Resolução de problemas nas aulas de Matemática: um estudo junto aos professores dos anos iniciais - Mastroianni, Maria Teresa Merino Ruz (2014)
Problem Solving represents an important line of research in Mathematics Education, expressing the posture of researchers and teachers willing to review the methodologies of the teaching-learning process of the school mathematics, looking for better results inside the classrooms and outside them. With the increase of the complex systems in today's world, the type of abilities needed for problem solving for the success beyond school have changed. However, there are still few researches about the development of concepts through problem solving, mainly problems which deal with the early years, in which the multitask teachers teach mathematics. These teachers have dealt with a variety of approaches, as a result of their historical paths and experiences. The present research, with a qualitative approach aims at investigating which conceptions a group of multitask female teachers from Elementary School in a private school from São Paulo have about the issue Problem Solving, being able to comprehend how they can influence their practice. The theoretical framework of the present investigation is based on the ideas of Guy Brousseau, specifically those related to the theory of didactic situations (TDS) and to the concept of didactic contract. As a subsidiary stream, a survey about the researches on the theme Problem Solving in Mathematics Education was done. Such theoretical movements tried to provide some basis to answer the leading questions, elaborated around the conceptions of the individuals on problem solving in mathematics classes, related to possible effects of the didactic contract which occur in the practice of these female teachers and the positioning of the pedagogical strategies employed, from the perspective of TDS. In order to answer the questions raised, a questionnaire has been used; its answers have made it possible to analyze the conceptions of six female teachers related to the theme. These teachers have had their classes observed, so that a comparison has been made between discourse and practice. The results show that the individuals of this research comprehend the importance of its critical role in the classes and value the mathematical thought of the students, although they still have some difficulty in organizing an antagonistic milieu , capable of provoking imbalance and searches for knowledge to be built through an investigative process, which indicates that, in practice, the individuals not always distinguish exercises from mathematical problems. Yet, some effects of the didactic contract over the relationships among teachers, students and the mathematical knowledge have been identified