Generalizaciones aritméticas, generalizaciones aritméticas sofisticadas y generalizaciones algebraicas en estudiantes de grado quinto de educación básica primaria (con edades de 10 y 11 años)

Resumen

This research shall address the problem of algebraic thinking in primary school while considering the necessity of possessing didactic knowledge to determine whether the production from students may actually be considered algebraic in order to promote its development. This research shall interpret the generalizations made by fifth grade students (aged 10 and 11) when addressing specific pattern sequence tasks during join work with the teacher. Semiotic means of objectification that may appear in their written, oral, and gestural productions shall also be described and the analyticity component analyzed, in addition to establishing generalization types and which of them correspond to algebraic production. This research is based upon the theory of objectification, the relation between semiotics and mathematics education, the proposal of early algebra and algebraic thinking, and the generalization of patterns. The methodological framework of this qualitative-interpretative research is multimodal analysis. The results show that the production from students corresponds to three types of generalizations: arithmetic, sophisticated arithmetic, or algebraic. Each characterization is analyzed with regard to their origin and presence in the generalization process and the transit between them. It was concluded that higher-level generalization is favored by classroom math activity and that the latter allows a higher level of conceptualization of the generalization process. The diversity of productions suggests that having broad didactic knowledge on the nature of generalizations is required to differentiate those that, albeit not algebraic, might be close to being algebraic and constitute a key element in the emergence of algebraic thinking by the student.