Creating constructivist environments and constructing creative mathematics
- 276 Downloads
Constructivism is not reducible to a set of rules to follow or actions to perform. However, we suggest that it is possible to define beliefs that must be held by teachers if they are to create constructivist environments for learning. In the first part of this paper we put forward as critical four tenets of belief and follow this with descriptions and analyses of classrooms in which the teachers' intentions are to create environments based on these beliefs. We examine the mathematical understanding actions of pupils in these classrooms to determine the relevance and validity of our claims.
KeywordsMathematical Understanding Creative Mathematic Understanding Action Constructivist Environment
Unable to display preview. Download preview PDF.
- Kieren, T. E.: 1990, “Understanding for teaching for understanding”,The Alberta Journal of Educational Research 36(3), 191–201.Google Scholar
- Kieren, T. E. and Pirie, S.E.B.: 1991,Characteristics of Growth of Mathematical Understanding. Unpublished paper presented at AERA annual meeting, Chicago, April.Google Scholar
- Minsky, M.: 1986,The Society of the Mind, Touchstone, Simon and Schuster, New York.Google Scholar
- Pirie, S.E.B. and Kieren, T. E.: 1989, “A recursive theory of mathematical understanding”,For The Learning of Mathematics 9(3), 7–11.Google Scholar
- Pirie, S.E.B. and Kieren, T. E.: 1990,A Recursive Theory for Mathematical Understanding—Some Elements and Implications. Unpublished paper presented at AERA annual meeting, Boston, April.Google Scholar
- Pirie, S.E.B. and Kieren, T. E.: 1991,A Dynamic Theory of Mathematical Understanding—Some Features and Implications. Unpublished paper prepared for the AERA annual meeting, Chicago, April.Google Scholar
- Sfard, A.: 1991, “On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin”,Educational Studies in Mathematics 22, 1–36.Google Scholar
- Steffe, L. and von Glasersfeld, E.: 1988, “On the Construction of the Counting Scheme”, in L. Steffe and P. Cobb (eds.),Construction of Arithmetical Meanings and Strategies, Springer-Verlag, New York.Google Scholar
- von Glasersfeld, E.: 1990, “Environment and Communication”, in L. Steffe and T. Wood, (eds.),Transforming Children's Mathematics Education, Lawrence Erlbaum, Hillsdale, NJ.Google Scholar