Formulação de problemas matemáticos na aprendizagem de números racionais por alunos do 4.º ano de escolaridade

In many countries, as in Portugal, Mathematics syllabus at different levels of education highlight problem solving, in some cases as a teaching strategy and in others as a mathematical ability to be developed by students. In addition to this activity, problem posing arises, which has deserved less attention at the level of curricular recommendations, although it may constitute a strategy for deepening mathematical concepts and developing the understanding of procedures. While in problem solving the student has to answer questions, in problem posing the student is challenged to contextualize situations using his language, knowledge and experiences. The formative potentialities of problem posing have led us to investigate how students in the fourth grade use and deepen their mathematical knowledge about non-negative rational numbers in that mathematical activity. In particular, we aim to know what kind of problems students formulate, the strategies of problem solving that they value and the traces of creativity that they identify in this activity. Given the nature of the objective, a qualitative and interpretative methodology was adopted. The collection of data is based on the collection of the written productions of students and the application of a questionnaire. The study reveals that students tend to formulate problems similar to the ones in school textbooks. In this formulation, students use the mathematical concepts relating to the non-negative rational numbers they have learned, creating, in most cases, plausible contexts. The study also reveals that students value the structure, the imagination, the originality, the playfulness and the degree of difficulty as traces of creativity in problem posing.