The Butterfly Effect -- Étienne Ghys .. . . . . . . . . . . 19rnWhither the Mathematics/Didactics Interconnection? Evolution and Challenges of a Kaleidoscopic Relationship as Seen from an ICMI Perspective -- Bernard R. Hodgson . . . . . . . . . 41rnMathematics Education in the National Curriculum—with Some Reflections on Liberal Education -- Lee Don-Hee . . . . . . . 63rnQuality Teaching of Mathematical Modelling: What Do We Know, What Can We Do? Werner Blum -- rn. . . . 73rnPart III Plenary Panels The TEDS-M: Important Issues, Results and Questions -- Konrad Krainer, Feng-Jui Hsieh, Ray Peck and Maria Teresa Tatto . . . . . . . . . . . . 99rnMathematics Education in East Asia -- Frederick K.S. Leung, Kyungmee Park, Yoshinori Shimizurn. . . . . 123rnand Binyan Xu Gender and Mathematics Education Revisited -- Gilah C. Leder . . . . 145rnPart IV Awardees Teaching Mathematics in Tomorrow’s Society: A Case for an Oncoming Counter Paradigm -- Yves Chevallard . . . . . . . . . . . 173rnMathematics for All? The Case for and Against National Testing -- Gilah C. Leder. . . . 189rnEarly Algebraic Thinking: Epistemological, Semiotic, and Developmental Issues -- Luis Radfordrn. . 209rnHow We Think: A Theory of Human Decision-Making, with a Focus on Teaching -- Alan H. Schoenfeld . . 229rnetcrn