Abstract
The theme of the present ICMI Study, ‘Mathematics Education as a Research Domain: A Search for Identity’ immediately leads to the question: ‘What is the object of this research?’ One direct answer that comes to mind is that it is mathematics. While this is true in some general sense, this answer is not satisfactory upon realization that the term ‘mathematics’ in the didactic context is full of ambiguity. In this context, at the onset, a more differentiated perspective on mathematical knowledge has to be introduced, highlighting the similarities and the differences between mathematics as a scientific discipline and mathematics as a school subject (cf. Chevallard 1991; Dörfler & McLone 1986).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bauersfeld, H.: 1978, ‘Kommunikationsmuster im Mathematikunterricht — Eine Analyse am Beispiel der Handlungsverengung durch Antworterwartung’, in H. Bauersfeld (ed.), Fallstudien und Analysen zum Mathematikunterricht, Schroedel, Hannover, 158–170.
Bauersfeld, H.: 1983, ‘Subjektive Erfahrungsbereiche als Grundlage einer Interaktionstheorie des Mathematiklernens und-lehrens’, in H. Bauersfeld et al. (eds.), Lernen und Lehren von Mathematik, Aulis, Cologne, 1–56.
Bereiter, C.: 1985, ‘Towards a Solution of the Learning Paradox’, Review of Educational Research 15, 201–226.
Cassirer, E.: 1955, The Philosophy of Symbolic Forms. Volume 2: Mythical Thought, Yale University Press, New Haven, CT.
Chevallard, Y.: 1991, La Transposition Didactique: Du Savoir Savant au Savoir Enseigné (2nd ed.), La Penseé Sauvage, Grenoble.
Dörfler, W. & McLone, R. R.: 1986, ‘Mathematics as a School Subject’, in B. Christiansen, A. G. Howson & M. Otte (eds.), Perspectives on Mathematics Education, Reidel, Dordrecht, 49–97.
Ernest, P.: 1993, ‘The Relation between Personal and Public Knowledge from an Epistemological Perspective’, Manuscript for the Conference on ‘The Culture of the Mathematics Classroom: Analyzing and Reflecting upon the Conditions of Change’, Osnabrück, Germany, October 11-15, 1993, Exeter University, Exeter.
Hefendehl-Hebeker, L.: 1993, ‘The Practice of Teaching Mathematics and Teacher Education’, Manuscript for the Conference on ‘The Culture of the Mathematics Classroom: Analyzing and Reflecting upon the Conditions of Change’, Osnabrück, Germany, October 11–15, 1993, Augsburg University, Augsburg.
Janvier, C.: 1983, ‘The Understanding of Directed Numbers’ in J. C. Bergeron and N. Herscovics (eds.), Proceedings of the Fifth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA). Vol. 2, International Group for the Psychology of Mathematics Education, North American Chapter, Montréal, 295–300.
Lave, J.: 1988, Cognition in Practice. Mind, Mathematics and Culture in Everyday Life, Cambridge University Press, Cambridge.
Lave, J. & Wenger, E.: 1991, Situated Learning — Legitimate Peripheral Participation, Cambridge University Press, Cambridge.
Lawler, R. W.: 1990, ‘Constructing Knowledge from Interactions’, Journal of Mathematical Behavior 9(2), 177–191.
Lytle, P. A.: 1992, Use of a Neutralization Model to Develop Understanding of Integers and of the Operations of Integer Addition and Subtraction, Master’s thesis, Concordia University, Montreal.
Lytle, P. A.: 1994, ‘Investigation of a Model Based on the Neutralization of Opposites to Teach Integer Addition and Subtraction’, in J. P. da Ponte & J. F. Matos (eds.), Proceedings of the Eighteenth International Conference for the Psychology of Mathematics Education, Vol. III, University of Lisbon, Lisbon, 192–199.
Otte, M, Reiß, V. & Steinbring, H.: 1979, ‘The Education and Professional Life of Mathematics Teachers’ in UNESCO (ed.), New Trends in Mathematics Teaching, UNESCO, Paris, 107–133.
Seeger, F. & Steinbring, H.: 1994, ‘The Myth of Mathematics’, in P. Ernest (ed.), Constructing Mathematical Knowledge: Epistemology and Mathematics Education, Studies in Mathematics Education Vol. 4, The Falmer Press, London, New York and Philadelphia, 151–169.
Steffe, L. P.: 1990, ‘The Learning Paradox: A Plausible Counterexample’, in L. P. Steffe (ed.), Epistemological Foundations of Mathematical Experiences, Springer, New York.
Steinbring, H.: 1986, ‘L’Indépendance Stochastique — un Exemple de Renversement du Contenu Intuitif d’un Concept et de sa Definition Mathématique Formelle’, Recherches en Didactique des Mathématiques 7(3), 5–50.
Steinbring, H.: 1989, ‘Routine and Meaning in the Mathematics Classroom’, For the Learning of Mathematics 9(1), 24–33.
Steinbring, H.: 1991, ‘The Concept of Chance in Everyday Teaching: Aspects of a Social Epistemology of Mathematical Knowledge’, Educational Studies in Mathematics 22, 503–522.
Steinbring, H.: 1994, ‘Symbole, Referenzkontexte und die Konstruktion mathematischer Bedeutung-am Beispiel der negativen Zahlen im Unterricht’, Journal für Mathematikdidaktik 3, 277–309
Wagner, R.: 1981, The Invention of Culture, University of Chicago Press, Chicago.
Wagner, R.: 1986, Symbols that Stand for Themselves, University of Chicago Press, Chicago.
Wittmann, E. C. & Müller, G.: 1990, Handbuch produktiver Rechenübungen. Bd. 1: Vom Einspluseins zum Einmaleins, Klett, Stuttgart.
Wood, T.: 1992, Funneling or Focusing: Patterns of Interaction in Mathematics Discussion. Paper presented in the Working Group 7, Language and Communication in the Mathematics Classroom at the 7th International Congress of Mathematics Education, Québec, August 17–23.
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
Steinbring, H. (1998). Epistemological Constraints of Mathematical Knowledge in Social Learning Settings. 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_34
Download citation
DOI: https://doi.org/10.1007/978-94-011-5470-3_34
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-4600-5
Online ISBN: 978-94-011-5470-3
eBook Packages: Springer Book Archive