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.
Reasoning by contradiction in dynamic geometry / Baccaglini Frank Anna; ANTONINI, SAMUELE; Leung Allen; Mariotti Maria Alessandra. - In: PROCEEDINGS OF THE PME CONFERENCE. - ISSN 0771-100X. - STAMPA. - 2:(2011), pp. 81-88. (Intervento presentato al convegno 35th Conference of the International Group for the Psychology of Mathematics Education tenutosi a Ankara, Turkey nel July 10-15, 2011).
Reasoning by contradiction in dynamic geometry
ANTONINI, SAMUELE;
2011
Abstract
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.
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