Problem Solving, Exploration, and Posing in the elementary school: contributions to the teaching and learning of combinatorics

Abstract

The present study aims to investigate the contributions of the Problem Solving, Exploration and Posing to the teaching and learning process of Combinatorics in the initial years of Elementary School, based on studies related to the teaching-learning methodology of Problem Solving and Combinatory Education. It`s a qualitative research, dedicated to describing and analyzing in detail the data collected through observations, field notes, written records made by the students and audio recordings. As subjects of the research, we adopted 16 students from a 5th grade classroom from an Elementary School in the municipal public network of Paraíba State, Brazil. The pedagogical actions carried out in a classroom context were supported by the classroom methodological perspective of Problem Solving, Exploration and Posing defended by Andrade (1998, 2017), as well as in studies that discuss the teaching and learning process of Combinatorics. In the opportunity, the four types of combinatorial problems (combination, arrangement, permutation and Cartesian product) that need to be approached in the initial years of Elementary School, based on combinatorial problems drawn from Pessoa's research (2009) and proposed by the students were worked out. It was concluded that the methodological proposal of the Problem Solving, Exploration and Posing contributes to the promotion of the combinatorial learning of the students, enabling the development of a reflective educational process. It was verified that the problematizations provoked during the Problem Solving, Exploration and Posing process potentiated the work of reflection on the invariants of the combinatorial problems, which favored the development of the combinatorial, generalizing and logical reasoning of the students, besides enabling the researchers to explore different dimensions of the proposed problems.