O ensino de análise combinatória pautado na aprendizagem, nos trabalhos em grupo e na comunicação matemática

Abstract

In response to the needs to make learning in mathematics, by the students, more meaningful, according to Ausubel's Meaningful Learning theory, we present this study in which we approach the possibility of students interacting with mathematical content, the significance of the mediator role of teacher as representative of knowledge, the importance and function of language in the formation of concepts and the implementation of Combinatorial Analysis teaching in a gradual and productive way. In this sense, we propose the following question: Will there be meaningful learning of Combinatorial Analysis, from a teaching proposal based on group work and mathematical communication, applied to a class of students from the Second Grade of High School in Chapecó- SC? To this end, we developed a teaching proposal, of Combinatorial Analysis, based on the resolution of problem situations, in order to develop combinatorial thinking in students from an environment that stimulates argumentation and discussions in small and large groups. To this, at first, the students solved problem situations about Combinatorial Analysis contents, without the use of any formula, using only their previous knowledge. After this, we present the contents of the Combinatorial Analysis and the formulas, and in the third moment the students solved exercises and problem situations by choosing which method they would like to solve them, in order to make the learning meaningful. The data collection was made from the tests applied during the meetings as well as the notes made in the logbook. The data analysis shows that this teaching proposal was able to contribute significantly to the process of teaching and learning of Combinatorial Analysis, as the students presented advances in the ability to solve problems involving counting principles. The comparison between the results of the diagnostic tests highlight a significant growth in the understanding of the concepts and in the resolution of combinatorial problems. In addition, the analysis reveals that the realization of group activities with emphasis on mathematical communication was fundamental for good results of the proposal. The data suggest that discussions in small and large groups, with encouragement of argumentation, contribute to the development of combinatorial thinking.