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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 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.

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.

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.

Notational Knowledge

Developmental and Historical Perspectives

Edited by Eva Teubal, Julie Dockrell and Liliana Tolchinsky

Permanent external representations in the form of drawings, maps, musical scores, figures, graphs, writing, numerals, hallmarks and signatures are part of our daily landscape and permeate most social activities almost from the moment we are born. This book is about humans’ appropriation, understanding and use of external representations.
The authors, all established researchers, present first hand research in the domain of notational knowledge. They reflect on the peculiar features and representational mechanisms of notational systems based on cultural conventions such as musical notation, graphs, writing, numerals and mathematical notation as well as on unique notations that children create in new situations. There are two chapter clusters in the book. The first cluster considers these systems from a historical perspective. Authors focus on the characteristics of these systems in different cultures and at different times and analyze the ways in which notation systems evolve and transform our social interactions, our ideas about language and about other domains of knowledge. The second cluster of chapters takes a developmental perspective. In these chapters the authors focus on the individual appropriation of these systems and highlight the interest for studying permanent external representation as a domain of human development. In particular, authors explore the ways in which notation systems are acquired, the extent to which children are sensitive to their distinguishing constraints and to the particular contents they come to represent and question the future of notations. Both the historical and the developmental perspectives are crucial for understanding the relations between culture and cognition. We can learn about the human mind through analyzing the social processes of invention and transformations of cultural artifacts and also through the individual and social process of appropriation of the cultural artifacts already created.
A common theme in the book is that permanent external representations are not just instruments for expressing given information or tools for communication, they are objects to think with. They not only keep record of existing knowledge but are themselves instrumental in the creation of new knowledge. There are conceptual, linguistic and esthetic distinctions that may be unattainable without notational means.
The book will be useful for students of psychology, philosophy, linguistics and education and for every one interested in understanding ways in which knowledge is generated, recorded and scrutinized.
Although there are other volumes on writing, literacy, and numeracy, and some chapters are available in other volumes on the history of writing, mathematics or musical notation, the present proposal is unique and timely for the range of notational systems it embraces, for including both an historical and a developmental perspective and for the number of theoretical frameworks it discusses.

How should I know?

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

Series:

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)

Series:

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.