Proceedings of the 13th International Congress on Mathematical Education : ICME 13 Part 1: Plenary Activities Thirteenth International Congress on Mathematical Education: An Introduction Gabriele Kaiser Uncovering the Special Mathematical Work of Teaching Deborah Loewenberg Ball Mathematics Education and Culture: A contemporary moral imperative Bill Barton Mathematics classroom studies Multiple lenses and perspectives Berinderjeet Kaur What is Mathematics  And why we should ask where one should experience or learn that and how to teach it Günter Ziegler Andreas Loos International Comparative Studies in Mathematics: Lessons and Future Directions For Improving Students’ Learning Jinfa Cai Ida Mok Vijay Reddy Kaye Stacey Transitions in Mathematics Education Ghislaine Gueudet Marianna Bosch Andrea A. diSessa Oh Nam Kwon Lieven Verschaffel Part 2: Awardees lectures ICMI Awards Ceremony Carolyn Kieran Jeremy Kilpatrick Mathematics Discourse in Instruction (MDI): A discursive resource as boundary object across practices Jill Adler The challenging relationship between fundamental research and action in mathematics education Michèle Artigue Elementary mathematicians from advanced standpoints a cultural perspective on mathematics education Alan Bishop Design and Development for Large Scale Improvement Hugh Burkhardt Malcolm Swan Making Sense of Mathematics Achievement in East Asia: Does culture really matter Frederick K.S. Leung Part 3: Reports of the Survey teams Digital Technology in Mathematics Education: Research over the last Decade Johann Engelbrecht Marcelo C. Borba Petek Askar George Gadanidis Salvador Llinares Mario Sánchez Aguilar Conceptualisation of the role of competencies knowing and knowledge in mathematics education research Mogens Niss Regina Bruder Núria Planas Ross Turner Turner Jhony Alexander Villa Ochoa Assistance of students with mathematical learning difficulties How can research support practice A summary Petra Scherer Kim Beswick Lucie DeBlois Lulu Healy Elisabeth Moser Opitz Mathematics teachers working and learning through collaboration Barbara Jaworski Olive Chapman Alison Clark Wilson Annalisa Cusi Cristina Esteley Merrilyn Goos Masami Isoda Marie Joubert Ornella Robutti Geometry education including the use of new technologies: a survey of recent research Nathalie Sinclair Maria Bartolini Bussi Michael de Villiers Keith Jones Ulrich Kortenkamp Allen Leung Kay Owens Part 4: Reports from the Thematic afternoon European Didactic Traditions in Mathematics Aspects and Examples from four Selected Cases Werner Blum Michèle Artigue Maria Alessandra Mariotti Rudolf Sträßer Marja Van den Heuvel Panhuizen German speaking traditions in mathematics education research Hans Niels Jahnke Rolf Biehler Angelika Bikner Ahsbahs Uwe Gellert Gilbert Greefrath Lisa Hefendehl Hebeker Götz Krummheuer Timo Leuders Marcus Nührenbörger Andreas Obersteiner Kristina Reiss Bettina Rösken Winter Andreas Schulz Andreas Vohns Rudolf vom Hofe Katrin Vorhölter What is and what might be the legacy of Felix Klein Hans Georg Weigand William McCallum Marta Menghini Michael Neubrand Gert Schubring Renate Tobies part 5: National presentations Argentinean National presentation Esther Galina Mónica Villarreal Teachers’ Professional Development and Mathematics Education in Brazil Victor Giraldo Mathematics Education in Ireland Maurice OReilly Thérèse Dooley Elizabeth Oldham Gerry Shiel National presentation of Japan Toshiakira Fujii Yoshinori Shimizu Hanako Senuma Toshikazu Ikeda National presentation of Lower Mekong sub region countries Fidel R. Nemenzo Masami Isoda Maitree Inprasitha Sampan Thinwiangthong Narumon Changsri Nisakorn Boonsena Chan Roth Monkolsery Lin Souksomphone Anothay Phoutsakhone Channgakham Nguyen Chi Thanh VŨ NHƯ Thư Hương Phương Thảo Nguyễn Teaching and learning mathematics in Turkey Huriye Arikan Part 6: Reports from the Topical Study Groups Topic study group no. 01 Early childhood mathematics education (up to age 7) Iliada Elia Joanne Mulligan Topic study group no. 02 Mathematics education at tertiary level Victor Giraldo Chris Rasmussen Topic study group no. 03 Mathematics education in and for work Diana Coben Geoff Wake Topic study group no. 04 Activities for and research on mathematically gifted students Florence Mihaela Singer Linda Jensen Sheffield Topic study group no. 05 Classroom practice and research for students with mathematical learning difficulties Lourdes Figueiras Rose Griffiths Topic study group no. 06 Adult learning Pradeep Kumar Misra Jürgen Maaß Topic study group no. 07 Populariztion of Mathematics Christian Mercat Patrick Vennebush Topic study group no. 08 Teaching and learning of arithmetic and number systems (focus on primary education) Pi Jen Lin Terezinha Nunes Topic study group no. 09 Teaching and learning of measurement (focus on primary education) Christine Chambris Barbara Dougherty Topic study group no. 10 Teaching and learning of early algebra Carolyn Kieran JeongSuk Pang Topic study group no. 11 Teachig and Learning of Algebra Rakhi Banerjee Amy Ellis Topic study group no. 12 Teaching and learning of geometry (primary level) Sinan Olkun Ewa Swoboda Topic study group no. 13 Teaching and learning of geometry secondary level Ui Hock Cheah Patricio G. Herbst Topic study group no. 14 Teaching and learning of probability Carmen Batanero Egan J. Chernoff Topic study group no. 15 Teaching and learning of statistics Dani Ben Zvi Gail Burrill Topic study group no. 16 Teaching and learning of calculus David Bressoud Victor Martinez Luaces Topic study group no. 17 Teaching and learning of discrete mathematics Eric W. Hart Cecile O. Buffet Topic study group no. 18 Reasoning and proof in mathematics education Guershon Harel Andreas Stylianides Topic study group no. 19 Problem solving in mathematics education Peter Liljedahl Manuel Santos Trigo Topic study group no. 20 Visualization in the teaching and learning of mathematics Michal Yerushalmy Ferdinand Rivera Topic study group no. 21 Mathematical applications and modelling in the teaching and learning of mathematics Jussara Araújo Gloria Ann Stillman Topic study group no. 22 Interdisciplinary mathematics education Susie Groves Julian Williams Topic study group no. 23 Mathematical literacy Hamsa Venkat Iddo Gal Topic study group no. 24 History of the teaching and learning mathematics Fulvia Furinghetti Alexander Karp Topic study group no. 25 The role of history of mathematics in mathematics education Constantinos Tzanakis Xiaoqin Wang Topic study group no. 26 Research on Teaching and Classroom Practice Yoshinori Shimizu Mary Kay Stein Topic study group no. 27 Learning and cognition in mathematics Gaye Williams Wim Van Dooren Topic study group no. 28 Affect beliefs and identity in mathematics education Markku Hannula Francesca Morselli Topic study group no. 29 Mathematics and creativity Demetra Pitta Pantazi Dace Kūma Topic study group no. 30 Mathematical competitions Maria Falk de Losada Alexander Soifer Topic study group no. 31 Language and Communication in Mathematics education Judit Moschkovich David Wagner Topic study group no. 32 Mathematics education in a multilingual and multicultural environment Richard Barwell Anjum Halai Topic study group no. 33 Equity in Mathematics Education (including Gender) Joanne Rossi Becker Bill Atweh Topic study group no. 34 Social and political dimensions of mathematics education Murad Jurdak Renuka Vithal Topic study group no.35 Role of ethnomathematics in mathematics education Milton Rosa Lawrence Shirley Topic study group no.36 Task design analysis and learning environments programme summary Jiansheng Bao Jere Confrey Topic study group no. 37 Mathematics curriculum development Anita Rampal Zalman Usiskin. Topic study group no.38 Research on resources (textbooks learning materials etc.) Lianghuo Fan Luc Trouche Topic study group no.39 Large scale assessment and testing in mathematics education Rae Young Kim Christine Suurtamm Topic study group no.40 Classroom assessment for mathematics learning Denisse Thompson Karin Brodie Topic study group no. 41 Uses of technology in primary mathematics education (up to age 10) Sophie Soury Lavergne Colleen Vale Topic study group no. 42 Uses of technology in lower secondary mathematics education (age 10 to 14) Lynda Ball Paul Drijvers Topic study group no. 43 Uses of technology in upper secondary education (age 14 to 19) Colette Laborde Stephen Hegedus Topic study group no. 44 Distance learning e learning blended learning Rúbia Barcelos Amaral Veronica Hoyos Topic study group no. 45 Knowledge in for teaching mathematics at primary level Carolyn Maher Peter Sullivan Topic study group no. 46 Knowledge in for teaching mathematics at the secondary level Ruhama Even Xinrong Yang Topic study group no. 47 Pre service mathematics education of primary teachers Keiko Hino Gabriel Stylianides Topic study group no. 48 Pre service Mathematics Education of Secondary Teachers Marilyn Strutchens Rongjin Huang Topic study group no. 49 In service education and professional development of primary mathematics teachers Akihiko Takahashi Leonor Varas Topic study group no. 50 In service education and professional development of secondary mathematics teachers Jill Adler Yudong Yang Topic study group no. 51 Diversity of theories in mathematics education Tommy Dreyfus Anna Sierpinska Topic study group no. 52 Empirical methods and methodologies David Clarke Alan Schoenfeld Topic study group No. 53 Philosophy of mathematics education Pau This book is open access under a CC BY 4.0 license. The book presents the Proceedings of the 13th International Congress on Mathematical Education (ICME 13) and is based on the presentations given at the 13th International Congress on Mathematical Education (ICME 13). ICME 13 took place from 24th 31st July 2016 at the University of Hamburg in Hamburg (Germany). The congress was hosted by the Society of Didactics of Mathematics (Gesellschaft für Didaktik der Mathematik GDM) and took place under the auspices of the International Commission on Mathematical Instruction (ICMI). ICME 13 brought together about 3.500 mathematics educators from 105 countries additionally 250 teachers from German speaking countries met for specific activities. Directly before the congress activities were offered for 450 Early Career Researchers. The proceedings give a comprehensive overview on the current state of the art of the discussions on mathematics education and display the breadth and deepness of current research on mathematical teaching and learning processes. The book introduces the major activities of ICME 13 namely articles from the four plenary lecturers and two plenary panels articles from the five ICMI awardees reports from six national presentations three reports from the thematic afternoon devoted to specific features of ICME 13. Furthermore the proceedings contain descriptions of the 54 Topic Study Groups which formed the heart of the congress and reports from 29 Discussion Groups and 31 Workshops. The additional important activities of ICME 13 namely papers from the invited lecturers will be presented in the second volume of the proceedings