Fenomenologia da Investigação Matemática na Educação Matemática

Abstract

In this thesis, we turn to the Investigation of Mathematics with the intention of comprehending it in the context of Mathematic Education. This approach is an intentional act and intertwined with the lived experience of the subject who experienced the interpretation. This brings to the research characteristics of Phenomenology and Hermeneutics, and from that position, we question: what is this; Mathematical Investigation in Mathematics Education? Searching for ways to face the theme, we highlight twelve academic works that have shown themselves significant in the field of Mathematical Inquiry in Mathematics Education, which we built the data with. With the hermeneutic-phenomenological movement accomplished, the Mathematical Investigation in Mathematics Education can be comprehended in two convergence regions that expressed it as a way to do Mathematics and as a way of teaching Mathematics. As a way of doing Mathematics, it values conjectures, tests, generalizations, and demonstrations as its modus operandi; and, as a Mathematics teaching method, it idealizes to the class the scientific experience of knowledge production in Mathematic, forging the making of the student and of the teachers to an imitating, an acting as the mathematician. The comprehension hermeneutically opened itself to a way of teaching Mathematics that underlies the everyday impersonality of Mathematical epistemology of the doing Mathematics of the Mathematician, valuing them. Besides, though, in principle, the Mathematical Investigation in Mathematics Education has been shown pretentiously open, there is the possibility of incurring in the closing of the investigative process upon attributing the opening characteristic exclusively to the initial situations and on presupposing an only making method. This implies the permanence of students and of teachers in a making that does not allow them to dare, in the genuine meaning of the word, to make Mathematics, which places in decline their authentic methods of being investigative individuals on being-with the Mathematics Investigation in Mathematics Education.