Development Teaching Theory and Teaching Guidance Activity in systematization of numbering system in the initial teacher education context

Abstract

This article investigates the development of mathematical thinking in the initial teacher training context in the Pedagogy Faculty of a university localized in the Southern of the State of Santa Catarina. The work investigates specifically the development of mathematical thinking at theoretical level mediated by the numbering system.  Throughout the semester 2020/2, an investigative developmental educational experiment was carried out with thirty-four students of the fourth and sixth semesters, enrolled in the Learning Unit (subject) Fundamentals and Methodologies of Mathematics for the Early Years of Elementary School, in the remote way. The method that supported the actions was the historical-dialectical materialist. One of the main characteristics of this method is based on the premise that the phenomenon investigated should be considered in its totality, in the inseparability between theory and practice. Research methodology adopted was the developmental educational experiment. Such methodology is linked to the understanding that is through teaching that one learns, and when learning, this one develops. However, it is not about any teaching but through a teaching organized based on contents and methods which make possible promoting develop theoretical thinking of students from their appropriation of scientifical knowledges. Investigative teaching experiment was organized from problems development, in Triggering Learning Situations context, and by four study actions. For data analysis, episodes that indicate the development of each study action were selected. We conclude that it is necessary to rethink the teaching organization of the numbering system since the early school years. The contact with only one of its particularities, the decimal, throughout Basic Education, hindered the appropriation of the essence of this system, making it impossible to correctly transit between one base and another, from its general relationship that gives rise to the different numerical bases. Therefore, it is necessary to rethink not only the initial training courses, but also the continuous training of teachers.