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

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Subject:   Mathematical maturity and lower-order 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

2  Math, as any discipline, can be thought of in terms of lower-order
knowledge and skills, and higher-order knowledge and skills. We have some
standardly accepted ideas on lower-order and higher-er 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 lower-order.

I believe it is necessary for a person to have both lower-order and
higher-order knowledge and skills within a discipline. However, in math and
many other disciplines I believe we spend far too much time teaching
lower-order 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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