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Re: writing equations
Posted:
Nov 28, 1996 9:11 PM


>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.
 Judy Roitman  "Glad to have Math, University of Kansas  these copies of things Lawrence, KS 66045  after a while." 9138644630  Larry Eigner, 19271996 



