RUMEC Reading List

Want to read a little background material?How about a lot of background material?

The RUMEC I Glossary edited by David J. DeVries. This document discusses the current working definitions of the terms associated with APOS Theory, including some helpful examples.

Books

• Mathematical Epistemology and Psychology by Evert W. Beth and Jean Piaget. Translated from the French by W. Ways. Publisher: Dordrecht, Hlland, D. Reidel; New York, Gordan and Breach 1966.
• Psychogenesis and the History of Science by Jean Piaget and Rolando Garcia; translated by Helga Feider. Columbia University Press, New York, 1989.
• Epistemology and Psychology of Functions by Jean Piaget et al. Dordrecht; Boston: D. Reidel Pub. Co. 1977
• The Concept of Function: Aspects of Epistemology and Pedagogy edited by Guershon Harel and Ed Dubinsky. MAA Notes Volume 25, 1992. ISBN 0-88385-081-8.
• Research Issues in Undergraduate Mathematics Learning: Preliminary Analyses and Results edited by James J. Kaput and Ed Dubinsky. MAA Notes Volume 33, 1994. ISBN 0-888385-090-7
• Research in Collegiate Mathematics Education I edited by Ed Dubinsky, Alan H. Schoenfeld, and James J. Kaput. CBMS Issues in Mathematics Education Volume 4, AMS/MAA, 1994. ISBN 0-8218-3504-1.

Papers

• E. von Glaserfeld, "Learning as a Constructive Activity" in Problems of Representation in the Teaching and Learning of Mathematics, edited by Claude Janvier, Lawrence Erlbaum Associates, Hillsdale, New Jersey, London, 1987.
• E. Dubinsky, "On Teaching Mathematical Induction, I." Journal of Mathematical Behavior v5 n3 p305-17 Dec 1986.
• E. Dubinsky, "On Teaching Mathematical Induction, II." Journal of Mathematical Behavior 8, 1989, 285-304.
• E. Dubinsky, "On Learning Quantification" in Mathematics Education The Present State of the Art (M. J. Arora, ed.) in press.
• E. Dubinsky, F. Elterman, C. Gong. "The Student's Construction of Quantification" in For the Learning of Mathematics, 1989.
• J. Cottrill, E. Dubinsky, D. Nichols, K. Schwingendorf, K. Thomas, and D. Vidakovic. "Understanding the Limit Concept: Beginning with a Coordinated Process Schema." in Journal of Mathematical Behavior (in press)
• J. Dautermann, E. Dubinsky, U. Leron, R. Zazkis. "On Learning Fundamental Concepts of Group Theory". Educational Studies in Mathematics. v27 n3 p267-305 Oct 1994.
• E. Dubinsky, "Reflective Abstraction in Advanced Mathematical Thinking", in Advanced Mathematical Thinking, edited by D. Tall, Kluwer, p. 95-126, 1991.
• D. Breidenbach, E. Dubinsky, J. Hawks, and D. Nichols, "Development of the Process Conception of Function", Educational Studies in Mathematics, 23 p. 247-285, 1992.

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Last Updated: Feb 13, 1997