This paper analyzes the role of abduction in proving process when students solve a geometrical problem. Solving a problem is like playing a game in which rules have to be defined. Two kinds of rules are considered: definitory rules that define the basic moves in the game and strategic rules that explain how to play the game. These two rules can be associated to two types of abductions that can be used to solve geometrical problems. The purpose of this paper is to compare these two abductions and to analyze their relationship with the deductive proof. In particular, the study reveals that abduction based on definitory rule can be an obstacle to the construction of the deductive proof, while abduction based on strategic rule seems to not be a challenge for students. In fact, this abduction is usually transformed into a deduction along the argumentation.
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.