Discussion:  Research Area 
Topic:  Mathematical maturity and lowerorder knowledge & skills 
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Subject:  Nitty Gritty 
Author:  Craig Russell 
Date:  May 16 2003 
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 lowlevel skills, midlevel
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 lowlevel skills as a prerequisite 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 tookit required Calculus as a prerequisite, 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
lowlevel 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 higherorder level.
 
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