The Role of Continuous Processes in Cognitive Development

Abstract

Abstract. Many scientists observing the cognitive development in children have noted distinct phases in the way they learn. One phase appears to be a gradual accumulation of experience. Another phase appears to be a reorganization of those experiences to make them more useful. In this paper we show how mathematical closure concepts can be used to abstractly model these cognitive processes.Closed sets, which we will call knowledge units, represent tight collections of experience, facts, or skills, etc. Associated with each knowledge unit is the notion of its generators consisting of those attributes which characterize it.Finally, we provide a rigorous mathematical model of these different kinds of learning in terms of continuous and discontinuous transformations. There are illustrations of both kinds of transformation, together with necessary and sufficient criteria for certain kinds of transformation to be continuous. By using a rigorous definition, one can derive necessary alternative properties which may be more easily observed in experimental situations.The formal mathematics is illustrated with reference to Lev Vygotsky's view of cognitive psychology, but it is not a verification of his model. We believe that this concept of "continuity" can be refined to test, and possibly verify, his and other models of cognitive behavior.

Two network transformations

“…The results of this paper would seem to support this contention. For example, closure is thought to be relevant to cognitive processing [9,27,28]. It is accepted that human cognition is realized by means of neural circuitry, or neural networks, of some form.…”

“…Neighborhood closure has been called "experiential" and "relational" closure in other papers[27,28].…”