I’ve been thinking a lot about the math learning discussed by Malcolm Gladwell in Outliers. In one part, a student takes twenty-two minutes to solve a single math problem. In another, a KIPP student takes twenty minutes to solve a math problem on the board with the help of his classmates .
Obviously, one way to master material is to have more time: at KIPP, ninety minutes of math class per day. Or in my own tutoring, a luxurious hour or more to discuss whatever the student wants to go over without any pressure or grades.
Slowing down and diving deep is awesome if you have time. But what do you do when you don’t have time?
When I was in eighth grade and routinely cried myself to sleep over my math homework, if someone had suggested to me that I spend twenty minutes on a single problem until I got it, I probably would have just cried harder. I, like many other students before and after me, had way too many problems to finish.
More time is not always an option.
However, as a student, I would have been a lot more open to the idea of slowing down and exploring if I only had to do it for a few problems. If I, or my teacher, had given myself permission and said, “Why don’t you just try to solve one of these problems, and take as much time as you need,” I would have been more willing to try diving deep.
I’m not talking about dumbing things down or making students less responsible. My philosophy has two parts. If you give a student a page of twenty math problems they don’t think they can do, they’ll feel pressured to do them all so at least they can show you they tried, but they probably only have time to attempt to do them poorly.
But if you give a student one to three difficult math problems instead of twenty, there’s a much better chance that the student will actually solve the problems. Doing it correctly, once, is more effective than doing it incorrectly or incompletely twenty times. And once they’ve untangled the process correctly, they’ll be in a better position to replicate that process later.
Also, reducing the amount of material can be used as a temporary measure to get a particular student through a rough patch and help them overcome a block.