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Edited by Jinfa Cai, Gabriele Kaiser, Bob Perry and Ngai-Ying Wong

What is effective mathematics teaching? This book represents the first purposeful cross-cultural collection of studies to answer this question from teachers’ perspectives. It focuses particularly on how teachers view effective teaching of mathematics. Teachers’ voices are heard and celebrated throughout the studies reported in this volume. These studies are drawn from many parts of the world representing both Eastern and Western cultural traditions. The editors and authors have deliberately included the views of teachers and educators from different cultural backgrounds, taking into account that beliefs on effective mathematics teaching and its features are highly influenced by one’s own culture.
The book will provide readers and scholars with the stimulus to take the ideas presented and expand on them in ways that help improve mathematics education for children, teachers and researchers in both the East and the West.

Rina Zazkis and Peter Liljedahl

This book presents storytelling in mathematics as a medium for creating a classroom in which mathematics is appreciated, understood, and enjoyed. The authors demonstrate how students’ mathematical activity can be engaged via storytelling. Readers are introduced to many mathematical stories of different kinds, such as stories that provide a frame or a background to mathematical problems, stories that deeply intertwine with the content, and stories that explain concepts or ideas. Moreover, the authors present a framework for creating new stories, ideas for using and enriching existing stories, as well as several techniques for storytelling that make telling more interactive and more appealing to the learner. This book is of interest for those who teach mathematics, or teach teachers to teach mathematics. It may be of interest to those who like stories or like mathematics, or those who dislike either mathematics or stories, but are ready to reconsider their position.

How should I know?

Preservice Teachers' Images of Knowing (by Heart ) in Mathematics and Science

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Kathleen T. Nolan

Elementary preservice teachers’school experiences of mathematics and science have shaped their images of knowing, including what counts as knowledge and what it means to know (in) mathematics and science. In this book, preservice teachers’ voices challenge the hegemony of official everyday narratives relating to these images.
The book is written as a parody of a physical science textbook on the topic of light, presenting a kaleidoscope of elementary preservice teachers’ narratives of knowing (in) mathematics and science. These narratives are tied together by the metaphorical thread of the properties of light, but also held apart by the tensions and contradictions with/in such a critical epistemological exploration. Through a postmodern lens, the only grand narrative that could be imag(in)ed for this text is one in which the personal lived experience narratives of the participants mingle and interweave to create a sort of kaleidoscope of narratives. With each turn of a kaleidoscope, light’s reflection engenders new patterns and emergent designs. The narratives of this research text highlight patterns of exclusion, gendered messages, binary oppositions, and the particle nature and shadowy texture of knowing (in) mathematics and science. The presentation format of the book emphasizes the reflexive and polyphonic nature of the research design, illustrated through layers of spoken text with/in performative text with/in metaphorical text.
The metaphor of a kaleidoscope is an empowering possibility for a critical narrative written to both engage and provoke the reader into imag(in)ing a critical journey toward possibilities for a different “knowing by heart” in mathematics and science and for appreciating lived experience narratives with/in teacher education.

Theorems in School

From History, Epistemology and Cognition to Classroom Practice

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Edited by Paulo Boero

During the last decade, a revaluation of proof and proving within mathematics curricula was recommended; great emphasis was put on the need of developing proof-related skills since the beginning of primary school.
This book, addressing mathematics educators, teacher-trainers and teachers, is published as a contribution to the endeavour of renewing the teaching of proof (and theorems) on the basis of historical-epistemological, cognitive and didactical considerations. Authors come from eight countries and different research traditions: this fact offers a broad scientific and cultural perspective.
In this book, the historical and epistemological dimensions are dealt with by authors who look at specific research results in the history and epistemology of mathematics with an eye to crucial issues related to educational choices. Two papers deal with the relationships between curriculum choices concerning proof (and the related implicit or explicit epistemological assumptions and historical traditions) in two different school systems, and the teaching and learning of proof there.
The cognitive dimension is important in order to avoid that the didactical choices do not fit the needs and the potentialities of learners. Our choice was to firstly deal with the features of reasoning related to proof, mainly concerning the relationships between argumentation and proof.
The second part of this book concentrates on some crucial cognitive and didactical aspects of the development of proof from the early approach in primary school, to high school and university. We will show how suitable didactical proposals within appropriate educational contexts can match the great (yet, underestimated!) young students’ potentialities in approaching theorems and theories.

Edited by Ángel Gutiérrez and Paulo Boero

"This volume is a compilation of the research produced by the International Group for the Psychology of Mathematics Education (PME) since its creation, 30 years ago. It has been written to become an essential reference for Mathematics Education research in the coming years.
The chapters offer summaries and synthesis of the research produced by the PME Group, presented to let the readers grasp the evolution of paradigms, questions, methodologies and most relevant research results during the last 30 years. They also include extensive lists of references. Beyond this, the chapters raise the main current research questions and suggest directions for future research.
The handbook is divided into five sections devoted to the main research domains of interest to the PME Group. The first three sections summarize cognitively oriented research on learning and teaching specific content areas, transversal areas, and based on technology rich environments. The fourth section is devoted to the research on social, affective, cultural and cognitive aspects of Mathematics Education. Finally, the fifth section includes two chapters summarizing the PME research on teacher training and professional life of mathematics teachers.
The volume is the result of the effort of 30 authors and 26 reviewers. Most of them are recognized leading PME researchers with great expertise on the topic of their chapter. This handbook shall be of interest to both experienced researchers and doctoral students needing detailed synthesis of the advances and future directions of research in Mathematics Education, and also to mathematics teacher trainers who need to have a comprehensive reference as background for their courses on Mathematics Education.

Making Connections

Comparing Mathematics Classrooms Around the World

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Edited by David Clarke, Jonas Emanuelsson, Eva Jablonka and Ida Ah Chee Mok

In this book, comparisons are made between the practices of classrooms in a variety of different school systems around the world. The abiding challenge for classroom research is the realization of structure in diversity. The structure in this case takes the form of patterns of participation: regularities in the social practices of mathematics classrooms. The expansion of our field of view to include international rather than just local classrooms increases the diversity and heightens the challenge of the search for structure, while increasing the significance of any structures, once found. In particular, this book reports on the use of ‘lesson events’ as an entry point for the analysis of lesson structure. International research offers opportunities to study settings and characteristics untenable in the researcher’s local situation. Importantly, international comparative studies can reveal possibilities for practice that would go unrecognized within the established norms of educational practice of one country or one culture. Our capacity to conceive of alternatives to our current practice is constrained by deep-rooted assumptions, reflecting cultural and societal values that we lack the perspective to question. The comparisons made possible by international research facilitate our identification and interrogation of these assumptions. Such interrogation opens up possibilities for innovation that might not otherwise be identified, expanding the repertoire of mathematics teachers internationally, and providing the basis for theory development.

Mathematics Classrooms in Twelve Countries

The Insider's Perspective

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Edited by David Clarke, Christine Keitel and Yoshinori Shimizu

This book reports the accounts of researchers investigating the eighth grade mathematics classrooms of teachers in Australia, China, the Czech Republic, Germany, Israel, Japan, Korea, The Philippines, Singapore, South Africa, Sweden and the USA. This combination of countries gives good representation to different European and Asian educational traditions, affluent and less affluent school systems, and mono-cultural and multi-cultural societies. Researchers within each local group focused their analyses on those aspects of practice and meaning most closely aligned with the concerns of the local school system and the theoretical orientation of the researchers. Within any particular educational system, the possibilities for experimentation and innovation are limited by more than just methodological and ethical considerations: they are limited by our capacity to conceive possible alternatives. They are also limited by our assumptions regarding acceptable practice. These assumptions are the result of a long local history of educational practice, in which every development was a response to emergent local need and reflective of changing local values. Well-entrenched practices sublimate this history of development. The Learner’s Perspective Study is guided by a belief that we need to learn from each other. The resulting chapters offer deeply situated insights into the practices of mathematics classrooms in twelve countries: an insider’s perspective.