Análise combinatória em sala de aula: Uma proposta de ensino-aprendizagem via resolução, exploração e proposição de problemas

Abstract

This research analyses how an approach in the classroom via Problem Solving, Exploration and Posing can potentialize the teaching and learning of Combinatorial Analysis. A literature review was performed aiming to understand the contributions of other researchers on the researched theme, so that it could be possible to realize what is possible to deepen and add for the scientific community, regarding the teaching and learning process of the Combinatorial Analysis. Besides this, an interview with mathematics teachers was performed, aiming to know their ideas on teaching and learning of Combinatory Analysis and, afterwards, scrutinize until where they could help to plan a sequence of activities. The research was conducted according to a qualitative approach, aiming to search meanings, interpreting and comprehend the information obtained. The modality of research 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 the one of the problem solving, exploration and posing, developed with a sequence of activities in a group of the 2nd year of Secondary School of a public school in the city of Alagoinha-PB, Brazil. During the intervention, this researcher acted as a researcher teacher, working in the classroom as a regent teacher, giving a utonomy to the students on the construction of the essential ideas of the Combinatory Analysis, in such a way that the author acted as a mediator and instigator. Data were collected during the lessons through observation and records of the materials used by the students, as well as sound recording. Twenty-one meetings were performed, totaling 25 lessons, each lesson lasting, at most, 45 minutes. The classroom was organized in groups of three students and, in some cases, in pairs, in order to carry out a cooperative and collaborative work, where it was considered important, in this process, the mutual respect among them, respecting the ideas arisen on the search of the problem solution. The results of the research highlighted that through the Mathematics teaching and learning approach via Problem Solving, Exploration and Posing it was possible to monitor the growth of the students, who created their own ideas to solve the problems, and, consequently, found multiple strategies for solution of them; posteriorly, justify their solutions, participating effectively of the construction of their knowledge. Besides this, the students engaged in activities of mathematical exploration, which enabled the comprehension of the essential ideas of Combinatorial Analysis, as well as assuming the role of investigators in the classroom, generalizing, formulating new problems and, afterwards, solving them. From which it follows that such methodology allows learning with more comprehension, strengthening the student to solve problems of Combinatorial Analysis with focus not only on the search of the problem solution, but also on the process of the solution and being able to go far beyond, like the performance of a work of problem posing and exploration.