Intro -- Acknowledgements -- Contents -- 1 International Comparative Studies in Mathematics: Lessons for Improving Students’ Learning -- 1 Introduction -- 1.1 How Are Large Scale Studies Used? -- 1.2 Unique Findings from Small Scale Studies -- 1.3 What Is an International Comparative Study? -- 1.4 What Lessons Can We Learn from International Comparative Studies? -- 2 Survey on State-of-the-Art -- 2.1 Lesson 1: Understanding Students’ Thinking -- 2.1.1 Findings from Two Examples -- 2.1.2 Needs and Benefits of In-depth Studies to Understand Students’ Thinking -- 2.1.3 Nurturing Creativity and Critical Thinking Skills -- 2.1.4 Calling for More In-depth, Small-Scale International Comparative Studies -- 2.2 Lesson 2: Examining the Dispositions and Experiences of Mathematically Literate Students -- 2.2.1 Country Profiles of the Processes of Mathematical Literacy -- 2.2.2 What Mathematics Experiences Build Mathematical Literacy? -- 2.2.3 Students’ Disposition Toward Formal and Applied Mathematics -- 2.3 Lesson 3: Changing Classroom Instruction -- 2.3.1 Complementary Roles of TIMSS Video Study and Learner’s Perspective Study -- 2.3.2 Lesson Structures and Lesson Events -- 2.3.3 Multiple Accounts of a Teacher’s Practice -- 2.3.4 The Episode of the Train-Ticket Problem -- 2.3.5 Lessons for the Implementation of Mathematical Tasks -- 2.3.6 Lessons for Changing Classroom Instruction -- 2.4 Lesson 4: Making Global Research Locally Meaningful: TIMSS in South Africa -- 2.4.1 Mathematics Achievement Trend Over 20 Years -- 2.4.2 Contextual Factors Influencing Educational Achievement -- 2.4.3 Student Progression and Pathways Through Secondary School -- 3 Summary and Looking Ahead -- References.