This is a response to the following article:

How to Fix Our Math Education (New York Times)

I think that the authors of this article have put the cart before the horse. Perhaps not having been in high school in quite some time, they have forgotten how math is actually learned. You cannot learn “applied mathematics” without first learning the very basics, like algebra and geometry. I agree that Americans would be well served to learn more practical mathematics, but this simply can’t happen without prerequisites. Yes, prerequisites, not corequisites. Some context could certainly help in teaching topics like algebra, where an example of an equation with a “mysterious variable x” could be something like an interest rate equation. However, the authors suggest teaching the exponential function. The exponential function is a function. Functions are a concept not even introduced until pre-calculus in some cases. You can’t understand what a function is until you have a strong grasp of algebra already.

In the data course, students would gather their own data sets and learn how, in fields as diverse as sports and medicine, larger samples give better estimates of averages.

This is called “hand-waving”. It’s great to motivate a topic, but unless you’re willing to follow up and go into the nitty-gritty details, it is not helpful because it doesn’t give the students any real skills. That larger samples give better estimates of averages is only a fact, not a skill. To quantify how large a sample needs to be for a certain scenario would require far more than just playing around with spreadsheets on a computer.

As for the statement that science and math were discovered together, I take exception. Back when Archimedes was already doing almost-calculus, physics was still talking about the four elements (air, fire, earth, water), biology still had spontaneous generation, and chemistry was still alchemy. In most cases, math illuminates science, not vice versa.

The problem is, of course, much broader than just math education. Everybody loves to bitch about the state of American education and the falling test scores in both math and English. I take the viewpoint that it is a cultural problem of undervaluing education, which has led to relatively low teacher salaries, which has led to this problem. Teaching is nobody’s idea of a glamorous profession, so we scrape the bottom of the college barrel for the near-dropouts, send them to teacher’s college for a year, then give them a classroom. I’m sure that many of them love teaching, but the ability just may not be there. It’s true that there are policy problems like No Child Left Behind, but I think that overall, we can start by just throwing money at the problem. Of course, change never starts at the political level. It starts at the cultural/social level, so until we change our attitudes towards education, it’s all just rearranging deck chairs on the Titanic.