Um estudo de combinatória com alunos de 5º ano do ensino fundamental - Silva, Jose Carlos Thompson (2019)
This thesis consists of a study focusing on mathematics education. The field research work took place in a fifth grade class of a municipal public school in Vitória, Espírito Santo. The central research question was: What strategies do fifth-graders use to solve and elaborate tasks involving combinatorial reasoning? It was based on the implicit combinatorial model, from the point of view of problem solving. It used a qualitative, interpretative and naturalistic perspective as methodological approach. In order to collect and produce data in 2018, a teaching experiment with seven tasks was carried out with this fifth grade class. For the choice of tasks for the teaching experiment, it was done a documentary study of a collection of didactic books and of masters and doctoral studies with a combinatorial focus. At the same time, it was done a research of historical-bibliographic character of combinatorial. Data collected and produced from 15 students in the class in the teaching experiment were analyzed. The results showed that the students used differentiated strategies in a nonsystematic and systematic way. It was concluded that it was necessary to work gradually and to explore problems of the same structure of combinatorial reasoning. In this context, it was necessary to ask intermediate questions that would aid in the comprehension of the statement and would draw the students' attention to the established parameters. We defend, in this thesis, that fifth year elementary students participating in this research use problem solving strategies that involve combinatorial reasoning. However, this reasoning needs to be explored and approached in an integrated and intentional way with other mathematical topics or concepts. In this way, it is possible to contribute to the students recognizing and amplifying these strategies in enumeration and counting procedures. In addition, they recognize the relationships between tasks involving the same structure from the point of view of combinatorial reasoning and are able to elaborating and solving similar ones.