Chapter 10 - Developing Student Understanding in Elementary School Mathematics: A Cognitive Perspective

Abstract

This chapter explores how considering the individual as a learner and part of a social context can help in the understanding of current implications from cognitive science for engaging children in mathematics and the ramifications of instantiating these ideas in the classroom context. The breadth and depth of work in cognitive psychology that addresses how children learn has been synthesized in a number of places. Theories of cognitive science do not lead to a single view of classrooms; instead they offer principles, from which decisions can be made about teaching mathematics. Developments in cognitive science convey a way of understanding different aspects of the mind, and modeling individual thinking and learning. This understanding of mental capacity and functioning has allowed researchers to go beyond thinking about the more general, yet powerful, notion that children learn from interacting with their environment. Sociocultural theorists advocate that learning occurs within social interaction. One way to understand the issues underlying the constructivist and sociocultural perspectives is to examine the role of the teacher within each perspective. Developing understanding is a cornerstone of both cognitive science and mathematics education. The connections between ideas enable an individual to search her mental structure, moving from connection to connection, in an attempt to gain access to and combine information.