Tommy Dreyfus is Emeritus Professor of Mathematics Education at Tel Aviv University in Israel and one of the Founding Series Editors of the IMPACT Mathematics series. He is an Advisory Editor of Educational Studies in Mathematics and a Contributing Editor of the Journal of Mathematical Behavior. He has previously edited several books including one in Routledge’s EARLI book series. Michèle Artigue is Emeritus Professor of Mathematics Education at the University Paris Diderot – Paris 7 in France. She was recently awarded the Felix Klein medal for life-time achievement in mathematics education research by the International Commission on Mathematical Instruction, and is a Knight of the French National Order of the Legion of Honour.Despina Potari is Professor of Mathematics Education at the University of Athens in Greece, and Guest Professor of Mathematics Education at Linnaeus University in Sweden. She is also Editor-in-Chief of the Journal of Mathematics Teacher Education. Susanne Prediger is Professor of Mathematics Education and head of the Institute for Development and Research in Mathematics Education at the University of Dortmund in Germany. She has authored numerous journal articles and book chapters and is currently President of ERME, the European Society for Research in Mathematics Education.Kenneth Ruthven is Emeritus Professor of Education at the University of Cambridge in England and Guest Professor in Mathematics Education at Karlstad University in Sweden and at the University of Agder in Norway. He is an Advisory Editor of the international journals Educational Studies in Math-ematics and Research in Mathematics Education and a Fellow of the Academy of Social Sciences.

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• 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 Hošpesová, 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

Tommy Dreyfus is Emeritus Professor of Mathematics Education at Tel Aviv University in Israel and one of the Founding Series Editors of the IMPACT Mathematics series. He is an Advisory Editor of Educational Studies in Mathematics and a Contributing Editor of the Journal of Mathematical Behavior. He has previously edited several books including one in Routledge’s EARLI book series. Michèle Artigue is Emeritus Professor of Mathematics Education at the University Paris Diderot – Paris 7 in France. She was recently awarded the Felix Klein medal for life-time achievement in mathematics education research by the International Commission on Mathematical Instruction, and is a Knight of the French National Order of the Legion of Honour.Despina Potari is Professor of Mathematics Education at the University of Athens in Greece, and Guest Professor of Mathematics Education at Linnaeus University in Sweden. She is also Editor-in-Chief of the Journal of Mathematics Teacher Education. Susanne Prediger is Professor of Mathematics Education and head of the Institute for Development and Research in Mathematics Education at the University of Dortmund in Germany. She has authored numerous journal articles and book chapters and is currently President of ERME, the European Society for Research in Mathematics Education.Kenneth Ruthven is Emeritus Professor of Education at the University of Cambridge in England and Guest Professor in Mathematics Education at Karlstad University in Sweden and at the University of Agder in Norway. He is an Advisory Editor of the international journals Educational Studies in Math-ematics and Research in Mathematics Education and a Fellow of the Academy of Social Sciences.

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• 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 Hošpesová, 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