Aprendizagem do conceito de função por meio de situações didáticas com microcontroladores digitais

Abstract

The purpose of the study was to investigate “How can the concepts of mathematical function be assimilated at levels of abstractions closer to reality without compromising the necessary mathematical formalism?”, Considering that the mathematics teaching model presents, in general, the contents in an abstract way, decontextualized and distant from the phenomena related to them. Based on the research problem, the work aimed to "define a teaching and learning process of mathematical function, integrated with the subject's action on a technological architecture". Specifically, the study sought to develop the technological framework based on digital microcontroller as a representation of mathematical function; discuss and analyze the development of didactic situations in an active method context that promote the subject's action to learn function concepts; and evaluate the experimental results to verify the learning of the formal concepts developed. Thus, to answer the research questions and achieve the proposed objectives, we opted for the qualitative approach in the experimental application modality, where through the planning, design, application and evaluation of a sequence of experiments, we did a pedagogical intervention in experimental character based mainly on the theoretical bases of genetic epistemology and Piaget and on the methodological assumptions of the didactic situations of Guy Brousseau. The first phase of the research refers to the characterization of the research subjects through the diagnostic test, the findings indicate that the subjects present difficulties of abstraction as a result of the predominantly empiricist pedagogical approach. Faced with this reality, we opted for the application of the didactic model based on the digital microcontroller as a source of abstractions of the concepts of mathematical function. This conceptual basis combined with the study of didactic situations brought the perspective of a new didactic-pedagogical dynamic in the classroom. This methodological implementation allowed the achievement of results that indicated favorable conditions for the learning and construction of mathematical knowledge, by stimulating the engagement and mobilization of action schemes that involve the function concepts initially expected.