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Tools and Mathematics: Instruments for Learning

John Monaghan, Luc Trouche, and Jonathan M. Borwein
Publication Date: 
Number of Pages: 
Mathematics Education Library
[Reviewed by
Woong Lim
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Tools and Mathematics: Instruments for Learning is one of a kind, serving as the encyclopedia of learning tools in mathematics. The volume of the book is quite daunting, with a total of 19 chapters, each very dense with content.

  • Part 1 (6 chapters) provides an overview of the book and discusses tool use in the history of mathematics.
  • Part 2 (5 chapters) reviews modern tools and theories in the learning of mathematics such as activity theory, the notions of situation and milieu, and the instrumental approach.
  • Part 3 (5 chapters) debates issues related to using tools in teaching mathematics with efforts to connect the epistemology and history of using tools to the practice of teaching mathematics.
  • Part 4 (3 chapters) focuses on the use of digital tools in mathematics and discusses emerging opportunities to teach and learn mathematics through the use of technology.

Classroom teachers may find this book too theoretical and philosophical; this may be especially true when looking for practical ideas to teach through the use of technology. I believe, however, that this book is a must-have reference for researchers and faculty in mathematics education. First, each chapter is rich with rich data, illustrations, history, mathematics, and critical perspectives, taking the reader into the minds of leading experts of tool use in mathematics. Second, and related, each part of the book has a discussion chapter that helps the reader reflect on preceding chapters and connect to emerging or related critical issues. In particular, I enjoyed reading the dialogues among the authors in these discussion chapters, as they provide intimate access to the thinking and humors of several brilliant minds. Third, the extensive references cited in the book could be an important source of future readings for novice academics, especially those within the U.S. context. Relying too much on recent studies for a literature review sometimes leads us to lose perspective on history and origin of the questions.

The authors exemplify how to capture the grand idea of tool use in mathematics education. Thanks to the breadth and depth of the book, this book will be successful as a course text or reference on your bookshelf. If you are a graduate student with interest in technology in mathematics education, you would appreciate the first six chapters to build your theoretical basis. I also recommend reading chapter 19 for new research ideas. If you are teaching mathematics education seminars, no matter what theories or practices your course may cover, I am confident you will find most chapters quite useful for a reading assignment.

Woong Lim ( is an Assistant Professor of Mathematics Education at University of New Mexico. His research interests include mathematics teacher education; and discourse, language, and equity in the mathematics classroom.

See the table of contents in the publisher's webpage.