Exercícios, problemas e explorações: Perspetivas de professoras num estudo de aula

Abstract

We analyze the perspectives about the tasks to propose to students of a group of five teachers of the second cycle of basic education participating in a lesson study. In the tasks, we distinguish between exercises, problems and explorations and give special attention to the development of mathematical reasoning. Data collection was carried out by participant observation and document collection, through the elaboration of a research journal, audio recording of the twelve sessions and video recording of the research class. The results show that, from the work done in the lesson study, the teachers accept the distinction between exercise, problem and exploration and value the realization of this latter type of task. They also recognize that pictorial representations may be the basis for the development of students’ problem-solving strategies. In addition, they turn out to value the realization of generalizations and justifications from students, recognizing that sometimes they are able to surprise the teacher for the originality of their problem-solving strategies. Finally, the teachers also assume that different kinds of tasks should be proposed to students, including tasks with a certain level of challenge.