Dealing with (Math) Overwhelm (1)
Sunday, October 31st, 2010I’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.
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What an interesting perspective! I love Gladwell’s books, but the way you’ve used his example to propose a solution to math overwhelm is fantastic! Totally opposite to what programs like Kumon routinely do. I’m guessing this can only work in the following situations:
1) When a teacher is working with a class of similar abilIty students like in the Gladwell example.
2) When a tutor or parent is working one on one with a student.
3) With independent learners
This is great food for thought for educators, parents and students alike. Thanks for putting this out there!
Caroline, welcome and thanks so much for stopping by! I’ve been enjoying your blog over at maths insider and I’m glad to see you here.
You’re totally right — this wouldn’t work in every situation all the time, but is more of a temporary way of reframing the situation so it doesn’t seem so overwhelming!
In one of her math books, Danica McKellar tells a sort of similar story about taking a math test and totally panicking–she wasn’t able to do the problems in the time allotted at all. For reasons Danica says that she still doesn’t completely understand, her math teacher let Danica keep working on the math test while everyone else went out to recess.
Within that extra time, Danica stopped panicking and successfully finished the test. This experience was actually a turning point for her in math.
So — we CAN change the parameters — increase the time or decrease the material — to help students change their mindset when they feel totally stuck and overwhelmed! But you’re right, not all the time 🙂
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Rebecca, as a former classroom math teacher for many years, I know you are right. There is so much institutional pressure to “get through the textbook”. Math teachers feel that they have to move quickly to get to the next page, next chapter . . . instead of doing what’s right for the students. If motivated, and encouraged, students can get just as much out of a 5 problem assignment if they can take their time, work collaboratively, and be creative. And . . . that learning will stick! They learn so much and so much better if we teachers just “get out of the way”, sometimes.
Agree! Thanks so much for stopping by and sharing your own experiences.
Anecdotally it seems that in other countries where students are less math-phobic, students have a lot more time to internalize the material. In his book “teach like your hair is on fire,” the great 5th grade teacher Rafe Esquith says something along the lines of, how crazy is it that we teach math by giving kids 500 problems, and then when they finish them, we say, here’s another 500 problems to do–the most important thing is that the kid is doing the *10* problems that are right for her — or something along those lines. Food for thought. 🙂
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