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Tuesday, November 21, 2006

Using math in the so-called real world?

So what do we say when we hear that all-too-familar question, “When am I ever going to use this in the real world?” [Grammatical footnote: logically speaking, that sentence should have two question marks at the end, one before and one after the closing quotation mark. But the official rules of American punctuation prevent me from doing that. Why? I suppose it’s because ?”? looks so ugly.]

Anyway, back to our question. My take on it is that the student who asks it rarely wants to listen to an answer. Usually it’s an indirect way of saying, “This is boring/confusing/hard to understand. Why do I have to learn it?” In other words, the subtext is a plea for more meaningful math (or whatever the subject is). But our tendency, as teachers, is to take the question seriously — as we should — and therefore to try to answer the question that was asked — rather than the question that was meant. We want our answers to be honest and to be perceived as responsive, but it’s hard to do both. So we say something like this: “You will need logarithms in surprisingly many situations in the future, such as chemistry, calculus, statistics, business courses, and even college psychology courses.” That’s somewhat honest: it’s the truth, but it’s not the whole truth. And it’s somewhat responsive: it does take the question seriously, but it provides an unsatisfactory answer to it, especially since the implication of the question is that school is not part of the real world.

Why is the answer unsatisfactory? It’s mostly because it merely postpones the question. Telling a student that she will “use” a concept in a later course only encourages her to ask the same question (quite appropriately) when taking that course. A similarly unsatisfactory answer, one that most teachers are understandably reluctant to give, is that logarithms will appear on the MCAS and the SAT II. Motivating a topic by citing its possible appearance (and it is only possible) on a standardized test satisfies no one and definitely does not answer the question. The reality is that future courses and standardized tests do constrain what we teach, but that’s not really what the student is asking.

So, what’s the honest answer? To my mind, the honest but brutal answer is to refuse to accept the terms of the question. The honest answer has two parts to it:
  • I don’t know, and you don’t know, exactly what you’re going to be doing in your future life. So don’t reject a topic just because it’s not included in your current plans. Maybe you’ll become a pharmacist and will need to understand reports of pharmaceutical tests... I can’t say whether you will use logs, but it’s better to leave the door open than to close it.

  • More important, our reason for selecting a topic is not that the content of that specific topic will be useful to you later on. Yes, it might turn out to be useful, but the most important life lessons you learn from studying any worthwhile topic, whether it be logarithms or fractals, polynomials or proofs, are those big, hard-to-test lessons: how to approach a difficult subject, how to reason quantitatively, how to organize knowledge, how to solve problems, how to explain your solutions, how to present your analysis, and so forth.
That’s what I’d like to say. That’s what I believe. But how many students would accept that as the honest answer it is?

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