You are not logged in.

 Discussion: Traffic Jam Applet tool Topic: exponents Related Item: http://mathforum.org/mathtools/tool/10/

 Post a new topic to the Traffic Jam Applet tool Discussion discussion
 << see all messages in this topic < previous message | next message >

 Subject: RE: exponents Author: lanius Date: Oct 4 2004
On Oct  2 2004, Alan Cooper wrote:
> 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.

So Alan, this is very intriguing. Would you please explain it further. What do
you mean by not a "fact of nature".

I know that at one point I lumped rules, conventions, and notations all into one
basket. You couldn't have 4/6, for example (as if that weren't a perfectly good
number). How do we help students differentiate the mathematically true, what I
think you are calling the facts of nature, from conventions or symbolic
expedients, however convenient they might be. BTW, does anyone know the history
of exponential notation?

Thanks,
cynthia

 Reply to this message Quote this message when replying? yes  no
Post a new topic to the Traffic Jam Applet tool Discussion discussion

Discussion Help