Formação de habilidades em modelagem matemática fundamentada no sistema didático Galperin, Talízina, Majmutov para licenciandos em Matemática

Abstract

The present study focuses on the formation of skills aimed at solving problem situations in the field of Mathematical Modeling, proposed in tasks to Mathematics undergraduates at the Federal University of Amazonas. To reach this objective, the Galperin, Talízina and Majmutov didactic system was assumed in the teaching and learning process, composing the so-called Mathematical Modeling Student Problem Situations Activity (MM SPSA). This system is based on the Historical Cultural Theory, in which the formation of skills occurs from the internalization of the guiding action, which is initially external (material) and moves through qualitative stages, called Galperin's Stages of Mental Actions, until it becomes action. internal (mental). The orientation of the activity is entitled Schema of a Complete Orienting Basis of Action (SCOBA), constituted here by four invariant actions, represented in the skills of: formulating the student problem; build the conceptual and procedural core; solve the problem; analyze the solution. Both actions and tasks follow the principle of Majmutov's Student Problem, in addition to the Direction of Study Activity of Talízina to guide the process of assimilation of skills in the classroom. The research is qualitative and quantitative, with a qualitative emphasis, whose instruments for collecting information adopted were pedagogical tests and observation guides. The results were evaluated according to criteria of execution in the accomplishment of the tasks and qualitative indicators of the actions carried out by the participating students. The first moment of the research was destined to the initial diagnosis to verify the real development zone of the students, noting flaws in the guiding base and the need for adequate (re)elaboration. With this, it was possible to design the didactic planning according to a system of tasks composed of contradictions, considering the starting level of the students and the stages of assimilation. After the implementation of the MM ASPD, the analysis of the results proceeded from the triangulation of performance levels, qualitative indicators and questionnaires. In view of this, it was found that 23% of the academics are able to solve the student modeling problem under materialized guidance, representing the beginning of the internalization of the experienced actions. With a higher relative frequency, 54% of the participants showed a reduction in explanation, increases in generalization and partial assimilation of actions, indicative of the formation of action in external verbal language. In addition, 23% showed independence and total assimilation of actions in the face of tasks that required greater creativity and generalization in their resolutions, thus reaching the stage of external language for themselves. Even in the face of difficulties faced in accessing the internet, manipulation of digital resources, obstacles in the execution of actions, advances were observed in the conscious orientation of students. In view of the above, the MM ASPD, guided by the didactic system Talízina, Galperin, Majmutov, contributes to the formation of skills as a consequence of the partial/total internalization of the invariant action scheme aimed at the practice of Mathematical Modeling.