I'll add in my $.02 on this thread with a few prefaces: One: As a
chemist, I might also be viewed as a different type of "unclean heathen
perverters of the purity of the true faith who use concepts in a
quick-and-dirty way without bothering to understand all the details of
what "really is" :-) " (in Larry Cartwright's description.)
First, in an earlier post, Larry had written "Years ago I acquired a
math major and certification, and was taught that math teachers (except
at the most elementary levels) shouldn't be thinking of apples and
oranges; they should be thinking about numbers in an abstract and
generalized manner." I think Larry put his finger on a crucial problem
that science educators face. Students are good at abstract problems
(5+6 = ___ or 4x + 3= 27) but cringe at "story problems." Because they
aren't thinking about apples and oranges, they wilt in the face of
problems like "Bob has three more oranges than Sue, and Sue has ..." or
"Find the mass of an orange peel given that that the diameter is 80 mm,
the peel is 5 mm thick, and the density is 0.6 g/cc." or "How many
oranges should a grocery store buy in order to optimize its profit,
given that....." etc.
I'd like to learn from the group how we get students across that divide:
from concrete science problem to the equation they need to solve... and
back to the scientific interpretation.
Second, in answer to Richard Grandy's question: "Perhaps you could give
an example of what other choices we might have made in inventing the
negative or irrational numbers." I'll report a story I heard about a
mathematics student who followed up the classroom introduction to
complex numbers by asking about "the number whose absolute value is
-1." The professor, I'm told, followed it up by working with the class
to invent a number system based on this new number.
--
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Dr. David W. Steyert steyert_dw@mercer.edu
Department of Chemistry (912)-752-4173
Mercer University
Macon, GA 31207
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