Discussion:  Research Area 
Topic:  Mathematical maturity and lowerorder knowledge & skills 
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Subject:  Mathematical maturity and lowerorder knowledge & skills 
Author:  Dave 
Date:  May 9 2003 
Piagetian developmental theory is an important component of accumulated
educational research. Math people tend to talk about "Math Muturity" and use
this term as they discuss math developmental theory.
Here are two topics that seem to me worth of discussion:
1. It appears that quite a bit of the math curriculum is being taught assuming a
developmentla level that is beyond where the average student (or, a number of
the students) are. The woprk of the von Hieles' in geometry support this
contention.
2 Math, as any discipline, can be thought of in terms of lowerorder
knowledge and skills, and higherorder knowledge and skills. We have some
standardly accepted ideas on lowerorder and higherer order, such as
Bloom's Taxonomy. Here is a quite different way of thinking about it.
Assertion for discussion: When referring to a piece of the math curriculum, if a
computer can do it, it is lowerorder.
I believe it is necessary for a person to have both lowerorder and
higherorder knowledge and skills within a discipline. However, in math and
many other disciplines I believe we spend far too much time teaching
lowerorder knowledge and skills. In essence, we are teaching students to
compete with the computer tools rather than to work with them.
 
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