O cálculo diferencial e integral e as oportunidades de aprendizagem profissional do futuro professor de matemática

Abstract

This research aims at understanding how Professional Learning Tasks for Teaching (TAP) are configured and connect concepts from Differential and Integral Calculus (CDI) with Mathematics in Basic Education, analysing how they contribute to the mobilization of professional knowledge among future Mathematics teachers. The investigation was based on teaching practices related to the concept of definite integral, These practices were treated as opportunities to articulate CDI contents with Basic Education demands. This is a qualitative study, developed through the Design-Based Research (DBR) methodology, applied in the context of a Mathematics Teacher Education Program. The TAP were designed from situations related to the Mathematics teaching in Basic Education. They required pre service teachers to understand students’ written productions, analyze mathematical strategies, considering teaching decisions and the comprehension about the learning processes related to fundamental ideas of Calculus. Among these ideas are the Riemann Sum, the formal definition of integral, the method of exhaustion, the Mean Value Theorem for Integrals, and the Fundamental Theorem of Calculus. Evidence of the mobilization of Mathematical Knowledge for Teaching (MKT), according to the model of Ball, Thames and Phelps (2008), was observed. Content Knowledge emerged through identification of connections between Calculus topics and Basic Education curriculum elements. Pedagogical Content Knowledge appeared in the reading of students’ reasoning and in the proposition of teaching strategies towards the construction of conceptual meanings. These propositions refered to current curriculum documents, indicating that CDI can offer elements for classroom practices in Basic Education content such as functions, sequences, geometry, variation and accumulation, as well as ideas related to infinity. To understand TAP contributions, the Professional Learning Opportunities for Teachers (PLOT) model was adopted. This model made it possible to recognize the professional learning opportunities generated throughout the process. The TAP present themselves as an instrument that connects academic mathematics with teaching practices and helps reduce historical discontinuities in teacher education.