Projects
days until the end of spring semester.days until Snakes on a Plane.
Boxes unpacked
Math article project
Finished mathematical core of article. Next: Write analytical core of article.
Dummit and Foote, Abstract Algebra
Finished section 1.6 (86 to go)
Silverman and Tate, Rational Points on Elliptic Curves
FInished 2.5 (31 to go)
Conway, Functions of One Complex Variable I
Finished section 7.5 (27 to go)
Munkres, Topology
Finished section 21 (60 to go)
Royden, Real Analysis
Finished section 2.4 (97 to go)
Nonfiction book project
Todo list uptodate
Fiction book project
1443 out of 100,000 projected words written.
Top 100 novels of all time
Reading Ulysses
IMDB top 250 films
Tengoku to jigoku next in queue.
Blogroll
This academic life
Academic CoachConfessions of a Community College Dean
Learning Curves
The Little Professor
My Hiding Place
New Kid on the Hallway
One Bright Star
Planned Obsolescence
Tall, Dark, and Mysterious
Math blogs
Ars MathematicaMathForge
MathPuzzle
Think Again
Archives

July 2003
August 2003
September 2003
October 2003
November 2003
December 2003
January 2004
February 2004
March 2004
April 2004
May 2004
June 2004
July 2004
August 2004
September 2004
October 2004
December 2004
January 2005
March 2005
April 2005
May 2005
June 2005
July 2005
August 2005
September 2005
October 2005
November 2005
December 2005
January 2006
February 2006
March 2006
April 2006
May 2006
Vito Prosciutto: Teaching community college math on the road to a PhD.
Tuesday, February 17, 2004
14:16Algebra  The Lizzie Method
So here's the short version of what it's all about: A sixteenyear old girl found a "new" way of factoring quadratic equations in the form ax^{2}+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 ax^{2}+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 x^{2}+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:
 Try it on their challenging problem to see if it really works.
 Write down the steps so she can use it when she teaches the material.