Noções introdutórias à ideia de função: uma trajetória hipotética de aprendizagem

Abstract

This work has as its intents: to investigate the construction, discussion and evaluation of a teaching planning that gives an introductory notion to the idea of function, inside a constructivist learning perspective; to investigate how the researches in the Mathematics Education field contribute to the teaching organization and to analyze Mathematics teachers performance before a teaching proposal with this characteristic. The theoretic foundation is based on the formula proposed by Simon (1995), about Hypothetical Learning Trajectory (HLT). The study achieved has qualitative aspect and had the involvement of two Mathematics teachers of a public school, in the state of Sao Paulo, and their work with seventy-seven students shared in two groups, all of them in their first year of High School. The data came through interviews, questionnaires and observations. Although the HTL has been worked out with tasks that include problems resolution, technology, interdisciplinary approaches and application in day-to-day situations, the HLT per se does not guarantee learning under a constructivist perspective, without the constant support of the teacher in the planning (re)organization. About the teachers, it is important emphasizing that the main challenge is to approach them of the academic researches and keep them in continuous learning process