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Re: writing equations
Posted:
Nov 28, 1996 2:33 PM


>Jennifer and Ralph have made some thoughtful contributions to Ladnor >Geissinger's original posting. While trying to deal with this issue in >a methods course I am teaching, I ran across a relevant discussion >published 25 years ago in the Mathematics Teacher (Nov, 1971). Robert >Exner and Peter Hilton presented pro and con (respectively) arguments >for teaching formal logic in high school. Some of the examples used in >the articles involved proving identities. Exner's position was very >similar to Ralph's. In fact, he used a cancellation property example >similar to Ralph's discussion of solving "x+3=0." > >Ed.Dickey@sc.edu
The issue of when to be precise about the obvious is always a difficult one. Reading Ralph's posting I found myself sceptical. I think most people (not just kids) would get very very frustrated  they would not understand what the fuss is about. I suspect that even kids who are precocious mathematically might not get the point  if you can immediately see that x+3 = 0 happens only when x = 3, what is the fuss about? And I can see kids giving Ralph the responses that he wants without having any idea why he wants them  a sort of keyword approach, as it were.
The problem I think is one of conflation  until a situation arises in which the distinctions Ralph points out need be made, one doesn't make those distinctions, one isn't even aware that those distinctions exist. When the distinctions are made in very simple situations, it's often hard to perceive what the distinctions are, and I'm not sure that simple situations are the place to introduce them.
I will give an example from my own teaching of how this problem arises. Take Euclidean geometry. In particular, take the parallel axiom. Why be fussy about it? Well, I use spherical geometry as a foil  oh, *that's* why we have to think carefully about the notion of "parallel." But without my foil I don't know how I'd get students to take the notion of "parallel" seriously.
I think the experience of classroom teachers would be very valuable here. Does Ralph's (and Exner's) method work? If not, what does work?
 Judy Roitman  "Glad to have Math, University of Kansas  these copies of things Lawrence, KS 66045  after a while." 9138644630  Larry Eigner, 19271996 



