Reviews for Mathematics Education Across Time and Place
"A strikingly original and engaging book about the global, historical and contemporary cultural activity that is the teaching and learning of mathematics. The extensive use throughout of creative non-fiction accounts (focused on such a hyper-rational subject) results in a lively, informative diversity of voices. Highly recommended."

--David Pimm,   author of Speaking Mathematically  and  Symbols and Meaning in School Mathematics
 "Mathematics Education Across Time and Place provides a historical, philosophical, educational, political and societal context about mathematics education over the last two millennia. The book is organized in eight chapters starting with the Greeks and Romans followed by a chapter on the Islamic Influence. The next three chapters take us from the Italian Renaissance to the mathematical practitioners of England to the French Revolution. The last three chapters move to early America, Canada and the twentieth century. The book has twenty-one essays in the form of stories, biographies, autobiographies, dialogues, speeches and letters, which gives the reader the experience and knowledge about mathematics education at different times and places around the world. Though the essays are fictional, they are scholarly writings based on historical documents and professional sources. O’Shea skillfully prefaces each essay with a brief commentary that provides a deeper context about the influence of historical developments and educational reforms on how and what mathematics was taught. So the narrative provides a thread that extends across 23 centuries, and winds through some lived experiences of mathematics educators from Athens to Zimbabwe.

As I read about the lives and the issues the mathematics educators faced, I find that a number of the issues are still relevant in today’s context. Learning mathematics in context with manipulatives is still pedagogically sound as it was a few thousand years ago. “We learnt division by dividing piles of apples between us, and he even seemed to see some mathematical purpose to those wonderful games we played with dice and knucklebones, not to mention the more complex game of chess” (page 10). Examples show how mathematics was used to solve problems in daily lives such as the development of accurate maps, the use of arithmetic in commerce, calculation of latitude and longitude with adoption of astronomy.

Most of the autobiographies included in this book come from an Euro-centric worldview. The inclusion of autobiographies from the Islamic world provides a unique opportunity to bring together Greek mathematics with its emphasis on geometry and number theory, and Hindu mathematics with its numeration system and focus on algebra and trigonometry (page 38). O’Shea acknowledges, “not included is any history pertaining to China, Japan, or India, as few students chose those areas, and reliable sources were difficult to find” (page xviii). We need to know about different worldviews, as “all people do mathematics because all cultures count, locate, measure, design, play, and explain” (page 309). Worldview is an expression of the creative process that connects all things. Indigenous peoples have historically applied the thought process of mathematics within cultural contexts, which are holistic. Most Indigenous cultures have an orientation to learning that is metaphorically represented in its art forms, its way of community, its language, and its way of understanding itself in relationship to its natural environment.

Thomas O’Shea has been retired for a number of years but his passion for mathematics education continues. This book is his labour of love; he truly is a maestro dei maestri (teacher of teachers). He achieves the purpose of the book to help mathematics teachers, teacher educators, and interested members of the public appreciate the path that we have followed to the present state of mathematics education. His use of imagination and story telling lets one understand the historical and social context for schools, schooling, and the place of mathematics in schools. The book is a pleasure to read; it enables one to reflect on the critical role of mathematical understanding in our personal and professional lives, in our history, and in our culture. I wholeheartedly recommend it to those interested in the teaching and learning of mathematics. The book is bound to expand the horizons of anyone interested in mathematics as a human endeavor."

--Kanwal Neel,  winner of the 1996 Prime Minister's Award for Teaching Excellence and in 2012  was awarded the Queen Elizabeth Diamond Jubilee Medal.



 Mathematics Education Across Time & Place. Over Two Millennia from Athens to Zimbabwe, by Thomas O’Shea. Victoria, Canada: FriesenPress, 2016.  In Canadian Mathematics Education Study Group Newsletter, May 2017.
 
Luis Radford, Université Laurentienne, Ontario, Canada
 
          Several years ago, Canadian educator Ted Aoki complained about the technological turn that education had taken since the dawn of the 20th century. Indeed, by then, several countries in Europe, North America, Eurasia and other parts of the world were moving quickly towards systematic and complex industrial forms of production. Such a colossal task required to rethink their educational systems. “Reform” was the name under which the curricular changes were conducted. Within this technologically oriented frame of mind, mathematics in those countries (and others that followed later) came to occupy an unprecedented place in the curriculum, often stealing school hours that so far were allocated to other disciplines. In 1914, the mathematician Gaston Darboux, president of the Academy of Science of France, in a speech addressed to the participants of an international conference on the teaching of mathematics, told his audience that teachers of literature were complaining that “Mathematics has become something very invasive” (Darboux, 1914, p. 193). And with this invasion came not only the problem of what to teach, but also how to teach it. It is at this precise moment that Ted Aoki’s complaint becomes relevant, as Aoki was among those who first understood with great clarity, and challenged forcefully, the educational orientations that ended up shaping the school of today in the manner of an industry and a consumerist business “that reduces human competence to instrumental reason and instrumental action” (Kaori in Pinar & Irwin, 2005, p. 113). Any foreseeable change can come only from a deep and daring collective reflection on mathematics, and its place and orientation in our schools. Certainly, such a reflection has to be carried out at different levels. We need to make teachers, prospective teachers, and other educational actors sensitive to the cultural, historical, political, and economic ideas underpinning contemporary education in general and mathematics education in particular. We need to reach deeper levels of social consciousness to envision mathematics education differently and to transform it in practice.

          Thomas O’Shea’s book Mathematics Education Across Time & Place is a most welcome contribution to this endeavour. Indeed, in order to envision mathematics education differently, we need to become aware of how mathematics education was practised before, in other contexts, and to understand how and why we have ended up where we are today. Without such a historical understanding no real grasp of reality seems possible. O’Shea’s book puts us on the right track. “The purpose of this book,” O’Shea notes, “is to help mathematics teachers, teacher educators, and interested members of the public appreciate the path that we have followed to the present state of mathematics education” (p. xx1). In the Preface, O’Shea mentions briefly his own trajectory, from Saskatchewan to Montreal to Australia to Malaysia to British Columbia. At Simon Fraser University, O’Shea had the opportunity to work with our late colleague Sandy Dawson, one of the most impressive mathematics educators I have had the chance to meet, and Len Berggren, a leading scholar in the history of Arabic Mathematics. The book Mathematics Education Across Time & Place is a result of the course Foundations of Mathematics Education that O’Shea designed, a task that was not accomplished without difficulties. As O’Shea notes,

                   As I designed the course, I recognized that students tend to think about mathematics education only in the day-to-day context                      in which they themselves are immersed. Much of what passes for professional development consists of struggles to contend                      with changes in the prescribed curriculum or with the most recent fashion in teaching. Little time is spent on trying to                                      understand larger societal, political, and educational forces that affect the curriculum and may help teachers to respond                                  thoughtfully to the question posed by students, “Why do we have to learn this stuff? I wished to devise some means to           
                   free them from the present and immerse them in a different time and place (O’Shea, 2016, p. xvi-xvii)

            To achieve this goal O’Shea devised an assignment: he asked his students to assume that they were mathematics educators at a certain point in history, and to prepare a mini-autobiography that should convey a sense of what life was like at the chosen historical time. In the autobiography, the students were invited to describe the societal conditions under which they taught, their approach to teaching, the students, and the mathematical content that they taught. They were free to investigate a real historical individual or to invent a fictional character. The assignment gave the students the opportunity to plunge into a different historical epoch, a different country with different needs, different people, and different conceptions of education. In brief, the assignment gave the students the opportunity to make the marvelous experience of alterity —the encounter of the Other— the first and unavoidably step towards the encounter with ourselves.

             The book presents a compilation organized by time and place of what the students produced: stories told as “straight autobiographies, as diaries, as letters to their grandchildren, as fragments of text found in an attic, and as poetry” (p. xvii). The chapters include Greece and Rome, Islam and its influence, the Italian Renaissance, 16th and 15th century mathematical practitioners of England, the French revolution, early America, Canada, and the 20th century. The students’ narratives are supported by an historical investigation of education and its cultural context. The Reference Section at the end of the book lists the historical sources and is certainly very valuable to those interested in the history of education, mathematics, and mathematics education. To give an example of the narratives, one of the sections of Chapter 3 (The Italian Renaissance) starts with an introduction of the character: “My name is Vitorio de la Francesca. I was born in Venice, Anno Domini 1614. My father was a wealthy merchant of silk fabrics.” The narrative provides an insightful view of the social, cultural, and intellectual contexts. It allows us to see a society revolving spiritually around the Church and economically around commerce and the emerging Western form of trade and craft capitalism —all tied up by the sense of family and responsibility that was the hallmark of Renaissance culture and its unresolved ethical tension between humanism and the new drive of profit. The narrative also brings forward the increasing social role of books that was to play such an essential role in the historical consolidation of the written tradition—one that left an indelible and profound imprint on Western thought: “My father was a passionate lover of books and he would always bring chests full of books from his travel to the East” (p. 97). The narrative brings back to life, in a fascinating and vivid manner, the historical opposition between those who defended the  use of Roman numerals and those who introduced the Arabic-Hindu numeric system, placing numbers and mathematical practices in their social and cultural contexts.

               The book Mathematics Education Across Time & Place is undoubtedly a great contribution to mathematics education. It invites us to see our discipline through historical lenses and enables us to imagine new ways to start moving beyond the technocratic stance in which we find ourselves currently immersed. The book will certainly be of interest to mathematicians, mathematics educators, teachers, and educators in general.

References
Darboux, G. (1914). Discours à la réunion d'ouverture de la conférence internationale de l'enseignement mathématique. L'Enseignement                      Mathématique, 16, 192-197.
Pinar, W. F., & Irwin, R. L. (Eds.) (2005). Curriculum in a new key: The collected works of Ted T. Aoki. Mahwah: Lawrence Erlbaum.


--Luis Radford received Laurentian University’s 2004-05 Research Excellence Award and the 2011 ICMI Hans Freudenthal Medal. From 2012 to 2016, he was Chair of the International Study Group on the Relations Between the History and Pedagogy of Mathematics (HPM). HPM is an affiliate group of the International Commission on Mathematical Instruction (ICMI). He is now vice-president of ICMI.