Sentidos e significados manifestos por licenciandos e pós-graduandos ao produzirem atividades de ensino de matemática na perspectiva lógico-histórica - Rezende, João Paulo (Universidade Federal de São Carlos, 2015)
This current research, of qualitative nature, has been led by the question: which senses and meanings can be produced by undergraduate and graduate students while they experience, study and create teaching activities from a logical-historical perspective? Our aim was to identify and analyze the senses and meanings manifested by two subjects that composed a group of ten undergraduate and three graduate students, who gathered virtually and in person, over a semester, to reflect collectively upon the organization of teaching by means of teaching activities founded by the logical-historical perspective. To conduct the research, we sought theoretical fundaments in the logical-historical dialectical perspective on theoretical constructs that deal with Teaching Orienting Activities (AOE in Portuguese) and with the concepts of sense and meaning studied by Vygostsky. The gatherings took place in the context of the Integration, Teaching, Research and Extension Curricular Activity (ACTEPE in Portuguese) entitled: “When the history of Mathematics becomes a teaching methodology,” and they were split in three blocks: the first was aimed at motivation to work under a logicalhistorical perspective; the second one, at the study and deep analysis of it; and the third one, at the organization of teaching activities founded by this perspective. The following instruments were used to constitute research data: a field journal; narratives; audio recording of the gatherings, which were transcribed; forums held in a virtual environment; and propositions of activities that were designed or adapted by the participants and presented in the last gatherings. Upon these propositions and three specific criteria, two participants, whose trajectories were followed along the sixteen gatherings, were selected. The senses and meanings manifested by the subjects, in the context of the present study, show that organizing teaching from a logical-historical perspective can allow the involved students to seize the concepts through the exercise of thinking about them, making it possible for the learners to feel the need for developing the concept. They also show that the conceptual nexuses - both internal and external - are important theoretical constructs when working under this perspective, for they perceive internal nexuses as those which are not made explicit to the students by a formal concept representation, but they are fundamental to understand it. This meaning makes it important to evince these nexuses to organize teaching. Nevertheless, it is necessary to learn them and history can make it possible, for it holds the conceptual development process and the product of that development.
Keywords: História da matemática; Lógico-histórico; Educação matemática; Atividade de ensino; The history of mathematics; Logical-historical; Mathematics education; Teaching activity; CIENCIAS HUMANAS::EDUCACAO