Conhecimento matemático para o ensino mobilizado por uma professora no contexto do estudo de aula

Abstract

The present dissertation is aimed to identify and analyze the subdomains of Mathematical Knowledge for Teaching, mobilized by a teacher of the early years of Elementary School during a Lesson Study cycle. The research is qualitative and interpretative in nature, carried out in the context of an extension project developed at the Universidade Tecnológica Federal do Paraná (UTFPR) and entitled Continuing Education in mathematics to teachers of the initial years of Elementary School. In this project, whose intention was to work collaboratively through Lesson Study, the group consisted of teachers educator, master's degree students and teachers of the 4th and 5th grades of elementary school who teach Mathematics in the municipal school system of Londrina - PR. Throughout 2019, eight face-to-face meetings were held, but this research analyzes only up to the third meeting of the group, a period that involved a complete Lesson Study cycle, composed of the planning, development and analysis (individual and collective) of a class. The research is based on the theoretical framework of Mathematical Knowledge for Teaching (MKT) proposed by Deborah Ball and collaborators. The focus of this research analysis was on the subdomains of Mathematical Knowledge for Teaching mobilized by the teacher Maria, who agreed to develop the lesson, planned by the group, with her 5th grade class. The data analyzed in this research were produced through audio and video recordings of the three face-to-face group meetings, by the researcher's participant observation and her logbook of these meetings, by video recording of the lesson developed by Maria and by audio recording of an individual reflection of this teacher. The analyses, divided into nine Episodes, show that almost all subdomains of MKT were mobilized by Teacher Maria, with the subdomains of Knowledge of Content and Teaching, Knowledge of Content and Students, and Specialized Content Knowledge being the most evident. We conclude that all stages of the Lesson Study cycle presented potential to mobilize subdomains of MKT and that certain aspects seem to have favored this, such as: the use of challenging mathematical tasks, the teaching approach based on exploratory teaching, the collaborative work in lesson planning and analysis, the use of tasks organized by the trainers to promote collective discussion among participants during lesson analysis. Based on this, as an Educational Product resulting from this professional masters research, a set of Professional Learning Tasks was proposed based on the analyses undertaken here and that we consider to have potential to promote the MKT development of teachers in initial or continued training.