Wednesday, January 5, 2011

New Math

So I was helping my oldest kiddo with his homework tonight.

Homework? I hear you say. Homework, in second grade?

Yep. Welcome to the brave new world of American childhood.

The Peep brings home one of these four- to five-page collections of foolscap every Monday and has to turn them in Friday morning. They are typically composed of a page of writing work, another of reading-and-comprehension, a couple pages of math, and a front page for the boy to record his reading, which is set at 20 minutes a night.He's terrible about it, of course, as you can probably remember from your school days. There's always something better to do than homework - blogging, for example - and the seven-and-a-half-year-old mind is a gossamer and flittery thing. So Mojo or I usually have to wrestle him into submission to get the work done. It is a process that all parties genially dislike.

Tonight we did the math worksheets.

I realized after I started that this was actually pretty sophisticated math for second grade. The sheet header showed a variety of domestic pottery labeled with prices in cents. The teapot is 72 cents, the glass 18, the frying pan 57, and so on. Down the page were a series of written questions, such as; "Alisha has 50 cents. She buys a glass. How much money does she have left?"

I sat down with the Boy and we looked at the first problem. We read it over. I looked at him.

"I have to think." he said. I waited. He thought.

"What should we do to start?" I asked.

"I'm thinking." he replied.

I waited.Finally I pointed to the example the sheet provided. "Look how they set up this problem. How can we do that here?" I asked.

"I'm still thinking." he replied. "It's time to stop thinking and do the problem." I hissed, at which he protested "I'm thinking! Mister Chun says we need to think about the problem!". His mom added that he was right, and he was told to think about the problems. I looked down at the page, frustrated.

"Do you know how to do this math problem, buddy?" I asked as neutrally as I could.

He frowned at the page. "I think I do." he said uncertainly. "Then what are you going to do?" I asked gently. He wrote down a number "nine" in the box with the problem. "That's the answer." he announced, in defiant hopefulness."No, it's not." I replied. "You don't know how to do these, do you?" I asked, wondering at the sort of math class that would start a kid on double-digit addition and subtraction without showing them how to convert tens into units.

So I showed him how, while you couldn't subtract the 8 from the 0 in the units column you could "break" a ten and convert it to ten "ones", then add the ten to the 0 and make it 10...then subtract 8 from 10 to get 2. And then you made a little mark striking out the tens value and reducing it by the one "ten" you moved. And subtracted the tens.

Little man was resistant at first until he saw how this method actually worked better than guessing or whatever sort of computation he was doing initially. By the time we reached the bottom of the second page he was anticipating me in "breaking down" the tens, converting single digits to teens, adding and subtracting.

The thing is, it took me a bit of thinking to remember how I do simple double-digit addition and subtraction; it wasn't nearly as intuitive as I thought it was. And explaining it to a second-grader was almost as difficult. But perhaps the most difficult part was understanding what it was he didn't understand and why. What seemed obvious to me was completely opaque to him; he couldn't make the cognitive jump from the written description to the setup of the numerical problem, and he couldn't do the simple unit addition and subtraction in his head as I could. It was difficult not to see his incomprehension as stupidity, and his math errors as carelessness.But he kept at it; he slowly worked through the word problems, set up the numerical problems, corrected his math errors, and carefully wrote down each answer. I don't think he ever enjoyed the process, but I think he got some satisfaction from doing the work correctly and well.

And then he hopped up and bounded happily down the hallway to the tub to splash and play with his toys, leaving me tapping the eraser of my pencil on the paper covered with childish handwriting, cartoon cups and plates, and wondering just what we had accomplished.

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