Conceito e representações de função via resolução, proposição e exploração de problemas: Um trabalho com alunos de graduação

Abstract

The present piece of research analyzes the essential understandings and difficulties of undergraduate students in the teaching-learning of function, and from this aspect, it proposes activities through resolution, proposition and exploration of problems that help the students from a licentiate degree in mathematics develop a better understanding of the concept and function representations, both in terms of understanding the concept and awakening the reflection on their practices as future mathematics teachers. On that account, we considered the difficulties reported in some studies (COELHO COSTA, 2004; COSTA, 2008; BRANDÃO, 2014; SILVA, 2013) and the five main ideas essential for the development of the function concept proposed by Cooney, Beckmann and Lloyd (2010), which are: concept of function, covariation and rate of change, families of functions, combination and transformation of functions and representations of functions. The chosen research methodology was based on the qualitative approach in the modality of pedagogical research (LANKSHEAR and KNOBEL, 2008), in which the teacher researches his/her own practice, and is open to changes in his/her conclusions and explanations, understanding broadly the situations and the challenges that arise. In the research development, questionnaires were applied in order to identify which essential understandings and difficulties were presented by the students. Afterwards, it was held a workshop about function for students of a mathematics licentiate course, where activities were applied based on the teaching methodology through resolution, proposition and exploration of problems, seeking to highlight the essential ideas worked in each activity. Among the results, we noticed that the students became more active, sought to reflect on their practices as future mathematics teachers and demonstrated having had a better understanding of the function concept and representations, since they were able to perceive the function concept in the course of the resolutions and identify the function representations that mostly contributed to the resolution of activities. We also emphasized that the students overcame the dependence of the teacher's confirmation, which was initially presented in relation to their answers, demonstrating more reliability in the verification of their resolutions; in addition, during the workshop, from our mediation, they did not present much resistance in assembling and analyzing the table. The students demonstrated a significant change in posture and reliability, as they sought to explore, in the proposed situations, aspects beyond those that were requested, and thenceforth, they verified their results. Thus, of the five great essential ideas, we have been able to develop the four essential ideas successfully: concept of function, covariation and rate of change, families of functions and function representations. Therefore, the teaching methodology through resolution, proposition and exploration of problems greatly contributed to the students becoming more active and that they could work the function concept and representations in a more understandable way, reflecting also on their practices as future mathematics teachers.