Combinatorial Analysis Teaching and Learning via problem Exploration, Solving and Posing in High School

Abstract

This research analyses how a classroom approach via Problem Exploration, Solving and Posing can potentialize the teaching and learning of Combinatorial Analysis. The research was conducted according to a qualitative approach, aiming to search meanings, interpreting and comprehend the information obtained, in a modality that can be characterized as teacher research, according to which the professor is the researcher of his or her own classroom (LANKSHEAR AND KNOBEL, 2008). The teaching and learning Methodology chosen to work in the classroom was of the Problem Exploration, Solving and Posing (ANDRADE, 1998; 2017), developed in a group of the 2^nd year of Secondary School of a public school, Brazil, through a set of problem situations regarding the content of Combinatorial Analysis. Data were collected through classroom observations and records of the materials used by the students, as well as sound recording. This article, it will highlight 7 meetings, totaling 7 classes, each one lasting no more than 45 minutes. During the intervention, the researcher acted as a teacher-researcher, working in the classroom both as researcher and as a regent teacher. He was a mediator and instigator of the students' teaching-learning process, giving them autonomy in the construction of the essential ideas of Combinatorial Analysis and developing thus reflections on the experience carried out. The results of the research showed that through the approach by Problem Exploration, Solving and Posing it was possible to monitor students’ growth, who launched their own ideas to explore and solve the problems proposed both by the teacher-researcher and by themselves. They used exploration and solving processes created by themselves in the student (s) - student (s) and teacher-student (s) dialogue. They also justified their explorations and solving, insights and processes, posing new explorations and problems, going beyond the solving process, effectively participating in the construction of their knowledge in Combinatorial Analysis. From which it follows that such methodology allows the student to learn with much more understanding and depth, empowering him to solve Combinatorial Analysis problems with a focus not only on the search for the solving of the problem, but could go much further, such as the performance of a work of problem exploration and posing from multiple perspectives.