​Chapter 1: Transforming mathematics instruction: What do we know and what can we learn from existing approaches and practices? Yeping LI, Texas A&M University, USA; Edward A. SILVER, University of Michigan, USA; Shiqi LI, East China Normal University, China.- Part I: Transforming Mathematics Instruction with a Focus on Changes in Instructional Practice.- Preface: David CLARKE.- Chapter 2: Modelling in mathematics classroom instruction - an innovative approach for transforming mathematics education: Katrin VORHÖLTER, University of Hamburg, Germany; Gabriele KAISER, University of Hamburg, Germany;Rita Borromeo FERRI, Kassel University, Germany.- Chapter 3: Guided reinvention: What is it and how do teachers learn this teaching approach? Michelle STEPHAN, University of North Carolina Charlotte, USA; Diana UNDERWOOD-GREGG, Purdue University Calumet, USA; Erna YACKEL, Purdue University Calumet, USA.- Chapter 4: Challenging mathematics with multiple solution tasks and mathematical investigations in geometry: Roza LEIKIN, University of Haifa, Israel.- Chapter 5: Transforming professional practice in numeracy teaching: Merrilyn GOOS, The University of Queensland, Australia; Vince GEIGER, Australian Catholic University, Australia; Shelley DOLE, The University of Queensland, Australia.- Chapter 6: Exploratory work in the mathematics classroom: João Pedro da PONTE, Instituto de Educação da Universidade de Lisboa, Portugal; Neusa BRANCO, Instituto de Educação da Universidade de Lisboa, Portugal; Marisa QUARESMA, Instituto de Educação da Universidade de Lisboa, Portugal.- Chapter 7: The affordances of using visibly random groups in a mathematics classroom: Peter LILJEDAHL, Simon Fraser University, Canada.- Part II: Transforming Mathematics Instruction with School Curriculum Changes.- Preface: Edward A. SILVER.- Chapter 8: Transforming mathematics education: The role of textbooks and teachers: Koeno GRAVEMEIJER, Eindhoven University of Technology, the Netherlands.- Chapter 9: Opportunities to develop algebraic thinking in elementary grades throughout the school year in the context of mathematics curriculum changes: Hélia OLIVEIRA, University of Lisbon, Portugal; Célia MESTRE, University of Lisbon, Portugal.- Chapter 10: Transformation of Japanese elementary mathematics textbooks: 1958-2012: Tad WATANABE, Kennesaw State University, USA.- Chapter 11: Changes in instructional tasks and their influence on classroom discourse in reformed mathematics classrooms of Chinese primary schools: Yu-Jing NI, The Chinese University of Hong Kong, Hong Kong SAR; Xiaoqing LI, Shen Zhen University, China; Dehui ZHOU, Hong Kong Shue Yan University, Hong Kong SAR; Qiong LI, Beijing Normal University, China.- Chapter 12: Improving classroom instruction in mathematics through exemplary lesson development: A Chinese approach: Rongjin HUANG, Middle Tennessee State University, USA; Yeping LI, Texas A&M University, USA.- Part III: Transforming Mathematics Instruction with Different Approaches in Teacher Education.- Preface: Peter SULLIVAN.- Chapter 13: Facilitating video-based professional development: Planning and orchestrating productive discussions: Hilda BORKO, Stanford University, USA, Jennifer JACOBS, University of Colorado, Boulder, USA, Nanette SEAGO, WestEd, USU, Charmaine MANGRAM, Stanford University, USA.- Chapter 14: Professional development for secondary school mathematics teachers using student work: Some challenges and promising possibilities: Edward A. SILVER, University of Michigan, USA, Heejoo SUH, Michigan State University, USA.- Chapter 15: Cases as a vehicle for developing knowledge needed for teaching: Margaret S. SMITH, University of Pittsburgh, USA. Justin BOYLE, University of New Mexico, USA, Fran ARBAUGH, Pennsylvania State University, USA, Gabriel STYLIANIDES, University of Oxford, UK.- Chapt