How do you figure the circumference of a circle ?

And why would you want to do that ?

In his final week as Chancellor of New York’s public schools, Mr. Joel Klein was interviewed on TV about his educational philosophy. Well, he opined, a child certainly must know how to figure the circumference of a circle.

Now I bet that Mr. Klein himself, a lawyer and educational administrator, never once had to figure the circumference of a circle after leaving high school. Perhaps he needed this knowledge for higher math in college, and perhaps not. I myself happen to remember the idea: 2πR, and of course I needed this knowledge when I studied trigonometry and calculus. So yes, I am not against teaching 2πR somewhere in high school, or, better yet, teaching how to find the formula if you happen to need it.

But compare this to mathematical ideas that everyone truly needs, and that are not taught in high school, at least not on a regular basis. Take the basic ideas of statistics, in particular the idea of sampling and the often-abused idea of “statistical significance.” These concepts are essential to all citizens because they enable a person to evaluate the (frequently false) claims made in the media about medical research, public opinion polls, and much else. (For a recent account of the misleading nature of scientific reporting — in the absence of an understanding of the basic ides of statistics — see the important article by Jonah Lehrer in the New Yorker of December 13, 2010.)

Here is one more example of the mindlessness of the current crop of “educational reformers” who preach the gospel of testing, large classes, charter schools, firing of teachers, and. overall, a disregard of Dewey’s concern for “the child and the curriculum.” See my previous posting here.

One thought on “How do you figure the circumference of a circle ?”

  1. I’m interested that no one has seen fit to comment on this smart post of yours. If nothing else, you’ve pinned down the absurd arrogance of the test-crazy educational “reformers” which anyone who has worked in a public school system, as I have (I’ve just retired last week) knows all too well.

    But beyond that, this particular problem — the circumference of a circle — is one I’ve loved to lay out to kids, and which all too many kids, ruined by ten years of deadening schooling, can no longer appreciate.

    Put correctly, It’s a question: What is pi?

    Answer: pi is the ratio between the circumference of a circle and that circle’s diameter.

    Demonstration: we take a shoelace that is the length of the diameter, and we start to loop it around the circle. Watch — the lace goes once, twice, three whole times … and there’s some extra. The extra distance is pretty close to one-seventh the length of the shoelace. But not exactly. In fact, it turns out to be one of those crazy numbers that never resolves.

    Now THAT, it seems to me, is a useful fact about the circumference of a circle. Understand that, and you know a lot of other things as well.

    Larry Houghteling
    lhoughteling@yahoo.com
    Please sign me up to get your intriguing post via email. Thanks

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