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(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?
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 (firstname.lastname@example.org)