Date: Jul 10, 2013 12:06 PM
Author: Louis Talman
Subject: Re: Using Rap to Learn Science

On Mon, 08 Jul 2013 16:07:09 -0600, Richard Strausz  
<Richard.Strausz@farmington.k12.mi.us> wrote:

> What would you have a geometry teacher do when facing a student who
> didn't master completing the square in his past?


This is a very good question, and our curricula beg it.

The obvious answer is "Send the student back to algebra, and don't let him
out of it until he knows enough algebra." Nor does "enough algebra" mean
simply "...how to complete the square". It means "...how to use the
underlying ideas of algebra to figure out how square completion has to
work." But the curriculum doesn't allow us to give that answer. The
effective answer, then, is that the teacher should give this student the F
in geometry that he deserved in algebra. This, of course, seems unfair.
It is, at the very least, misleading.

Everyone in the discussion so far, seems to be treating square completion
as a technique to be memorized---and the song reinforces this overly
simplistic notion. I think that's the wrong way to go; square completion
is an example of algebraic transformation that flows from an understanding
of underlying patterns. Students should come out of algebra understanding
that they can develop the transformations they need when they need them.
That kind of understanding is part of understanding algebra and what it's
for.

The difficulty here is one that no one has mentioned: This student is in a
geometry course, and not in an algebra course, and so his grade should
reflect what he knows about geometry---and not what he knows about
algebra. But algebra is prerequisite to this geometry course, and the
student doesn't have the handle on algebra that the curriculum presumes he
has. And the real question is not "What would you do...?" but "Why does
the system allow this (and worse!) to happen?"

- --Louis A. Talman
Department of Mathematical and Computer Sciences
Metropolitan State University of Denver

<http://rowdy.msudenver.edu/~talmanl>