The Post of Many Questions (and few answers)

I’ve been pondering this question for a long time, but it came to me in a new form today. Why do we make kids learn math?  Mathematicians and math teachers, of course, consider it a self-evident truth that you cannot be a fully functioning human being–or at least not a fully functioning citizen of the United States–unless you can do calculus, or at the very least, algebra.  Of course, it’s not surprising that professional math people think that way; after all, we need people to pay us to teach their kids math, or tutor their kids when they’re failing math, or write new curricula because kids are getting bad test scores (and to write those tests that kids do badly on).  What’s interesting is that no one else seems to question that supposedly self-evident truth either–except occasionally the kids being forced to learn eight thousand different algorithms for factoring a polynomial.  We happily put aside music, art, theater, even history and social studies in schools in order to make more time for math.

At the same time, there doesn’t seem to be any particular downside attached to not being able to do math.  Innumeracy seems to me to be treated as a sort of minor inconvenience–on par with, say being unable to draw or not knowing anything about music. It’s the sort of thing you toss out in a conversation: “Oh, I was never very good at math.” And the other person says, “neither was I” or, if the other person is good at math, he or she just looks vaguely embarrassed and says “I guess I was lucky, I had good math teachers” or, “I was always good at following thre rules.” At any rate, innumeracy doesn’t seem to carry any of the stigma that illiteracy carries in our culture.  If anything, there is more of a stigma attached to being good at math (I have quite literally had people back away from me when I told them I was a graduate student in math). And yet, there seems to be an endless stream of stories in the news about how the US is falling behind in math and therefore we are headed for an inevitable collapse and will never be able to compete with the rest of the world.  See for example (from a few years ago) this article in the NY Times.  There seems to be very little objection when the SAT gets revamped to add *harder* math. I suspect it would be political suicide for a politician, of any stripe, to suggest that maybe schools don’t need to push more students through calculus.

All of this leads me to a bunch of questions, none of which I have answers to:

1) How did math make its way into our education system, and how did it get to its current form? Math is not, of course, a monolithic thing, although in my experience, people have no idea that there is anything to math beyond the standard set of topics covered in school (admittedly, a few people know there are things called “multi-variable calculus” and “linear algebra”). Essentially everyone goes through various types of arithmetic, followed almost invariably by algebra 1, geometry, algebra 2 (whatever “algebra 1″ and “algebra 2″ are supposed to be) something called “trigonometry” or “pre-calculus” or “functions and something” covering trigonometry, usually some analytic geometry, exponential and logarithmic functions, and maybe a few other miscellaneous topics. Some students are allowed to stop around algebra 2, and more around pre-calculus. For those who are in very high-powered schools, or who want to go to competitive colleges, or who are deemed “good at math”, this series is inevitably followed by calculus (usually the AP version–a rant which I will save for another time).  There are occasional variants on this sequence, such as the so called “integrated math”, but these mostly just take the same topics and put them in a slightly different order.  There are many other parts of math, which we don’t bother to teach. Why not?  Another way to put this is: what are the real reasons we insist that everyone should learn math (and these particular mathematical topics) in school?

2) On a related note, how did math acquire its exalted position in Western culture? I don’t really think you can answer question 1 without answering this one.

3) What are the stated justifications for teaching math the way we teach it? In other words, what do teachers tell sceptical students? What to school boards tell sceptical government bodies? What do mathematicians tell the rest of the world? about why it’s so important that everyone learn math.

4) Are those good reasons? And, are we actually accomplishing the goals we claim to have for teaching math? I’ll be up front here: I’ve yet to hear an argument for teaching the kind of math we teach that I’ve found very convincing. I’d love to hear more though.

5) Are there good reasons to make sure everyone learns some math? If so, what kinds of math?

6) A related question: why do so many people find math so incredibly difficult to learn? There’s not question that math is difficult, but I really have trouble believing that the answer is that most people are too stupid to learn math.

All of these are really more sociological/historical/political questions than mathematical ones (except maybe the last one, which is more of a psychological question). Not being a historian or a sociologist, I don’t really know where to start looking for answers. Any suggestions? I’m interested in your (yes, your) take on why we teach math. Any resources you know of?

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3 thoughts on “The Post of Many Questions (and few answers)

  1. G says:

    You make an interesting weblog, some articles a bit long and some lengthy questions. Let me give part of an answer for #1.

    Mathematics in various forms or levels has been part of human culture and has become traditional. People have developed ways to count and measure so they could predictably manage quantities. Since we are a specie that explores, we have developed technlological skills from our specie’s beginning. This again relied on Mathematics – more counting and measuring. People conduct business, or trade. Again, counting must be used so that the trading parties can assure eachother of fairness in the bargaining.

    Obviously, since we are explorers, and often curious (some of us, not always all of us), some people explored numbers and shapes and their relationships to see how they are related. Some of this was found to be practical (meaning useful). Notice that in numbers, we have more kinds of numbers than just the whole, counting numbers; we have number values between the whole numbers – meaning FRACTIONS.

    Our technological development is probably what makes the more advanced modern Mathematics useful, and learning this Mathematics takes longer to learn. It is basically more complicated than just simple operations with whole numbers and simple fractions. Generally many people prefer not to spend so much effort trying to learn more Mathematics than they believe they would need – it would take too long, and would be too much effort.

    Maybe later, I will try to answer a couple more of your questions. Some of them deserve thoughtful answers.

  2. G says:

    More about your question #1,
    The courses in high school Mathematics which are the best are Algebra 1, Algebra 2, and Geometry. After those, curricula become less consistant. Not really bad, just less consistant.

    One good reason for the Algebra courses in high school, including “PreCalculus” if that one is offered, is to give students better tools for mathematical modeling of quantitative information. In case a student is on a true college preparatory path for university education for the sciences or engineering, relearning any of this Math in college will be easier than trying to learn it for the first time.

    Anyway, the “Algebra” is important. Modeling is very useful. If one can create a faithful mathematical model, then one may use this model in the development of a software program intended to process information or solve a scientific or engineering problem situation. (too many examples, so please do not ask me to give examples).

    Why “Calculus”? Probably this is not so important in high school. I see no great point in pushing students to learn Calculus UNTIL their Algebra knowlegde is more secure. I found Algebra 1 and Algebra 2 to be more practical. They gave me a far stronger sense for handling Arithmetic; they are much closer to the kind of Math that I often used. I found Algebra to be great for simple finance applications and many blend situations which were describable with simple systems of equations.

  3. The problem with math is not that it’s enforced in schools, but that it’s taught in the most useless and ineffective manner possible. It is forced down students’ throats as random tidbits of abstract information, without providing a solid and concrete base of knowledge. Students are then required to regurgitate it for tests, and nobody really cares if they could ever apply the concept in a useful way in real-life dealings.

    So, the question must not be “SHOULD math be taught?” but “HOW should math be taught?”

    Which answers none of your questions and creates more. 🙂

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