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Discussion: Research Area
Topic: Mathematical maturity and lower-order knowledge & skills


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Subject:   Nitty Gritty
Author: Craig Russell
Date: May 16 2003
I'm not sure what the gist of your response was, and upon reading my message to
which you responded, I see that I was too vague!

Let me say, first, that I don't think we should teach (or expect) the students
to compete with computers.  We need to teach low-level skills, mid-level
skills, and higher order skills (though at higher order, the word "skills"
sounds too limiting).  What we can't afford to do, as the examples you listed
illustrate, is to use mastery of low-level skills as a pre-requisite for
exposure to higher order mathematical thinking skills.  That only serves to
limit the access of otherwise active thinkers.  

An example I remember from my undergraduate days (over 20 years ago!) is the
Economics course I took--it required Calculus as a pre-requisite, and there
were several graduate students in the course who really struggled with the
mechanics of taking derivatives (calculating and using the chain rule are fairly
low-level skills in Calculus), but their understanding of economics was still
possible because their exposure to the concepts of rate of change (or marginal
whatever in economics) was at a higher-order level.

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