Desenvolvimento do pensamento algébrico em um experimento de ensino sobre sequências

Abstract

The present research, of a formative nature, aimed to observe the development of algebraic thinking with which 8th year students from a school in the Minas Gerais State Education Network can develop relationships between thinking and algebraic language, when in contact with situations that present regularities. We carried out five interventions through Teaching Experiments, comprising Objects of Knowledge and Skills within the thematic unit of Algebra, present in the National Common Curricular Base (BNCC), which involve, in particular, the generalization of sequences and the use of algebraic language. The data used was obtained through: (i) transcription of the meeting footage; (ii) researcher's field diary; (iii) observer’s field diary; (iv) student registration. We concluded that the format of group discussions established by the students promoted an environment of collective construction of meanings, where we were able to perceive the characteristics of algebraic thinking and the use of algebraic language (rhetorical, syncopated or symbolic). We were able to observe that some students often relied on Arithmetic, demonstrating the arithmeticism found by Lins. Secondarily, we sought to observe what sensitivities of students during the process of teaching and learning algebraic objects; in this case, generalizations. We observed that as students experience a given algebraic object, the greater their autonomy and self-esteem will be to mobilize the necessary knowledge. Finally, we built a Didactic Sequence, the result of adaptations that we perceived necessary for the activities used in carrying out the Teaching Experiment, whose objectives are to develop algebraic thinking, promote initial student contact with the formalization of symbolic algebraic language, in order to provoke the construction of meanings for these objects, and to provide learning.