Professora, qual é a conta? - elos entre as situações-problema e os diálogos de estudantes do Ensino Fundamental

Abstract

This work is a qualitative research whose object of study was based on dialogue in Mathematics classes and its relationship with the acquisition and expansion of the concepts of multiplicative structures, having as theoretical support Vergnaud's studies on the resolution of situations of multiplicative structures and the contributions of Alro and Skovsmose around the concept of dialogical communication. The performance of students in a fifth-year class was compared in three distinct stages: in a pre-test, in a didactic intervention and in a post-test. Using Gitirana et al. as a reference, multiplicative comparison situations focused on the students' context were considered according to the two classes of this multiplicative axis: (i) unknown relationship and (ii) unknown referent or referred. A protocol with six questions was applied for each of the three phases of the research. Taking action research as inspiration, we investigated what happens to students' resolutions during and after dialogic processes promoted by interventionist didactic actions in which two roles were assumed concomitantly: that of teacher in charge of the group investigated and that of researcher in education. With a dive into the focus group, made up of four children, developments in the students' reasoning were observed. The results showed that, through dialogues in small groups followed by plenary sessions, the students compared and reformulated some calculations, including division, an operation required in the more complex problems that were addressed. Dialogues in action led students to recognize the nature of comparative multiplication situations in a self-evaluative process that included error correction, constructive criticism, advice, support and praise, all carried out carefully and horizontally in moments of exchange and interactions between children and the teacher. It was concluded that any situation in the Multiplicative Conceptual Field can and should be well worked on with students in the initial grades as long as a set of actions is guaranteed, such as: care with the use of the language used in preparing the statements; encouraging the action of asking as a strategy for making implicit schemes explicit; promotion of individual and group moments for interaction between students; openness to sharing and analyzing different perspectives; and overcoming the treatment of error as something absolute and to be eliminated. Investigating communication and interaction processes between teachers and children in the early years is a fruitful topic for the field of Mathematics Education. suggestion for future research, especially in the exploration of other multiplicative axes. There should be more reach to this theory by teachers in the initial years, as it is powerful in supporting the diagnosis of potentialities and intervention in the face of students' weaknesses in the mathematical learning process.