The National Centre for Excellence in Teaching Mathematics (NCETM) was set up in England by the UK Government as a national infrastructure to provide effective strategic leadership for mathematics-specific continuing professional development (CPD). The National Centre aims to raise the professional status of all those engaged in the teaching of mathematics so that the mathematical potential of learners will be fully realised. The National Centre has also initiated a research programme to identify the characteristics of effective CPD for teachers of mathematics. Within the first phase of this SEG 4/6 teachers and CPD coordinators will animate the discussion by presenting a critical overview of the factors that they have identified as being key to innovative and effective CPD for teachers of mathematics. After this introductory phase the participants will work in 4/6 sub-groups (led by a discussant), each one critically engaging with a particular approach to CPD. Within the final phase of the SEG similarities and differences between the identified perspectives will be highlighted and a research agenda will be proposed.