I would agree that "context" does not _equal_ "application."
I would, in our terms, define applications as a subset of problems
that can developed within a meaningful "context." The point is
for students to be able to do, and to understand what they've done;
more than solving _a_ particular problem. Rather, we want to have them
attack problems written in a form where the context is meaningful (from
life, business, mathematics, industry, society...) and the problem doens't
just boil down to "ok, that was the story, now solve this problem...."
We shouldn't limit our problems to applications that come from
industry or business, but the curriculum could certainly stand more!
These real problems may not be what that student will be doing in ten
years, but they certainly don't have "[any] bearing on their known
future." We can not limit ourselves to problems which we know students will
enjoy and find in their future life. Rather, problems from industry
or wherever can serve to enlighten students about careers and interests
they knew very little about! Not to mention the motivation for the study
of math.
Students who can make connections between mathematics and the workplace
will not be "throw-away employees" they'll be "keepers" since they will
be able to enjoy life long learning and not be dependent upon society
to educate them, house them, ...
Thanks for your comments, Rob
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