DOCUMENTA MATHEMATICA, Extra Volume ICM III (1998), 735-746

Maria G. Bartolini Bussi

Title: Drawing Instruments: Theories and Practices from History to Didactics

Linkages and other drawing instruments constitute one of the most effective fields of experience at secondary and university level to approach the theoretical dimension of mathematics. The main thesis of this paper is the following: By exploring, with suitable tasks and under the teacher's guidance, the field of experience of linkages and other drawing instruments, secondary and university students can 1) relive the making of theories in a paradigmatic case of the historical phenomenology of geometry; 2) generate `new' (for the learners) pieces of mathematical knowledge by taking active part in the production of statements and the construction of proofs in a reference theory 3) assimilate strategies for exploration and representative tools (such as metaphors, gestures, drawings, and argumentations) that nurture the creative process of statement production and proof construction. This thesis will be defended by referring to research studies already published or in progress.

1991 Mathematics Subject Classification: MSC 97A15 98A15

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