PracticePracticePractice

I have to do something today besides sit around thinking and writing about math . . .

But all that other stuff can wait!

I'm going to be quick, which means this is off the top of my head:

1. Carolyn's friend Gerry on multiplication

For what it's worth, I think he's dead right about the value of mental multiplication.

I've mentioned that I taught a little after-school class in Singapore Math this winter. In every class I had the kids do mental math.

We did a lot of mental multiplication with the explicit purpose of implanting the distributive property inside everyone's heads.

I'm constantly pushing Christopher to do mental multiplication for this very reason.

He now 'knows' the distributive property; I think he can actually write it out in its 'letter form,' i.e. a(b + c) = ab + ac. (I think.)

He also, I think, knows -- and understands -- that the multiplication algorithm is based on the distributive property.

He knows that when you're doing a problem like:

21
x23

(sorry for the funky alignment; neither Carolyn nor I has been able to figure out how to insert extra spaces in the text thus far . . . )

. . . anyway . . . Christopher knows that when you take the 3 times the 2 you are multiplying 3 x 20; he knows that you are splitting the problem up into smaller multiplication problems and then adding the products together, which you can do because of the distributive property.

But even though he knows all this, I swear he's not as good at mental multiplication as the kids in my Singapore Math class (which Christopher boycotted). Nor does he seem to understand mental multiplication.

He didn't get the practice my Singapore Math kids did, and he's still not really making the connection that the same thing that lets you do the standard multiplication algorithm can be used to multiply numbers in your head or to very quickly multiply numbers horizontally.

His knowledge is still inflexible; he's not generalizing it to other situations and contexts. He's not seeing the connections.

This brings me to --

2. Carolyn's post on practice

This is a HUGE subject, but here are my first thoughts.

I've found that practice per se isn't such a hard thing to get kids to do.

My Singapore Math kids loved the timed worksheets I gave them. (I used the 'Fast Facts' worksheets from Saxon Math.) They used to ask to do more of them, because they made it into a competition. They were revved!

I'd have my timer out, and the kids would call out Done! when they finished the sheet; then I'd call their time & they'd subtract it from the starting time of 5 minutes and write it down on their score sheets.

(I gave each child his own 'Singapore Math' notebook with a Saxon score sheet in the front. So each week they could compare their new score to their previous scores.)

Now, you'd think this could go seriously awry, with the slow kids feeling defeated. I was worried about this myself, since I had kids ranging all the way from a fourth grader who may have been classified with some level of special needs (I have no idea--the parent seemed to indicate this) to a fifth grader whose parents immigrated from China and who's probably one of the best math students in the school.

That's a range.

But nobody's ego got crushed. Exactly the opposite.

Since they all had their own score sheets, they were competing against themselves as well as against the class. They also did different worksheets, depending on whether they'd hit the 5-minute mark on the worksheet from the week before.

As soon as somebody could do the 'Fast Facts' addition sheet, he or she moved on to the 'Fast Facts' subtraction sheet. So the faster kids were doing harder worksheets, and the slower kids were doing easier worksheets.

I guess that's like handicapping in golf, right? (I don't play golf, so I don't know.)

Let's just say that levelled the field considerably, and no one seemed to feel remotely humiliated because they were still doing subtraction when someone else was doing multiplication. They just liked the race.

And they all picked up speed incredibly quickly; I was amazed.

I had one child who, the first time he did a 5-minute addition worksheet, took -- gosh, I don't know -- upwards of 8 or even 10 minutes to get through it.

This child has perfect handwriting and is painstaking when he writes numbers, which was slowing him down, so the second day I actually wrote the answers for him so he wouldn't lose time just on penmanship.

But here's the miracle.

This kid did zero practicing in between classes, and yet by the third class he was coming in under the 5-minute deadline.

I couldn't believe it, and I don't know how he did it. He just . . . got faster. They all did.

They were achieving personal bests every week.

This gets back to Carolyn's post on group learning and Wichita Boy's post about competition: under the right circumstances, practice is fun.

I think the problem for Christopher & Ben is that they're sitting at a table with their mom who is forcing them to do math.

If they were sitting at a table with their friends, and everyone was doing math, it would be different. I happen to know for a fact that this is true, because a couple of times Christopher's friends Drew & Marc, who are fraternal twins, have done a Saxon Math lesson with us. Their mother told them they had to, so they did.

When the three of them are doing Saxon Math together, they peddle.

I've been thinking about group learning ever since Carolyn wrote about it, and I'm turning into a believer.

But more on that later.


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I see I've gotten off-track.

I meant to talk about Carolyn's observations on practice and expertise.

I'll have to do that later, but in the meantime the single best article I've seen on this subject is here.


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I wonder if you could get kids to practice the viola if you put 3 of them in a room together and set the timer.


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