Tuesday, March 06, 2007

Learning math

I'm not in favor of schools in general, for many reasons, but mostly because I don't believe the structure necessary to keep children paying attention to the teacher is good for them or actually helps with the learning process. That said, I did find a wonderful essay written by a teacher at the Sudbury Valley School, by the name of Daniel Greenberg. The essay is available online, but is also published in his book "Free at Last: The Sudbury Valley School". The reason I like this article, written by a teacher, is that he talks about teaching math, and the means, methods and results are quite amazing, and the implications just warm my unschooling heart. I'm going to quote the whole thing here.

And 'Rithmetic
Sitting before me were a dozen boys and girls, aged nine to twelve. A week earlier, they had asked me to teach them arithmetic. They wanted to learn to add, subtract, multiply, divide, and all the rest. "You don't really want to do this," I said, when they first approached me. "We do, we are sure we do," was their answer. "You don't really," I persisted. "Your neighborhood friends, your parents, your relatives probably want you to, but you yourselves would much rather be playing or doing something else." "We know what we want, and we want to learn arithmetic. Teach us, and we'll prove it. We'll do all the homework, and work as hard as we can." I had to yield then, skeptically. I knew that arithmetic took six years to teach in regular schools, and I was sure their interest would flag after a few months. But I had no choice. They had pressed hard, and I was cornered. I was in for a surprise.
My biggest problem was a textbook to use as a guide. I had been involved in developing the "new math," and I had come to hate it. Back then when we were working on it -- young academicians of the Kennedy post-sputnik era -- we had few doubts. We were filled with the beauty of abstract logic, set theory, number theory, and all the other exotic games mathematicians had played for millennia. I think that if we had set out to design an agricultural course for working farmers, we would have begun with organic chemistry, genetics, and microbiology. Lucky for the world's hungry people that we weren't asked. I had come to hate the pretensions and abstruseness of the "new math." Not one in a hundred math teachers knew what it was about, not one in a thousand pupils. People need arithmetic for reckoning; they want to know how to use the tools. That's what my students wanted now. I found a book in our library, perfectly suited to the job at hand. It was a math primer written in 1898. Small and thick, it was brimming with thousands of exercises, meant to train young minds to perform the basic tasks accurately and swiftly.
Class began -- on time. That was part of the deal. "You say you are serious?" I had asked, challenging them; "then I expect to see you in the room on time -- 11:00AM sharp, every Tuesday and Thursday. If you are five minutes late, no class. If you blow two classes -- no more teaching." "It's a deal," they had said, with a glint of pleasure in their eyes. Basic addition took two classes. They learned to add everything -- long thin columns, short fat columns, long fat columns. They did dozens of exercises. Subtraction took another two classes. It might have taken one, but "borrowing" needed some extra explanation. On to multiplication, and the tables. Everyone had to memorize the tables. Each person was quizzed again and again in class. Then the rules. Then the practice.
They were high, all of them. Sailing along, mastering all the techniques and algorithms, they could feel the material entering their bones. Hundreds and hundreds of exercises, class quizzes, oral tests, pounded the material into their heads. Still they continued to come, all of them. They helped each other when they had to, to keep the class moving. The twelve year olds and the nine year olds, the lions and the lambs, sat peacefully together in harmonious cooperation -- no teasing, no shame. Division -- long division. Fractions. Decimals. Percentages. Square roots. They came at 11:00 sharp, stayed half an hour, and left with homework. They came back next time with all the homework done. All of them. In twenty weeks, after twenty contact hours, they had covered it all. Six years' worth. Every one of them knew the material cold.
We celebrated the end of the classes with a rousing party. It wasn't the first time, and wasn't to be the last, that I was amazed at the success of our own cherished theories. They had worked here, with a vengeance. Perhaps I should have been prepared for what happened, for what seemed to me to be a miracle. A week after it was all over, I talked to Alan White, who had been an elementary math specialist for years in the public schools and knew all the latest and best pedagogical methods. I told him the story of my class. He was not surprised. "Why not?" I asked, amazed at his response. I was still reeling from the pace and thoroughness with which my "dirty dozen" had learned. "Because everyone knows," he answered, "that the subject matter itself isn't that hard. What's hard, virtually impossible, is beating it into the heads of youngsters who hate every step. The only way we have a ghost of a chance is to hammer away at the stuff bit by bit every day for years. Even then it does not work. Most of the sixth graders are mathematical illiterates. Give me a kid who wants to learn the stuff -- well, twenty hours or so makes sense." I guess it does. It's never taken much more than that ever since.

Twenty weeks, twenty hours. Six years' worth of math taught the "traditional" way. This is just so amazing, I never, even as an eclectic/unschooly homeschooler, would have thought you could do math this way. I went to public school K through 12. Everyone knows it takes lots of time to teach math. Well. This calls for a radical change in thinking about how learning happens. These kids were ready to learn, asking to be taught. This is obviously the key. And it just can't happen this way in a normal school setting. Sudbury isn't a normal school, so it worked for these kids with this teacher. There is no reason that this can't work for homeschoolers, and for other subjects besides math. What do you think?

Stumble Upon Toolbar


John said...

Does this mean that I helped or hindered your learning when I lied about you getting correct answers when we were kids using that plastic multiplication table thingy?

Silvia said...

That's just evil. No wonder I still have trouble with my multiplication tables!