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Conceptions and Consequences of Mathematical Argumentation, Justification, and Proof
This book aims to advance ongoing debates in the field of mathematics and mathematics education regarding conceptions of argumentation, justification, and proof and the consequences for research and practice when applying particular conceptions of each construct. Through analyses of classroom practice across grade levels using different lenses - particular conceptions of argumentation, justification, and proof - researchers consider the implications of how each conception shapes empirical outcomes. In each section, organized by grade band, authors adopt particular conceptions of argumentation, justification, and proof, and they analyse one data set from each perspective. In addition, each section includes a synthesis chapter from an expert in the field to bring to the fore potential implications, as well as new questions, raised by the analyses. Finally, a culminating section considers the use of each conception across grade bands and data sets.
Learning Mathematics
This volume emphasizes students' inferred mathematical experiences as the starting point in the theory-building process. The book addresses conceptual constructions, including multiplicative notions, fractions, algebra, and the fundamental theorem of calculus, and theoretical constructs such as the crucial role of language and symbols, and the importance of dynamic imagery.
The Emergence of Mathematical Meaning
This book grew out of a five-year collaboration between groups of American and German mathematics educators. The central issue addressed accounting for the messiness and complexity of mathematics learning and teaching as it occurs in classroom situations. The individual chapters are based on the view that psychological and sociological perspectives each tell half of a good story. To unify these concepts requires a combined approach that takes individual students' mathematical activity seriously while simultaneously seeing their activity as necessarily socially situated. Throughout their collaboration, the chapter authors shared a single set of video recordings and transcripts made in an Amer...
Mathematics Teacher Education
Currently there is substantial exchange and communication between academic communities around the world as researchers endeavour to discover why so many children 'fail' at a subject that society deems crucial for future economic survival. This book charts current thinking and trends in teacher education around the world, and looks critically at the inservice education of maths teachers. The contributors explore the processes , practices and issues in teacher education projects in ten countries and these are then discussed and related to current philosophies of teacher education. The book provides an insight into the successes and shortcomings of many different approaches to maths education.
Early Childhood Math Routines
One of the many challenges facing early childhood teachers is how to meet academic standards while creating learning environments that honor young children’s mathematical curiosity. In Early Childhood Math Routines Empowering Young Minds to Think, author Toni Cameron introduces us to a set of short whole-group and partner routines designed to engage young children in meaningful math thinking and build problem-solving communities. With contributions from Patricia Gallahue and Danielle Iacoviello, Cameron reimagines traditional math routines and introduces brand new routines that focus on the important mathematical ideas of early childhood. Through stories, classroom examples, and resources,...
Awakening Children's Minds
Parents and teachers today face a swirl of conflicting theories about child rearing and educational practice. Indeed, current guides are contradictory, oversimplified, and at odds with current scientific knowledge. Now, in Awakening Children's Minds, Laura Berk cuts through the confusion of competing theories, offering a new way of thinking about the roles of parents and teachers and how they can make a difference in children's lives. This is the first book to bring to a general audience, in lucid prose richly laced with examples, truly state-of-the-art thinking about child rearing and early education. Berk's central message is that parents and teachers contribute profoundly to the developme...
Issues in Mathematics Teaching
This book presents the key debates that the mathematics teacher will need to understand, reflect on and engage in as part of their professional development. Issues in Mathematics Teaching is suitable for those at initial training level right through to practising mathematics teachers. Its accessible structure enables the reader to pursue the issues raised as each chapter includes suggestions for further reading and questions for reflection or debate.
Radical Constructivism in Mathematics Education
Mathematics is the science of acts without things - and through this, of things one can define by acts. 1 Paul Valéry The essays collected in this volume form a mosaik of theory, research, and practice directed at the task of spreading mathematical knowledge. They address questions raised by the recurrent observation that, all too frequently, the present ways and means of teaching mathematics generate in the student a lasting aversion against numbers, rather than an understanding of the useful and sometimes enchanting things one can do with them. Parents, teachers, and researchers in the field of education are well aware of this dismal situation, but their views about what causes the wide-s...
The State of Mathematics Achievement
The Nation1s Report Card on mathematics achievement in all 50 States in grades 4, 8 and 12. Covers: achievement by population subgroups (gender, region, type of school., etc.); proficiency by content area; course-taking patterns; student performance; instructional approaches; calculators and computers; characteristics of math teachers, and much more. Charts and tables.
Transforming Children's Mathematics Education
Eminent scholars from around the globe gathered to discuss how educational systems would change if the prevailing principles of constructivism were applied to three major aspects of those systems -- knowledge and learning, communication, and environment. This volume provides documentation of the proceedings of this important meeting - - the Early Childhood Action Group of the Sixth International Congress on Mathematics Education. This international assembly, representing such diverse disciplines as mathematics and math education, epistemology, philosophy, cognitive science, psycholinguistics, and science education, is the first to examine early childhood mathematics education from constructivist and international perspectives in addition to formulating recommendations for future work in the field.
