The Great Algebra Debate

Earlier in the summer, veteran sociologist Andrew Hacker caused a stir by arguing that algebra shouldn't be a mandatory course in high schools and colleges:

Education Realist reviews the numbers and responds:

These numbers, on the surface, don’t support the conventional wisdom about math performance: namely, that elementary school teachers need improvement and that the seeds of our students’ failure in higher math starts in the lower grades.

Elementary students are doing quite well. It’s only in advanced math, when the teachers are much more knowledgeable, with higher SAT scores and tougher credentialling tests, that student performance starts to decline dramatically.

What these numbers do suggest is that as math gets harder, fewer and fewer students achieve mastery, or anything near it. What they suggest, really, is that math knowledge doesn’t advance in a linear fashion. Shocking news, I know. We have all forgotten the Great Wisdom of Barbie. ...

Anyway. With numbers like these, it’s hard not to just see this entire debate as insanely pointless. In California, at least, tens of thousands of high school kids are sitting in math classes that they don’t understand, feeling useless, understanding deep in their bones that education has nothing to offer them. Meanwhile, well-meaning people who have never spent an hour of their lives  trying to explain advanced math concepts to the lower to middle section of the cognitive scale pontificate about teacher ability, statistics vs. algebra, college for everyone, and other useless fantasies that they are allowed to engage in because until our low performers represent the wide diversity of our country to perfection, no one’s going to ruin a career by pointing out that this a pipe dream. And of course, while they’re engaging in these fantasies, they’ll blame teachers, or poverty, or curriculum, or parents, or the kids, for the fact that their dreams aren’t reality.

If we could just get whites and Asians to do a lot worse, no one would argue about the absurdity of sending everyone to college.

Until then, everyone will divert themselves by engaging in this debate—which, like many kids stuck in the hell of unfair expectations, will go nowhere.

I'm a little less cynical.

First, America has made a vast effort since 1983 to teach students more math, and the test scores suggest that it has been mildly successful.

Second, it's worth trying to pound some abstract math into everybody's heads just to find out which ones can do it.

Third, there are massive diminishing returns to pounding, however. The Gates Foundations' pushing for requiring Algebra, Geometry, and Algebra II to graduate from public school is overkill.

Fourth, we need a lot of effort and publicity put into figuring out what kinds of non-abstract math are useful. Consider construction, for example. Economic historians sometimes use carpenters' wages as an index to compare wages over the centuries because carpenters have been around since before Jesus, and will probably be around for a long time in the future, too. Think about five categories of individuals in regards to construction work:

  • Unemployable
  • Laborer
  • Carpenter
  • Contractor
  • Developer

The differences between Unemployable and Laborer are presumably mostly due to character. But differences in math skills can matter in moving up the ladder. It would be useful to have a curriculum for mastering practical arithmetic for students who don't have what it takes for abstract math.

Fifth, the algebra v. statistics question is a good one. I was always mediocre at pure abstract thinking, but, for some reason, am good at very simple statistical thinking (and I am good at pulling up examples out of my memory). That's a major reason why my insights are so orthogonal to almost everybody else's. I don't really know why that is.

Would teaching more statistics at a younger age do much for the quality of discourse in America? I don't know. In some ways, probabilistic thinking is an old man's game. It may not appeal much to the young, who are more imaginative, abstract, and idealistic.