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what should we say to AP students about the word "model"?
Posted:
Jul 31, 1996 5:50 PM
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< see previous message for lead-in to the following >
(2) The draft version of the Teacher's Guide quotes (on p.31) Hoaglin &
Moore as asserting that "data are numbers with a context". Some may
regard that as a bit oversimplified, but I like it, and think it captures
something important in only a few words.
Then I got thinking about the word "model," which surely is used in
multiple ways in mathematics and in statistics, as well. I have seen
instances in which it was asserted or implied that "an equation is a
model," (see endnote 1) but that seems to me to be a bit too simple to be
useful. Is y = 2x - 5 a model? If so, a model of what?
Then it occurred to me that, a la Hoaglin & Moore, it might be a useful
to start with the notion that "models are equations with a context".
What do others think?
Endnotes:
1. In the draft version of Kime & Clark, Explorations in College Algebra,
Wiley, 1996, we find on p.93 the following: "Can we find an equation
that describes the relationship between female infant weight and age?
Such an equation is called a _mathematical model_." Actually, the
context is there, but the second sentence doesn't mention it. But maybe
it assumes it???
==============================================
Bruce King
Department of Mathematics and Computer Science
Western Connecticut State University
181 White Street
Danbury, CT 06810
(kingb@wcsub.ctstateu.edu)
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