Ensino-aprendizagem de análise combinatória através da resolução de problemas: um olhar para a sala de aula

Abstract

This research seeks to outline a mapping of the Combinatorial Analysis teaching and learning, through practice in the classroom, using mathematics teaching and learning through problem solving and exploration, the result of a reflective look at our own practice as teacher-researcher. The research begins with an investigation in the field of Mathematics Education with the theme "Combinatorial Analysis teaching and learning". In developing this work, it was possible to observe the actual classroom practice reflected in the discussions and ideas relevant to the content of Combinatorial Analysis by the theoretical perspectives. Thus, the central ideas in the teaching and learning process in this matter were clarified and exposed the methodological perspectives in the use of mathematics teaching and learning through problem solving and exploration that content, when developed in real classrooms, not idealized. On the whole, bring a wander reflective on the subject of combinatorial analysis, problem solving, social constructivism, philosophy of mathematics and mathematics education, and educational research as a methodology with the school routine, making use of observations, records of the classes and materials used by students. In interventions, it was experienced various difficulties relevant to Combinatorial Analysis teaching and learning, as the distinction between arrangement and combination problems, which leads to the failure to perceive, to understand the problem, by the students, if the order the grouping of the elements is not relevant or in the count. The research provides contributions to the content of Combinatorial Analysis and a better understanding of the use of problem solving and exploration in the classroom, as a method of teaching and learning. In developing the survey, the routine requires the attention of the teacher as an essential element in making pedagogical. Then come taunts and reflections on the research with the everyday classroom, which imply a critical eye to it. This teaching practice entails an opportunity to change the status quo and the emancipation of students. It means therefore the search for a pedagogy that may be constituted as resistance to oppression in schools.