Networking of Theories as a Research Practice in Mathematics Education

1. Front Matter

   Pages i-xii

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2. Introduction

   1. Front Matter

      Pages 1-1

      PDF

   2. Starting Points for Dealing with the Diversity of Theories

      • Angelika Bikner-Ahsbahs, Susanne Prediger, Michèle Artigue, Ferdinando Arzarello, Marianna Bosch, Tommy Dreyfus et al.

      Pages 3-12

   3. Description of the Data: Introducing the Session of Carlo, Giovanni, and the Exponential Function

      • Cristina Sabena

      Pages 13-28

3. Diversity of Theories

   1. Front Matter

      Pages 29-29

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   2. Introduction to the Approach of Action, Production, and Communication (APC)

      • Ferdinando Arzarello, Cristina Sabena

      Pages 31-45

   3. Introduction to the Theory of Didactical Situations (TDS)

      • Michèle Artigue, Mariam Haspekian, Agnès Corblin-Lenfant

      Pages 47-65

   4. Introduction to the Anthropological Theory of the Didactic (ATD)

      • Marianna Bosch, Josep Gascón

      Pages 67-83

   5. Introduction to Abstraction in Context (AiC)

      • Tommy Dreyfus, Ivy Kidron

      Pages 85-96

   6. Introduction to the Theory of Interest-Dense Situations (IDS)

      • Angelika Bikner-Ahsbahs, Stefan Halverscheid

      Pages 97-113

4. Case Studies of Networking

   1. Front Matter

      Pages 115-115

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   2. Introduction to Networking: Networking Strategies and Their Background

      • Susanne Prediger, Angelika Bikner-Ahsbahs

      Pages 117-125

   3. The Epistemic Role of Gestures: A Case Study on Networking of APC and AiC

      • Tommy Dreyfus, Cristina Sabena, Ivy Kidron, Ferdinando Arzarello

      Pages 127-151

   4. Context, Milieu, and Media-Milieus Dialectic: A Case Study on Networking of AiC, TDS, and ATD

      • Ivy Kidron, Michèle Artigue, Marianna Bosch, Tommy Dreyfus, Mariam Haspekian

      Pages 153-177

   5. The Epistemological Gap: A Case Study on Networking of APC and IDS

      • Cristina Sabena, Ferdinando Arzarello, Angelika Bikner-Ahsbahs, Ingolf Schäfer

      Pages 179-200

   6. Topaze Effect: A Case Study on Networking of IDS and TDS

      • Angelika Bikner-Ahsbahs, Michèle Artigue, Mariam Haspekian

      Pages 201-221

5. Reflections

   1. Front Matter

      Pages 223-223

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   2. Beyond the Official Academic Stage. Dialogic Intermezzo

      • Stefan Halverscheid

      Pages 225-233

   3. Networking as Research Practices: Methodological Lessons Learnt from the Case Studies

      • Angelika Bikner-Ahsbahs, Susanne Prediger

      Pages 235-247

   4. Reflection on Networking Through the Praxeological Lens

      • Michèle Artigue, Marianna Bosch

      Pages 249-265

How can we deal with the diversity of theories in mathematics education? This was the main question that led the authors of this book to found the Networking Theories Group. Starting from the shared assumption that the existence of different theories is a resource for mathematics education research, the authors have explored the possibilities of interactions between theories, such as contrasting, coordinating, and locally integrating them.

The book explains and illustrates what it means to network theories; it presents networking as a challenging but fruitful research practice and shows how the Group dealt with this challenge considering five theoretical approaches, namely the approach of Action, Production, and Communication (APC), the Theory of Didactical Situations (TDS), the Anthropological Theory of the Didactic (ATD), the approach of Abstraction in Context (AiC), and the Theory of Interest-Dense Situations (IDS).

A synthetic presentation of each theory and their connections shows how the activity of networking generates questions at the theoretical, methodological and practical levels and how the work on these questions leads to both theoretical and practical progress. The core of the book consists of four new networking case studies which illustrate what exactly can be gained by this approach and what kind of difficulties might arise.

• Abstraction in Context (AiC)
• Action, Production and Communication Theory (APC)
• Anthropological Theory of the Didactic (ATD)
• Connecting math education theories
• Diversity of didactical theories in math education
• Epistemic processes in mathematics education
• Interest Dense Situation Theory (IDS)
• Networking as research practice
• Networking theories in mathematics education
• Semiotic resources in the classroom
• Social interactions in mathematics classes
• Theory of Didactical Situations (TDS)
• Topaze effect

“The Networking Theories Group has produced a highly commendable book for anyone interested in theories in mathematics education. … for those with an open mind and willingness to make this effort, a lot could be learned. … this book is a forerunner for more such work, not only on networking but also on the emergence of new theories or development of existing ones.” (Arthur Bakker, Educational Studies in Mathematics, Vol. 93, 2016)

• Fachbereich 03 für Mathematik und Informatik, AG Didaktik der Mathematik, University of Bremen, Bremen, Germany

  Angelika Bikner-Ahsbahs

• Institute for Development and Research in Mathematics Education, TU Dortmund University, Dortmund, Germany

  Susanne Prediger

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