Atribuição de significado para a modelagem matemática em um design de formação de professores que ensinam matemática

Abstract

To become a teacher, there is a training process during which aspects related to didactics, approaches to the content to be taught, and content knowledge are studied. Throughout a professional career, knowledge is built from experience to assist in day-to-day practice. However, for the implementation of certain methodological approaches, in addition to teaching experience, specific preparation is required, which generally takes place in training environments. Mathematical Modelling is a pedagogical alternative in which, through the investigation of extra-mathematical situations, students apply mathematical knowledge and build new knowledge to find solutions to one or more problems under study. For this alternative to be present in the classroom, it is argued that teachers who teach mathematics should be familiar with it and feel prepared to work with it. The Teacher Training Design in Mathematical Modelling was developed during 2023, organized according to the following axes: learning about, learning through, and teaching using Mathematical Modelling, with the aim of guiding teachers to develop practices with modelling, in addition to serving as the context for data production for this research. The goal of this research is to investigate, "What meaning does a teacher who participated in a training design assign to Modelling?", especially when planning and implementing practices with modelling. Data production was supported by audio and video recordings, written notes, responses to questionnaires, and interviews. This investigation is based on Peircean Semiotics, regarding the production of interpretants as signs produced by the interpreter that pertain to meaning-making, as well as on the theoretical assumptions of Mathematical Modelling. The analyses are guided by Grounded Theory. During the initial coding, analyses were conducted on the statements of one of the teachers in training, a participant in the design, during three in-person meetings. We complemented the initial codes with an analysis of the practices developed by the teacher during axial coding, organizing these codes into categories based on their common characteristics. Finally, focused coding was carried out by verifying the categories in the final interview data. It was concluded that the meaning assigned by the teacher in training was supported by four categories: Teacher Actions, Student Actions, Characteristics of Mathematical Modelling, and Knowing Mathematical Modelling. Each category has subcategories, which identify how the teacher interpreted Modelling through the signs expressed. Thus, the training design was structured as a means of meaning-making in which learning about modelling allowed the teacher to understand modelling; learning through modelling shaped the teacher's actions, and teaching using modelling prompted a focus on student actions and the characteristics of mathematical modelling in practice. The educational product consists of a digital booklet with texts, links, and videos that can guide a teacher interested in learning about Mathematical Modelling and implementing it in their classes.