The Washington meeting, centerpiece of the ICMI study "what is research in mathematics education, what are its results?", evidenced the great variety and the complexity of the answers one can try to propose to these questions. The question of results was essentially understood from the point of view of actual teaching, which makes the question difficult since it is not very easy to show precisely a direct effect of research on practice, but the meeting made clear that the social relevance of research in mathematics education is as crucial as its theoretical relevance and methodological validity. To answer the question of what research is, is even more complex. The basic relationships of research in mathematics education with both theory and practice led to the recognition of two different paradigms : action-research, rooted in the field of practice and aiming at its transformation, theory-oriented-research for which the field of practice is an object of knowledge theoretically rooted. It is not my purpose here to discuss these positions, I see the emphasis on the existence of different paradigms has both a progressive move and a way to avoid the difficulties. The discussion will continue.
An other point must be addressed that is vitally important for many researchers in mathematics education : who are we as professional? For some of us, part of our job is to teach, another part is to conduct research. To which extent does our professional development, and the development of our institutions, depend on the latter? At this point the question "what is research in mathematics education?" takes an other meaning which today needs an answer more urgently than the question at a theoretical level. In fact, we know that these foundational questions are open in every field. Let's consider the questions "What is research in geography?", "What is research in computer-science?", "What is research in mathematics, and applied mathematics?", "What is research ...?". One may be tempted to give the answer : "Research in mathematics education is what researchers in mathematics education do". If so, who are these people as professionals in universities, research centers, institutes of different kind? Are they academics of a different specie than those in other domains?
I suggest, as a first concrete step, to take the question "what is research?" from this point of view. It will lead us back to the foundational question. And, through the question "what reasearchers in mathematics education do?" we will again have to address the ICMI question "what are their results?". But the first pragmatic step is needed to clarify the field, at least in order to make it more "readable" to the academic world. So, I suggest that the ICMI be asked to set up a body, working group, or advisory group, whose mission would be to clarify the framework in which our PROFESSIONAL COMMUNITY OF ACADEMIC RESEARCHERS IN MATHEMATICS EDUCATION develops at an international level. Among the questions to which we need an answer one could mention :
- How are researchers in mathematics education educated, in particular, what is required in the doctoral courses and what are the criteria for completing a doctorate in different countries?- How does the career of young researchers develop? What are the criteria for obtaining positions and advancing in them? Could we establish a picture of developments over the last decade?
- What is the status of the main places where research in mathematics education is done? To whom and how are teams or laboratories in mathematics education accountable?
- What are the standards of scientific quality and the criteria for accepting a paper for publication in international research journals on mathematics education?
- How are the relations between research and the field of practice organized?
One question of major importance is : what are our links to mathematics as an academic field and to mathematicians? At this point I would like to propose for discussion the following claim : "researchers in mathematics education are responsible for the methods and the theoretical frameworks they refer to and build; they are responsible for the organisation of their field of research; but they share with mathematicians the responsibility for ensuring that mathematics is present in their research". It is within ICMI that we are likly to find the best way to establish relevant links between researchers in mathematics education and mathematicians. The task I propose may help us to be more clearly visible and understandable to the mathematicians of IMU, and through that to mathematicians of our own countries as well as to the academic community in general. It may even help us to make sense of the differences we aknowledged during the Washington discussions and which are of a more foundational nature. In some countries associations of researchers in mathematics education already exists. The body established by ICMI might involve representatives of these associations as well as representatives of international groups like PME and TME and others such as regional research groups. But this question could be considered later, when some consensus has been reached about the relevance of the present proposal.
Grenoble, 23 July 1994
Nicolas Balacheff