Investigação da generalização do pensamento aritmético como forma de ascensão ao pensamento algébrico

Abstract

The objective of this research was to investigate the process of meaning-making established through students' Activities in Learning Triggering Situations (LTS) that enabled the development of algebraic thinking based on the generalization of arithmetic thinking. With the research objective defined, we formulated the following guiding question: What meanings are produced by students in the final years of elementary school, through Learning Triggering Situations, that enable the development of algebraic thinking? We hypothesized that students' difficulties in studying algebra stemmed from issues related to arithmetic. Therefore, our main objective was to analyze the development of algebraic thinking through LTS that explored the generalization of arithmetic thinking. The specific objectives were: (1) to analyze whether the mobilization of algebraic conceptual nexuses in LTS produces meanings that contribute to the development of algebraic thinking; (2) to analyze whether the LTS foster Study/Learning Activities; and (3) to analyze the role of pedagogical organization in the production of meanings. The development of this research was grounded in the historical-cultural theory, which is based on the development of individuals through their engagement with history and the cultural environment in which they are embedded, while also considering the unique subjectivity of each individual. The methodology employed in this research was based on the analysis of meaning-making nuclei, derived from the dialogues of the participants in the research environment, as influenced by the proposed tasks and learning contexts throughout the research process. The identified meaning-making nuclei highlighted three central aspects of the development of algebraic thinking: (1) the transition from arithmetic language to generalization, where students began to identify patterns and regularities; (2) the generalization of arithmetic to the formation of the concept of variables, demonstrating the relationship between numbers and symbols; and (3) the integration of algebraic language, geometric figures, fluency, and interdependence, fostering a broader and more theoretical understanding of algebra. The research methodology adopted was based on a logical-historical framework and the materialist historical-dialectical method. Additionally, categories related to the concept of school education grounded in social praxis were employed, such as work, contradiction, mediation, necessity, and motive. The results emphasize how the LTS, grounded in the cultural-historical theory, contributed to the formation of mathematical meanings and the development of theoretical algebraic thinking, enabling students to identify patterns, understand variables, and interpret complex mathematical situations.