Problem posing of Combinatory Analysis as a starting point: classroom episodes

Abstract

This article advocates that the posing of problems should occupy a prominent place in mathematics classes.  Thus, this study aims to analyze how a classroom approach via Problem Posing can enhance the teaching-learning of Combinatorial Analysis.  The research is based on a qualitative approach, aiming to seek meanings, interpret and understand the information obtained.  The research modality is characterized as pedagogical, according to which the teacher is the researcher of his/her own classroom (LANKSHEAR and KNOBEL, 2008).  The methodology chosen to work in the classroom was the Problem Posing, and developed in a 2nd year high school class at the State Elementary and High School Agenor Clemente dos Santos, located in the town of Alagoinha-PB.  In this article, six meetings stand out - totaling seven classes, each class lasting a maximum of 45 minutes.  However, we went deeper into the description and analysis of a meeting (two classes), which focused on the posing of Combinatorial problems. The results of the research showed that students perceived the relationship of words with the essential ideas of Combinatorial Analysis.  Thus, it appears that they were able to make relations of a mathematical idea in different contexts.  Consequently, the development of this activity fostered the acquisition of several ideas that were implicit in the formulated problem, providing the students with the perception of the relationships between mathematics and their social reality.  It is concluded that, in the proposal of problem posing, in which the students acted as protagonist of their learning, the common discoveries were shared, defending decision making, and a consensus was reached on all the work done in the debate, in order to promote the deepening of the main concepts of Combinatorial Analysis, as well as the development of mathematical thinking.