Abstract
As I view it, the topic of the relations between practice and theory in mathematics education conveys two main problems. The first problem concerns the relationship between mathematics as a practical activity, and mathematics as a theoretical body of knowledge. The second problem concerns mathematics education, and the relationship between the teacher’s activity in the classroom and research in mathematics education and psychology. I think that, for both problems, we need a theory of practice and of articulation between theory and practice. This theory must be quite general since it does not concern mathematics or mathematics education alone, but all human activities. To do this, we also need some practice of theory, or theorizing. And we need examples, since theory without examples is usually incomprehensible.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Brousseau, G.: 1981, ‘Problèmes de Didactique des Décimaux’, Recherches en Didactique des Mathématiques 2(1), 37–128.
Da Rocha Falcao, J.: 1992, Représentation du Problème, Ecriture de Formules et Guidage dans le Passage de l’Arithmétique à l’Algèbre. Thèse, Université Paris V.
Piaget, J.: 1971, Genetic Epistemology, Norton, New York.
Piaget, J.: 1980, Adaptation and Intelligence, University of Chicago Press, Chicago.
Vergnaud, G.: 1981, L ‘Enfant, la Mathématique et la Réalité, Peter Lang, Bern
Vergnaud, G.: 1982, ‘A Classification of Cognitive Tasks and Operations of Thought Involved in Addition and Subtraction Problems’, in T. P. Carpenter, J. M. Moser, & T. A. Romberg (eds.), Addition and Subtraction: A Cognitive Perspective, Lawrence Erlbaum Associates, Hillsdale, New Jersey.
Vergnaud, G.: 1983, ‘Multiplicative Structures’, in R. Lesh and M. Landau (eds.), Acquisition of Mathematics Concepts and Processes, Academic Press, New York, 128–203.
Vergnaud G.: 1990, ‘Epistemology and Psychology of Mathematics Education’, in J. Kilpatrick & P. Nesher (eds.), Mathematics and Cognition, A Research Synthesis by the International Group for the Psychology of Mathematics Education, Cambridge University Press, Cambridge, 14–30.
Vygotsky, L.: 1962, Thought and Language, The MIT Press and J. Wiley & Sons, New York, London.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media New York
About this chapter
Cite this chapter
Vergnaud, G. (1998). Towards A Cognitive Theory of Practice. In: Sierpinska, A., Kilpatrick, J. (eds) Mathematics Education as a Research Domain: A Search for Identity. New ICMI Studies Series, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5470-3_15
Download citation
DOI: https://doi.org/10.1007/978-94-011-5470-3_15
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-4600-5
Online ISBN: 978-94-011-5470-3
eBook Packages: Springer Book Archive