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Topic: Mathematical maturity and lower-order knowledge & skills

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Subject:   I hadn't responded yet
Author: grc
Date: May 16 2003
but only hit the Enter key accidentally and it posted my message before it was

What is happening right now is going far beyond students needing to understand
something as simple as taking a derivative.  

It seems to me, looking at it from the outside, that the universities don't
really have a grasp of what is going on at the k-12 levels, even the 9-12
levels.  The schools, also, do not appear to be aware of what is happening with
mathematics at the research level in industry and the universities and how
dramatically the trickle effect will impact the level of mathematics that will
be required of students in the future in areas of study that heretofore did not
require much math.  

Computers are taking math modeling into fields where it really couldn't go
before, or didn't for whatever reasons.  To some degree, this is going to have a
systemic affect, in biology, for instance.  Biology long considered their
systems to be too complex for math to deal with, felt they were above math, so
to speak, so biology really didn't (as economics has and does) have to address
math, very much.  Now they are having to take math very seriously, so that
biology students are going to be required to know more and more math, because
math biology is a frontier that is here to stay and has a long and fruitful
journey ahead of it.  

As time passes, more students are going to be required by their degree programs
to take a minimum of Calculus and Analytic Geometry I, so that students who do
not have the math skills to pass such a class will be left out of more
disciplines than ever before.  This is what I mean by academic repercussions.
Math research that is way beyond what most students or people will ever reach in
their careers is making a fundamental impact on academics at many different

That was my point, is that the need for hands-on math skills is increasing,
and then, of course, the computer is important, too.  They both matter, and I
don't know where the middle ground is, or where compromise becomes sacrifice in
math education.

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