In proof by reductio ad absurdum, the impossibility of a mathematical object is drawn from the deduction of a contradiction. The relationship between the statement and the contradiction is logical in nature and it is one of the main obstacles for students. An analysis of indirect argumentations produced by students in geometry enlightens how they sometimes by-pass this obstacle transforming the geometrical figure so that the (false) proposition becomes true and the link between the contradiction and the statement is reconstructed. This analysis reveals some interesting differences in the treatment of the contradiction in argumentations and in proofs, identifying important difficulties in understanding proof by contradiction.

Indirect argumentations in geometry and treatment of contradictions

ANTONINI, SAMUELE
2008-01-01

Abstract

In proof by reductio ad absurdum, the impossibility of a mathematical object is drawn from the deduction of a contradiction. The relationship between the statement and the contradiction is logical in nature and it is one of the main obstacles for students. An analysis of indirect argumentations produced by students in geometry enlightens how they sometimes by-pass this obstacle transforming the geometrical figure so that the (false) proposition becomes true and the link between the contradiction and the statement is reconstructed. This analysis reveals some interesting differences in the treatment of the contradiction in argumentations and in proofs, identifying important difficulties in understanding proof by contradiction.
2008
9789689020066
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/137118
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