Contribuições do ensino desenvolvimental de Davydov para a formação de conceitos teóricos de matriz

Abstract

The object of this research is the formation of scientific concepts. It is linked to Research Line 2: Theories of knowledge and pedagogical practices, of the Academic Postgraduate Program in Education of the Instituto Federal de Goiás - Goiânia Campus. The aim is to understand and answer the following research question: What contributions can a teaching experiment on the concept of matrices, in the light of Davidov's Developmental Teaching Theory, make to the formation of theoretical thinking in basic education students? To this end, a literature review was initially carried out, which revealed few studies focused on the formation of mathematical concepts, using the theory of developmental teaching and, when refining the search for the term matrices, no study was found that linked the two themes. This showed the greater potential of the research. As a result, the studies of theorists such as Davidov and Libâneo were used to support the criticism and ineffectiveness of the current system of content transmission that takes place on the school floor, and the development of a formative didactic experiment was suggested as a resource, aimed at the formation of theoretical thinking through the ascent from the abstract to the concrete, based on the six actions proposed by Davidov. The research also drew on the theories of Marx, Vigostki, Leontiev and Elkonin in order to support its theoretical development and practical analysis, with emphasis on the importance of social interactions for cognitive development. At the central of the research is the understanding of the subject in action, during the development of the didactic experiment, emphasizing the importance of the teacher's mediation in this teaching-learning process. We sought to build a relationship, through a dialectical process, between school teaching and the students' local community, with the aim of contextualizing teaching in an individual social way. The formative didactic experiment, as an intervention method, was developed in a 2nd grade high school class at a state public school in Anicuns, in the countryside of Goiás. The experiment was analyzed, involving categories that are specific to cultural-historical theory, such as: mediation, concept formation (theoretical and empirical thinking), moving from interpersonal to intrapersonal communication and study activity. The work seeks to analyze, from a qualitative perspective, the conceptual appropriations of mathematical content, with a focus on matrices, in addition to arousing the student's interest in the study of the object; bringing the concepts closer to their daily lives; overcoming empirical teaching; enabling theoretical teaching; contributing to the student's effective development; teaching from historically produced and socially valid knowledge; providing opportunities for teachers and students from the field school to appropriate theoretical contributions. The results concluded from the analysis made it possible to understand that the students had appropriated the scientific concepts. In conclusion, this study aims to fill a gap in educational research by exploring new approaches to teaching matrices in secondary school. Theoretical and practical contributions emerge from the application of the Theory of Developmental Teaching, promoting a deeper and more contextualized understanding of mathematical concepts.