## Thursday, October 06, 2011

(Congratulations to anyone who actually read this post after seeing the title!)

Many years ago, MAD magazine had a piece about joke courses for college football players. The one I remember was called “Subtraction: Addition’s Tricky Pal.”

The Boy is discovering that there’s some truth to that.

He’s struggling with “borrowing.” Say you want to subtract 235 from 700. Turning the last zero into a ten requires borrowing from the digit before, but that’s a zero, so...

Oh, the humanity.

I learned “borrowing” sometime during the Carter administration, so I’m a little fuzzy on the step-by-step of teaching it. I suggested thinking of 700 as seventy ‘tens.’ To borrow a ten for the last column would leave you with 69 tens. Then, in order from right to left, ten minus five is five, nine minus three is six, and six minus two is four. 465, done and done.

That doesn’t seem to take, though. The idea of “seventy tens” seems a little too abstract.

He’s fine when just borrowing from a single digit. 82 minus 28 is fine, since borrowing from the 8 still leaves enough to subtract the 2. But borrowing across multiple digits remains mysterious.

Trying to convey ‘borrowing’ to a ten year old really brings home the difference between knowing how to do something and knowing how to teach it. I’ve walked him through problems step by step, narrating each step as I go, and he seems to follow. Then I have him try a few problems, and he does great. But it’s gone by the next day. It doesn’t stick.

His frustration is palpable and insidious. He’ll get back worksheets with middling grades, but the middling grade really just reflects a single mistake repeated over and over again. He honestly wants to get it right, but just can’t seem to hold the concept for very long.

I’m okay with him learning to struggle a bit, since that’s a valuable life skill. (Sometimes I think the only way in which my social science grad school training prepared me for my current job was in teaching me how to take a punch.) But I don’t want him to get so discouraged that he starts to doubt his own abilities. I don’t want him to become the kid who writes off math as something you’re either born with or not, like wiggling your ears.

He can’t be the first bright, motivated kid to have trouble holding on to a mathematical concept overnight. So I’m sending out this message in a bottle -- okay, in a blog -- hoping that someone has found a way to help that kind of concept stick in the mind of a ten year old.

Wise and worldly readers, have you found a way to explain this sort of math that’s both simple enough for a ten year old, and sticky enough to make it to the next day? TB and I would be terribly grateful for anything that works.

(Program note: We’re trekking across several states over the next few days, so the next post will be on Tuesday the 11th.)