Uma análise das ações do professor que apoiam o raciocínio matemático na disciplina equações diferenciais ordinárias em cursos de Engenharia

Abstract

This work aims to identify and discuss the teacher's actions that support students' mathematical reasoning during the performance of an exploratory task in an Engineering class in the discipline of Ordinary Differential Equations (ODE). The research is qualitative, and the data were produced in a natural classroom environment of the ODE discipline, whose teacher of the class is the research advisor. The discipline was offered jointly to two engineering courses at the Federal Technological University of Paraná (UTFPR) Londrina campus, the Chemical Engineering and Environmental Engineering courses. During the classes, the teacher worked on an exploratory task involving first-order ODE, and the mathematical model addressed was Newton's Law of Cooling. The mathematical task involved taking water temperature measurements, developing a mathematical model using an ODE, and analyzing the model. Audio recorders and the students' written production were used for data recording. Based on the transcription of the dialogues captured by the recorders, the data were analyzed considering categories of teacher actions defined a priori: inviting, guiding/supporting, informing/suggesting, and challenging. The analyses of the interactions in the classroom over the three days of the task development revealed that the teacher's actions supported the students' mathematical reasoning, leading them to formulate conjectures, justify and validate their answers, and the teacher challenged them to seek generalizations. The conclusions indicate that the task proposed and developed in the classroom engaged the students in several activities – such as collecting data on water temperature, developing a mathematical model, and exploring in the GeoGebra software –, always mediated by the teacher's actions. Although most of the teachers’ intentions were positive, it was observed that the teacher directed the students' thinking, indicating the path to be followed. This practice, although understandable, may have limited the students' autonomy and reduced the level of cognitive challenge of the mathematical task in some situations. However, it is important to highlight that the teacher sought to balance the necessary support and promote student autonomy. At the end of the research, an educational product was developed consisting of pedagogical material intended for teachers who teach ODE in Higher Education who wish to understand what actions can support students' mathematical reasoning.