I pull up a chair next to her and ask where she's stuck.
"I don't get it," she says.
"Get what?"
"All of it."
"Where did you get stuck?"
"Right here," she points.
"What is the goal?"
"I don't know."
"What are you trying to do?"
"Solve for x."
"And what is x?" I ask.
She shrugs her shoulders.
"X is the independent variable. X is that thing that we get to decide in life. X is how many hours you work or tacos you buy or how fast you're driving on the way to San Diego." This isn't my classroom and I'm not sure if I should be doing this, but I plow forward.
"So, you're trying to figure out the meaning behind what you can control. You're trying to solve something. And here's the beauty of it: you can't break an equation."
"What do you mean?"
"You can always plug it in and if it's wrong, you can go back to the first level and try again."
"Like a video game?" she asks.
"Exactly. It's like baseball with as many strikes as you want. So go forward and backwards. Make mistakes. Then when it doesn't work, ask yourself why it didn't work and then go back to the first level."
"So, I can mess up?"
"Yeah, you should be messing up. If you don't mess up on anything, you need to ask for harder problems to solve."
"That makes sense."
She goes back to her paper and messes it up, confusing negative and positive integers and forgetting that 7/7 or 9/9 or 5/5 all equal one. But as she talks through it conceptually, she doesn't run out of lives. There is no Game Over. She doesn't strike out. The journey doesn't stop.
And regardless of the mixed metaphors and the confusing, meandering points I tried to make, she doesn't look so scared to tackle the algorithm.
I'm stealing this. Tomorrow, 1st Period.
ReplyDeleteBeautiful post about real teaching. But I can't help but think how can we measure this to prove that you are an effective teacher? (sarcasm about how ridiculous teacher evaluations are).
ReplyDeleteI personally find this to be a better judgement of you than any "score."
I love this! It is going straight into my livebinder so that I read it every year before teaching linear equations :)
ReplyDeleteI love your post for what it is. However, as a maths teacher I feel compelled to share a couple of my equations stories as alternative paths this story could have taken.
ReplyDeleteOne is on determining that the problem was in understanding why we had to isolate x in the first place. It also echoes your story in the theme of not making assumptions and listening to the students to discern what really is bothering them.
And the other one is Teaching equations big-picture style - a story of a lesson that focuses on what students already know and putting equations in perspective.
Finally, there's the Problems vs Exerciseswhich probably is most aligned with your post but still with a mathematical lesson bent.
I feel like I'm spamming you with links but that's not the point. The point is that our encounters with kids is an evolving narrative. It can go many different ways and each one (quite likely) is an opportunity to learn.
cheers.
Dear Doyle,
ReplyDeleteI'd love to see what you're doing in terms of stealing it :)
Dear Mike,
Thanks for the kind words. Your points on merit pay really resonate with me.
Dear Jeannette,
I'm glad it was practical for you. It's a part of what makes me odd, though.
Dear Malyn,
Thank you for the links. Those are awesome. We need to talk math some day :)