A generalização de padrões matemáticos com estudantes do ensino fundamental - Campos, Mylena Simões (2023)
The generalization of mathematical patterns is a possibility for the development of mathematical thinking, specifically algebraic thinking, in students at any level of education, as well as the potential for developing advanced mathematical thinking. From this perspective, this research aimed to answer the following question: In what way do elementary school students generalize mathematical patterns and develop algebraic thinking? To answer this question, the objective was to investigate how elementary school students generalize mathematical patterns and develop algebraic thinking. The theoretical framework encompassed discussions on the following topics: a) mathematical thinking, including discussions on advanced mathematical thinking; b) algebraic thinking; c) mathematical patterns; d) generalization of mathematical patterns and e) generalization strategies. Regarding the method, a qualitative research study of the case study type was conducted, involving a group of eight students from the 7th grade of a public school located in Marataízes-ES. Data was collected through: i) participant observation, in which the researcher observed the students solving tasks taken from their textbooks that involved the generalization of mathematical patterns; ii) the students’ notes, which were the tasks solved by them; iii) a conversation circle, where participants could comment and discuss how (or what) they thought in order to generalize the proposed patterns. The results showed that recursive counting strategies and the multiple of the difference with and without adjustment were chosen by the students to generalize the patterns, with the native language being the main means of representation. Furthermore, the presence of advanced mathematical thinking processes in the students' solutions is highlighted, confirming the idea that the generalization of mathematical patterns also concerns the development of advanced mathematical thinking.