Moreover, "the system" (at least at my institution and I suppose yours) allows it - even demands it - all the way into college. And it's damaging to students in the name of trying to help them.
At 09:06 AM 7/10/2013, Louis Talman wrote: >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>