Invited Lectures from the 13th International Congress on Mathematical Education.

• Superior document: ICME-13 Monographs
• Author: Kaiser, Gabriele.
• TeilnehmendeR: Forgasz, Helen.; Graven, Mellony.; Kuzniak, Alain.; Simmt, Elaine.; Xu, Binyan.
• Place / Publishing House: Cham : : Springer International Publishing AG,, 2018.; ©2018.
• Year of Publication: 2018
• Edition: 1st ed.
• Language: English
• Series: ICME-13 Monographs
• Physical Description: 1 online resource (777 pages)

Table of Contents

• 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.