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