Interfaces between Mathematical Practices and Mathematical Education

1. Front Matter

   Pages i-xvi

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2. Foundations of Mathematics Buried in School Garbage (Southern Mesopotamia, Early Second Millennium BCE)

   • Christine Proust

   Pages 1-25

3. From the Practice of Explanation to the Ideology of Demonstration: An Informal Essay

   • Jens Høyrup

   Pages 27-46

4. Catholicism and Mathematics in the Early Modernity

   • Jorge Alberto Molina

   Pages 47-67

5. “Je n’ai point ambitionnée d’être neuf”: Modern Geometry in Early Nineteenth-Century French Textbooks

   • Jemma Lorenat

   Pages 69-122

6. The Impact of Teaching Mathematics Upon the Development of Mathematical Practices

   • Gert Schubring

   Pages 123-141

7. A Multiple Perspective Approach to History of Mathematics: Mathematical Programming and Rashevsky’s Early Development of Mathematical Biology in the Twentieth Century

   • Tinne Hoff Kjeldsen

   Pages 143-167

8. Teaching as an Indicator of Mathematical Practices

   • Carlos Tomei

   Pages 169-180

9. Back Matter

   Pages 181-190

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This contributed volume investigates the active role of the different contexts of mathematics teaching on the evolution of the practices of mathematical concepts, with particular focus on their foundations. The book aims to deconstruct the strong and generally wide-held conviction that research in mathematics constitutes the only driving force for any progress in the development of mathematics as a field. In compelling and convincing contrast, these chapters aim to show the productive function of teaching, showcasing investigations from countries and regions throughout various eras, from Old Babylonia through the 20^th Century. In so doing, they provide a critical reflection on the foundations of mathematics, as well as instigate new research questions, and  explore the interfaces between teaching and research.

• Complementarity of teaching and research
• Relation of teaching to the foundations of mathematics
• Origins of mathematics
• Teaching as reproduction
• The origin of proof
• The Zilsel-thesis and the Merton-thesis
• Institutional origins of modern science
• Practical geometry in the 16th Century
• Catholicism and mathematics in the 17th Century
• Modern geometry in 19th Century French textbooks
• Historical conditions of production of mathematics

• Department of Mathematics, Federal University of Rio de Janeiro, Brazil

  Gert Schubring

Gert Schubring is a retired member of the Institut für Didaktik der Mathematik, a research institute at Bielefeld University, and at present is visiting professor at the Universidade Federal do Rio de Janeiro (Brazil). His research interests focus on the history of mathematics and the sciences in the eighteenth and nineteenth centuries and their systemic interrelation with social-cultural systems. One of his specializations is history of mathematics education. He has published several books, among which is Conflicts between Generalization, Rigor and Intuition: Number Concepts Underlying the Development of Analysis in 17th–19th Century France and Germany (New York, 2005).

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