Knowledge Of Proportional Reasoning and its Teaching: a study on tables and manipulative materials

Abstract

This research aims to identify and understand the professional knowledge of teachers who teach mathematics in the early years regarding the development of proportional reasoning among their students through collective discussion on tables and manipulative materials during the resolution of two problem situations. The research uses the multidimensional model of mastery of mathematical knowledge for teaching as a theoretical framework proposed by Ball, Thames, and Phelps, categorizing the professional knowledge of teachers who teach the subject. The methodological procedures adopted involve a qualitative approach, using data collected during a group study session with six teachers who teach mathematics in the initial years. The activities proposed during the study session require recognizing and using the principles of proportionality. The strategies adopted by the teachers to solve the situation initially involved mental calculations and visual representations. Teachers' difficulties in operating with rational numbers and proportions were identified, but the development of proportional reasoning was also observed throughout the discussion and group reflection. The use of resources such as manipulative materials and proportion tables, proposed by Lamon, was an effective tool to help teach rational numbers and encourage the development of proportional reasoning.