Using Arguments, Proofs, and Refutations in Geometry Classes as Contributions to the Development of the Student's Critical Sense

Abstract

In the present paper, we evaluated how to contribute to the improvement of critical sense of the students in the mathematics classes. Specifically, for the purpose of promoting this way of thinking, named critical sense, we exposed a group of 6th grade students to an environment of argumentations and refutations applying a sequence of didactic activities that leads them to demonstrate the result of Plane Geometry: “the sum of the internal angles of any triangle is 180°”. Next, using this result, that they determined the sum of the internal angles of any polygon through a process of logical inference. In the tasks, which involved the communication of validations, the students were encouraged to make manipulations, to question, and to raise hypotheses, always aiming to build the necessary knowledge and geometric relationships, making their learning meaningful. To support our actions, we relied on Van Hiele and his theory on the development of geometric thinking, as well as on Balacheff and his works whereby him explore argumentations and refutations to the construction of mathematic validations. In analyzing the results, we based ourselves on Carraher and his criteria to characterize an individual as a critical thinker. Thus, we show that the development of critical thinking can be favored through pedagogical work that involves students in the construction of geometric validations, while observing the geometric learning levels proposed by Van Hiele.

Keywords:
Critical Sense; Argumentation; Proof; Refutation; Geometry