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Jürgen Maasz and Wolfgang Schlöglmann

During the last fifteen years, research on affect has been of considerable interest to the mathematics education community. Researchers with an interest in mathematics and gender had a look at aspects of affect in their research studies right from the beginning. Similarly many studies of mathematical problem solving had a growing interest in affect. The main focus of research are now student beliefs and teacher beliefs which are identified as important factors for those influencing learning and teaching.
The thirteen chapters of this book involve many aspect of research on affect like theoretical problems of defining beliefs, the complex relationship between content knowledge and affect, espoused beliefs and teaching practice, domain-specific beliefs as well as the relationship between special learning conditions and affective reactions.

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.

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.

In Doubt

- about Language, Mathematics, Knowledge and Life-Worlds

Ole Skovsmose

During years a main part of Ole Skovsmose’s research has addressed educational issues. He has developed the notions of landscapes of investigation, mathematics in action, students’ foreground, and ghettoising with particular reference to mathematics education. In this book he addresses more general issues related to mathematics.
Ole Skovsmose tries to show that mathematics, like any other language, includes presumptions, ideas, and priorities. Mathematics does not provide a step out of the metaphysics that accompanies natural language, as suggested by many, who see mathematics as the language of objectivity. By investigating how mathematics forms part of technological endeavours, Ole Skovsmose explores how also mathematics itself embraces a range of metaphysical assumptions.
This observation has implications for how we interpret the most general aspects of human life. Thus, Ole Skovsmose sees our life-worlds as fabricated and mathematics as being crucial to this fabrication. It constitutes part of the human condition, although it can be a highly dubious and frightful constitution.

Mathematical Action & Structures of Noticing

Studies on John Mason’s Contribution to Mathematics Education

Edited by Stephen Lerman and Brent Davis

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.
Among the many markers of his esteemed career was the 1984 publication of Thinking Mathematically (with Leone Burton and Kaye Stacey). It has become a classic in the field, having been translated into many languages and in use in countries around the world. Thinking Mathematically and other writings in his substantial body of work are used with advanced high school students, with pre-service and practicing teachers, and by researchers who are interested in the nature of doing and learning mathematics.
This book is not, and at the same time is, a tribute to the enormous contributions made by Mason to mathematics education. It is not a tribute book because every chapter is a report of research and thinking by the authors, not simply a statement of appreciation. All engage with how others have taken Mason’s ideas forward to extend their own research and thinking. At the same time it is a tribute book. It is about how research and teaching has been inspired by Mason through his substantial opus and his vibrant presence in a network of mathematics educators.

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.

Edited by Christopher Andersen, Nora Scheurer, María del Puy Leonor Pérez Echeverría and Eva Teubal

Learning and teaching complex cultural knowledge calls for meaningful participation in different kinds of symbolic practices, which in turn are supported by a wide range of external representations, as gestures, oral language, graphic representations, writing and many other systems designed to account for properties and relations on some 2- or 3-dimensional objects. Children start their apprenticeship of these symbolic practices very early in life. But being able to understand and use them in fluid and flexible ways poses serious challenges for learners and teachers across educational levels, from kindergarten to university.
This book is intended as a step in the path towards a better understanding of the dynamic relations between different symbolic practices and the acquisition of knowledge in various learning domains, settings and levels. Researchers from almost twenty institutions in three different continents present first hand research in this emerging area of study and reflect on the particular ways and processes whereby participation in symbolic practices based on a diversity of external representations promotes learning in specific fields of knowledge.
The book will be useful for persons interested in education, as well as cognitive psychologists, linguists and those concerned by the generation, appropriation, transmission and communication of knowledge.

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.

Words and Worlds

Modeling Verbal Descriptions of Situations

Series:

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.

The Psychology of Mathematics Education

A Psychoanalytic Displacement

Series:

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.