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The Body in Mathematics
An embodied perspective on mathematical thinking, teaching and learning has grown from early theoretical and empirical work in the 90’s to a diverse and productive collection of approaches today. The aim of this book is to survey the landscape of these approaches and to provide empirical examples of research and an in-depth analysis of the most influential perspectives on embodiment and mathematics. More particularly, the book clarifies differences and points of contact among several theoretical and methodological frameworks that all take embodiment as a core construct in understanding mathematical thinking, and illustrates in a concrete way the affordances of each of these frameworks. Contributors are: Dor Abrahamson, Martha W. Alibali, Corey Brady, James A. Dixon, Laurie Edwards, Virginia J. Flood, Susan Gerofsky, Christina Krause, Ricardo Nemirovsky, Matthew Petersen, Luis Radford, Wolff-Michael Roth, Anna Shvarts, and Ashwin Vaidya.
Knowledge and Interaction
Decades of research in the cognitive and learning sciences have led to a growing recognition of the incredibly multi-faceted nature of human knowing and learning. Up to now, this multifaceted nature has been visible mostly in distinct and often competing communities of researchers. From a purely scientific perspective, "siloed" science—where different traditions refuse to speak with one another, or merely ignore one another—is unacceptable. This ambitious volume attempts to kick-start a serious, new line of work that merges, or properly articulates, different traditions with their divergent historical, theoretical, and methodological commitments that, nonetheless, both focus on the highl...
Cscl 2
CSCL 2: Carrying Forward the Conversation is a thorough and up-to-date survey of recent developments in Computer Supported Collaborative Learning, one of the fastest growing areas of research in the learning sciences. A follow-up to CSCL: Theory and Practice of an Emerging Paradigm (1996), this volume both documents how the field has grown and fosters a meaningful discussion of how the research program might be advanced in substantive ways. Recognizing the long-standing traditions of CSCL work in Europe and Japan, the editors sought to broaden and expand the conversation both geographically and topically. The 45 participating authors represent a range of disciplinary backgrounds, including a...
Planting the Seeds of Algebra, PreK2
The subject of algebra has always been important in American secondary mathematics education. However, algebra at the elementary level has been garnering increasing attention and importance over the past 15 years. There is consequently a dire need for ideas, suggestions and models for how best to achieve pre-algebraic instruction in the elementary grades. Planting the Seeds of Algebra will empower teachers with theoretical and practical knowledge about both the content and pedagogy of such instruction, and show them the different faces of algebra as it appears in the early grades. The book will walk teachers of young children through many examples of K-6 math lessons and unpack, step by step, the hidden connections to higher algebra. After reading this book, teachers will be better equipped ...
Symbolizing, Modeling and Tool Use in Mathematics Education
This book explores the option of building on symbolizing, modeling and tool use as personally meaningful activities of students. It discusses the dimension of setting: varying from the study of informal, spontaneous activity of students, to an explicit focus on instructional design, and goals and effects of instruction; and the dimension of the theoretical framework of the researcher: varying from constructivism, to activity theory, cognitive psychology and instructional-design theory.
Approaches to Algebra
In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. This theory of measure is limited to exact measure. Operations on magnitudes cannot be actually numerically calculated, except if those magnitudes are exactly measured by a certain unit. The theory of proportions does not have access to such operations. It cannot be seen as an "arithmetic" of ratios. Even if Euclidean geometry is done in a highly theoretical context, its axioms are essentially semantic. This is contrary to Mahoney's second characteristic. This cannot be said of the theory of proportions, which is less semantic. Only synthetic proofs are considered rigorous in Gr...
Psychology and the Conduct of Everyday Life
Psychology and the Conduct of Everyday Life moves psychological theory and research practice out of the laboratory and into the everyday world. Drawing on recent developments across the social and human sciences, it examines how people live as active subjects within the contexts of their everyday lives, using this as an analytical basis for understanding the dilemmas and contradictions people face in contemporary society. Early chapters gather the latest empirical research to explore the significance of context as a cross-disciplinary critical tool; they include a study of homeless Māori men reaffirming their cultural identity via gardening, and a look at how the dilemmas faced by children ...
What is a Mathematical Concept?
Leading thinkers in mathematics, philosophy and education offer new insights into the fundamental question: what is a mathematical concept?
