Conhecimentos evidenciados nos cursos de formação inicial para o ensino dos números racionais

Abstract

This work aims to identify what knowledge and arguments are evidenced in the teaching of rational numbers in the process of initial teacher training, observing possible relationships between academic mathematics addressed in higher education courses and school mathematics worked in Basic Education with respect to the teaching of students rational numbers. The participants were students and professors of the classroom courses in Mathematics Degree at the Federal University of Sergipe (Universidade Federal de Sergipe – UFS) and the Federal Institute of Education, Science and Technology of Sergipe (Instituto Federal de Educação, Ciência e Tecnologia de Sergipe – IFS). This was a qualitative research, and the data were collected through the application of questionnaires, bibliographic review, documents from the undergraduate courses at UFS and IFS, interviews and records in the field diary carried out during the meetings. Regarding knowledge, we considered the categories of Ball, Thames and Phelps (2008) which, supported by Shulman's ideas (1986), indicate the knowledge necessary to teach Mathematics. As for the argumentation, we are based on the model of Sales (2011) and Attie (2016), which point out the categories of explanative and justificative argumentation. The analysis of the instruments applied was based on Content Analysis (CA), following the guidelines of Bardin (2011). Observing our data, we found that it is common for undergraduate students to use Explanatory Argumentation to argue procedures related to rational numbers. When asked why some processes are valid, many were unable to provide a justification. Therefore, it was noticeable that there are difficulties for students in using argumentation in the mathematical procedures in question, to validate properties. In this way, we demonstrate that there is a need for training that provides and enhances the process of legitimacy of mathematical concepts and that invests in the argumentative process of undergraduate Mathematics students.