Monday, February 18, 2013

If π is good, is 2π better? How about 2πr?

Okay, quick math quiz: what does this formula mean?
2πr= C

If you answered "two times pi times diameter equals the Circumference," you'd be kinda' right... and you'd probably also be kinda' wrong. 

You'd be kinda' right because that would calculate the correct answer for the circumference of a circle. But you'd be kinda' wrong because the relationship (as taught to kids -- and most likely to 80% of adults) is not "two quantities of pi times the radius."

Instead, kids are taught that the circumference of a circle is πd (or about 3.14 diameters). So when you change diameter into multiples of the radius, it should stay together as a unit (d= 2r). And so the formula should read 2r•π= C.

Ahh, but that's not what we write in textbooks.

Instead of letting the kids get accustomed to 2r as a unit to represent d, we rewrite the formula to better match algebraic convention (or to match trigonometric understandings): none of which makes sense to a middle schooler. So instead of 2r•π= C (or even π•2r= C), they get 2πr= C which totally blows their chance at following along with what has been measured and summarized into a formula format.

Now, if we used τ (tau) instead, it might be easier yet. With that little replacement (where τ is the ratio C/r... or the number of radii that can fit along the outside of a circle), the formula becomes even easier!

τ•r= C or r•τ= C

And that would be GREAT! Except that the official state test requires them to be able to calculate -- BY HAND -- the area and circumference of a circle using "3.14" and "22/7" as estimates of pi.

*head thwack*

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