عنوان

Interfaces between mathematical practices and mathematical education /

303001617X

3030016188

9783030016173

9783030016180

3030016161

9783030016166

Interfaces between mathematical practices and mathematical education /

[Book]

Gert Schubing, editor.

Cham, Switzerland :

Springer,

[2019]

1 online resource (201 pages)

International studies in the history of mathematics and its teaching

Includes bibliographical references and indexes.

Intro; Introduction; Contents; About the Authors; Chapter 1: Foundations of Mathematics Buried in School Garbage (Southern Mesopotamia, Early Second Millennium BCE); 1 Basic Knowledge, Fundamental Knowledge; 2 The Mathematical Curriculum in Nippur Schools; 2.1 Elementary Level; Metrological Tables; A Multiplication Table; A Table of Reciprocal (ERM 14645); 2.2 Intermediate Level; An Extraction of Reciprocals; The Calculation of the Surface of a Square; 2.3 Advanced Level; 2.4 Linear Paradigm; 3 The Role of Factorization in Calculating Reciprocals.

4 The Role of Coefficients in Problems of Volumes5 Conclusion: The Linear Paradigm and How to Get Out of It; Appendix; References; Chapter 2: From the Practice of Explanation to the Ideology of Demonstration: An Informal Essay; 1 Arguing from the Locally Obvious; 2 Critique; 3 Demonstration, Critique, and the Culture of Liberal Arts; 4 Axiomatization; 5 And Then?; References; Chapter 3: Catholicism and Mathematics in the Early Modernity; 1 The Place of Mathematics in Seventeenth Century Culture; 2 Institutional Aspects; 3 Accepting the Mysteries of Faith; 4 Against Scepticism.

5 Usefulness to Theology6 Philosophical Conceptions; 7 Conclusions; References; Chapter 4: "Je n'ai point ambitionnée d'être neuf": Modern Geometry in Early Nineteenth-Century French Textbooks; 1 Introduction; 2 Historiography of Mathematics Textbooks; 3 Finding Textbooks; 4 Claims for Novelty By Textbook Authors; 4.1 The Majority View; 4.2 Textbooks with Modern Geometry; Dupin; Garnier; Biot; Vincent; Didiez; Bergery; Terquem; 5 New Objects; 5.1 Poles and Polars; Copy and Paste; Constructive Innovations; New Applications and Properties; 5.2 Centers and Axes; Similitude Without Radicals.

Chapter 6: A Multiple Perspective Approach to History of Mathematics: Mathematical Programming and Rashevsky's Early Development of Mathematical Biology in the Twentieth Century1 Introduction; 2 A Multiple Perspectives Approach to History of Mathematics; 3 Two Episodes: Mathematical Programming and Mathematical Biology; 3.1 Mathematical Programming in the USA and the Significance of World War II; 3.2 Beginning of Mathematical Biology and Interdisciplinary Research; 3.3 The Significance of Teaching and Education; 4 Conclusion; References.

Uniting Similitude with Radicals5.3 Imaginaries; 6 Reception; 7 Conclusion; References; Chapter 5: The Impact of Teaching Mathematics Upon the Development of Mathematical Practices; 1 Introduction: Issues of Methodology; 2 Examples for Introducing the Interface Approach; 3 The Notion of Element and of Elementarisation; 4 The Impact of Teacher Education; 5 An Early Teaching of Set Theory in Germany; 6 Non-Euclidean Geometry in German Gymnasien; 6.1 About the Contents of Wagner's Schoolbook; 7 Conclusion; References; Sources; Publications.

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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 20th 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.

Springer Nature

com.springer.onix.9783030016173

9783030016166

Mathematics-- Study and teaching.

Education.

Mathematics.

EDU029010

JNU

JNU

PB

Schubring, Gert

20200823073238.0

pn

[Book]

Y