O trabalho com regularidades em sequências e o desenvolvimento do pensamento algébrico: conhecimentos docentes especializados para a implementação de tarefas no 2º Ano dos Anos Iniciais do Ensino Fundamental - Senhora, Gustavo Gomes Moreno (2024)
The present research, qualitative in nature and bibliographic in scope, aimed to understand the necessary teaching knowledge required for a mathematics teacher instructing second-grade students in the early years of elementary school, when implementing tasks focused on numerical and figural sequences, aligned with the skills established by the BNCC, with the intent of fostering the development of algebraic thinking, specifically in its functional thinking aspect. We based our study on the MTSK theoretical model to identify the specialized teaching knowledge needed to implement these tasks, specifically in relation to the domain of mathematical topics, understanding the structure of mathematics, its teaching, and the characteristics of its learning. We also drew on the ideas of Blanton, Kaput, Martins, Pittalis and their collaborators, Rocha, and Viseu on algebraic thinking and one of its facets: functional thinking. We developed a set of three tasks on regularities in numerical and figural sequences, anchored in skills prescribed in the National Common Curricular Base (BNCC) for the second year of the early grades, within the Algebra thematic unit, so that, from an analysis of these tasks, we could identify the specialized knowledge previously mentioned that should be activated in teaching practice to implement them. As main results, for knowledge of Mathematics topics, we highlighted an understanding of the specificities of figural sequences, which involve not only the difference in the quantity of figures and symbols from one term to another, but also the way these symbols and figures are visually organized in each term of the sequence; regarding the understanding of the structure of Mathematics, we emphasized the importance of connections with mathematical topics at more advanced educational stages, such as functions, arithmetic progressions, and geometric progressions; for knowledge of Mathematics teaching, we underscored the organization of teaching strategies to activate different forms of mathematical thinking, exploring, for example, the recognition, naming, and comparison of/among planar and spatial figures, as well as the translation or rotation of these figures; and for knowledge of learning characteristics, we stressed the teacher’s understanding of the possible difficulties students may face when dealing with tasks that, for instance, explore and require precise descriptions of sequence regularities