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defense of factoring (was:equation with inverse trig fcn???HELP)
Posted:
Apr 13, 1998 5:19 PM


My defense of factoring is that I want students to learn that: 1) there is a connection between the factors and roots of a polynomial 2) there is a connection between the coefficients and roots of a polynomial.
I think practice with factoring and multiplying simple polynomials is one good way to lead students to that understanding. Of course there are other ways, maybe better ways, to emphasize these ideas. And for some students, the simple arithmetic of factoring becomes a memorized algorithm and they lose sight of these two ideas.
One thing I have particularly noticed is that factoring by grouping helps students get the idea that they can treat larger chunks, like 2x+1, just the same way as they would a variable like y.
Hey, I can make this relevant to apcalc now! That idea, first learned in beginning algebra I hope, is crucial to understanding the chain rule (and its inverse, usubstitution for integration). So I hope we keep teaching factoring by grouping! If not, we need to replace it with some other situation that makes the students see this idea of chunking.
Joshua Zucker



