• Teachers’ questionnaires: two hundred and seventy three teachers of children 3 – 8 years completed questionnaires about children’s mathematical marks and ‘written’ mathematics. The teachers came from four areas of England – three cities and one rural county
• Telephone interviews: we conducted interviews with a sample of teachers who had completed questionnaires, allowing us to explore aspects of teachers’ beliefs and practice conferencing children’s mathematical graphics;
• Nursery study – India: conducted in nursery and primary schools in rural southern India, focusing on teaching
• Study to compare teacher-modelling and teacher-given examples in one of our own classrooms – children 4 – 5 years of age
• Assessing the contribution of teacher-modelling on children’s developing mathematical graphics. We assessed the effects of teacher-modelling mathematics for genuine purposes during the course of one term, with children 5 – 6 years of age;
• Creativity and mathematics: teachers’ perspectives. Creativity and mathematics: we explored teachers’ and practitioners' perceptions of creativity in mathematics through questionnaires with over 200 teachers across England. Reflecting on creativity and cognitive challenge.
• Cambridge Nursery Mathematics Learning Network: Nursery teachers and practitioners monitoring and understanding the development of children's learning as they progress towards standard abstract symbols and standard written calculations, and analyse and promote the pedagogy that underpins deep level learning in mathematics.
• Researching Effective CPD in Mathematics Education (RECME): (2007 - 2009). We are delighted that the Researchers identified many positive aspects of Children’s Mathematics Network Groups as a powerful means of CPD. These findings confirm our own beliefs in teachers and practitioners:

• to co-construct pedagogical theories and understanding of children’s mathematical thinking
• in the importance of collaborative dialogue
• in the significance of research for teachers - and in teachers as researchers
• in the need to trust teachers and to give them back their professionalism in order to empower them
• of the value of ‘grassroots’ networks ‘owned’ and shaped by the teachers and practitioners themselves

The findings also support the success of local CM Network groups in supporting high levels of children’s mathematical thinking and contributing to deepening understanding of the standard abstract symbolism of written mathematics. This is captured in a comment from the RECME research team: ‘The standard of the mathematical understanding, thinking and reasoning was far higher than the specified curriculum objectives for children of this age’.