In my earlier post on the meaning of understanding, I describe
understanding of mathematics as making connections: To
understand is to make connections. These connections are not
done in random. Concepts are linked with other concepts in order
to create a richer image for the new concept that is being
learned. To understand therefore is to form concept image. And a
concept image is not formed by defining the concept. The
definition of a concept is different from the concept image. Let
me share with you a an excerpt from my paper which discusses
this idea. You can view the references here. Understanding the
definition does not imply understanding the concept. In order to
understand a concept one must have a concept image for it. One’s
concept image includes all the non-verbal entities, visual
representations, impressions and experiences that are created in
our mind by a mention of a concept name (Vinner, 1992). Vinner
stressed that the concept definition is not the first thing that
is learned in understanding