Algebra

In Sunday's New York Times, Andrew Hacker asks "Is Algebra Necessary?" and answers, Generally, no. The reactions to this article that I noticed (over at Hacker News, as it happens) were strongly negative.

I find that I am of several minds about this one.

First, I have seen algebra fetishized by some. The Washington Post used to carry a columnist who was sure that 8th-grade algebra was necessary to the nation's future. She wrote well and set forth her arguments forcefully. Yet I wondered. The Montgomery County schools--which she covered--had more problems than under-enrollment in 8th grade algebra; students were getting to high school not knowing arithmetic they should have learned in the middle grades. I came to think that eventually there would be a movement for third grade algebra, which would have predictable results: the schools would teach what they could, and call it algebra; the parents of the young Gausses and Noethers would write furious letters to the Post about deficiencies in the algebra teaching; and the rest of the parents would shake their heads and wonder what came next.

Second, Hacker's proposal matches many I see. If something turns out to be hard, let's not do it. I don't know that this is the best way to run school systems.

Third, some of his reasoning seems questionable to me:

The toll mathematics takes begins early. To our nation’s shame, one in four ninth graders fail to finish high school. In South Carolina, 34 percent fell away in 2008-9, according to national data released last year; for Nevada, it was 45 percent. Most of the educators I’ve talked with cite algebra as the major academic reason.

Or could it be--as the folks at Hacker News suggest--that algebra can't be fudged with easy grades for bad work, the way softer courses can?

Fourth, good teachers are scarce, and good math teachers are scarcer. Some of what Hacker describes must no be  a deficiency in the students so much as in the teachers and the curricula. Of course, it would be easier to write an outstanding algebra text than to reform mathematics education in a school system, let alone a state or nation.

Fifth, can one consider a college student academically ready if he or she cannot master the rudiments of logic? And if not, are the rudiments of logic easier to master than algebra?

Finally, it is hard not to recall the numbers of obviously intelligent persons who have confessed--the boasters I don't count--that they could not master algebra. I suspect that many of them simply encountered bad teachers, and were too young to know how to ignore the teacher and work from the text. Yet some probably could not manage it, others didn't, and many went on to useful careers in academia or elsewhere.