Intro -- Preface -- Contents -- 1 Practice-Based Initial Teacher Education: Developing Inquiring Professionals -- Abstract -- 1.1 Introduction -- 1.2 Inquiring Professionals -- 1.3 Inquiry Within Practice-Based Initial Teacher Education -- 1.4 Developing an Inquiry Stance Within Rehearsals -- 1.5 Developing an Inquiry Stance in Classroom-Based Rehearsals -- 1.6 Supporting Teaching Inquiry-Orientated Standards -- 1.7 Challenges and Implications Going Forward -- Acknowledgements -- References -- 2 Mathematical Experiments-An Ideal First Step into Mathematics -- Abstract -- 2.1 Mathematical Experiments and Science Centers -- 2.2 Mathematikum Giessen -- 2.3 Some Experiments -- 2.4 Books and Easy-to-Built Experiments -- 2.5 Two Critical Questions -- 2.5.1 Are These Experiments at All? -- 2.5.2 Is This at All Mathematics? -- 2.6 Effects and Impact on the Visitors -- References -- 3 Intersections of Culture, Language, and Mathematics Education: Looking Back and Looking Ahead -- Abstract -- 3.1 School Versus Home -- 3.2 Some Context -- 3.3 Towards a Two-Way Dialogue Home-School -- 3.4 Cultural Aspects -- 3.5 Language Aspects -- 3.6 The Case of Larissa -- 3.7 Looking Ahead -- Acknowledgements -- References -- 4 The Double Continuity of Algebra -- Abstract -- 4.1 Introduction -- 4.2 From University to Secondary School -- 4.2.1 Pythagorean Triples -- 4.2.2 The Algebraic Method from a Higher Standpoint -- 4.2.3 Using Norms to Construct Triangles with a 60� Angle -- 4.2.4 What Is to Be Learned from This? -- 4.3 From Secondary School to University -- 4.3.1 Ptolemy's Theorem -- 4.3.2 A Question from a Secondary School Class -- 4.3.3 What Is to Be Learned from This? -- 4.4 Implications for Teaching Abstract Algebra -- References -- 5 A Friendly Introduction to "Knowledge in Pieces": Modeling Types of Knowledge and Their Roles in Learning -- Abstract.

5.1 Introduction -- 5.1.1 Overview -- 5.1.2 Empirical Methods -- 5.2 Two Models: Illustrative Data and Analysis -- 5.2.1 Intuitive Knowledge -- 5.2.2 Scientific Concepts -- 5.3 Examples in Mathematics -- 5.3.1 The Law of Large Numbers -- 5.3.2 Understanding Fractions -- 5.3.3 Conceptual and Procedural Knowledge in Strategy Innovation -- 5.3.4 Other Examples -- 5.4 Cross-Cutting Themes -- 5.4.1 Continuity or Discontinuity in Learning -- 5.4.2 Understanding Representations -- References -- 6 History of Mathematics, Mathematics Education, and the Liberal Arts -- Abstract -- 6.1 By Way of Introduction: David Eugene Smith -- 6.1.1 Religio Historici -- 6.2 History of Mathematics and Mathematics Education -- 6.3 The Liberal Arts -- 6.4 Concluding Words -- References -- 7 Knowledge and Action for Change Through Culture, Community and Curriculum -- Abstract -- 7.1 "Mathematics for All" -- 7.1.1 Ethnomathematics and Ecological Systems Theory -- 7.2 Culture, Community and Curriculum -- 7.2.1 Theoretical Frameworks -- 7.2.2 Connections to Hawai'i and the Pacific -- 7.3 Knowledge and Action for Change -- 7.3.1 Educational Context in Hawai'i and the Pacific -- 7.3.2 Preparing Teachers as Leaders -- 7.4 Further Discussion -- References -- 8 The Impact and Challenges of Early Mathematics Intervention in an Australian Context -- Abstract -- 8.1 Introduction -- 8.2 Failure to Thrive When Learning Mathematics -- 8.3 The Extending Mathematical Understanding (EMU) Intervention Approach -- 8.4 Using Growth Point Profiles to Identify Children Who May Benefit from an Intervention Program -- 8.5 Progress of Students Who Participated in an EMU Intervention Program -- 8.6 Longitudinal Impact on Mathematics Knowledge and Growth Points Over Three Years -- 8.7 Impact of EMU Intervention on Children's Confidence for Learning Mathematics.

8.8 Issues Related to Effective Intervention Approaches -- 8.9 Conclusion -- Acknowledgements -- References -- 9 Helping Teacher Educators in Institutions of Higher Learning to Prepare Prospective and Practicing Teachers to Teach Mathematics to Young Children -- Abstract -- 9.1 Introduction -- 9.2 The Need for EME -- 9.3 A Guide for Teacher Educators -- 9.3.1 What Do We Teacher Educators Want Our Students to Know? -- 9.3.1.1 The Mathematics -- 9.3.1.2 The Development of Mathematical Thinking -- 9.3.1.3 Formative Assessment and Understanding the Individual -- 9.3.1.4 Pedagogical Goals and Methods -- 9.3.2 Overcoming Negative Feelings -- 9.4 The DREME Modules -- 9.5 My Course -- 9.5.1 Who Are You? -- 9.5.2 What Concerns You? -- 9.5.3 Learning About the Math -- 9.5.4 Learning About Children's Thinking -- 9.5.5 Assessment -- 9.5.6 Analyzing Videos -- 9.5.7 Clinical Interview -- 9.5.8 Pedagogy -- 9.5.9 Picture Books -- 9.6 Conclusion -- References -- 10 Hidden Connections and Double Meanings: A Mathematical Viewpoint of Affective and Cognitive Interactions in Learning -- Abstract -- 10.1 Introduction -- 10.2 Theoretical Fundamentals -- 10.2.1 Affective-Cognitive Reference System: The Zig-Zag Path in Mathematical Reasoning -- 10.2.2 Affective-Cognitive Reference System Model -- 10.3 Determining the Local Affect-Cognitive Structure -- 10.3.1 Considerations for the Analysis of the Cognitive Mathematical Dimension -- 10.3.2 Modeling the Local Structure of Affect in the Individual: Routines and Bifurcations -- 10.4 Modeling Local Affect Structure in a Group -- 10.4.1 Implicative Data Analysis -- 10.4.2 Results of the Modeling of Local Affect Structure in a Group -- 10.5 Conclusion -- Acknowledgements -- References -- 11 The Role of Algebra in School Mathematics -- Abstract -- 11.1 Introduction -- 11.2 Different Profiles in Mathematics Education.

11.3 Equal Rights to Education -- 11.4 Reasons for Low Emphasis on Algebra -- 11.5 Pure and Applied Mathematics -- 11.6 How to Learn the Mathematical Language Algebra -- 11.7 Summary and Further Research -- References -- 12 Storytelling for Tertiary Mathematics Students -- Abstract -- 12.1 About Stories and Storytelling -- 12.2 History of Storytelling -- 12.3 Literature on Storytelling in Education -- 12.4 Storytelling for Tertiary Mathematics -- 12.5 Features of Storytelling -- 12.6 Data Gathering -- 12.7 Feedback -- 12.8 Critical Reflection -- 12.9 Examples of Stories -- References -- 13 PME and the International Community of Mathematics Education -- Abstract -- 13.1 Introduction -- 13.1.1 Some General Features of PME -- 13.1.2 PME Spirit Through the Lens of Its Goals, Conferences, Proceedings and Books -- 13.2 First Views on the Research Presented at PME -- 13.2.1 The Theoretical Basis That Is Used to Frame Findings -- 13.2.2 Methods Used to Approach Questions -- 13.3 Development and Changes in PME Research on Mathematics Learning -- 13.3.1 General Features of Trends in This Research -- 13.3.2 Learning as It Is Expressed in the Accumulation of Learners' Responses (as Individuals) to Purposeful Tasks in Tests and Questionnaires (Quantitative Research) -- 13.3.3 Theory in the Center -- 13.3.4 Constructivism and Socio-cultural Approaches, as Catalysts for Classroom Research or Vice-Versa -- 13.3.5 Research in the Mathematics Classroom and the Mathematics that is Taught and Learned in the Classroom -- 13.3.6 Networking-Connecting Theoretical Approaches for Better Interpretation of Empirical Findings -- 13.4 Factors Influencing PME's Development-Examples from Research on Mathematics Teachers -- 13.4.1 The Development of Research on Teachers and Teaching in PME -- 13.4.2 Trends Impacting the Development of Research on Teachers and Teaching.

13.4.3 What Can We Learn from Research on Teachers and Teaching? -- 13.5 Epilog -- References -- 14 ICMI 1966-2016: A Double Insiders' View of the Latest Half Century of the International Commission on Mathematical Instruction -- Abstract -- 14.1 Introduction -- 14.2 1908-1982: Foundation, (Re)Formation and "The First Crisis" Around ICMI -- 14.3 1983-1998: Consolidation and Expansion -- 14.4 1999-2016: Calm Waters, but with "A Second Crisis" Around ICMI -- 14.5 ICMI and the Field of Mathematics Education -- References -- 15 Formative Assessment in Inquiry-Based Elementary Mathematics -- Abstract -- 15.1 Introduction -- 15.2 Background of the Study -- 15.2.1 Assessment -- 15.2.2 Inquiry-Based Approach in Mathematics Education and Assessment -- 15.3 Empirical Study -- 15.3.1 Goals and Organization of the Study -- 15.3.2 Preparation of the Educational Experiments -- 15.3.3 Data and Their Analysis -- 15.4 Selected Findings and Discussion -- 15.4.1 Formulation of Learning Objectives -- 15.4.2 Supporting Self-Assessment and Formative Peer Assessment -- 15.4.3 Correctness of Solution of the Problem and Peer Assessment -- 15.4.4 Peer Assessment and Institutionalization of Knowledge -- 15.4.5 Other Methods of Formative Assessment in Our Experiments -- 15.5 Concluding Remarks -- 15.5.1 Formative Assessment and Teachers -- 15.5.2 Formative Assessment and Pupils -- 15.5.3 Formative Assessment and Culture -- Acknowledgements -- Appendix 1: Assessment Tools Worksheet 1: Find Out How Many Lentils There Are in a Half-Kilogram Package. (Colored Parts Are Intended for Peer Assessment.) -- References -- 16 Professional Development of Mathematics Teachers: Through the Lens of the Camera -- Abstract -- 16.1 Introduction -- 16.2 The VIDEO-LM Project: Rationale, Theoretical Roots, and Framework -- 16.2.1 The Six-Lens Framework.

16.2.2 Features of Using SLF in Video-Based PD Sessions.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2023. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.