Atenção seletiva e teoria dos campos conceituais: articulação para a aprendizagem da noção de relações métricas no triângulo retângulo

Abstract

The objective of this research was to elaborate a didactic sequence with the potential to mobilize the students' selective attention, for the development of learning the notion of metric relations in the right triangle. For this, there is methodological support in Classic Didactic Engineering (CDE) by Artigue (1996), namely: with the stages of Preliminary Analysis and Conception and Priori Analysis. Through the first stage, it was possible to establish the epistemological obstacles associated with the historical construction of knowledge of metric relations in the right triangle, the obstacles to teaching and learning in the classroom, the competences provided for in normative documents for education, as well as the strategies proposed by textbooks. Through the data of this analysis, it was possible to establish as theoretical support the Theory of Conceptual Fields (TCF) and the construct of selective attention with the model of the Theory of Guided Search (TGS), for the elaboration of didactic actions that have the potential to mobilize the attentional focus and provide the development of the conceptual field of metric relationships. In the Conception and Prior Analysis stage, the five moments for the didactic sequence were outlined, with the description of their objectives and importance, in addition to predictions of expected behaviors that correspond to effective learning. Two reference matrices were elaborated for the analysis of aspects of tests based on the TGS and general aspects of the activities of the didactic sequence, which were used for the internal validation of the sequence, done through the application of a questionnaire. It was found that the proposed didactic sequence has the potential to mobilize selective attention to the development of learning metric relations in the right triangle, by proposing dynamics with different resources and different types of situations in which this concept can be used. Some articulations between Cognitive Neuroscience and Didactics of Mathematics were evidenced through the planning of didactic situations, by favoring the functioning of the brain in the learning process.