Equações do 2° grau e o sistema didático zankoviano: um olhar para o desenvolvimento do estudante

Abstract

This research, based on historical-dialectical materialism, assumes relevance in the area of Education and Mathematics Education due to the limited access, in Brazil, to the works and productions of L. V. Zankov and the contributions of the didactic and methodological elements of the Zankovian system to the process of obutchénie and development of mathematical concepts and to the Theory of Developmental Obutchénie. In the search for an answer to the central question - what are the contributions of the process of obutchénie of 2nd degree equations based on the Zankovian system for the development of the student? -we set as a general objective to analyze the contributions of the process of obutchénie of 2nd grade equations based on the Zankovian system for the development of the student. As specific objectives, we sought to investigate potentialities and/or limits of a task, composed of seven steps, elaborated in the principles of the Zankovian system, for the integral development of the students, and to analyze possible contributions of a microcycle experiment organized in the perspective of the Zankovian system, for the process of obutchénie of the 2nd degree equations concept. We used the microcycle experiment as the research methodology, being carried out with 24 ninth grade students from a public school in Uberlândia - MG. An educational task consisting of seven steps was organized. For analysis purposes, we organized the empirical material in two isolates, consisting of episodes and scenes, discussing the movements made possible in the unfolding of the stages of the task, as well as the students' actions and reflections when facing the proposed problem situations. Through the analyses performed, there is evidence that students have appropriated the concept of 2nd degree equations and the relevance of the concepts of fluency, variable, variation field and algebraic language for the process of obutchénie of algebra. During the process, students justified their actions by means of the needs that drove them, allowing the attribution of new quality to the development of theoretical knowledge. Moreover, the task organized according to Zankovian principles allowed the development of the students' cognitive, ethical, moral, emotional and volitive dimensions, concatenated with the appropriation of the concept of 2nd degree equations.