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Topic: writing equations
Replies: 8   Last Post: Dec 1, 1996 1:47 PM

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Posts: 243
Registered: 12/6/04
Re: writing equations
Posted: Nov 28, 1996 2:33 PM
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>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."

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"

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."
913-864-4630 | Larry Eigner, 1927-1996

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