Situações-problema do campo conceitual aditivo: um estudo acerca dos conhecimentos dos professores dos anos iniciais do ensino fundamental do norte do Espírito Santo

Abstract

Considering that the knowledge of teachers reflects in the teaching given to students, this research, which presents an excerpt on the Additive Conceptual Field from the perspective of the Theory of Conceptual Fields (TCC) of Gérard Vergnaud, starts from the question: What are the contributions of a process of continuing education on TCC for the expansion of knowledge about the Additive Conceptual Field, by teachers of the early years of elementary school in the north of Espírito Santo? In the search to answer this question, this study proposes to investigate the contributions of an extension course of the Federal University of Espírito Santo (UFES) on the educational applications of TCC, in the expansion of knowledge about the Additive Field, by these teachers. Data were collected from this extension course, with the participation of 14 teachers who worked in classes of the initial years of elementary school in 9 different state schools, located in 6 municipalities in the north of Espírito Santo, in the year 2022. This qualitative research, developed through a case study with the use of elements of Didactic Engineering, employs as data collection instruments: activities carried out in schools by the participants of the course, activities developed in the face-to-face meetings, questionnaire and video recordings. The analyses indicate that before the studies on TCC in the extension course, the problems elaborated by the participants were mostly classified as prototypes, simpler types among the categories of the Additive Field. The identification of the theorems in action employed by the teachers in the resolutions reveals the mobilization of true and false theorems. A second elaboration of problems, after the studies on the Additive Field in the course, shows greater diversification of the categories. These results, as well as the analyses of the teachers on the ways of solving problems in this field by their students and the answers to the questionnaire about their perspectives in relation to the contributions of TCC to teaching practice, confirm that the course contributed to the expansion of knowledge about TCC by teachers, and consequently, so that the diversity of situations involved in the Additive Field reaches the students for whom they teach.