Formação continuada de professores de ciências e de matemática no contexto da modelagem na perspectiva epistemológica de Stephen Toulmin

Abstract

Modeling can consist of a methodological possibility to move towards a conceptual construction that considers the complexity of the relations between science and mathematics. Based on this premise, the following research problem was investigated in this work: How do the conceptual relationships evolve on the scientific and mathematical modeling identified in teachers in these areas of teaching in an environment of continuing education characterized by the confrontation of these subjects with situations in the context of modeling, in an environment of reflection, discussion and accomplishment of activities, proposed in a discipline at the Graduate level? The main objective was to identify possible conceptual relationships between the areas of Science and Mathematics, expressed by teachers in continuing education, as well as to investigate the process of evolution of these relationships in the context of modeling throughout a discipline of the Post-Graduate Program Education in Science: Life Chemistry and Health (PPGECQVS) at the Federal University of Santa Maria (UFSM), taught in the first semester of 2019 and with the participation of six students. As an epistemological reference to guide the research, Stephen Toulmin's ideas were sought, for which, similarly to Darwinian Theory, scientific concepts also have natural selection and, thus, can be possible to think of a conceptual evolution. The analysis of the conceptual evolution of the participants of the discipline was made in view of the Theory of Conceptual Fields. The central preoccupation was to propose productive situations and analyze evidence on their possible contributions to the conceptualization process in the context of modeling. The research was qualitative and consisted of a field study of the case study type. The data records consisted of: previous questionnaire; students' productions during the course (concept maps, Gowin diagrams V, didactic units and other elaborated materials); transcription of audio recordings of classes; interview after the end of the course. The analysis of the collected data was made from the Discursive Textual Analysis (ATD). Two DTAs were executed: (a) One of the inductive type through which the participants' previous conceptions about modeling were identified; (b) Another of the deductive type, taking into account the records produced in the other meetings of the discipline, investigating the possible contributions of the situations proposed for the conceptual evolution of the participants around the theme addressed. At ATD (b) the eight formative needs for the science teacher listed by Carvalho and Gil-Pérez (2011) were adopted as a priori categories, namely: to know the subject to be taught; questioning the teaching ideas of “common sense”; acquire theoretical knowledge about science learning; knowing how to critically analyze “traditional education”; know / prepare activities; knowing how to direct students' work; know how to evaluate; knowing how to use research and innovation. As a main result of the investigation, it was found that the evolution of conceptual relationships on scientific and mathematical modeling in the teachers participating in the discipline occurred: based on the concept of interdisciplinarity; through the diversity of situations presented, especially in the moments of practical activities that accentuated the ruptures and continuities of the progressive control in the context of modeling; as were sought to teach and learn from a constructivist perspective.