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Topic: Mathematical maturity and lower-order knowledge & skills

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Subject:   RE: Creativity and intuition
Author: moursund
Date: Aug 4 2004
Robert Sternberg has developed a three component model of intelligence
( ). One of the three components is creativity.
According to Sternberg and others, we can design curriculum that helps increase
and focus creativity. Since we (math teachers) value creativity in math, we
should design our curriculum, instruction, and assessment in a manner that
fosters, encurages, rewards, etc. math creativity. Mathematical creativity is a
component of math maturity, and at the highest levels of math maturity we expect
to see a high level of math creativity.

Especially when working with students who are gifted in math, we see intuitive
leaps and insights that are sort of mind boggling. I understand this, but at the
same time I hold in mind a statement from Herbert Simon (early leader in
computers and artificial intelligence; Nobel prize winner; ) who said
"Intuition is frozen analysis." I believe he was talking about business
intuition, and he was referring to the idea that having a good intuition about
business problems comes from analyzing lots of business problems. Some students
have very good math intuition when they really haven't lived long enough and
studied math long enough to have analyzed a large number of math problems.

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