Wednesday, February 27, 2013

HB 1350: Math Remediation and How Not to Need It

Virginia House Bill 1350, which has passed both the House and the Senate, provides for "math remediation."

http://lis.virginia.gov/cgi-bin/legp604.exe?131+ful+HB1350EH1

This reminds me of a cool true story about how a primary school teacher, not otherwise a very good or well liked teacher, taught advanced math to everybody. I've cited other things my fourth grade homeroom teacher said (not in Gate City!) as things that ought to get a teacher fired...but by the time we left fourth grade I think all thirty-five of us were just about ready for eighth grade algebra. This is something I've been asked to share with homeschooling readers, so here's the story.

I am not good at math. I was not good at math. Early in the year I was sent home with a nasty note to the effect that some schools might not require everyone to learn the multiplication table in grade three, but this one did, so would my parents please make sure I'd learned it before I came back to school in the morning. Other kids were going swimming. My parents said that I could still get in some swimming if I memorized the multiplication table fast. So I did. Only I was still dysnumeric; the fact that I've learned the multiplication table, and the addition table, does not keep me from making idiotic mistakes in multiplication and addition. I'm not capable of being "taught" not to be dysnumeric, but after grade nine I learned to cope with it.

And everybody knew,'cos Piaget said, that nobody under age ten is capable of understanding multiplication well enough to learn division or fractions. My teacher understood that as well as he understood that several of us were still nine or even eight years old, when he started teaching us advanced arithmetic.

He told us that a doctor had advised him to drink less coffee for his health, so if he started to feel drowsy, what he was supposed to do to wake himself up was work out a math problem. We were free to ignore him. We were also free, just in case we were feeling drowsy too, to shout out the answer for each step in the math problem the teacher was working out on the chalkboard.

So at least once a day, and sometimes eight or ten times, whenever a critical number of people started looking out the window and waiting for other people to finish something, this teacher would set up a math problem on the chalkboard. "5280 divided by 365. If you know the answer, shout it out. 365 into 5..."

"Won't go," a few kids would shout.

"365 into 52..."

"Won't go!" more of us would shout.

"365 into 528..."

"One time!" Everybody would get into it.

"Next step?"

"Multiply!"

"One times 365 is 365..."

"Subtract!"

"528 minus 365 is..."

And so on. Absolutely no pressure. No comparisons. No nagging. We were just watching a grown-up do something grown-ups did, and being encouraged to pay attention to the details of it.

We had a thick, intimidating math book. "New math" was the current fad. It allowed teachers to toss out simple exercises in geometry, just for fun, to liven up arithmetic lessons. Thanks to "new math" that book contained exercises in long division, fractions, decimals, ratios, percentages, solid and plane geometry, non-decimal number systems, and I think compound interest.

Before spring break, we were all doing those exercises. The book explained a long, complicated, oldfashioned way to set up division problems. "Just ignore that. It's oldfashioned. You all know how to divide, multiply, subtract, and bring down." We all did. The book explained fractions, decimals, non-decimals in the same way the teacher did. We did those exercises too.

I was nine years old. According to Piaget, I didn't understand the idea of division. Actually I think I understood it pretty well, although I wasn't ready to explain it to people who didn't. According to Piaget, I'd merely learned by rote how to do a few tricks. Well, that's as it may be. I have never had any trouble doing those tricks, in high school, in college, or in adult life, beyond the basic fact that I'm dysnumeric. There may well have been a time when "Division is the reverse of multiplication" was just a thing I'd heard adults say, and a time when I understood it. I don't remember any transition between those times.

In any case, that rote learning did me no harm at all. I don't think it did anyone any harm. I think kids are wired for a certain amount of rote learning. They hear adults saying things, they repeat them in ways that show that they didn't understand them, and then one day they're teenagers or adults and they do understand those things. As long as there's no pressure on children to learn things by rote, there's no danger in it. A parrot may learn to say that 63 divided by 7 equals 9 and think that that's a song lyric or a given name. A child may learn to say that 63 divided by 7 equals 9, without thinking what that means, and then later, when the child's brain has developed further, the child sees that of course if you have 63 of something and want to divide it into 7 piles you put 9 in each pile.

This was not a special school for bright students, although I don't remember any evidence that anyone had major brain damage. You could do what my teacher did with any student, or students; with any subject, not only math. It's how one-room schools work; students on the lower level learn by observing what those on the higher level do.

Next year we came back home, just in time for me to be in the class of the world's worst math teacher, the one who had a good system but couldn't make a move without oozing emotions: she was menopausal, an undiagnosed diabetic, she hated fifth grade math, she hated fifth grade kids. She liked to inflict pain. Some kids I knew who'd been good students up to grade five started failing math and developing mental blocks in grade five. I didn't. I already knew everything the hateful fifth grade teacher was supposed to be teaching us, so her hostility didn't touch me--although I didn't like her, personally, any more than anyone else did. I had nothing to worry about in sixth or seventh grade math, either; the teachers were nice, some of the "new math" games were fun, I already knew all the concepts, and I was still dysnumeric.

Eighth grade algebra was different. That class had a real old-school teacher. We were ready to learn the concepts, and that teacher made sure that everyone had learned the concepts by making us set up our own equations, not just work out the exercises in the book. I think that's an excellent way to identify students who really need any "remediation."

But these days the academic standards seem so low...why can't children learn the things we're being told they can't learn? Why do we need the "at least even this generation of little brain-damaged trolls can learn this much" approach called Common Core, which Karen Bracken calls an anti-American plot to make American children ignorant? What's wrong with a little rote learning in place of coffee for the teacher? No pressure, no trauma. Divide. Multiply. Subtract. Bring down. Your children can do that. If I can learn anything to do with numbers, you know your children can.

There was, now that I think about it, another wonderful thing my unlovable fourth grade teacher did. He never told our class, "You are smarter or better educated than other children. You already know everything other children your age are going to be struggling to learn, about math, for the next three years." That was true, but it wasn't something middle school students need to think much about. I don't know whether my fourth grade teacher had any spiritual consciousness or even much public spirit. Maybe he was just self-serving. When children aren't told that they've learned something that's supposed to be especially difficult, and can therefore consider themselves especially clever, they are free to formulate the thought, "I had a good teacher."