I love being wrong. Really, I do.
Sometimes when we embrace our "wrongness" we figure out what is right.
Case in point: Math.
Until recently, I held to certain beliefs about how to approach math that verged on religious fervency (it doesn't matter if you hate it, do it!).
Paralyzed by the fear that unless I pushed a certain methodology, my underlings would perform poorly on the SAT's, I continued to force feed a curriculum whose claim-to-fame is the mastery of standardized testing in the field of mathematics (homeschoolers: you know that of which I speak).
Then it happened. One of my enlightened friends (I am grateful to have a few) forwarded something to me called A Mathematician's Lament by Paul Lockhart. A twenty-five page mathematician's argument, originally written in 2002, on how we have really mucked-up the study of arithmetic in schools. I read the first two pages and knew that I was reading something that was going to profoundly challenge my long-held ideas about our approach to math . I dare you not to be moved...changed.
Sapare Aude
"Dare to Know"
Lockhart draws a brilliant connection between music and art and math that never would have occurred to me. But he's dead right. At the end of page 2, he states:
"Sadly, our present system of mathematics education is precisely this kind of nightmare (Raising Autodidact's note: read pages 1-2 to understand the "nightmare"). In fact, if I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done - I simply wouldn’t have the imagination to come up with the kind of senseless, soul - crushing ideas that constitute contemporary mathematics education."
Ouch. He continues...
"Everyone knows that something is wrong. The politicians say, “we need higher standards.” The schools say, “we need more money and equipment.” Educators say one thing, and teachers say another. They are all wrong. The only people who understand what is going on are the ones most often blamed and least often heard: the students. They say, “math class is stupid and boring,” and they are right."
Wow. You mean when my kids complain about their math curriculum and say they "hate it," they aren't just being difficult?
Parcheesi, anyone?
Reading the first two pages of "Lockhart's Lament" threw me into a kind of existential crisis. Everything I had been thinking and practicing for the last seven years might be utterly and totally wrong. Not only that, maybe what we had been doing was causing more harm than good.
In answer to the question, "But don't we need third graders to be able to do arithmetic?" Lockhart's answer is, "Why? You want to train them to calculate 427 plus 389? It’s just not a question that very many eight-year-olds are asking. " My nine-year-old was eight last year, I can attest to this fact.
Then Lockhart says, "For that matter, most adults don’t fully understand decimal place-value arithmetic, and you expect third graders to have a clear conception? Or do you not care if they understand it? It is simply too early for that kind of technical training. Of course it can be done, but I think it ultimately does more harm than good. Much better to wait until their own natural curiosity about numbers kicks in."
See, I told you this was subversive stuff. Not for the faint-of-heart. Now he really had me.
So, what do you do with young children in math class, Mr. Lockhart?
And then Mr. Lockhart says, "Play games! Teach them Chess and Go, Hex and Backgammon, Sprouts and Nim, whatever. Make up a game. Do puzzles. Expose them to situations where deductive reasoning is necessary. Don’t worry about notation and technique, help them to become active and creative mathematical thinkers."
At this point this resonated so completely with my personal approach to learning, I had to thump myself on the head, and ask "Why on earth was I not already applying this to math?" Well, because I'm afraid, of course. Afraid that it won't "work."
As it happens, a few months before reading "The Lament" I was introduced to the Life of Fred Math series authored by Stan Schmidt. It was described to me as a way to engage children in math without boring the pants off them or making them crazy. I was intrigued. My kids are solid math students, but it is possibly their least favorite subject. It is simply how the material is presented. You don't have to hold a "dog-and-pony show" to capture their attention, but you do have to find the elegance and art in the subject matter. It seemed this "Fred" fellow might be on to something.
So who exactly is Fred, and what about his life has anything to do with math? According to the Life of Fred Math web-site:
"Fred Gauss was born on the western slopes of the Siberian mountains. By the end of the final book, he is six years old. In his everyday life he first encounters the need for each new part of mathematics, and then comes the mathematics. Never again will students have to ask their perennial question: “When are we ever gonna use this stuff?”
No, Fred is not a real person. In fact, he's roughly thirty-six inches tall and teaches at a university named KITTENS. My nine-year old started the series about a month ago. Sometimes he reads "Fred" at his desk, sometimes while he's curled up on the couch. I often hear him laugh out loud at the story line. This is definitely a first. I have never noticed audible laughing during math-time before.
I told my twelve year old last month that as soon as he finished his current math curriculum, we were going to stop and take a break. He's looking forward to starting his own "Fred" book. In fact, "Fred" can take you all the way up to two years of college calculus and a year of college statistics. My oldest took his last cookie-cutter exam on Friday and let out a whoop. He ran around the house for about five minutes celebrating the fact that he didn't have to open that old math book ever again.
Sometimes letting go of what isn't working is hard, because we're convinced it's the only way. For me, this involves staying open to being wrong, sometimes on a daily basis. I don't feel threatened by being wrong, it's just a necessary part of trying to figure things out.
We're gonna try "Fred" around here for a while, and see what happens. Maybe it will work, maybe it won't. But I think we're headed in the right direction.
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