Argumentative orchestration in the mathematical modelling cycle in the classroom

Abstract

Given the importance of modelling in mathematics classrooms, and despite the extensive body of research on teacher support for promoting the mathematical modelling cycle in the classroom, authors have overlooked how teacher support for argumentation can contribute to this cycle. This study is aimed at characterizing teacher support for argumentation in the mathematical modelling cycle in the classroom. We analyzed 10 class episodes taken from the cases of two teachers, Soledad and Ángeles. The episodes were analyzed considering teacher support for argumentative orchestration (communicative strategies and pattern recognition). In the two cases studied, we found that argumentative orchestration exhibited different types of overall presence and recurrence throughout the stages of the mathematical modelling cycle, with communicative strategies being more present across the board and more recurrent in the mathematical modelling cycle than pattern recognition strategies.

Knowledge and Beliefs on Mathematical Modelling Inferred in the Argumentation of a Prospective Teacher When Reflecting on the Incorporation of This Process in His Lessons

“…An innovative aspect of this research is that we inferred the knowledge and beliefs based on the argumentation of the prospective teacher studied, which we analyzed from unusual theoretical references, namely, from the pragma-dialectical perspective [33] for the analysis of a critical discussion through four stages (confrontation, opening, argumentation, and concluding stages); and from the diagramming technique [34], which allows, on one hand, to make a spatial map of the argumentation, considering the language and, on the other hand, to shape the written reasoning. In the literature review, we have not found works that infer prospective teachers' knowledge and beliefs from the analysis of the structure of the argumentation, which they realize when they reflect on their practice, with models other than Toulmin's [35] (among others, the works of [36,37]). Similarly, unlike the research commented in the literature review [23][24][25][26][27][28][29], where knowledge and beliefs are extracted through the application of questionnaires and interviews with items aimed at individuals clearly expressing their knowledge and beliefs; in this study, we opted for argumentation as a means to infer these elements indirectly.…”