Monday, July 30, 2012

Is Algebra Necessary?

Political scientist Andrew Hacker has a thought-provoking article in the Times arguing that teaching algebra to all students is a huge waste of effort, and blocks many otherwise promising students from pursuing higher education:
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. Shirley Bagwell, a longtime Tennessee teacher, warns that “to expect all students to master algebra will cause more students to drop out.” For those who stay in school, there are often “exit exams,” almost all of which contain an algebra component. In Oklahoma, 33 percent failed to pass last year, as did 35 percent in West Virginia. . . .

Another dropout statistic should cause equal chagrin. Of all who embark on higher education, only 58 percent end up with bachelor’s degrees. The main impediment to graduation: freshman math. The City University of New York, where I have taught since 1971, found that 57 percent of its students didn’t pass its mandated algebra course. The depressing conclusion of a faculty report: “failing math at all levels affects retention more than any other academic factor.” A national sample of transcripts found mathematics had twice as many F’s and D’s compared as other subjects.        
As an alternative, Hacker proposes courses that focus on how math is actually used in our society:
Instead of investing so much of our academic energy in a subject that blocks further attainment for much of our population, I propose that we start thinking about alternatives. Thus mathematics teachers at every level could create exciting courses in what I call “citizen statistics.” This would not be a backdoor version of algebra, as in the Advanced Placement syllabus. Nor would it focus on equations used by scholars when they write for one another. Instead, it would familiarize students with the kinds of numbers that describe and delineate our personal and public lives. . . . This need not involve dumbing down. Researching the reliability of numbers can be as demanding as geometry. More and more colleges are requiring courses in “quantitative reasoning.” In fact, we should be starting that in kindergarten.
The teaching of abstract math is something I have changed my mind about in adulthood. I loved math in school, especially geometry and calculus, and I was good at it. I loved learning how many different phenomena could be reduced to the same set of equations. I thought people who complained about math were either stupid or lazy.

But as part of my plan to stop imposing my own ideas on other people, I have given up my enthusiasm for math. For all that we live in a technological society dominated by equations, how many of us actually use math, other than arithmetic and basic statistics? As an archaeologist I am sort of a scientist, and yet I have never used algebra on the job, let alone calculus or trig. There is a great deal of irrationality about forcing so many students through difficult classes in things they will never use, and which will keep many from going on with their educations. Why not just stop?

There are some telling objections to such a reform. One is that math is intellectually difficult and therefore mind-stretching. I believe that minds strengthen with use, especially among young people, and that as the hardest subject most kids take math is therefore the one doing the most to strengthen their brains. As Hacker says, we could devise other kinds of courses that would be as difficult, but I doubt we would. Most likely we would replace trig with something much easier, and so students would study even less than they do now and learn even less.

Another is that math trains our minds for abstract, symbolic reasoning, and in a world of computers this is quite important. I have many friends who shifted into computer careers in adulthood, after pursuing things like English or History in college. Would they have been able to do this if they had not been through the whole course of required abstract math? I doubt it. Much of what primary and high school education does is keep people's options open, and any student who stopped taking math would quickly find options in science and engineering closed. Of course, only a few percent of us end up as scientists and engineers, so maybe this is a purely theoretical objection.

People sometimes say that a high school or even college diploma "doesn't mean anything." Removing math from the curriculum would take away one thing that it does still mean: that the student has sufficient intelligence and willpower to pass algebra. But is that a goal worth the misery imposed on millions by these requirements?

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