This book is about the creation and production of textbooks for learning and teaching mathematics. It covers a period from Antiquity to Modern Times. The analysis begins by assessing principal cultures with a practice of mathematics. The tension between the role of the teacher and his oral mode, on the one hand, and the use of a written (printed) text, in their respective relation with the student, is one of the dimensions of the comparative analysis, conceived of as the ‘textbook triangle’. The changes in this tension with the introduction of the printing press are discussed. The book presents various national case studies (France, Germany, Italy) as well as analyses of the internationalisation of textbooks via transmission processes.
As this topic has not been sufficiently explored in the literature, it will be very well received by scholars of mathematics education, mathematics teacher educators and anyone with an interest in the field.
Author(s): Gert Schubring
Series: International Studies in the History of Mathematics and its Teaching
Publisher: Springer
Year: 2023
Language: English
Pages: 212
City: Cham
Preface
Contents
Chapter 1: Why Study Historical Books Intended for Teaching?
1.1 Textbooks as Interface
1.2 Social History
1.3 Methods for Textbook Analysis
1.3.1 What Is Meant by ‘Context’?
1.3.2 Hermeneutics
1.3.2.1 The Development of Hermeneutics
1.3.2.2 A Subjectivist Variant: Dilthey, Heidegger, Gadamer
1.3.2.3 Questioning this Variant in Science
1.3.2.4 Material or Objective Hermeneutics
1.3.2.5 A Brazilian Blossom
1.4 Main Dimensions of Textbook Analysis
1.4.1 Institution as Co-author
1.4.2 Textbook Knowledge as Common Property
Chapter 2: Textbooks Before the Invention of the Printing Press: Orality and Teaching
2.1 The Poles of Orality and Writing
2.2 Mesopotamia
2.3 Egypt
2.4 China
2.5 Greece and Hellenism
2.6 India
2.7 Islamic Cultures
2.8 European Middle Ages
Chapter 3: Textbooks in the Era of the Printing Press: The Emergence of Modern Textbooks
3.1 Conflicts in Introducing the Printing Press
3.2 The First Printed Mathematics Books: For Commercial Context
3.3 First Printed Versions of Euclid’s Elements
3.4 Printing Diagrams
Chapter 4: Differentiation of Textbook Development During Pre-modern Times
4.1 Textbooks for New Publics and for New Areas
4.2 The Growth of Algebra Textbooks
4.3 General Textbooks for Mathematics
4.3.1 The Controversy Between Amauld and Prestet on Negative Quantities
4.3.2 From the Seventeenth to the Eighteenth Century in France
4.4 The Sonderweg in France
4.5 New Areas in Mathematics and Their Textbooks: Analytic Geometry and Differential and Integral Calculus
4.6 Summarising the Stratification of Textbook Publics in Pre-modern Times
Chapter 5: Elements: Elementarisation- Structure of the Discipline
5.1 D’Alembert’s Concept of Élémens
5.2 How Textbooks Came into Being
5.3 Composition of Textbooks
5.4 Textbook Methodology
5.5 How to Use Good Elements in Studying
Chapter 6: The Period of the French Revolution
6.1 The Excessive Enthusiasm for Livres Élémentaires
6.2 The Concours for livres élémentaires
6.3 Results and Effects of the concours
6.4 French State Policy for livres classiques
Untitled
Chapter 7: Lacroix as an Entrepreneur: His Struggle for the Textbook Market
7.1 The Monopoly of Lacroix’s Cours
7.2 Lacroix: A Textbook Author at the Level of the Inventors
7.3 The “Common” Knowledge
7.4 The Quarrel with Legendre About the Market
7.5 The Cultural and Epistemological Pressures: The Case of Algebra
7.6 Methodological Comments
7.7 Translations of Lacroix’s Cours
Chapter 8: Textbook Versus the Autonomy of the Teacher: The Prussian Case
8.1 Independence of the Teachers
8.2 The Local Production of Schoolbooks
8.3 Crelle’s Misunderstanding
8.4 Differentiation of the Schoolbook as a Kind of Publication
Chapter 9: Cultural Specificity of Textbooks: The Case of Legendre in Italy
9.1 The French Anti-euclidean Approach in Geometry and Legendre’s Geometry
9.2 The Decision in Italy for Euclid
9.3 Legendre’s Critics in Italy
9.4 Criticism in Gemany
9.5 The Analytic Against the Synthetic
9.6 Cultural Consequences of the Classicist Conception
Chapter 10: Transmission of Textbooks from Metropoles: The Nineteenth Century
10.1 France
10.2 Spain
10.3 Portugal/Brazil
10.4 Latin America
10.5 United States
10.6 Islamic Countries
10.7 Germany
10.8 Russia
10.9 Greece
10.10 The Netherlands
10.11 England
Chapter 11: An Outlook to the Twentieth Century
11.1 Segmentation and ‘Nationalisation’ of Mathematics to Be Taught
11.2 Interfaces Between School Mathematics and Academic Mathematics
11.3 Who Are the Textbook Authors?
11.4 The Growing Diversification of Textbook Material
11.5 The Textbook Triangle Reassessed
Bibliography
Sources
Publications
List of Figures Which Needed a Reproduction Permission
Index
