Thirteenth International Congress on Mathematical Education: An Introduction -- Gabriele Kaiserrn........... 3rnUncovering the Special Mathematical Work of Teaching -- . Deborah Loewenberg Ball ... 11rnMathematics, Education, and Culture: A Contemporary Moral Imperative -- Bill Barton.... 35rnMathematics Classroom Studies: Multiple Lenses and Perspectives -- Berinderjeet Kaur .... 45rn “What is Mathematics?” and why we should ask, where one should experience and learn that, and how to teach it -- Günter M. Ziegler and Andreas Loos. ......... 63rnInternational Comparative Studies in Mathematics: Lessons and Future Directions for Improving Students’ Learning . -- . Jinfa Cai, Ida A.C. Mok, Vijay Reddy and Kaye Stacey.......... 79rnTransitions in Mathematics Education: The Panel Debate -- Ghislaine Gueudet, Marianna Bosch, Andrea A. diSess -- Oh Nam Kwon and Lieven Verschaffel ........... 101rnEtc.rn