A comunicação e a comunicação matemática presentes no quinto ano do Ensino Fundamental e o desenvolvimento do pensamento algébrico

Abstract

Based on changes to the legal documents governing Brazilian schools, which now mandate the teaching of algebra from the early years, and the low scores presented in large-scale assessments that measure the mathematical skills of Brazilian students, we realize it is highly relevant to propose investigations aimed at understanding the development of algebraic thinking in the early years. In this qualitative research, our main objective is to investigate the presence and use of mathematical communication in the math classes of a generalist teacher who teaches a 5th-grade class in elementary education (EFAI). We seek to answer the question: what is the presence and use of mathematical communication in the math classes of a teacher who teaches a 5th-grade class, especially in a proposal involving the teaching and learning of algebra? We adopt the Theory of Objectification (TO), a historical-cultural educational theory developed by Luis Radford, as our theoretical framework. For data production, different data collection methods were used, and we based our data analysis on the multisemiotic method. The various semiotic means mobilized by the students and the teacher during the activity were observed, and the data were organized and structured into four categories: 1: Communication as affection; 2: The reflective teacher and their views on an algebraic activity; 3: Mathematical communication in the classroom: joint labor and algebraic thinking; 4: Ask and listen to ensure before asserting. From the analysis of each category, we were able to highlight the relationships between the language and communication used by the researcher, with emphasis on the processes experienced within the school. We also inferred that the teacher's training and professional development courses she attended have not yet allowed for the development and enhancement of her own algebraic thinking and, consequently, her explorations and actions carried out jointly with the students did not permit many advances in the development of algebraic thinking. From the interactions between the researcher and the teacher, we also identified potential formative opportunities within school-based investigations that use TO as a guiding framework for investigative processes. We observed that, often, the teacher and students used arithmetic thinking to solve the proposed algebra challenge and noticed that there were no explorations leading to broader understandings. We suggest that the theme of mathematical communication and the development of algebraic thinking in the early years, especially addressing the notions of equality and equivalence, can be potent and necessary for further research and investigations