The more time I spend working with high school students, I wish I could travel back in time and change how my students were taught to approach math. I have so many students who choose not to participate or share their answer with the class for fear of being wrong. For them, it is better to sit silently and never understand than to speak up and potentially be wrong.
As a math major, I have written many, many proofs. Last semester, I took a class where we proved all of the most important theorems that allow us to do calculus. Unlike math, writing proofs never came easily for me. When asked, I often told people that I chose to major in math because there is only one right answer. Well, as you likely know, proofs are an exception to that rule. There is no one right way to prove something. There are long proofs, short proofs, elegant proofs, and gadget proofs. However I soon learned that the best way to finding a proof that worked was to just start trying. Some days I would spend hours writing down mathematical statements, trying to find connections. Instead, I would find myself surrounded by crumpled notebook paper. With each failed attempt, I learned more about the problem. I gained new insights to further guide my attempts. And, eventually, I would usually discover the right combination of mathematical statements to get my proof rolling. Looking back, it is those proofs that I am most proud of.
A few weeks ago, I came across a passage in a book (If You Want to Walk On Water, You've Got to Get Out of the Boat) regarding this topic of failure. John Ortberg writes,
"Failure does not shape you; the way you respond to failure shapes you. Sir Edmund Hillary made several unsuccessful attempts at scaling Mount Everest before he finally succeeded. After one attempt he stood at the base of the giant mountain and shook his fist at it. "I'll defeat you yet," he said in defiance. "Because you're as big as you're going to get--but I'm still growing." Every time Hillary climbed, he failed. And every time he failed, he learned. And every time he learned, he grew and tried again. And one day he didn't fail."
How can I create a classroom culture where failure is not looked at as a defining feature but as an opportunity to grow? Math is learned by doing, by trying, by making mistakes, and by trying again. But, how do I get my students to try?