Concepções sobre a Matemática e trabalho investigativo

Abstract

Investigative activities provide students with lively and gratifying experiences — stimulating learning processes such as generalizing, particularizing, symbolizing, communicating, analyzing, exploring, conjecturing, and proving. Previous research, although scarce, points their potential but also their problems. These result from incorrect conceptions that students often hold about mathematics and learning. This research intends to show how they work in this activities and develop their conceptions. Based in four investigational tasks and using a case study, it analyzes how a sixth-grade student gets involved in this kind of activity. The student, Francisco, shows great interest in the proposed tasks. Firstly he does not go beyond formulating conjectures. Progressively, he carries out tests, refines his conjectures, and sketches justifications. He reveals growing autonomy, confidence, and willingness to take risks in his reasoning. In the beginning, he does not relate to the group but at the end he interacts with his colleagues. Initially very dependent from the teacher to validate results, he recognizes himself as a mathematical authority. These activities contribute for his acquiring of a new conception of mathematics as a developing science, of the role of the teacher as a facilitator, and regarding classroom tasks, as desirably challenging. The study concludes that the open and challenging nature of tasks, the working procedures of the teacher, and the dynamic of the classroom yielded opportunities for reasoning and interaction that were uptaken by this student. It also shows that a significant enrichment of crucial aspects of students’ conceptions is possible and suggests that investigative work in the classroom deserves clear attention in educational research, indicating new leads for future work.