PROFESSIONAL TEACHING KNOWLEDGE AND ITS RELATIONSHIP WITH THE IDEA OF PROPORTIONALITY

Abstract

This study aims to analyze the professional knowledge of teachers who teach Math in the 5th year of elementary school, whose students (average age 9-10 years old) stood out in the SARESP (System of Evaluation of Educational Achievement of São Paulo). The study is a field research that involves a group of five teachers at a public school in São Paulo, Brazil. Data collection included a questionnaire and semi-structured interviews with the tasks performed by students. Theoretically, this research is based both on theories that discuss issues related to teacher training and in studies investigating questions about teaching multiplication and division of natural numbers. The first approach was based on studies of Shulman. Regarding educational issues associated with the mathematical object, we used the Theory of Conceptual Fields by Vergnaud. Overall, the data analysis identified that the group of school teachers work collectively. However, it was observed that the difficulties in teaching practice can be influenced by the lack of knowledge of teacher about the mathematical content since we observed weaknesses in their arguments for using the calculation procedure. This study indicates the need to revisit the ways to dealing with multiplicative and proportionality, in particular in the initial training courses and continuing education.

Keywords: Mathematics Education, Professional Teaching Knowledge, Teaching and Learning, Proportionality.