ENSINO DO CONCEITO DE FUNÇÃO POR MEIO DE PROBLEMAS: CONTRIBUIÇÕES DE DAVYDOV E DE MAJMUTOV.

Abstract

Situated in the didactic, this research is focused on teaching and learning of the mathematical concept of function. The Brazilian scientific literature within the mathematics education shows that the learning difficulties related with the concept of function, are associated with teaching methodologies. Teaching through problem solving is an alternative, but in general, are not singled out theories or teaching methods by problems with potential to promote change. Emphasizing the historical-cultural approach, it sought to clarify the issue: how to structure the teaching approaching the theories Davydovs developmental teaching and Majmutovs problem-based teaching for what the student to learn the concept of function? Besides the analysis of the teaching-learning of concept of function on the basis of historicalcultural theory, the research aimed to: clarify the nuclear aspect of the concept of function as the basis for its teaching; analyze the teaching theories of Davydov and Majmutov discussing their similarities and differences; point out the benefits and limitations of the teaching of function based on these theories. For teaching the concept of function, it is considered the Bourbakis approach, which points as nuclear element, essential to the understanding of this concept, the specificity of the relationship between the elements of the sets involved. The methodological procedures were literature and field research, and the latter consisted of a formative didactic experiment in 1st year Teaching Integrated Technical High School of an area of the Instituto Federal de Goiás. The tools to collect the data were observation, semistructured interviews and diagnostic tools of student learning. The analysis sought to confront the initial learning situation of students with one identified after teaching by problems in the formative didactic experiment. The results showed that the privileged teaching theories complement each other and are close in some respects: 1) Teaching must be focused on the development of theoretical thinking of students; 2) Students should learn from research processes and not ready conclusions; 3) The teaching and learning must provide active and creative appropriation of knowledge by the student; 4) The tasks of the students must contain problems to be solved through investigation, contemplating the existent contradictions in the objects of knowledge. In addition, the qualitative changes in the relations of the students with the concept of function have shown signs of development of theoretical thinking, as advocated by Davydov and cognitive independence as advocates Majmutov. The contradictions and limitations were related to low workload of math classes, with little time for reflection, and the difficulty to dissuade students from individual study habit, transmissive and passive, in favor of collective study, reflective and active. It is concluded that the teaching structured with problems based in theory Davydov and on theory Majmutov, presents possibilities for effective learning of mathematical concepts, particularly of concept of function.