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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.
Preface
Why Study Historical Books Intended for Teaching?
Textbooks as Interface
Social History
Methods for Textbook Analysis
What Is Meant by ‘Context’?
Hermeneutics
The Development of Hermeneutics
A Subjectivist Variant Dilthey, Heidegger, Gadamer
Questioning this Variant in Science
Material or Objective Hermeneutics
A Brazilian Blossom
Main Dimensions of Textbook Analysis
Institution as Co-author
Textbook Knowledge as Common Property
Textbooks Before the Invention of the Printing Press Orality and Teaching
The Poles of Orality and Writing
Mesopotamia
Egypt
China
Greece and Hellenism
India
Islamic Cultures
European Middle Ages
Textbooks in the Era of the Printing Press The Emergence of Modern Textbooks
Conflicts in Introducing the Printing Press
The First Printed Mathematics Books For Commercial Context
First Printed Versions of Euclid’s Elements
Printing Diagrams
Differentiation of Textbook Development During Pre-modern Times
Textbooks for New Publics and for New Areas
The Growth of Algebra Textbooks
General Textbooks for Mathematics
The Controversy Between Amauld and Prestet on Negative Quantities
From the Seventeenth to the Eighteenth Century in France
The Sonderweg in France
New Areas in Mathematics and Their Textbooks Analytic Geometry and Differential and Integral Calculus
Summarising the Stratification of Textbook Publics in Pre-modern Times
Elements Elementarisation- Structure of the Discipline
D’Alembert’s Concept of Élémens
How Textbooks Came into Being
Composition of Textbooks
Textbook Methodology
How to Use Good Elements in Studying
The Period of the French Revolution
The Excessive Enthusiasm for Livres Élémentaires
The Concours for livres élémentaires
Results and Effects of the concours
French State Policy for livres classiques
Untitled
Lacroix as an Entrepreneur His Struggle for the Textbook Market
The Monopoly of Lacroix’s Cours
Lacroix A Textbook Author at the Level of the Inventors
The “Common” Knowledge
The Quarrel with Legendre About the Market
The Cultural and Epistemological Pressures The Case of Algebra
Methodological Comments
Translations of Lacroix’s Cours
Textbook Versus the Autonomy of the Teacher The Prussian Case
Independence of the Teachers
The Local Production of Schoolbooks
Crelle’s Misunderstanding
Differentiation of the Schoolbook as a Kind of Publication
Cultural Specificity of Textbooks The Case of Legendre in Italy
The French Anti-euclidean Approach in Geometry and Legendre’s Geometry
The Decision in Italy for Euclid
Legendre’s Critics in Italy
Criticism in Gemany
The Analytic Against the Synthetic
Cultural Consequences of the Classicist Conception
Transmission of Textbooks from Metropoles The Nineteenth Century
France
Spain
Portugal/Brazil
Latin America
United States
Islamic Countries
Germany
Russia
Greece
The Netherlands
England
An Outlook to the Twentieth Century
Segmentation and ‘Nationalisation’ of Mathematics to Be Taught
Interfaces Between School Mathematics and Academic Mathematics
Who Are the Textbook Authors?
The Growing Diversification of Textbook Material
The Textbook Triangle Reassessed
Bibliography
Sources
Publications
List of Figures Which Needed a Reproduction Permission
Index