Engenharia Didática em um processo de formação continuada: um estudo de conhecimentos de uma professora de matemática

Abstract

This investigation has the general objective of analyzing the knowledge of a Mathematics teacher who participates in a process of continuing education based on the Didactic Engineering stages. For this, we considered as a base researches that deal with the process of continuing education, which present criticisms in actions that don’t take into account the reality of the teacher and his or her absence during the process of conception of formation, for the proposition of a formative process that sought to overcome possible difficulties. As a theoretical basis to the research, we used the Theory of Conceptual Fields proposed by Vergnaud, which provides a theoretical framework about the individual’s cognitive development in the face of the proposed situations, especially the ideas of the operative knowledge and predicatives of subject and knowledge in action. Besides, we were guided by the Didactic Engineering that we used as a contribution in the development of the moments of the proposed training, starting from the phases that compose it. In this sense, we proposed an extension course for Mathematics teachers in the city of Coxim - MS, in order to execute a training process that was guided by the phases that compose the Didactic Engineering research methodology. The extension course, which had the participation of a Mathematics teacher who taught in classes from the 6th to the 9th, was developed in 14 meetings, weekly, in the 2nd semester of 2018. Considering the needs and interest of the teacher, the topics covered were fractions, decimal numbers, systems of equations of the 1st degree and metric relations in the circumference. For each topic, we went through the moments that constitute Didactic Engineering, carrying out the preliminary study of the theme, elaboration and a priori analysis of the didactic sequence, the experimentation and a posteriori analysis and the validation of the sequence. We organized like this, because we believed that during the meetings it would be possible to go through situations that contributed to the formation of the teacher, both in mathematical and didactic aspects. The data analyzed in the research came from audio recordings and the meeting logbook, in addition to the teacher's plans. In our analysis, we showed that the teacher frequently manifested the operative form of knowledge, with the mobilization of procedures and resolution algorithms in the face of the proposed situations. However, when trying to justify these strategies, she found it difficult to relate properties, relationships and justifications involved in the situation, components of the predicative form of knowledge. In this sense, during the meetings, there were situations that destabilized the mathematical knowledge of the teacher, leading her to moments of reflection, enabling the construction of knowledge. In relation to didactic knowledge, we found that the teacher mobilized some elements related to the emphasis of situations that favored the use of resolution techniques, in addition to believing that her students needed her help to solve the activities, so that we model this knowledge as didactic knowledge in action. During the formative process, the teacher was faced with situations, such as a posteriori analysis of the activities, which led her to rethink her choices, showing traces of new didactic knowledge. Finally, we highlight the use of Didactic Engineering in the process of continuing education for teachers, presenting some limits of the professional context that hinder the work, such as the need to follow the school timetable and calendar, and potentialities, of which we highlight the use of elements of Didactic Engineering during the teacher's work, such as the precepts of a priori and a posteriori analysis.