Tools and Mathematics

ISBN-13: 9783319023953 / Angielski / Twarda / 2016 / 483 str.

John Monaghan;Luc Trouche;Jonathan M. Borwein

Opis

This book is an exploration of tools and mathematics and issues in mathematics education related to tool use. The book has five parts. The first part reflects on doing a mathematical task with different tools, followed by a mathematician's account of tool use in his work. The second considers prehistory and history: tools in the development from ape to human; tools and mathematics in the ancient world; tools for calculating; and tools in mathematics instruction. The third 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 fourth 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: task and tool design and new forms of activity via connectivity and computer games.

Spis treści

Preface.- 1.Introduction to the book.- 2.Doing mathematics with tools: one task, four tools.-

3.The life of modern Homo Habilis Mathematicus: Experimental computation and visual theorems.- 4.Tools, human development and mathematics .- 5.The development of mat

hematics practices in the Mesopotamian scribal schools.-  6.Discussions of Part A chapters.- 

7. Developments relevant to the use of tools in mathematics.-  8.Constructionism.- 9.Activity theoretic approaches.- 10.Didactics of mathematics: concepts, roots, interactions and dynamics from France.- 11.Discussion of issues in chapters in Part B.-  

12.Integrating tools as an ordinary component of the curriculum in mathematics education.- 13.The calculator debate.- 14.        Tools and mathematics in the real world.- 15.Mathematics teachers and digital tools.- 16.        Tasks and digital tools.- 17.Games: artefacts in gameplay.- 18.Connectivity in mathematics education: Drawing some lessons from the current experiences and questioning the future of the concept.- Epilogue.

O autorze

Jonathan M. Borwein, FRSC is Canada Research Chair in Collaborative Technology at Dalhousie University. He received his Doctorate from Oxford in 1974 and has been on faculty at Waterloo, Carnegie Mellon and Simon Fraser Universities. He has published extensively in optimization, analysis and computational mathematics and has received various prizes both for research and for exposition.

Blurb

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.