The rationale for this Survey Team (ST), commanded by the International Program Committee of ICME 11, is that:

"Notions and concepts of theory play key roles in mathematics education research, as they do in any scholarly or scientific discipline. On closer inspection, the notion, concept, and nature of what is termed “theory” in such research are very varied indeed, as are the roles, uses and implications of theories employed in mathematics education research. In other words, the term "theory" does not have one universal meaning in our field. Moreover, concrete theories put to use with regard to mathematics education originate in several different disciplines, many of which are external to mathematics education research itself. The task of this ST is to identify, survey, and analyse different notions and roles of "theory" in mathematics education research, as well the origin, nature, uses, and implications of specific theories pertaining to different types of such research."

This task defines a very important problematique in mathematics education research but, even if this problematique is clear, its treatment is problematic. Of course, the investigation of this problematique can be different and we can produce different answers.

In this ST, to carry out this task, we will consider three levels corresponding to some questions. The first level is a preliminary interrogation about: how to do a survey? What are the data? What are the tools for doing this survey? What are the criteria? Are these criteria theoretical or empirical? Have we common or different tools for doing this task? What are our assumptions about this task? This level is a methodological level but it is too an epistemological one: our practice and assumptions of mathematics education research found what we do in order to achieve this task.

A second level is a results level. We produce different surveys and we identify and analyse different roles and functions of “theory” in mathematics education research. We must point out different results of these surveys and these results are depending on the data and tools used in this work.

A third level is a reflexive level. We want to compare our different methodologies and assumptions in doing this task. What are the different types of theory? What is a theory in mathematics education research? What is the role of theory in the autonomy and identity of mathematics education as a scientific domain?

These three levels organise our text in three parts and we conclude by some “open questions”. We organized the ST from an preliminary individual work. We got five papers and this common paper is the result of the collective work. Three of us tended to work especially in the first and second level, and the other two in the third level but this is just a trend. Sometimes for further developments we will make reference to these preliminary papers because we cannot include their full content in this paper.