Learning related to the multiplicative field in solving proportional fourth problems in the 6th year of Elementary School: the case of Mariana

Abstract

Understanding elementary arithmetic operations has historically been one of the pillars of school life. In the transition from the initial years to the final years of elementary school, this is generally one of the mathematical skills that students are expected to have built up. However, national assessments show that this expectation has not been realized in most Brazilian public schools. In view of this, based on the Conceptual Fields Theory, a set of tasks on the multiplicative field was designed and developed in a 6th grade class at a public school in Ouro Preto (MG). This article analyzes the process experienced by a student when solving problems involving the proportional fourth. The research, which was qualitative in nature, was carried out over a period of four months, during regular math class times, and focused on the learning of notions associated with the multiplicative field. The data was produced through audio and video recordings of some of the activities carried out, the researcher's field diary, records produced by the student throughout the work and an interview with her. The results show that the student used different procedures throughout the process and that, although her answers do not allow us to specify exactly which strategy she adopted at each moment, mathematical knowledge about the fourth proportional was mobilized. Other learning was also identified (relating to classmates and the teacher, knowing how to listen to classmates and the teacher, constructing and expressing arguments, etc.) which played an important role in the process. The work carried out proved to be a possibility for learning mathematical concepts involved in the multiplicative field, favoring the transition and adaptation of schemes from additive to multiplicative thinking.