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

Tuesday, February 17, 2004

Algebra - The Lizzie Method 

Teaching factoring of quadratics in the form ax2+bx+c is always a challenge, so when Vlorbik pointed me to this discussion at the now-defunct isomorphisms, I was intrigued to see what was said.

So here's the short version of what it's all about: A sixteen-year old girl found a "new" way of factoring quadratic equations in the form ax2+bx+c and the local newspaper wrote a breathless article extolling the virtues of what she did.

Most of the commentary at isomorphisms focused on the idea that her process isn't really revolutionary in a mathematical sense. And this is true. But from a pedagogical perspective, what she's done is actually rather useful.

The text that we use for beginning Algebra at the high school where I'm student teaching offers one method for factoring ax2+bx+c: Guess and check. It's possible to use some educated guessing to shorten the process, but it's still a lot of work and students will generally not get far factoring this sort of problem.

What I've found works well (and what my mentor teacher uses) is known by a variety of methods: Factoring by grouping, the split method, the ac method, the British method (the supplementary materials for our textbook include this approach), and who knows what other names are lurking out there.

The "Lizzie" method, on the other hand, eliminates the somewhat difficult final step in the ac method which requires factoring by grouping or a bit of educated guess and check. The process is actually remarkably straightforward, and what I found was that by the third problem, about 90% of the class was successfully factoring polynomials with a leading coefficient (and the remaining 10% were having difficulty because they still had trouble with the simpler process of factoring polynomials in the form x2+bx+c). If you teach math, definitely check out the Lizzie method. So far every teacher that I've shown it to has responded with the following reaction:

  1. Try it on their challenging problem to see if it really works.
  2. Write down the steps so she can use it when she teaches the material.

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