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Re: CL # 4, Some comments
Posted:
Nov 9, 1996 2:43 PM
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On Sat, 9 Nov 1996, Ralph A. Raimi wrote:
> On Sat, 9 Nov 1996, Andre TOOM wrote:
>
> > Here Ralph takes for granted that every mathematical question
> > has exactly one correct answer.
>
> Yes, if you include "I don't know", and "This question is not a
> mathematical question."
How about "There is no answer," or "There is insufficient information"?
Or, are these in the second category?
> There are those who say things like "A quadratic
> equation has more than one correct answer." This is incorrect. A
> quadratic equation is not a question at all.
>
> It might be a clause in a mathematical question, though, e.g. "For
> what real values of x will x^2-5x+6=0?" -- to which the correct answer
> is, "For x=2 and for x=3." That's one answer, not two, and it should be
> observed that it has a capital letter on one end and a period on the
> other, even though as an English sentence it is a bit elliptical.
>
>
> > However, there is a fashion among modern educators to avoid
> > unique answers and promote situations where it is impossible to
> > say which answer is correct.
>
> Such situations might involve mathematics, but the fuzzy part is
> generally social and not mathematical. To the question, "Which form of
> measurement here would be most convenient?", there might not be one
> correct answer; but such a question is not a mathematical one. Here a
> parliamentary approach is best, with each participant guaranteed a right
> to the floor at some time in the debate.
>
Could we say socio-mathematical? The example above seems to be an
interesting example. I'm not sure resorting to English sentence
structure is a good way to say that there is one solution. We do talk
about TWO roots/zeros of x^2-5x+6, don't we? We can say there is a set
of values of x for which this expression equlas 0.
Anyway, I can see a possible line of discussion starting with an argument
whether x=2 or x=3 is the answer, to the idea that maybe there are more
than one value that satisfies the condition. Then, treating a set of all
values that satisfy the given as ONE solution. But, treating this set as
ONE solution seems to contain both mathematical as well as social
(society of mathematicians?) aspect.
Tad Watanabe
Towson State University
Towson, Maryland
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