Executive Summary
This article presents the type of approach that we selected for researching a set of related issues concerning the practices of teachers of (in) mathematics. Our working hypothesis, which takes as a basis a considerable amount of previously completed research, can be summed up as follows: Teachers’ practices can be handled as a multidimensional, complex, and coherent system. In particular, this perspective provides a rationale for discussing the practices of a given teacher without having to specify the context.
We begin by elaborating upon the dual approach selected, in which we bring out the interconnections among practices from the perspective of their relationship with the mathematics-learning path of the students concerned and from the point of view of the teaching profession. In other words, we are concerned not only with the teaching procedures implemented by the teacher, which are analyzed in terms of the potential learnings of students, but also with the teacher as actor, whose activity is examined in the context of a particular professional field. The analyses dealing with teaching methods are presented according to three dimensions involving course contents and classroom sequences, the latter analyzed in terms of in-class discussions/dialogue and the forms of students’ work. Following this, we discuss our proposed methodology for further developing research that implements this approach. Teacher practices are analyzed on the basis of four components that are related, on the one hand, to the activities of students and, on the other hand, to the institution and the individual teacher.
As is brought out in our conclusion, the knowledge about practices that emerges from research based on this approach can, in turn, generate new questions about the learnings of students and teacher education.