Would US Education Be Better If We Replaced Algebra Requirements With Stats & Logic?

from the reshuffling dept

By now you may have heard about the NY Times article from over the weekend in which political science professor Andrew Hacker makes the somewhat contrarian suggestion that the US education system would function much better if we ditched algebra requirements. The whole article is worth reading, but the basic gist of it is that many people who end up dropping out of school do so in part because of trouble they have in getting past basic algebra. It's a key stumbling block.
California's two university systems, for instance, consider applications only from students who have taken three years of mathematics and in that way exclude many applicants who might excel in fields like art or history. Community college students face an equally prohibitive mathematics wall. A study of two-year schools found that fewer than a quarter of their entrants passed the algebra classes they were required to take.

"There are students taking these courses three, four, five times," says Barbara Bonham of Appalachian State University. While some ultimately pass, she adds, "many drop out."

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.
I will admit that my initial reaction to this article was to scoff and think that it's ridiculous. Understanding basic algebra, to me, seems fundamental to understand a variety of other important things -- including some forms of logic and statistics. So, I wondered how dropping algebra as a requirement might make those already lacking fields even worse.

However, Hacker's piece actually suggests something of a solution: potentially replacing algebra with a form of statistics, which is rarely a required course.
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.

It could, for example, teach students how the Consumer Price Index is computed, what is included and how each item in the index is weighted - and include discussion about which items should be included and what weights they should be given.
I will admit to being unsure how such a class will work without a basic underpinning in algebra. However, conceptually, what Hacker is saying makes sense. Focusing on the formulaic side of algebra isn't particularly practical for many people. I could see how classes that focus on practical mathematical skills around statistics and logic, could actually be a lot more useful. And while he says these don't need to be "backdoor" algebra classes, I'm not so sure that's a bad thing. Having people understand the basics of algebra by putting them in realistic situations they understand, and showing how to apply such things in a useful manner doesn't seem like such a bad idea...

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  1. identicon
    Anonymous Coward, 31 Jul 2012 @ 6:29am

    Re: my intuition tells me...

    What terrible questions.

    An elephant stands on a platform supported by a beam. If you need a beam four inches thick to support an elephant six feet tall, how thick a beam do you need to support a ten-foot elephant? This ignores the cube-square law and is not as simple as multiplying the beam's thickness by 1 2/3.

    A pizzeria takes telephone orders. Taking one order takes one minute. During peak hours, the telephone is silent for an average of two minutes between orders. How many orders are lost during peak hours because the phone's busy? Not enough information, such as call volume and the number of employees, phones, & phone lines. Additionally, telephone calls (despite having what you can call an average call time and average idle time) follow a poisson distribution. Given the right information, and using an Erlang-C formula to figure this out would yield a result much different from expectations from just doing the math on the averages you supplied.

    Incidentally, the answer uses a statistical model, not an algebraic model.

    Which gets heatstroke faster, a large short-haired dog, or a small long-haired dog?Hopefully the small one, but this has way too many unstated factors to be answered successfully.

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