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Oriented by complexivist and ecological discourses, teaching and learning seem to be more about expanding the space of the possible and creating the conditions for the emergence of the as-yet unimagined, rather than about perpetuating entrenched habits of interpretation. Teaching and learning are not about convergence onto a pre-existent truth, but about divergence – about broadening what is knowable, doable, and beable. The emphasis is not on what is, but on what might be brought forth. Thus learning comes to be understood as a recursively elaborative process of opening up new spaces of possibility by exploring current spaces.

This working group focused on connection between and among mathematics education research and mathematics, the foundation disciplines, and practice, The practice. The premise was that insularity from any or all of these critical domains is a threat to the quality and progress of the field. We organized our work to examine how productive fostered, we explored actual and possible connections between mathematics education and other disciplines. We investigated how mathematics education research interacts with mathematics as a disciplines, as well as with theory and practice of scholarship in other fields, with an eye on practice, we also explored new approaches to research that seek to bridge traditional divides among theory, basic research, and problems of teaching and learning. We set out to learn about productive interactions among disciplinary communities in the context of research in mathematics education. We asked: What are some of the barriers to such interactions? What special roles do mathematics and mathematicians and mathematics as a discipline have? and what roles might they have? in mathematics education research? We asked similar questions about the roles of other disciplines. We examined what is entailed in deriving questions about the roles of other disciplines. We examined what is entailed in deriving questions directly from issues of practice and in working closely with practitioners. We considered what is afforded and what pitfalls exist in designing theoretically-focused experiments in practice.

In this article, the author focuses on some of the problems involved in offering an appropriate university Masters module for teachers who want to improve their practice and move beyond the intuitive. The article claims that this is a highly complex task, which in the first place will demand several radical changes in focus and attention. The author describes the fundamental theoretical framework on which this module will be based, and also gives an insight from a related assignment as to what might be expected from the course. South African Journal of Higher Education Vol.16(2) 2002: 25-31

In this chapter, contrasting views on the contributions that teachers as researchers are making to the field of mathematics education are used as a springboard to examine developments over the past decade. On the one hand, there is a growing movement for more teachers to become involved in a critical exploration of their practice through such methods as critical reflection, action research, and lesson studies. The contrasting position makes the claim that these activities have done little to add to the body of knowledge on mathematics education. The chapter starts by scanning the literature in mathematics education and then takes a step back and explores the broad roots and issues of the teacher-researcher movement. A particular example of teachers studying for a higher degree in teaching provides an opportunity to explore the interface between the two contrasting positions. The chapter closes with an appeal to academics in mathematics education to seek ways to listen to and engage with the informed voices of teachers.