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Semiotics in Mathematics Education

Epistemology, History, Classroom, and Culture

Series:

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.

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.

Margaret Walshaw

Education has a long tradition of opening itself up to new ideas and new ideas are what Working with Foucault in Education is all about. The book introduces readers to the scholarly work of Michel Foucault at a level that it neither too demanding not too superficial. It demonstrates to students, educators, scholars and policy makers, alike, how those ideas might be useful in understanding people and processes in education. This new line of investigation creates an awareness of the merits and weaknesses of contemporary theoretical frameworks and the impact these have on the production of educational knowledge.
Working with Foucault in Education engages readers in selected aspects of education. Its ten chapters take a thematic approach and include vignettes that explore issues relating to curriculum development, learning to teach, classroom learning and teaching, as well as research in contemporary society. These explorations allow readers to develop a new attitude towards education. The reason this is possible is that Foucault provides a language and the tools to deconstruct as well as shift thinking about familiar concepts. They also provide the means for readers to participate in educational criticism and to play a role in educational change.