As our Kindergarten daughter races down the road to education, I’ve decided to do a little reading to try to keep up. Fortunately, her teacher literally wrote the book on mathematics instruction, so I have an obvious place to start. Her wonderful book is a great reminder that math is not about numbers or computation, but about curiosity and thinking and determination. I’m kind of sad reading it, honestly, because though I enjoyed certain aspects of math in school (geometry and basic algebra and physics were fascinating to me), I finally quit taking math classes after getting bogged down in advanced algebra. Then and now, I have a real sense of defeat about it. But now I wonder if I had possessed more determination, or perhaps had teachers who helped me to see beyond my short-term struggles, whether I might have come through with a more positive outlook on math. Maybe my life would look much different now.
But the best part of the book so far isn’t as much about math as it is about life. Ms. Wedekind (which is what I will call her, forever) displays a lovely streak of contrarianism when it comes to a certain classroom practice. Where most of us did elementary-school math with a pencil and eraser, she insists that her students use a pen. And she coaches them not to obliterate their mistakes with the ink, blacking out the numbers beyond recognition. Instead, she tells them to simply draw a single line through the mistake and keep working.
It is a way of acknowledging and accepting our failures, to be sure. To get beyond our shame at making mistakes, and our hesitancy to explore new options. To avoid the pitfall of perfectionism. But more than that, it is a way of mapping our thinking. The worst thing for a teacher to see, she says, is a single correct answer to a problem on the page. It is much better to see how the student got to that conclusion. To better understand their process. ‘Pathway to learning’ is her nomenclature, and it obviously applies to a lot more than Kindergarten.
There are an almost infinite number of ways to solve a problem, and we can all learn from the approaches of each other. You can add ’5 + 2′ and get ’7′ simply because you know that, or you can count up to seven, or draw seven marks on the page, or take ’5′ at face value and count on two more, or vice versa. Or, you can draw five detailed busts of George Washington next to two pictures of squirrels. Or line up five blocks next to two coins. Or you might happen to know that ’4 + 2′ equals ’6′, so you take one away from 5 and then give it back later. Or maybe you remember that ’6 + 2′ equals ’8′, so you just solve that problem and subtract the ’1′ later. Or you can completely mess up the whole thing, then cross out your work and try again. The point is the journey, not the destination. Show your work, so that we can all learn from it.
So as the noise of the Season of Resolutions begins to fade into the background, I’m going to try to do some things less well in the new year. To make a few mistakes. To embrace my imperfections. To reveal the pathways of my learning. To blog some things that I will disagree with someday soon. To write things, if only so I can read them in ten years and see what– and how– I was thinking. 2012, you don’t scare me.