Theories of Mathematical Learning

By Leslie P. Steffe; Pearla Nesher et al. | Go to book overview

13
The Theory of Conceptual Fields
Gérard Vergnaud CNRS, France
INTRODUCTION AND DEFINITIONS
The theory of conceptual fields aims to provide, with a few concepts and a few principles, a fruitful and comprehensive framework for studying complex cognitive competences and activities, and their development through experience and learning. By complex cognitive competences and activities, I understand those that are developed in education, at work, and in ordinary experience, and that are required to face both routine situations that do not demand great adaptation of former knowledge, and nonroutine situations (or problems) that do demand some new combination of former knowledge and ultimately some construction or discovery of new knowledge.This theory is exemplified here by various examples drawn from the psychology of mathematics education, but it is also fruitful for other domains, including social knowledge and physical education. Several of its ideas have been proposed by other scientists before--notably Piaget ( 1950, 1971, 1980) and Vygotsky ( 1962, 1978), and other authors like Russell ( 1910, 1940), Tarski ( 1971), de Saussure ( 1972), Newell and Simon ( 1972), and Bruner ( 1966). But this theory puts these ideas together in an original fashion with new definitions for such essential points as:
What is a concept?
What is a scheme?
What is conveyed by the distinction signifier/signified?

One reason for referring to such authors as those just mentioned is that a science that is not cumulative is not a science. According to this criterion, one

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