that down the road if Ella doesn't know 4 x 6, she'll repeat to herself inside, "4...8...12...16...20...24!"