| Description |
1 online resource |
| Series |
Mathematics education library |
|
Mathematics education library.
|
| Contents |
Foreword; Preface; Contents; About the Authors; Part I: Setting the Scene; Chapter 1: Introduction to the Book; 1.1 Introduction; 1.2 The Purpose and Scope of This Book; 1.3 What Is a Tool?; 1.3.1 Johnś Attempt to Address This Question; 1.3.2 Lucś Attempt to Address This Question; 1.4 The Structure of the Book; References; Chapter 2: Doing Mathematics with Tools: One Task, Four Tools; 2.1 Introduction; 2.2 Bisecting an Angle with a Straight Edge and a Compass; 2.3 Bisecting an Angle with a Protractor; 2.4 Bisecting an Angle with a Dynamic Geometry System; 2.5 Bisecting an Angle with a Book |
|
Chapter 3: The Life of Modern Homo Habilis Mathematicus: Experimental Computation and Visual Theorems3.1 Introduction; 3.1.1 Who I Am and How I Got That Way; 3.1.2 What Follows; 3.1.3 Some Early Conclusions; 3.2 Visual Theorems and Experimental Mathematics; 3.2.1 Visual Theorems; 3.2.2 On Picture-Writing; 3.2.2.1 Proofs Without Words; 3.3 Experimental Mathematics; 3.3.1 Experimental Mathodology; 3.3.2 When Science Becomes Technology; 3.3.2.1 Minimal Configurations; 3.3.3 Mathematical Discovery (or Invention); 3.3.4 Digital Assistance; 3.3.5 The Twentieth Centuryś Top Ten Algorithms |
|
3.3.6 Secure Knowledge Without Proof3.3.7 Is ̀Free ́Software Better?; 3.4 A Dozen or So Accessible Examples; 3.5 Simulation in Pure Mathematics; 3.5.1 Monte Carlo Simulation of pi; 3.5.2 Finding a Region of Convergence; 3.6 Case Studies I: Dynamic Geometry; 3.6.1 Case Study Ia: Iterative Reflections; 3.6.2 Case Study Ib: Protein Conformation; 3.7 Case Studies II: Numerical Analysis; 3.7.1 Case Study IIa: Trefethenś 100 Digit Challenge; 3.7.2 Case Study IIb: Algorithms for Polylogarithms; 3.8 Case Studies III: Randomish Walks; 3.8.1 Case Study IIIa: Short Walks; 3.8.1.1 The Three-Step Walk |
|
3.8.1.2 The Four-Step Walk3.8.2 Case Study IIIb: Number Walks; 3.8.3 Case Study IIIc: Normality of Stoneham Numbers; 3.9 Conclusion; References; Chapter 4: Tools, Human Development and Mathematics; 4.1 Introduction; 4.2 Tool Use and Phylogenesis; 4.3 Ancient Greece; 4.3.1 Discussion of This Proof; 4.3.2 Tools; 4.3.3 Oral and Written Mathematics; Communities of Practice; 4.4 Ancient Indian Square Roots; 4.5 Abaci; 4.6 Tools for Calculation in Europe Circa 1600; 4.7 Discussion: Insights on Tool Use Over Time; References |
|
Chapter 5: The Development of Mathematics Practices in the Mesopotamian Scribal Schools5.1 Introduction; 5.2 A Critical Moment; 5.3 The Computation Practices and Their Support in Scribal Schools; 5.4 Evidencing Computing Artefacts Complementing the Usage of Tablets and Memory; 5.5 Analysing the Algorithm for Calculating a Reciprocal, a Way for Entering the Spirit of Mesopotomian Computation; ; 5.6 Conclusion and Discussion; References; Chapter 6: Discussions of Part I Chapters; 6.1 Introduction; 6.2 Interactions with John and Jon Follow-Up; 6.2.1 Writing and Mathematics, a Dual Invention? |
| Summary |
This book is an exploration of tools and mathematics and issues in mathematics education related to tool use. The book has four parts. The first part sets the scene with a reflection on doing a mathematical task with different tools, a mathematician's account of tool use in his work and historical considerations of tool use. The second part opens with a broad review of technology and intellectual trends, circa 1970, and continues with three case studies of approaches in mathematics education and the place of tools in these approaches. The third part considers issues related to mathematics instructions: curriculum, assessment and policy; the calculator debate; mathematics in the real world; and teachers' use of technology. The final part looks to the future and digital tools: task design; the importance of artefacts in gameplay; and new forms of activity via connectivity |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (EBSCO, viewed May 12, 2016) |
| Subject |
Mathematics -- Study and teaching.
|
|
MATHEMATICS -- Essays.
|
|
MATHEMATICS -- Pre-Calculus.
|
|
MATHEMATICS -- Reference.
|
|
Mathematics -- Study and teaching
|
| Form |
Electronic book
|
| Author |
Trouche, Luc, author.
|
|
Borwein, Jonathan M., author.
|
| ISBN |
9783319023960 |
|
3319023969 |
|
3319023950 |
|
9783319023953 |
|
