1 Mathematical investigations in the classroom: A collaborative project1

Abstract. This paper presents some work developed through a collaborative project involving mathematics teachers and teacher educators, aimed at the development of classroom tasks involv-ing students in mathematical investigations and the study of related teaching styles. We give a general overview of the project and present one task dealing with the concepts of powers and ex-ponents. Then, we describe how it was used in the classroom (grade levels 5-7), and present our experience about the role and the activity of the teacher in the process of organizing, conducting and reflecting about this kind of activity. Why mathematical investigations in the classroom? Modern society requires from everyone a reasonable fluency in mathematics. It is specially important to be able to interpret information framed in mathematical lan-guage (numerical and graphical) and to think mathematically (seeking patterns and rela-tionships and reasoning). However, mathematics is usually regarded as a most difficult subject. Students frequently view it just as doing computations and getting the correct answers. They tend to assume a dualist view in which things are either right or wrong. In many countries, including Portugal, the evaluations of students ’ learning, attitude