Concepções e competências de professores especialistas em matemática em relação ao conceito de fração em seus diferentes significados

Abstract

This study aimed to identify and analyze the concepts and skills of specialist teachers in mathematics who work in the 3rd or 4th cycle of primary education in relation to the concept of fraction. For this, the study aimed to answer the following research question: "What are the concepts and skills presented by specialist teachers in mathematics who work in the 3rd or 4th cycle of primary education on the concept of fraction in their different meanings?" To answer this question, first we seek theoretical support to subsidize the development of the study. This support came from the ideas contained in Vergnaud Conceptual Fields Theory and theoretical ideas of Kieren and Nunes in relation to the different meanings of the fraction. Then a diagnostic tool was developed consisting of four units: (a) profile, (b) development of problem situations, (c) answers the problems and situations (d) skills. This tool administered to 21 teachers who were divided into two groups: group 1 (G1) consisting of 11 teachers who were working in the 3rd cycle of primary education (6 and 7 grades) and group 2 (G2) comprised 10 teachers they were working in the 4th cycle of primary education (8 and 9 grades) distributed in six schools. In relation to conception the teachers from both groups showed a narrow fraction, only to face two meanings: part-whole and multiplicative operator. In addition, there was an emphasis on treating only fractionally from the standpoint of the algorithm. Regarding the competence G2 presented as more competent than the G1. We conclude that based on the fact that the G1 had a higher rate of confusion in using the ratio as a fraction, and showed a higher rate of use of perception as the main strategy for teaching fractions, thus distancing from the content present in this logical invariants and, when appropriate, allow a solid understanding