Luis F. Lara y Carmen Samper
Abstract: In this article, we report some of the results obtained in a case study in which we analyze a group of high school (14-16 years old) students’ interaction when they solve a geometric problem within an environment that favored proving activity. Particularly, the behavior of the students is described and interpreted using the integration of the Toulmin and Habermas models, proposed by Boero, Douek, Morselli y Pedemonte (2010). With the first model, we analyze the formulation of arguments (argumentative behavior); with the second one, we study the three aspects that characterize rational behavior (epistemic, teleological, and
communicative). This study permits establishing that the students, after having participated in a course where inquiry and justification are favored, have an argumentative and rational behavior that is in accordance with that of a person with greater mathematical maturity, as they justify the conjecture they formulated as solution to a problem.
Keywords: proving activity, type of argument, rational behavior.
