Vito Prosciutto: Teaching community college math on the road to a PhD.

Friday, February 20, 2004

I generally don't link to Joanne Jacobs... 

... but doing an internet search on "The Lizzie Method" turned up this discussion at her site and reminds me of why I ignore her site.

Much like at isomorphisms, the commenters revel in the ignorance of the reporter on the story, but here they reveal their own ignorance.

factoring polynomials - a fairly important operation in college-level math and in the mathematical sciences, but it only works well when there is a whole-number answer.
Actually, not quite. You can factor when there is a rational solution to a quadratic equation. The applications of factoring also go beyond solving quadratics: It's also important for working with rational expressions, a subject covered in Algebra I (which is hardly "college-level" mathematics).
Or it is possible to derive the quadratic formula by trying to apply this method to arbitrary coefficients, through several pages of algebra.
Um, no, it's not possible to derive the quadratic formula using this method (finding factors p and q of ac that sum to b is not possible without specific values for a, b and c). The quadratic formula is derived by completing the square. I did this in Advanced Algebra yesterday. It's short enough that I didn't bother to write the derivation in my class notes, but to get from ax2+bx+c=0 to the quadratic formula takes 6 steps.
why she's getting praised for a method that's so difficult
Difficult? It's by far the simplest and easiest to teach method for factoring ax2+bx+c that I've found. The quadratic formula, incidentally, is of limited use for simplifying rational expressions.
Lizzie seems to me to be FOILing backwards
Um, factoring is taking a product and writing it as a product of two factors (thus the name). So of course it's going to look as if she's FOILing backwards. The problem is figuring out how to get from the product to the factors. It's much harder than it seems.

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