I worry that we’re pushing many kids to grasp math at higher levels before they are ready. When they struggle, they begin to dread math, and eventually we lose thousands of students who could be the scientists and engineers of tomorrow. If we held back and took more time to ground them in the basics, we could turn them on to math.
We’re asking young kids to move up in mathematics too far, too soon, in other words. Patrick goes on to focus especially on a push in California to get more younger kids taking Algebra and cross-references it with a Duke University study showing negative effects of the same sort of program in North Carolina.
I’m in complete agreement with this op-ed, although thankfully I haven’t felt that push so much with my own kids, ages 3, 6, and 8. There have been hints of pushing algebra a little too early for my taste but for the most part, it’s fairly intelligently built in to the curriculum; and in any event my kids’ teachers have not applied pressure to move up unless kids want to and they’re ready.
Where I see the effects of an early push into higher levels of math is in another subject that is often pushed down too far: Calculus. Here, whether it’s in an AP Calculus class in high school or the traditional freshman calculus class in college, the effects of early pushes to higher levels of mathematics are greatly compounded. Issues with arithmetic, algebra, geometry, and trigonometry tend to get amplified in calculus, which needs facility with all those subjects. When you look at graphics like these that show an enormous increase in the number of students taking AP Calculus in high school, it’s no wonder that the MAA and the NCTM would put out a joint statement about calculus, essentially saying: Stop teaching this subject in high school until students are strong on the basics.
It’s important to note that being “strong on the basics” means more than just mechanical fluency. One of the teachers quoted in the op-ed says that “In the lower grades, more time has to be devoted to practicing basic computational skills so that they are internalized and eventually come naturally.” Yes, but internalizing a skill takes more than mere practice. It takes thinking about that practice and becoming comfortable with it — including, as much as possible, understanding why the computational skill you are practicing works. Kids can’t just learn to compute; they have to be taught to compute in a way that makes sense to them, that scales up to harder problems, and then be given chances to do that scaling-up process themselves. This isn’t easy, and it’s like cooking a tough piece of meat — you have to use low heat over a long period of time.
And if I could connect this to another recent post, it’s another point where I have issues with the overzealous use of computation-heavy teaching resources like Khan Academy. KA videos stress computational fluency. There is nothing wrong with this, but when we begin to think that this is all mathematics is, the pathway is laid for thinking that the faster one learns how to compute, the more advanced one’s understanding of math is, and pretty soon kids end up in calculus needing an intuition and conceptual fluency with previous subjects that they just don’t have, because it didn’t magically appear when they learned how to compute.