Aprendizagens sobre frações a partir da abordagem exploratória em um estudo de aula

Abstract

Learning about fractions, especially in elementary school, characterizes an important dimension of mathematical learning, so that its teaching presupposes different contexts and activities with the potential to explain students' ways of thinking. The exploratory approach to mathema tics makes it possible to explain students' thinking and strategies to express their understanding of curricular topics. The research, of a qualitative and interpretative nature, sought to highlight and discuss the mathematical learning of 7th grade studen ts on the topic of fractions from an exploratory approach in a class study. The investigation, based on the theoretical assumptions of the class study and the exploratory approach, was carried out in the context of the investigation class, 3rd stage of the class study, developed in a class of the 7th grade of Elementary School at Escola Municipal Santa Terezinha, from Faxinal dos Guedes, SC. The class study, organized in 12 meetings of 2 hours each, was carried out with four Mathematics teachers from the mu nicipal network, who were engaged in the planning of the investigation class, which addressed the topic fractions. The empirical material of the study was constituted through the application of a questionnaire to the students before the investigation class , elaboration of field notes, the observations made by the teachers and the accomplishment of interviews with the students at the end of the class study. The data were analyzed from the perspective of the evidentiary paradigm, prioritizing the examination of resolution strategies, the mathematical representations mobilized, the reasoning processes and the generalizations made by the students in the development of the proposed task for the investigation class. The analysis of the empirical material evidenced three categories: (i) fraction meanings, (ii) fraction representations and (iii) students' justifications and conclusions about fractions, making it possible to highlight important learnings. Students' learning about fractions was characterized by the dif ferent understandings of the meanings of fraction explored from the proposed task, the mobilization of different representations to solve it, as well as the arguments and justifications formulated for the results found. This aspect was enhanced in the coll ective discussion, through the sharing of representations, interpretations and generalizations and the identification of errors, uncertainties or irresolutions, which in the end made it possible to systematize conclusions and the results obtained, in the s ame way as the development of reasoning ability and mathematical communication. Thus, the exploratory approach favored students' mathematical learning insofar as it allows the development of mathematical skills such as problem solving, mathematical reasoni ng and mathematical communication, giving rise to mathematical ideas, which are systematized in collective discussion.