First, I don't think rigor is traditional. Rigor came along only around the
turn of this century, a relative newcomer in the mathematics timeline. The
kind of mathematical reasoning that evolved into rigor, however, goes back
as far as the history of the subject and is pretty easily accessible.
In looking back at how I grew into whatever abilities I have with
mathematical logic, I believe getting hold of elementary processes like
factoring played a big role. It gave me opportunities to learn helpful
skills in the larger concept of problem solving such as inspection,
identification and classification. I firmly believe that many of the topics
and skills under fire in this discussion are not entirely the content of
what we are trying to teach our students, but simply the tools with which we
try to model a kind of thinking that can serve people well throughout life.
As for tempting students with "real world" applications, let's be
reasonable. Most students who lack the motivation to learn the simple
system of ideas that go into factoring are probably not thinking, "If only
this course were full of complicated models of the economic interdependence
of a global economy I'd be doing fine."
--Tony Armstrong
Somerset Community College
Somerset, KY
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