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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 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.

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.

Key Works in Radical Constructivism

(edited by Marie Larochelle)

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Ernst von Glasersfeld

Key Works on Radical Constructivism brings together a number of essays by Ernst von Glasersfeld that illustrate the application of a radical constructivist way of thinking in the areas of education, language, theory of knowledge, and the analysis of a few concepts that are indispensable in almost everything we think and do. Ernst von Glasersfeld’s work opens a window on how we know what we know. The present work grew out of a desire to make more accessible this line of thought, to highlight its originality and consistency, and to illustrate its fecundity in the domains of cognition and learning.
The first three parts of this book contain texts by Glasersfeld that outline the constructivist approach and explicate the frequently drastic reconceptualizations he has suggested. Both the last part and the postscript consist of commentaries by Edith Ackermann, Jacques Désautels, Gérard Fourez, Leslie P. Steffe and Kenneth Tobin, scholars in the fields that Glasersfeld has been concerned with. They examine a number of critical aspects pertaining to (radical) constructivism’s current and future development, often tracing out paths that warrant further exploration and reflection, in particular concerning the sociopolitical dimension of knowledge.
Key Works on Radical Constructivism is intended as a reference book for researchers, educators, and students of education—and for anyone interested in grasping, or deepening their grasp of, radical constructivism’s tenets, ambitions and concerns. Readers will discover in this collection of firsthand contributions the contours of a bold, contemporary debate about a most compelling current of thought.

Mathematisation and Demathematisation

Social, Philosophical and Educational Ramifications

Edited by Uwe Gellert and Eva Jablonka

In this volume scholars from diverse strands of research have contributed their perspectives on a process of mathematisation, which renders social, economical or political relationships increasingly formal. At the same time, mathematical skills lose their importance as they become replaced by diverse technological tools; a process of demathematisation takes place. The computerization of financial transactions, calculation of taxes and fees, comparison of prices as well as orientation by means of GPS, visualisation of complex data and electronic voting systems—all these mathematical technologies increasingly penetrate the lifestyle of consumers. What are the perils and promises of this development? Who is in charge, who is affected, who is excluded?
A common concern of all the authors of this volume is an attempt to draw attention to issues related to the formatting power of mathematics and to its role as implicit knowledge, which results in a process of demathematisation. This process, having once received considerable attention, is now threatened to be eclipsed by the proliferation of a discussion of school mathematics, which shows a tendency of cutting off its own philosophical and political roots. Taken together, the contributions reveal a rather complex picture: They draw attention to the importance of clarifying epistemological, societal and ideological issues as a prerequisite for a discussion of curriculum.

Stepping Stones for the 21st Century

Australasian Mathematics Education Research

Edited by Gilah C. Leder and Helen Forgasz

Over the years a number of "must read" articles and book chapters have appeared—work that has formed the foundational stepping stones of mathematics education research for the 21st century. Twelve such seminal articles have been reproduced in this book. Each is accompanied by two independent appraisals of the longer term impact of the work within and beyond the mathematics education research community. Collectively these writings cover a wide range of topics and provide a broad overview of the outstanding contributions of Australasian mathematics education research prior to 2000.