Invited Lectures from the 13th International Congress on Mathematical Education

1. Front Matter

   Pages i-x

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2. Practice-Based Initial Teacher Education: Developing Inquiring Professionals

   • Glenda Anthony

   Pages 1-18Open Access

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3. Mathematical Experiments—An Ideal First Step into Mathematics

   • Albrecht Beutelspacher

   Pages 19-29Open Access

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4. Intersections of Culture, Language, and Mathematics Education: Looking Back and Looking Ahead

   • Marta Civil

   Pages 31-48Open Access

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5. The Double Continuity of Algebra

   • Al Cuoco, William McCallum

   Pages 49-63Open Access

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6. A Friendly Introduction to “Knowledge in Pieces”: Modeling Types of Knowledge and Their Roles in Learning

   • Andrea A. diSessa

   Pages 65-84Open Access

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7. History of Mathematics, Mathematics Education, and the Liberal Arts

   • Michael N. Fried

   Pages 85-101Open Access

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8. Knowledge and Action for Change Through Culture, Community and Curriculum

   • Linda Furuto

   Pages 103-114Open Access

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9. The Impact and Challenges of Early Mathematics Intervention in an Australian Context

   • Ann Gervasoni

   Pages 115-133Open Access

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10. Helping Teacher Educators in Institutions of Higher Learning to Prepare Prospective and Practicing Teachers to Teach Mathematics to Young Children

    • Herbert P. Ginsburg

    Pages 135-154Open Access

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11. Hidden Connections and Double Meanings: A Mathematical Viewpoint of Affective and Cognitive Interactions in Learning

    • Inés M. Gómez-Chacón

    Pages 155-174Open Access

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12. The Role of Algebra in School Mathematics

    • Liv Sissel Grønmo

    Pages 175-193Open Access

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13. Storytelling for Tertiary Mathematics Students

    • Ansie Harding

    Pages 195-207Open Access

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14. PME and the International Community of Mathematics Education

    • Rina Hershkowitz, Stefan Ufer

    Pages 209-228Open Access

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15. ICMI 1966–2016: A Double Insiders’ View of the Latest Half Century of the International Commission on Mathematical Instruction

    • Bernard R. Hodgson, Mogens Niss

    Pages 229-247Open Access

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16. Formative Assessment in Inquiry-Based Elementary Mathematics

    • Alena Hošpesová

    Pages 249-268Open Access

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17. Professional Development of Mathematics Teachers: Through the Lens of the Camera

    • Ronnie Karsenty

    Pages 269-288Open Access

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18. Powering Knowledge Versus Pouring Facts

    • Petar S. Kenderov

    Pages 289-306Open Access

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19. Mathematical Problem Solving in Choice-Affluent Environments

    • Boris Koichu

    Pages 307-324Open Access

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20. Natural Differentiation—An Approach to Cope with Heterogeneity

    • Günter Krauthausen

    Pages 325-341Open Access

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The book presents the Invited Lectures given at 13^th International Congress on Mathematical Education (ICME-13). ICME-13 took place from 24^th- 31^st 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 – the biggest ICME so far - brought together about 3500 mathematics educators from 105 countries, additionally 250 teachers from German speaking countries met for specific activities. The scholars came together to share their work on the improvement of mathematics education at all educational levels.. The papers present the work of prominent mathematics educators from all over the globe and give insight into the current discussion in mathematics education. The Invited Lectures cover a wide spectrum of topics, themesand issues and aim to give direction to future research towards educational improvement in the teaching and learning of mathematics education. This book is of particular interest to researchers, teachers and curriculum developers in mathematics education.

• mathematics education
• mathematics learning
• mathematics teaching
• mathematics teachers
• ICME-13
• 13th congress on Mathematical Education
• Empirical Studies in Mathematics Education
• Theoretical Reflections on Mathematics Education
• Tertiary Mathematics Education
• Secondary Mathematics Education
• Primary Mathematics Education
• Society of didactics of Mathematics
• Mathematics educators
• improvement of mathematics education
• Global mathematics trends
• Open Access
• learning and instruction

• University Hamburg, Hamburg, Germany

  Gabriele Kaiser

• Monash University, Clayton, Australia

  Helen Forgasz

• Rhodes University, Grahamstown, South Africa

  Mellony Graven

• Université Paris Diderot, Paris, France

  Alain Kuzniak

• University of Alberta, Sherwood Park, Canada

  Elaine Simmt

• East China Normal University, Shanghai, China

  Binyan Xu

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