College-level counting

[Computer’s still a few time zones away, bike-without-adapter is still primary means of transportation – and I have an apartment to move to the mainland. And I’ll be away, again, this time south of the border, for part of July, so don’t expect anything interesting or substantial in this space for quite some time.]

In the meantime, a discussion topic: how mathematics education went so horribly awry that we now teach this stuff in college. Actually, let me flip that one around: why do we bother teaching this material – integers, fractions, areas of plane figures, basic algebra – in elementary school and junior high in the first place?

I know why I think students should learn it, but I wonder if educators and curriculum developers at that level can answer that question, given that basic mathematics is so often so poorly retained. I certainly wonder what insight those educators would offer when confronted with the fact that more and more colleges are offering remedial classes, especially in math, than ever before; that in many cases, it is unwise for us college math instructors to assume that our students have anyknowledge of prerequisite material. What sort of subject is grade-school math, that it is absorbed so poorly?

If I were to invent a language with counterintuitive syntax and bizarre vocabulary that bore no relation to that of any Western language, and if I were to teach my invention to a classroom full of schoolchildren, some would excel. Others would do decently. In any event, most, I figure, would pass. But a year later, nearly everyone in my class will have forgotten my crazy language, save a few words that they heard in memorable contexts.

Why would they remember it, after all? They have no need for it, and the lessons they took were nowhere reinforced in their day-to-day lives. This is how so many college students see math: as something that they need to learn because their teachers said so, but something that is so poorly connected to the rest of their lives that they have no reason to remember (let alone apply, let alone use) any of it.

At the risk of sounding like an obnoxious student, I’m asking those who teach this material the first time: what’s the point of any of this? Why do we have to learn it? What does it have to do with anything?

…and given whatever those answers are…why is math so seldom worked into any aspect of children’s lives outside the mathematics classroom before they graduate from high school?

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