I see children as instinctively creative and analytic, innately mathematical. School done wrong, particularly math class done wrong, has a way of putting out this light inside of young people. This is a story about seeing it happen.
I teach at Saint Ann’s School, where grades are not allowed and creativity holds perhaps the highest value. When you strip away grades as the source for authority and remove standard course content, “the leadership of the teachers arises from their intellect and accomplishment,” quoting the mission. “There is no other source of status.” Remove those things, and classes can spend their time learning from each other, driven by passionate personal interest.
In sharp contrast, I am spending part of my summer teaching math to incoming fifth and sixth graders at a small private summer session. The demands on me are simple. Get the kids a head start on next year. Do what’s in the book. Have them do every page in six weeks. This means we have to do about seven pages a day. Homework is given letter grades each day. Incomplete work must be made up, and poor work must be corrected. Ignoring the fact that these homemade books are full of misguided activities and tons of typos and mistakes, the primary focuses are arithmetic, terminology, and standard tricks for deciphering “what they’re asking.” Much of it could be classified as mathematical busy work. A lot of the content and techniques are new to students, but they have to move quickly to “just doing it” in order to get through the work load.
What keeps me there is the thought that in my time with the kids, I can get them through the busy work, narrating along the way, and then stoke their mathematical fires by challenging them with really compelling and inviting math problems. I felt great about last year, but one of my current students has really shaken me up, today especially.
* * *
He really struggles to complete his homework, always saying how distracted he gets. Doing so many problems each day, he struggles to work “at pace.” And yet, this guy gets on a roll whenever he relies on his intuitive number sense. He wants “his strategy.” “I’m just trying to find a strategy,” he says, finishing too few problems again. He analyzes what he’s doing to the point that he slows down to think until he’s figured out exactly how it works. In short, this kid can’t do all of the work, because he’s thinking too much about it!
Having seen the change in his face when his strategy clicks, and he starts nailing it, today was particularly hard. Long dividing two decimals was tricky for him, and kicking himself for being slow again, his face lit up. “I think I figured something out,” he said, “math is like just doing work.”
I was gutted, but I knew exactly where he was coming from. The demands are simple: do the work until it’s done. The program doesn’t care how he thinks. Get the work done. Despite my backing, the head teacher pushed to bring him down to fourth grade. He was embarrassed enough for her to change her mind, but the trouble was clear. This student is in a learning environment too rigid to give him thinking time.
* * *
He possesses a unique knack for numerical reasoning. He has so much to celebrate and enjoy developing, but he’s being rushed through tons of material and busy work for the sake of “high standards.” The book asks almost nothing of his own naturally creative math insight, so he does little thinking for homework. Class time tells him he’s too distracted and too slow, so his only regular time with mathematics is negative. And so, he slowly writes off his positive experiences with problem-solving.
Mathematics requires time to think and create. Asking students to blow through grunt work with handed down shortcuts is foolish. Students need time to make up their own strategy. In fact, making up the strategy is the part that’s mathematics. Take that away and you’re just doing work.