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 a concept but the experiences associated with it, which becomes part of one’s concept image. Vinner believes that in carrying out cognitive tasks, the mind consults the concept image rather than the concept definition. Continue reading “Why it is bad habit to introduce math concepts through their definitions”