Criatividade e geração de ideias em atividades de modelagem matemática

Abstract

This research aims to investigate moments of idea generation in mathematical modeling activities. The research can be characterized as qualitative and the participating subjects were the students of the Mathematical Modeling discipline of the fourth year of a degree course in Mathematics at a university in the state of Paraná. Since idea generation is directly linked to creativity, we are based on authors who deal with creativity (AMABILE, 1982 and 2011; ALENCAR; FLEITH, 2003a and 2003b; GONTIJO, 2007a; LUBART, 2007) and models of creativity (AMABILE, 1982 STERBENG; LUBART, 1991; CSIKSZENTMIHALYI, 1999). In this research the subjects developed modeling activities proposed by the researcher. For the elaboration and monitoring of mathematical modeling activities, we base ourselves on the works of Almeida, Silva and Vertuan (2012), about the cognitive actions of students during mathematical modeling activities. To analyze how an idea is considered by a group of people, we rely on Csikszentmihalyi's (1999; 2014) creativity model. For this, the data collection took place during the development of activities in the classroom, from the use of audio recorders. Prior to data collection, the researcher spent a period of seven weeks making observations in the class in order to note topics of interest for the preparation of proposals for mathematical modeling activities. During this observation period the researcher used a field agenda to write down pertinent information to the research. The data organization was made through the adaptation of a temporal organization tool proposed by Shoenfeld (1992). After the temporal organization, the recordings analyzes were made based on the theoretical foundation about creativity and creativity models. To answer the questions in this research, we highlight Episodes of Interest during the analysis. These episodes are times when subjects came up with ideas and how these ideas were considered within the group during the resolution. We are more specifically interested in student group brainstorming when developing mathematical modeling activities. Our objective is to investigate at what moments the generation of ideas occurs during the development of Mathematical Modeling activities with students of a Mathematics Degree course, undertaken in groups, and what implications do these ideas trigger in the investigation of the problem. In this context, in our research, we aim to analyze the moments of ideas generation in student groups during the development of mathematical modeling activities. Do mathematical modeling activities make it possible for students to generate ideas? When do ideas come up? How does the group manage the ideas that come up? Which ideas are selected and which are discarded by the group? Is it possible to infer why some ideas are considered and others discarded by students? And what attitudes of the teacher can stimulate the generation of ideas? Our goal is to identify and analyze the moments of idea generation and the implications of these moments during the development of a modeling activity in groups of students, in this case, already started in mathematical modeling. From the analysis and based on the theoretical foundation, we infer that countless ideas are generated during modeling activities, specifically during the first twenty minutes. In this period of time the main action of the students was the phase of interaction. We emphasize that the affinity, prior knowledge and experiences that the subjects had with the themes of the proposed activities were fundamental for the development of the activities. In addition, judgment has emerged constantly among students and this fact has a direct impact on ideas that arise and are rejected, or even ideas that are no longer presented in the context of discussions