This field-spanning book will set out the broad advances in knowledge which have accumulated in the 21st century through the sustained exchange of ideas and collaboration between mathematics education researchers, considering both european and global perspectives. It is split in to three main sections focusing on content domains and processes, aspects of mathematics teaching and learning, and linguistic and social perspectives, and concludes with two lively international discussion chapters. Each section will include coverage of recent developments, current status and future outlook of global research making this book a fascintaing compendium of state of the art mathematical knowledge.

Foreword Preface The European Society for Research in Mathematics Education: Introduction by its former presidents Ferdinando Arzarello, Paolo Boero, Viviane Durand-Guerrier and Barbara Jaworski Chapter 1. From geometrical thinking to geometrical working competencies Alain Kuzniak, Philippe R. Richard, Paraskevi Michael-Chrysanthou Chapter 2. Number sense in teaching and learning arithmetic Sebastian Rezat, Lisser Rye Ejersbo Chapter 3. Algebraic thinking Jeremy Hodgen, Reinhard Oldenburg, Heidi Strømskag Chapter 4. Research on probability and statistics education: trends and directions Arthur Bakker, Corinne Hahn, Sibel Kazak, Dave Pratt Chapter 5. Research on university mathematics education Carl Winsløw, Ghislaine Gueudet, Reinhard Hochmuth, Elena Nardi Chapter 6. Argumentation and proof M. Alessandra Mariotti, Viviane Durand-Guerrier, Gabriel J. Stylianides Chapter 7. Theory-practice relations in research on applications and modelling Morten Blomhøj, Jonas Bergman Ärlebäck Chapter 8. Early years mathematics Esther S. Levenson, Maria G. Bartolini Bussi, Ingvald Erfjord Chapter 9. Mathematical potential, creativity and talent Demetra Pitta-Pantazi, Roza Leikin Chapter 10. Affect and mathematical thinking: Exploring developments, trends, and future directions Markku S. Hannula, Marilena Pantziara, Pietro Di Martino Chapter 11. Technology and resources in mathematics education Jana Trgalová, Alison Clark-Wilson, Hans-Georg Weigand Chapter 12. Classroom practice and teachers' knowledge, beliefs, and identity Jeppe Skott, Reidar Mosvold, Charalampos Sakonidis Chapter 13. Mathematics teacher education and professional development Alena HoSpesová, José Carrillo, Leonor Santos Chapter 14. Mathematics education and language: Lessons and directions from two decades of research Núria Planas, Candia Morgan, Marcus Schütte Chapter 15. Diversity in mathematics education Guida de Abreu, Núria Gorgorió, Lisa Björklund Boistrup Chapter 16. Comparative studies in mathematics education Eva Jablonka, Paul Andrews, David Clarke, Constantinos Xenofontos Chapter 17. History and mathematics education Uffe Thomas Jankvist, Jan van Maanen Chapter 18. Theoretical perspectives and approaches in mathematics education research Ivy Kidron, Marianna Bosch, John Monaghan, Hanna Palmér Chapter 19. ERME as a Group: Questions to mould its identity Marcelo C. Borba Chapter 20. Communication, cooperation, and collaboration: ERME's magnificent experiment Norma Presmeg