Estratégias alternativas de ensino em disciplinas matemáticas: contribuições no desenvolvimento de competências do futuro engenheiro

Abstract

The teaching of mathematics in Engineering programs faces the continuous challenge of aligning conceptual rigor with the development of professional competencies demanded by the job market. Given this scenario, this thesis aims to understand the role of alternative teaching strategies, in mathematics courses, in the development of the competencies expected of Engineering graduates. This is a qualitative research, configured as a bibliographic study that uses meta-synthesis (qualitative metaanalysis). The corpus of analysis was composed of two sets of documents: international articles and nine master's dissertations produced within a research group at the Federal Technological University of Paraná (UTFPR), which investigate the Task Resolution Episodes (TREs) strategy in the context of Differential and Integral Calculus. The analysis of the international articles, conducted through a systematic review using the Methodi Ordinatio methodology, sought to identify research on the mathematical competencies developed and the teaching strategies that promote them. For the dissertations, the data analysis (including practice records and theoretical discussions) was performed using vertical and horizontal reading procedures, seeking convergences and patterns. The results indicate that, while the international literature points to a vast range of active methodologies, the in-depth analysis of TREs reveals a central cognitive mechanism: the intentional mobilization of Mathematical Reasoning (MR). Based on the Discursive Textual Analysis (DTA) by Moraes and Galiazzi (2011), the contributions of the TREs in the analyzed dissertations were categorized, resulting in the following categories: a) Intuitive Construction of Mathematical Concepts; b) Development of Mathematical Reasoning; c) Promotion of Creativity; d) Collaborative Work and Communication; e) Integration between Theory and Practice; f) Development of Autonomy; g) Improvement of the Assessment Process; h) Fostering Critical Thinking; i) Exploration of Digital Technologies. It is concluded that the MR processes, such as conjecturing, justifying, and generalizing, stimulated by investigative tasks, constitute the cognitive basis for the development of professional competencies essential to engineers, such as system modeling, technical communication, and the capacity for innovation, as advocated by the National Curricular Guidelines. The thesis culminates in the proposal of a "Didactic Manual" that materializes the findings, offering teachers a tool for planning and analyzing classes focused on MR development, bridging the gap between theory and classroom practice.