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Re: writing equations
Posted:
Nov 28, 1996 9:11 PM
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>On Thu, 28 Nov 1996, Judy Roitman wrote:
>>
>>
>> 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.
> Ms. Roitman is quite right, and introducing distinctions before
>differences appear is poor policy (cf W.o.Ockham). And I should have
>introduced the difference sooner than the pair of linear equations, in my
>imaginary (abbreviated!) lesson in equations, but thought I had made the
>point. In the case of x+3=0, one could pose the question -- in English
>-- "Find all positive numbers x such that x+3=O." Then the kids who are
>untroubled by logic can 'solve the equation' by 'subtracting 3 from both
>sides' and gee, what happened? Did they make a mistake or something?
> Logic is not truth tables, it is at the bottom of civilized life.
>
But Ralph, a lot of kids would just say that "Find all positive numbers x
such that x+3=O" is a trick question (okay, it is a command, but they would
call it a question) and I suspect that they still would not appreciate the
point.
I'm not talking about what *should* be. I'm talking about how to turn what
is into what should be.
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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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