Mathematics, Education and History

• Introduction.- Part I - Theoretical and/or conceptual frameworks for integrating history and epistemology of mathematics in ME.- I.1: The history of artefacts as a resource in mathematics education, and inquiry reflective learning environments.- I.2 History of mathematics and teachers’ education: on otherness and empathy.- I.3 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 Facilitating source-centered history of mathematics in Danish upper-secondary mathematics education.- II.2 Involving students in original research with primary sources: A graduate course in the History of Mathematics Education.- II.3 Algebra without context is empty, visualizations without concepts are blind.- II.4 History of mathematics in German textbooks - typology of tasks.- Part III - Empirical investigations on implementing history and epistemology in ME.- III.1 Geometry and visual reasoning to introduce algebraic language as Liu Hui and Al-Khwarizmi did.- III.2 Missing curious fraction problems: the unknown inheritance and the unknown numbers of heirs.- III.3 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 Liu Hui shares his views with young students.- IV.2 Experimentation on the effects of mathematical diversity: Using ancient cuneiform mathematics on conceptual and nature of sciences aspects.- IV.3 Making domain-specific beliefs explicit for prospective teachers – an example of using original sources.- IV.4 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 The Pantograph – a historical drawing device for math teaching.- V.2 Expanding contexts for teaching upper secondary school geometry.- V.3 Learning new mathematics from old: Euclid’s art after Bath.

“This book covers all levels of education, from primary school to tertiary education, with a particular focus on teacher education. It is a valuable contribution to the literature on mathematics education.” (Ubiratan D’Ambrosio, zbMATH 1445.97003, 2020)“I would recommend any novice considering using the history of mathematics in their teaching to read this piece. It thoughtfully asks the relevant questions necessary for such an endeavor, outlines the history of efforts made in working towards a “fruitful and harmonious interplay among History, Education and Mathematics” and then offers this most recent contribution of experiences and suggestions. … This is a good, useful and readable book.” (Frank Swetz, MAA Reviews, August, 2018)