Releitura do processo de aprendizagem de estudantes repetentes de Cálculo I

Abstract

In this doctoral research in mathematics education we investigate how university students who are repeating the discipline of Differential and Integral Calculus I (Calculus I) solve tasks about limits of functions of a real variable, what mistakes they make and the causes that lead them to fail or to give up the discipline. Thus, we searched for the repeating students’ information related to (i) studying habits; (ii) learning expectations related to Calculus and (iii) previous difficulties related to mathematical concepts. We analyzed the reasons that led them to repeat this discipline and led them to believe they were not able to learn it (ERNEST, 1989; GÓMEZ CHACÓN, 2003). We also tried to understand their successes and their mistakes while they were determining the limits of functions of a real variable (CURY, 2008). To do so, we understood and identified conceptual and procedural mistakes (operational mistakes) while they were calculating limits (SKEMP, 1976; CORNU, 1991; TALL, 1991). We developed a qualitative research in which the professor researcher worked together with the Calculus professor throughout the first semester in 2014. Thirty eight repeating students in Calculus I participated in this research and they all were undergraduate students of Agronomy and Teaching in Agricultural Sciences at the Federal Institute of Espírito Santo (IFES), Campus Itapina. We collected data by observing classes and through students’ tasks, questionnaires and interviews. Then, we enunciated some results of this study. In relation to the studying habits we identified that the discourse and the practice of the students were divergent. They were becoming conscious about this contradiction and started learning to change their studying habits during the semester. We connected students’ learning expectations to the emotional and cognitive aspects, such as beliefs, conceptions and attitudes related to the discipline of Calculus I. We found that we had to change our university professor posture and to break with our pedagogical practices which were far from students’ reality. We believe that with this behavioral change it was possible to motivate them to believe that they were able to overcome obstacles and learning limitations. We verified that there is a relationship between difficulties in learning Calculus and the lack of previous knowledge about mathematical contents. Therefore, we started to review these contents in parallel with the contents of Calculus, but not in an isolated way in the beginning of the semester, as we did before. This integrated work of mathematical concepts helped us to understand and to analyze the repeaters’ mistakes. We also used the analysis of mistakes as a pedagogical strategy to make the mistakes visible to the professor and to the students. Furthermore, we succeed in identifying epistemological difficulties about some specific concepts of Calculus. In summary, we observed that these differentiated pedagogical strategies of the professor researcher encouraged the learning of Calculus and enabled a change of posture by the university students. Therefore, as a thesis we believe that we need to work with repeating students of Calculus I in in-service courses, differently from the way that it is taught in specific mathematics courses. Also, we need to actively engage the students in the process of teaching and learning Calculus.