Uma proposta de ensino de frações por meio de cálculos de segmentos: desvendando o objeto por meio dos experimentos mentais

Abstract

This text is part of the basic requirement for the defense in the Graduate Program in Mathematics Education, aiming to obtain the Master's degree. The central question of this work is: what relationships can be developed in the contrast between the formal and the intuitive in the study of operations with fractions in basic education? The objectives outlined to answer the research question are: i) to understand the different ways of conceptualizing fractions within basic education; ii) to draw a parallel between the formal and intuitive aspects present in the operational process of fractions; iii) to develop mental experiments that allow a better understanding of the proposed theme in the research; iv) to record the different interpretative forms and meanings produced during the application of these experiments in basic education as an alternative teaching methodology. In seeking to achieve these objectives, this study presents a qualitative, bibliographic, and explanatory research, belonging to the research line of Teaching and Learning, based on studies that aim to build a relationship between Mathematics and language through Peirce's semiotics, and adopting the principle of complementarity applied to semiotic, didactic, historical, and epistemological studies of Mathematics and the development of mental experimentation processes. Based on these studies, a didactic proposal for teaching fractions is developed, which uses Mental Experiments as a teaching methodology. The application of this alternative teaching methodology for Mathematics was carried out in the basic operations with fractions, using segments and employing Euclidean geometry as a system of representation.