Much research in recent years has centred on the knowledge required by school teachers to teach mathematics. This has focused particularly on the roles of content and pedagogical knowledge and their interaction. The concept of pedagogical content knowledge (PCK) introduced by Shulman has received considerable attention in the mathematics education community and has been elaborated by Ball and colleagues in their extensive and influential work on Mathematics Knowledge for Teaching (MKT). In contrast, however, the knowledge required by mathematics teacher educators (i.e. mathematics educators who teach mathematics and/or mathematics pedagogy courses to teachers) has received relatively little attention but is an emerging field of research interest. A discussion group drawing on the latest research and thinking in the area is timely to set directions for future research in what is likely to be a growing and an important area of research in mathematics education. The aims of the discussion group are, therefore, to:

• Facilitate discussion of key issues related to the knowledge required by mathematics teacher educators.
• Identify different emergent strands in research that can be related to this area.
• Summarise research and research/theoretical perspectives related to knowledge for mathematics teacher education.

The following three broad areas frame the territory of the discussion. These will be posted on the DG website and it is anticipated that they will evolve and/or be added to over the period leading up to ICME-12.

• To what extent are the various knowledge types for mathematics teachers described by Shulman, Ball et al. and others applicable/transferable to mathematics teacher educators? How does the knowledge needed by mathematics teacher educators differ from that required by mathematics teachers? Is it a kind of meta-knowledge or something as distinct from the knowledge for teaching mathematics as knowledge for teaching science is?
• Who researches mathematics educators’ knowledge? What are the dilemmas and opportunities associated with researching ourselves? What evidence is there of the knowledge required by mathematics teacher educators? What measures/criteria are there for successful mathematics teacher education and how are they connected to mathematics teacher educators' knowledge? What methodologies might be effective in building such an evidence base?
• How is knowledge for mathematics teacher education acquired? How is the transition from mathematics teacher to mathematics teacher educator made and what is gained or lost in the transition? To what extent and in what ways is knowledge for teaching mathematics necessary for mathematics educators? What theories of learning are useful? What models are/should be used (e.g., apprenticeship, Generic tertiary teaching courses)?
• Why might it be important to articulate knowledge for mathematics teacher educators? What contribution can understanding it make to our work and to mathematics education more broadly? Who wants to know about this knowledge and why?