SUNY series, Reform in Mathematics Education - Böcker

Two of the most important concepts children develop progressively throughout their mathematics education years are additivity and multiplicativity. Additivity is associated with situations that involve adding, joining, affixing, subtracting, separating and removing. Multiplicativity is associated with situations that involve duplicating, shrinking, stressing, sharing equally, multiplying, dividing, and exponentiating.This book presents multiplicativity in terms of a multiplicative conceptual field (MCF), not as individual concepts. It is presented in terms of interrelations and dependencies within, between, and among multiplicative concepts. The authors share the view that research on the mathematical, cognitive, and instructional aspects of multiplicative concepts must be situated in an MCF framework.

Two of the most important concepts children develop progressively throughout their mathematics education years are additivity and multiplicativity. Additivity is associated with situations that involve adding, joining, affixing, subtracting, separating and removing. Multiplicativity is associated with situations that involve duplicating, shrinking, stressing, sharing equally, multiplying, dividing, and exponentiating.This book presents multiplicativity in terms of a multiplicative conceptual field (MCF), not as individual concepts. It is presented in terms of interrelations and dependencies within, between, and among multiplicative concepts. The authors share the view that research on the mathematical, cognitive, and instructional aspects of multiplicative concepts must be situated in an MCF framework.

Today new ways of thinking about learning call for new ways for monitoring learning. Reform in School Mathematics builds from the vision that assessment can become the bridge for instructional activity, accountability, and teacher development. It places teachers in key roles while developing the theme that we cannot reform the way in which school mathematics is taught without radically reforming the ways the effects of that teaching are monitored. Among others, this volume addresses the issues of the specification of performance standards, the development of authentic tasks, the measure of status and growth or a combination, the development of psychometric models, and the development of scoring rubrics. The new models proposed in this book give teachers a wealth of non-traditional assessment strategies and concrete ways to obtain measures of both group and individual differences in growth.

Provides middle school teachers with a firm pedagogical foundation based on the manner in which students learn the mathematics being taught.This book is written primarily for middle grade teachers who are discovering that they now want to teach in ways that create positive mathematical learning environments and instigate rich classroom discourse. Many of these teachers are finding that their mathematical preparation did not address the complexities underlying the mathematics they now want to teach.In Part One, the authors provide a foundation for the mathematics of these grades, particularly the mathematics that grows out of concepts of number, quantity, and arithmetic operations. In Part Two, through three case studies, the authors demonstrate to teachers how a deeper understanding of the mathematics they teach can enhance classroom instruction.The book interweaves research and classroom practice. Mathematics teacher educators, researchers, curriculum developers, textbook authors, and supervisors of mathematics programs will find this book to be useful. Teachers, both prospective and practicing, will benefit most from this book when the chapters are used as catalysts for discussion in classes or professional development programs.

Presents the emerging field of ethnomathematics from a critical perspective, challenging particular ways in which Eurocentrism permeates mathematics education and mathematics in general.This collection brings together classic, previously published articles and new research to present the emerging field of ethnomathematics from a critical perspective, challenging particular ways in which Eurocentrism permeates mathematics education. The contributors identify several of the field's broad themes-reconsidering what counts as mathematical knowledge, considering interactions between culture and mathematical knowledge, and uncovering hidden and distorted histories of mathematical knowledge. The book offers a diversity of ethnomathematics perspectives that develop both theoretical and practical issues from various disciplines including mathematics, mathematics education, history, anthropology, cognitive psychology, feminist studies, and African studies written by authors from Brazil, England, Australia, Mozambique, Palestine, Belgium, and the United States.