Explaining the Roles of Definitions in Mathematics IV

Share Cognitive Science Implications for Teaching Mathematics
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Role #4: They are the core element of every simple concept.   See 21 Feb blog.  Study the blog on 26 JUN 18.

Simple mathematics concepts are constructed with a definition as a central core tightly wrapped in several layers of illuminating information.

Therefore, for any one of teaching, learning, or studying to be effective it is necessary that both the instructor and the learner know precisely the stipulative definitions of all the words being used.

A baseball consists of a central core tightly wrapped in several layers of different materials. Construction of a golf ball is similar.  As a matter of fact, many familiar objects, including the earth, have similar constructions.

On a more abstract level, simple mathematics concepts are similarly constructed.

It is convenient to think of a simple mathematics concept as a central core (definition) tightly wrapped in several layers of illuminating information.

Complex mathematics concepts consist of many simple mathematics concepts joined together.

 

 

If a learner desires to learn mathematics (opposed to training to do certain computations) that learner must begin by learning simple concepts of mathematics.  To learn those simple concepts the learner must memorize the core definition and study that definition together with the layers of illuminating information.

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