Compreensão de ideias essenciais ao ensino-aprendizagem de funções via resolução, proposição e exploração de problemas

Abstract

In this present research we have investigated understandings of essential ideas of functions by students and we have analyzed the contributions of the methodology for learning-teaching Mathematics via solving, posing and exploration of problems. Our focus has turned to literature from Algebra School to the learning-teaching of the concept of function. There are many researches about teaching of functions that reveal the importance of this theme. We have taken as theoretical references the learningteaching of functions along the curriculum with the multiple representations of functions and the development of essential understanding of functions by Cooney, Beckmann and Lloyd. To work in the classroom we have chosen solving, posing and exploration of problems using interaction and mediation as links to the formation of concepts accordingly to Vygotsky s ideas. The research was qualitative in pedagogical research way according to Lankshear and Knobel, in which the teacher research his own classroom practice. For the survey data we have used notes, descriptions and lessons analysis as well as students productions. Fieldwork was conducted with a group of student from first year High School in the Public School of State of Pernambuco in the Recife city, the action/interaction in the classroom has occurred with the formation of groups, providing work of performance in the Proximal Development Zone. The descriptions and lessons analysis pointed out basically conceptual and conversion difficulties among different representations of functions and the results have showed that an understanding of essential ideas about functions occurs by transitions among these ideas in multiple interpretations, characteristics and connections to one another. The final conclusion of this study has shown that solving, posing and exploration of problems have allowed possibilities of developing essential understanding of functions as well as broader contextual extensions in citizenship promoting.