Reasoning in geometry

Hershkowitz, Rina, Duval, Raymond, Bartolini Bussi, Maria G., Boero, Paolo, Lehrer, Richard, Romberg, Thomas, Berthelot, R., Salin, M. H. and Jones, Keith (1998) Reasoning in geometry. In, Mammana, Carmelo and Villani, Vinicio (eds.) Perspectives on the teaching of geometry for the 21st Century: An ICMI study. (New ICMI Study Series, 5) ICMI Study 9 Conference on Perspectives on the Teaching of Geometry for the 21st Century (27/09/95 - 02/10/95) Dordrecht, NL. Kluwer Academic Publishers, pp. 29-83. (doi:10.1007/978-94-011-5226-6_3).

Abstract

This chapter deals with the specific features of reasoning in geometry, including general aspects and specific case studies for different age groups carried out in different countries. The five sections of the chapter discuss and illustrate examples of main new trends in reasoning in geometry. The sections comprise a meta-cognitive analysis of geometrical reasoning processes and their interactions with other thinking processes, two sections that discuss theory and curriculum development that demonstrate what is called now “learning geometry from context”, a section on the roles of pupils’ spatial knowledge in geometry learning, and an analysis of how pupils interweave intuitive-visual reasoning and deductive reasoning. Together, the sections illustrate three main trends in learning geometrical reasoning; reasoning in building proofs, reasoning in geometry from contexts, and visual reasoning.

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Contributors

Author: Keith Jones

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