Amazing.
Someone who is actually saying the things that my wife and I have been talking about. She is a math teacher and has been developing techniques to make it easier for high-school kids to do some of the things they need to do, but the fundamental problem is that they need to be able to master their multiplication tables before things like factoring and solving quadratics become easy (quick, what are two number that add up to 12 and whose product is 35?).
She has adapted someone else's technique for dealing with sum, difference, product and division of rational funtions (of one variable and to first order) to ordinary fractions to give her students quick ways of doing these things and taking care of the bookkeeping.
One of the interesting ones in the technique she has taught them about adding fractions (different than above).
If you have 1/(na) and 1/(nb) then she suggets that they extract the common factor (1/n) and then use cross multiplication, because they love doing that for some reason (of course, its a bit more complicated than that) and then multiply by the pre-extracted factor. This all helps them use the LCM and handle the bookkeeping.
The neat thing, however, is that the same techniques can be used with multiplying rational functions and reduces the headaches if they can see common factors (which is often an issue in and of itself).
So, anyway, I agree pretty much totally with you.
I do wish you would provide some way to email you ...
So many educators are out of touch and push technology as the solution to all education ills.
Richard, you can email me at drsarcasm@hotmail.com
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