A interseccionalidade entre o sistema didático, contrato didático, a relação ao saber e as perspectiva das estruturas multiplicativas com ênfase na análise combinatória.

Abstract

This research has as general objective to analyze the practice of the teacher who teaches Mathematics in the Early Years with emphasis on the content of Combinatorics Analysis, we have as specific objectives: To investigate the practice of the professor, emphasizing the teaching of combinatorics analysis, the starting from the discussion of the theoretical notion of the didactic contract and understanding how the teacher relates to the content of combinatorial analysis. What justifies this investigation from a scientific point of view is the existing gap in the academy of research on combinatorics in general, especially in the Early Years of Elementary Education in our country, as research in this area began to emerge in the mid-2000s . What motivates this investigation beyond the enchantment for the area of mathematical knowledge, specifically the interest in understanding more effectively about how the teaching practice of those who teach Mathematics is happening and the ways of teaching combinatorial content, as well as, the possibility of contributing to a study that serves as a reference in the mathematical educational field. In this investigation we will aim to answer the following problematizing question: How is the teaching practice of teachers who already work in classrooms and what is their relationship with knowledge, Combinatorial Analysis? When considering the hypothesis that understanding the relationship that the teacher has with the combinatorial analysis content directly implies the way of teaching it in the classroom. We opted for the methodology of scientific research of a qualitative nature, of the empirical type, which occurred from the bibliographical research to the field research. The sources used were diversified, since theses, dissertations, articles, books, and others that were produced in the investigation process of our object of study were used. For the review of previous studies, we will consider the period from 1987 to 2019, where they were mapped in the annals of the National Meeting of Mathematics Education ENEM, which is the most important event at the national level, as it brings together the universe of segments involved with Mathematics Education : Basic Education teachers, Teachers and Students of Degrees in Mathematics and Pedagogy, Graduate Students and Researchers. The data collection instruments will be the videography of the classes. The theoretical references that will support this investigation are the concepts of Didactic System and Didactic Contract by Brousseau (1996, 2008), as well as in the writings of Brito Menezes (2006), Almeida (2016), Borba (2018) Relação ao Saber by Charlot ( 2000, 2001, 2005, 2013) and Combinatorial Analysis in Borba's Early Years (2010). The context of this investigation will involve the research space of a municipal elementary school in the city of Pombal, in the sertão of the state of Paraíba. In this way, it was noticeable that there are some phenomena of Combinatorics that are extremely important to develop a meaningful and effective teaching of Mathematics in the classroom that strengthens the Teacher-student relationship, because if the content is mediated by a certain knowledge to be taught /learned it is possible to insert it in the Early Years in order to facilitate the understanding of students in the multiplicative field and that the student does not have an arduous “shock” between the Initial Years and Final Years.