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Subject:   RE: exponents
Author: Alan Cooper
Date: Oct 2 2004
On Oct  1 2004, PWR wrote:
> . . .To me, the rules are both logical and easy,
> but my students usually seem to find them too
> numerous and confusing. . .

Perhaps you find them easy *because* you find them logical.
I believe that if we insist on students understanding and explaining "rules"
rather than memorizing and reproducing them, then they, like us, may see that
there is really only *one* rule of exponents - namely that a whole number power
corresponds to repeated multiplication - and that the rest all follow quite
easily from this.

Once whole number exponents have been fully understood, then the definitions of
negative and fractional powers can be seen as natural and convenient choices of
notation (which they are) rather than facts of nature (which they are not).

The failure to clearly identify such distinctions is actually one of the most
confusing things about our subject, and perhaps explains the sense of
frustration and anger with which many people leave it.

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