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Roza Leikin, Abraham Berman and Boris Koichu

This book breaks through in the field of mathematical creativity and giftedness. It suggests directions for closing the gap between research in the field of mathematics education and research in the field of creativity and giftedness. It also outlines a research agenda for further research and development in the field.
The book consists of a balanced set of chapters by mathematicians, mathematics educators, educational psychologists and educational researchers. The authors of different chapters accept dynamic conception of creativity and giftedness.
The book provides analysis of cognitive, affective and social factors associated with the development of creativity in all students and with the realisation of mathematical talent in gifted students. It contains theoretical essays, research reports, historical overviews, recommendations for curricular design, and insights about promotion of mathematical creativity and giftedness at different levels.
The readers will find many examples of challenging mathematical problems intended at developing or examining mathematical creativity and giftedness as well as ideas for direct implementation in school and tertiary mathematics courses. They will also find theoretical models that can be used in researching students’ creativity and giftedness. Research reports enlighten relationships between excellence in mathematics and creativity and examine different aspects of inquiry-based environment as a powerful way for developing mathematical creativity in school students. The readers can also learn about characteristics of creativity of research mathematicians.

Words and Worlds

Modeling Verbal Descriptions of Situations

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Edited by Lieven Verschaffel, Brian Greer, Wim Van Dooren and Swapna Mukhopadhyay

In this book, the reader is invited to enter a strange world in which you can tell the age of the captain by counting the animals on his ship, where runners do not get tired, and where water gets hotter when you add it to other water. It is the world of a curious genre, known as "word problems" or "story problems". It originated in the ancient civilizations of Egypt, China, and India, and is the subject of daily rituals among students and teachers in mathematics classrooms all around the world. An international group of scholars with a shared interest in this phenomenon explore multiple aspects of this world from multiple perspectives. These discussions take us deep into philosophical issues of the relationships between words, mathematical systems, and the physical and social worlds we all inhabit. Empirical investigations are reported that throw light on how students and their teachers experience and interpret this activity, raising profound questions about the nature and purposes of mathematics teaching/learning in general and how it could be improved.

Nordic Research in Mathematics Education

Proceedings from NORMA08 in Copenhagen, April 21-April 25, 2008

Edited by Carl Winsløw

This volume presents the “state-of-the-art” of Nordic research on mathematics education within four broadly defined areas:
the study and design of mathematics teaching in classrooms
the identity and education of mathematics teachers
the use of new technology in mathematics education
meanings and challenges of providing mathematical education to all citizens in modern societies.
It provides the reader with insights into research done not only by scholars from the Nordic countries (Denmark, Finland, Norway, Sweden and Iceland), but also by colleagues from the rest of Europe—and even other parts of the world.
While the principal research questions addressed are universal in nature, their investigation in concrete contexts will inevitably relate to more contingent issues and conditions. This book offers both in-depth view into the reality of mathematics teaching in the settings studied by the authors, syntheses by world renowned scholars of current problems and methods within each of the four areas, and cross-links to studies done in different countries, as represented both by this book and by the wealth of referenced literature it draws upon. Each of the book’s four sections therefore provides rich material for studies within the corresponding areas, for the beginner as well as for the expert.
The chapters of the book result from the work of the fifth Nordic congress in research on mathematics education, which was held in Copenhagen in April 2008. It includes 32 full research papers, 8 agendas and reports from discussions in working groups, and 22 short communications.

The Handbook of Mathematics Teacher Education: Volume 4

The Mathematics Teacher Educator as a Developing Professional

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Edited by Barbara Jaworski and Terry Wood

The Handbook of Mathematics Teacher Education, the first of its kind, addresses the learning of mathematics teachers at all levels of schooling to teach mathematics, and the provision of activity and programmes in which this learning can take place. It consists of four volumes.
Volume 4 of this handbook has the title The Mathematics Teacher Educator as a Developing Professional. The volume seeks to complement the other three volumes by focusing on knowledge and roles of teacher educators working with teachers in teacher education processes and practices. In this respect it is unique. Chapter authors represent a community of teacher educators world wide who can speak from practical, professional and theoretical viewpoints about what it means to promote teacher education practice.
The volume is in 3 main sections. In the first we focus on Challenges to and Theory in Mathematics Teacher Education. Here authors write from perspectives of theory and/or challenge and relate this to examples and insights from their practice. The second section, Reflection On Developing as a Mathematics Teacher Educator has four autobiographical chapters in which authors delineate their experiences as teacher educators and relate these to theoretical and/or moral standpoints. In Section 3, Working With Prospective and Practising Teachers: What We Learn; What We Come to Know, authors write from perspectives on practice—in many cases, the practices in which they themselves have engaged—and relate this to theoretical perspectives and rationales for teacher education programmes.
The volume also has an introductory chapter in which the purpose and content of the volume is set out, and a final chapter that syntheses themes and issues from the chapters as a whole, offering an overview of the field and suggesting future directions.
Bibliographical Information for the complete set:
VOLUME 1:
Knowledge and Beliefs in Mathematics Teaching and Teaching Development
Peter Sullivan, Monash University, Clayton, Australia and Terry Wood, Purdue University, West Lafayette, USA (eds. )
paperback: 978-90-8790-541-5, hardback: 978-90-8790-542-2, ebook: 978-90-8790-543-9
VOLUME 2:
Tools and Processes in Mathematics Teacher Education
Dina Tirosh, Tel Aviv University, Israel and Terry Wood, Purdue University, West Lafayette, USA (eds. )
paperback: 978-90-8790-544-6, hardback: 978-90-8790-545-3, ebook: 978-90-8790-546-0
VOLUME 3:
Participants in Mathematics Teacher Education: Individuals, Teams, Communities and Networks
Konrad Krainer, University of Klagenfurt, Austria and Terry Wood, Purdue University, West Lafayette, USA (eds. )
paperback: 978-90-8790-547-7, hardback: 978-90-8790-548-4, ebook: 978-90-8790-549-1
VOLUME 4:
The Mathematics Teacher Educator as a Developing Professional
Barbara Jaworski, Loughborough University, UK and Terry Wood, Purdue University, West Lafayette, USA (eds. )
paperback: 978-90-8790-550-7, hardback: 978-90-8790-551-4, ebook: 978-90-8790-552-1

Philosophy, Learning and the Mathematics Curriculum

Dialectal Materialism and Pragmatism related to Chinese and U.S. Mathematics Curriculum

Xuehui Xie and Phil Francis Carspecken

Mathematics curriculums used in progressive classrooms of the United States and in classrooms of the People’s Republic of China presuppose markedly different philosophies. Xie and Carspecken reconstruct different assumptions operating implicitly within mathematics curriculums developed by the Ministry of Education in China and NCTM in the United States. Each curriculum is constructed upon a deep structure holistically integrating presuppositions about the nature of the human self, society, learning processes, language, concepts, human development, freedom, authority and the epistemology and ontology of mathematical knowledge. Xie and Carspecken next present an extended discussion of the two main philosophical traditions informing these curriculums: dialectical materialism in the case of the Chinese mathematics curriculum, and Dewey’s instrumental pragmatism in the case of NCTM. Both philosophies were developed as movements out of Hegelian idealism while retaining the anti-dualist and anti-empiricist insights of Hegel’s thought. The history of dialectical materialism and Dewey’s instrumentalism is carefully examined by the authors to identify both similarities and sharp differences in the resulting mature philosophies. Drawing upon more recent philosophies of intersubjectivity (Brandom, Habermas) and dialectical materialist psychologies (Vygotsky, Luria), the authors conclude this book with arguments for overcoming the limitations of a purely instrumentalist framework and for expanding potentialities implicit within dialectical philosophies. This book will be of value to a broad audience, including mathematics educators, philosophers, curriculum theorists, social theorists, and those who work in comparative education and learning science.

The Psychology of Mathematics Education

A Psychoanalytic Displacement

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Edited by Tony M. Brown

This book paints an alternative and contemporary portrait of psychology within mathematics education, drawing on psychoanalytic practices and theory. Mathematics education is still a fairly new social science that began as an adjunct to the practice of mathematics in schools some forty years ago, defined by a marriage with cognitive psychology. As a consequence school mathematics has often been seen as a scientific enterprise centred on the operation of individual minds confronting mathematical ideas. Meanwhile, psychoanalysis had earlier come into existence through the work of Sigmund Freud. And for much of his life Freud had similarly seen his work as scientific, a view that later fuelled mainstream practices in psychology. Yet Freud’s engagement with his patients combined with his literary capabilities produced surprising results defining humans in ways that transcended mere scientific assessment. Rather his accounts of humans weaved a rich social tapestry in which individuals were understood relationally to those who shared their world. And through re-telling the story lines of their lives individuals were able to create alternative futures. This dimension of Freud’s work provoked an alternative tradition, best exemplified in the work of Lacan, in which narrative-based understandings linking humans to the social world replaced cognitive models centred on controlling individuals through particular understandings of normality. Through its eleven chapters this book provides accounts of how children, teachers, researchers and mathematical learning can be understood differently, towards emphasising how they are each consequential to the many ways in which the world can be created and described.

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Edited by Helen Forgasz, Anastasios Barkatsas, Alan J. Bishop, Barbara Clarke, Stephen Keast, Wee Tiong-Seah and Peter Sullivan

Every four years, beginning in 1984, the Mathematics Education Research Group of Australasia (MERGA) produces a review of Australasian research in mathematics education. The authors of the chapters in this volume have summarised and critiqued research conducted during the period 2004-2007. The research foci for the period are reflected in the chapter titles. Working under tight funding opportunities and the shadow of demanding research accountability measures, the research undertaken has, nonetheless, been rigorous, far-ranging, and at the cutting edge. In bringing this regular review of the best of Australasian mathematics education to a broader international audience for the first time, readers will recognise the outstanding contributions made by Australasian mathematics education researchers and the potential their findings have to inform and direct future directions in the field.

Semiotics in Mathematics Education

Epistemology, History, Classroom, and Culture

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Edited by Luis Radford, Gert Schubring and Falk Seeger

Current interest in semiotics is undoubtedly related to our increasing awareness that our manners of thinking and acting in our world are deeply indebted to a variety of signs and sign systems (language included) that surround us.
Since mathematics is something that we accomplish through written, oral, bodily and other signs, semiotics appears well suited to furthering our understanding of the mathematical processes of thinking, symbolizing and communicating. Resorting to different semiotic perspectives (e. g., Peirce’s, Vygotsky’s, Saussure’s), the authors of this book deal with questions about the teaching and learning of mathematics as well as the history and epistemology of the discipline. Mathematics discourse and thinking and the technologically-mediated self of mathematical cultural practices are examined through key concepts such as metaphor, intentionality, gestures, interaction, sign-use, and meaning.
The cover picture comes from Jacob Leupold’s (1727) Theatrum Arithmetico-Geometrico. It conveys the cultural, historical, and embodied aspects of mathematical thinking variously emphasized by the contributors of this book.

Edited by Gerald Kulm

This book presents a coherent collection of research studies on teacher knowledge and its relation to instruction and learning in middle-grades mathematics. The authors provide comprehensive literature reviews on specific components of mathematics knowledge for teaching that have been found to be important for effective instruction. Based on the analysis of video data collected over a six-year project, the chapters present new and accessible research on the learning of fractions, early concepts of algebra, and basic statistics and probability.

The three sections of the book contain chapters that address research on the development of mathematics knowledge for teaching at the undergraduate level, instructional practices of middle-grades teachers, and the implications of teacher knowledge of mathematics for student learning. The chapters are written by members of a research team led by the Editor that has been working for the past six years to develop practical and useful theories and findings on variables that affect teaching and learning of middle grades mathematics.

Mathematics knowledge for teaching is a topic of great current interest. This book is a valuable resource for mathematics education researchers, graduate students, and teacher educators. In addition, professional developers and school district supervisor and curriculum leaders will find the concrete examples of effective teaching strategies useful for teacher workshops.

Edited by Erkki Pehkonen, Maija Ahtee and Jari Lavonen

The Finnish students’success in the first PISA 2000 evaluation was a surprise to most of the Finns, and even people working in teacher education and educational administration had difficulties to believe that this situation would continue. Finland’s second success in the next PISA 2003 comparison has been very pleasing for teachers and teacher educators, and for education policymakers. The good results on the second time waked us to think seriously on possible reasons for the success. Several international journalists and expert delegations from different countries have asked these reasons while visiting in Finland. Since we had no commonly acceptable explanation to students’success, we decided at the University of Helsinki to put together a book “How Finns Learn Mathematics and Science?”, in order to give a commonly acceptable explanation to our students’success in the international PISA evaluations. The book tries to explain the Finnish teacher education and school system as well as Finnish children’s learning environment at the level of the comprehensive school, and thus give explanations for the Finnish PISA success. The book is a joint enterprise of Finnish teacher educators. The explanations for success given by altogether 40 authors can be classified into three groups: Teacher and teacher education, school and curriculum, and other factors, like the use of ICT and a developmental project LUMA. The main result is that there is not one clear explanation, although research-based teacher education seems to have some influence. But the true explanation may be a combination of several factors.