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PNA, v7 n2 p63-73 2013

This paper addresses contributions that dynamic geometry systems (DGSs) may give in reasoning by contradiction in geometry. We present analyses of three excerpts of students' work and use the notion of pseudo object, elaborated from previous research, to show some specificities of DGS in constructing proof by contradiction. In particular, we support the claim that a DGS can offer guidance in the solver's development of an indirect argument thanks to the potential it offers of both constructing certain properties robustly, and of helping the solver perceive pseudo objects. [This paper was originally published as Baccaglini-Frank, A., Antonini, S., Leung, A., & Mariotti, M. A. (2011). Reasoning by contradiction in dynamic geometry. In B. Ubuz (Ed.), "Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education" (Vol. 2, pp. 81-88). Ankara, Turkey: PME.]

Descriptors: Geometry, Thinking Skills, Mathematical Logic, Mathematical Concepts, Problem Solving, Persuasive Discourse, Logical Thinking, Secondary School Students, Secondary School Science, Video Technology, Case Method (Teaching Technique), Educational Practices, Educational Strategies, Teaching Methods, Foreign Countries

Universidad de Granada Didáctica de la Matemática: Persamiento Numerico, FQM-193. Campus de Cartuja, Granada, Spain 18071. Tel: +34-958-241503; Fax: +34-958-246359; e-mail: pna[at]; Web site:

Autor: Baccaglini-Frank, Anna; Antonini, Samuele; Leung, Allen; Mariotti, Maria Alessandra


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