Learning Concepts in Mathematics

Refer to the diagram.

Construction of a Simple Concept
Construction of a Simple Concept

Begin at the heart (the definition) of the simple concept.  Memorize that definition because it is a stipulative definition.  Understanding is minimal at this time.

To enhance understanding the instructor and student must use ELABORATION (see post of 12 APR 18) to supply the concentric rings around the definition.  This is the time for examples, pictures and diagrams, connection to previously learned knowledge, exercises, any kind of classification, any other information which improves understanding.

Not all forms of elaboration happen immediately.  In fact, Elaboration of this concept should continue as it is incorporated into more complex concepts.

After some time the student will understand the concept so well that its precise stipulative definition will not seem to be memorized, rather it will simply be the only reasonable statement defining the concept.  By this time the student will be able to provide elaboration of his own beyond those originally provided by the instructor or instructional material.


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