Formação de professores a partir da vivência e da análise de práticas exploratório-investigativas e problematizadoras de ensinar e aprender matemática

Abstract

We start with a brief history of the research and practice of teaching and learning math with problem solving. For that, we trace the international evolution of this field of study and practice, above all in North America by NCTM with its contribu- tion to this line of research in Brazil. We end this first part relating the principle historical tendencies in problem solving with math modeling with the appearance after 2000 of mathematical studies. In the second part of this work, we describe six approaches to use problem solving and mathematical research in the preparation of teachers of math. We discuss some of the impact of these approaches in the professional development of teachers. In the thrid part we present and analyze an episode with exploratory-investigative characteristics that occurred in a classroom, highlighting the production of knowldege situated in the practice of teaching and learning math. We use as a tool for analysis a triad of teaching conceived by Potari & Jaworsky (2002) and that interrelates mathematical challenge, sensibility of the teacher in relation to the students, and guidance of learning. We conclude with an attempt to redimension the place and role of exploratory-investigative practices and problem solving in the work of teachers and in the preparation of teachers who teach math.