## The Harvard study on math and science education

There was a Harvard study released this week linking high school math to success in college science classes (which I’m inclined to file under “Very Obvious Stuff”), and now it’s beginning to make the rounds of my favorite blogs. So far the most interesting take is Rob over at Galactic Interactions: A cynical take on a study about high school science. He basically says that while they’re learning mathematical facts and tricks in high school, they’re not understanding the math.

First, though, I do want to agree that a solid grounding in math is essential. I have observed, and have heard other faculty comment, that students come into college not understanding algebra….

But let me suggest that there is another thing underlying the results of this study. That is, high school science is, in general, not taught the way it should be… and, college science is, in general, taught assuming students learned

nothingin high school science…

It’s an excellent post, followed by a number of very interesting comments, so I didn’t try to reproduce much of it here.

If Rob is right that high schools aren’t doing a good job of teaching math, then how does it help college science achievement? One reason may be that the students who take advanced math courses in high school (probably with the intention of taking science classes in college) would learn math even from a *bad* math class, or in spite of it, or without it altogether. They’re interested in the material. They work harder at the material, they find their own books, they even rearrange their schedules to find the best teachers.

Being on college track, they are required to take the class, and we might be reading too much significance into the fact that they took it. Their high achievement isn’t due to the fact that they took the class, it’s due to the fact that *they* took the class, as opposed to the poor achievers who tend to seek easier classes.

One of the themes explored in the comments to Rob’s post is that it’s difficult to test for understanding. Science is a process, not just a body of knowledge; we know how to test for the latter but testing the former ain’t so easy. This is equally true with math as with science. So students arrive at college with a “magical incantation” approach to math, having memorized a lot of formulas, and able to apply them to recognized types of problems on paper, but not necessarily ‘getting it’.

I am skeptical that there *is* a “right” way to teach math in high school, though. Invidivuals vary widely. My own math education crashed and burned in school; decades later I learned of undiagnosed dyslexia, which makes it so difficult to read numbers and symbols. (I had always thought I was just stupid.) Later still, I found that I can wrestle effectively with math concepts to whatever extent I can keep it all in my head; the problem occurs when the math goes to paper and I have to read what’s on the paper. So I keep pecking away at algebra and geometry and before I die, damn it, I’ll get a functional grasp of calculus.

There’s no “one size fits all” approach to math education. What works for me won’t necessarily work for you, and neither of those approaches may work for that other guy. I’m pretty sure we’ll have to get better at the messy process of identifying what will work for each person. And notice I said “person”, not “child” because I believe there’s a tendency to regard children as somehow other than persons. We squeeze ‘em into the school system and try to extrude ‘em out the other end just in time for their remedial classes in college.

What gets me is the population like me, good at math but becomes uninterested in school. Teachers haven’t seemed to learn that doing the same thing over and over again ruins interest in the topic.

Unfortunately there aren’t many ways to teach multiple learning styles to multiple students without more teachers.

It’s just another reason why Montessori Schools seem very appetizing.

Beside several good ways to teach math, there are several bad ways. The one that infuriates me this morning is the test-preparation way: Instead of teaching algebra, teach how to do algebra problems. This doesn’t lead anywhere, because every problem is a special case. The student passes the test (or not), but doesn’t understand the basis for the next chapter. Again he learns by rote to get through the next test. This is as boring as memorizing how to fill out a tax form, and as useful. A few years later I explain mixture problems and the student says, “So you divide both sides by whatever number is here, right?” If I were a Zen master, I’d hit him with a stick and he would be enlightened.