This book explores the idea that mathematics educators and teachers are also problem solvers and learners, and as such they constantly experience mathematical and pedagogical disturbances. Accordingly, many original tasks and learning activities are results of personal mathematical and pedagogical disturbances of their designers, who then transpose these disturbances into learning opportunities for their students. This learning-transposition process is a cornerstone of mathematics teacher education as a lived, developing enterprise. Mathematical Encounters and Pedagogical Detours unfold the process and illustrate it by various examples. The book engages readers in original tasks, shares the results of task implementation and describes how these results inform the development of new tasks, which often intertwine mathematics and pedagogy. Most importantly, the book includes a dialogue between the authors based on the stories of their own learning, which triggers continuous exploration of learning opportunities for their students.

Our objective is to publish a book that lays out the theoretical constructs and research methodologies within mathematics education that have been developed by Paul Cobb and explains the process of their development. We propose to do so by including papers in which Cobb introduced new theoretical perspectives and methodologies into the literature, each preceded by a substantive accompanying introductory paper that explains the motivation/rationale for developing the new perspectives and/or methodologies and the processes through which they were developed, and Cobb’s own retrospective comments. In this way the book provides the reader with heretofore unpublished material that lays out in considerable detail the issues and problems that Cobb has confronted in his work, that, from his viewpoint, required theoretical and methodological shifts/advances and provides insight into how he has achieved the shifts/advances. The result will be a volume that, in addition to explaining Cobb’s contributions to the field of mathematics education, also provides the reader with insight into what is involved in developing an aggressive and evolving research program. When Cobb confronts problems and issues in his work that cannot be addressed using his existing theories and frameworks, he looks to other fields for theoretical inspiration. A critical feature of Cobb’s work is that in doing so, he consciously appropriates and adapts ideas from these other fields to the purpose of supporting processes of learning and teaching mathematics; He does not simply accept the goals or motives of those fields. As a result, Cobb reconceptualizes and reframes issues and concepts so that they result in new ways of investigating, exploring, and explaining phenomena that he encounters in the practical dimensions of his work, which include working in classrooms, with teachers, and with school systems. The effect is that the field of mathematics education is altered. Other researchers have found his "new ways of looking" useful to them. And they, in turn, adapt these ideas for their own use. The complexity of many of the ideas that Cobb has introduced into the field of mathematics education can lead to a multiplicity of interpretations by practitioners and by other researchers, based on their own experiential backgrounds. Therefore, by detailing the development of Cobb’s work, including the tensions involved in coming to grips with and reconciling apparently contrasting perspectives, the book will shed additional light on the processes of reconceptualization and thus help the reader to understand the reasons, mechanisms, and outcomes of researchers’ constant pursuit of new insights.

John Mason has been a prominent figure in the research field of mathematics education for several decades. His principal focus has been thinking about mathematical problems, supporting those who wish to foster and sustain their own thinking and the thinking of others.

This volume presents multiple perspectives on the uses of the history of mathematics for teaching and learning, including the value of historical topics in challenging mathematics tasks, for provoking teachers’ reflection on the nature of mathematics, curriculum development questions that mirror earlier pedagogical choices in the history of mathematics education, and the history of technological innovations in the teaching and learning of mathematics. An ethnomathematical perspective on the history of mathematics challenges readers to appreciate the role of mathematics in perpetuating consequences of colonialism. Histories of the textbook and its uses offer interesting insights into how technology has changed the fundamental role of curriculum materials and classroom pedagogies. History is explored as a source for the training of teachers, for good puzzles and problems, and for a broad understanding of mathematics education policy. Third in a series of sourcebooks from the International Commission for the Study and Improvement of Mathematics Teaching, this collection of cutting-edge research, stories from the field, and policy implications is a contemporary and global perspective on current possibilities for the history of mathematics for mathematics education. This latest volume integrates discussions regarding history of mathematics, history of mathematics education and history of technology for education that have taken place at the Commission's recent annual conferences.

Mathematics is generally considered as the only science where knowledge is uni form, universal, and free from contradictions. „Mathematics is a social product - a 'net of norms', as Wittgenstein writes. In contrast to other institutions - traffic rules, legal systems or table manners -, which are often internally contradictory and are hardly ever unrestrictedly accepted, mathematics is distinguished by coherence and consensus. Although mathematics is presumably the discipline, which is the most differentiated internally, the corpus of mathematical knowledge constitutes a coher ent whole. The consistency of mathematics cannot be proved, yet, so far, no contra dictions were found that would question the uniformity of mathematics" (Heintz, 2000, p. 11). The coherence of mathematical knowledge is closely related to the kind of pro fessional communication that research mathematicians hold about mathematical knowledge. In an extensive study, Bettina Heintz (Heintz 2000) proposed that the historical development of formal mathematical proof was, in fact, a means of estab lishing a communicable „code of conduct" which helped mathematicians make themselves understood in relation to the truth of mathematical statements in a co ordinated and unequivocal way.

This book is centrally concerned with how mathematics education is represented and how we understand mathematical teaching and learning with view to changing them. It considers teachers, students and researchers. It explores their mathematical thinking and the concepts that this thought produces. But also how these concepts acquire cultural layers that mediate our apprehension. The book examines some of the linguistic and socio-cultural filters that influence mathematical understanding. But above all it introduces some contemporary theories of human subjectivity, in which subjectivity is seen primarily as consequential to, rather than productive of, our attempts to represent or categorise the world in which we live. That is, our sense of who we are results from our attempts to see ourselves against the various versions of the world that we encounter. Such theories trouble the very notion of mathematical "concepts" as apprehended by "humans". And in foregrounding this concern with subjectivity the book considers mathematics rather differently to styles more familiar in many instances of mathematics education research. The book proposes that mathematics can provoke us to think differently about our world and as a result enable our transformative capacities. Such an orientation may disturb our understanding of what mathematics is, how it exists in an "objective" sense, insofar as mathematical objects can be derived from social filters being applied to the world, but also serve as filters on the world capable of producing new social entities.

An Invitation to Critical Mathematics Education deals with a range of crucial topics. Among these are students’ foreground, landscapes of investigation, and mathematics in action. The book is intended for a broad audience: educators, students, teachers, policy makers, anybody interested in the further development of mathematics education. The book discusses concerns and preoccupation. This way it provides an invitation into critical mathematics education.