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This book includes 18 peer-reviewed papers from nine countries, originally presented in a shorter form at TSG 25 The Role of History of Mathematics in Mathematics Education, as part of ICME-13 during . It also features an introductory chapter, by its co-editors, on the structure and main points of the book with an outline of recent developments in exploring the role of history and epistemology in mathematics education. It serves as a valuable contribution in this domain, by making reports on recent developments in this field available to the international educational community, with a special focus on relevant research results since 2000.

The 18 chapters of the book are divided into five interrelated parts that underlie the central issues of research in this domain:

1. Theoretical and conceptual frameworks for integrating history and epistemology in mathematics in mathematics education;

2. Courses and didactical material: Design, implementation and evaluation;

3. Empirical investigations on implementing history and epistemology in mathematics education;

4. Original historical sources in teaching and learning of and about mathematics;

5. History and epistemology of mathematics: Interdisciplinary teaching and sociocultural aspects.

This book covers all levels of education, from primary school to tertiary education, with a particular focus on teacher education. Additionally, each chapter refers to and/or is based on empirical research, in order to support, illuminate, clarify and evaluate key issues, main questions, and conjectured theses raised by the authors or in the literature on the basis of historical-epistemological or didactical-cognitive arguments.

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Introduction - K. M. Clark, T.H. Kjeldsen, S. Schorcht & C. Tzanakis

Part I - Theoretical and/or conceptual frameworks for integrating history and epistemology of mathematics in ME

I.1 : M. W. Johansen & T. H. Kjeldsen - The history of artefacts as a resource in mathematics education, and inquiry reflective learning environments

I.2 D. Guillemette - History of mathematics and teachers´ education: on otherness and empathy

I.3 I. Witzke, K. M. Clark, H. Struve & G. Stoffels - ÜBERPRO: addressing the transition from school to university: Initial results from a case study

Part II Courses and/or didactical material: Design, implementation and evaluation

II.1 K. Danielsen,, E. Gertz, & H. K S›rensen- Facilitating source-centered history of mathematics in Danish upper-secondary mathematics education

II.2 P. Baggett, & A. Ehrefeuc
ht - Involving students in original research with primary sources: A graduate course in the History of Mathematics Education

II.3 Y. Weiss-Pydstrygach & R. Kaenders - Algebra without context is empty, visualizations without concepts are blind
II.4 S. Schorcht - History of mathematics in German textbooks - typology of tasks

Part III - Empirical investigations on implementing history and epistemology in ME

III.1 I. Guevara-Casanova & C. Burgués-Flamarich - Geometry and visual reasoning to introduce algebraic language as Liu Hui and Al-Khwarizmi did

III.2 M.T. Sanz,. & B. Gómez - Missing curious fraction problems: the unknown inheritance and the unknown numbers of heirs

III.3 A. Bernardes & T. Roque - History of matrices: promoting commognitive conflicts and encouraging reflection on meta-discursive rules in prospective teachers

Part IV- Original
historical sources in teaching and learning of and about mathematics

IV.1 V. Tsiapou - Liu Hui shares his views with young students

IV.2 C. de Varent - Experimentation on the effects of mathematical diversity: Using ancient cuneiform mathematics on conceptual and nature of sciences aspects

IV.3 S. Spies I. Witzke - Making domain-specific beliefs explicit for prospective teachers - an example of using original sources

IV.4 J. Lodder - Primary historical sources in the classroom: Graph Theory and spanning trees

Part V - History and epistemology of mathematics: Interdisciplinary teaching and socio-cultural aspects

V.1 S. Schöneburg - The Pantograph - a historical drawing device for math teaching
V.2 P. Kotarinou, Ch. Stathopoulou & E. Gana - Expanding contexts for teaching upper secondary school geometry

V.3 S. Lawrence - Learning new
mathematics from old: Euclid´s art after Bath

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