Diagrammatic reasoning mobilized by 1st year elementary school students in a mathematical modelling activity

Abstract

In this paper, we aim to highlight the knowledge of students in a 1st-year elementary school class in a modelling activity under a semiotic interpretation of diagrammatic reasoning. We understand that mathematical modelling is a pedagogical alternative in which, based on a problematic situation in reality, mathematical procedures are used to reach a solution to what is being investigated. The knowledge is supported by Peircean semiotics, more specifically, in the mobilization of diagrammatic reasoning, made possible in the construction, experimentation, and observation of semiotic diagrams produced by students. The qualitative analysis supported by the triangulation process took into account the 25 first-year students of a municipal school in the interior of Paraná as subjects, the diagrams produced in the development of the modelling activity as objects and the phenomenon consists of the mobilization of the diagrammatic reasoning that emerged either through students' needs or at the teacher's request. Data were obtained through audio and video recordings and through inscriptions produced individually or collectively. The results showed that the mobilization of diagrammatic reasoning was carried out in the diagrams produced jointly between students and teacher, mainly to advance the generation of more sophisticated mathematical representations, such as tables and graphs, in which new knowledge was constructed. Furthermore, the interaction between colleagues and the communication undertaken with the entire class based on a theme close to the students promoted interest in developing the activity.

Mathematics Education; Mathematical Modelling; Peircean semiotics; Diagrams; Early years