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There are many questions about the mathematical preparation teachers need. Recent recommendations from a variety of sources state that reforming teacher preparation in postsecondary institutions is central in providing quality mathematics education to all students. The Mathematics Teacher Preparation Content Workshop examined this problem by considering two central questions: What is the mathematical knowledge teachers need to know in order to teach well? How can teachers develop the mathematical knowledge they need to teach well? The Workshop activities focused on using actual acts of teaching such as examining student work, designing tasks, or posing questions, as a medium for teacher learning. The Workshop proceedings, Knowing and Learning Mathematics for Teaching, is a collection of the papers presented, the activities, and plenary sessions that took place.
"A joint publication with Educational Development Center and Bank Street College of Education."
"This book is the third in an important trilogy of edited collections on the teaching and learning of primary mathematics. To each book the editor, Ian Thompson, has attracted a team of expert contributors, and himself set the characteristically high standard of writing and clarity... When, in 10 or 20 years' time, people want to know about the state of English primary mathematics at the turn of the 21st century, they will turn to this volume. You would do well to read it now." Mathematics in Schools "This is the third book in the popular series edited by Ian Thompson that brings together an impressive array of contributing authors. Current issues are discussed in an informed but concise way that makes research accessible to the wider community of mathematics educators." Julia Anghileri, University of Cambridge This book explores the effect that the National Numeracy Strategy and its successor, the Primary Strategy, have had on the way in which mathematics is taught in primary schools. Prominent contributors examine the Strategies' recommendations from the perspective of their own research areas or interests, and discuss the issues involved, including: Ideas for extending current practice Suggestions of important aspects of mathematics teaching that are being given little or no emphasis Alternative approaches that could be integrated into current practice Aspects of current practice that need to take account of recent research findings or emerging issues. Each chapter discusses implications for teaching and learning primary mathematics. The book will be particularly useful for trainees, practising teachers, mathematics coordinators and numeracy consultants. Contributors: Mundher Adhami, Mike Askew, Carol Aubrey, Margaret Brown, Ann Dowker, Rosemary Hafeez, Steve Higgins, Keith Jones, Lesley Jones, Valsa Koshy, Alison Millett, Claire Mooney, Laurie Rousham, Malcolm Swan, Ian Thompson, Helen J Williams.
The second edition continues the mission of bringing together important new mathematics education research that makes a difference in both theory and practice. It updates and extends the Handbook’s original key themes and issues for international research in mathematics education for the 21st century, namely: priorities in international mathematics education research lifelong democratic access to powerful mathematical ideas advances in research methodologies influences of advanced technologies. Each of these themes is examined in terms of learners, teachers, and learning contexts, with theory development being an important component of all these aspects. This edition also examines other catalysts that have gained increased import in recent years including a stronger focus on the teacher and teacher practice, a renewed interest in theory development, an increased focus on the mathematics needed in work place settings, and a proliferation of research designs and methodologies that have provided unprecedented opportunities for investigating (and ultimately improving) mathematical teaching and learning. This edition includes ten totally new chapters; all other chapters are thoroughly revised and updated.
This volume reflects an appreciation of the interactive roles of subject matter, teacher, student, and technologies in designing classrooms that promote understanding of geometry and space. Although these elements of geometry education are mutually constituted, the book is organized to highlight, first, the editors' vision of a general geometry education; second, the development of student thinking in everyday and classroom contexts; and third, the role of technologies. Rather than looking to high school geometry as the locus--and all too often, the apex--of geometric reasoning, the contributors to this volume suggest that reasoning about space can and should be successfully integrated with other forms of mathematics, starting at the elementary level and continuing through high school. Reintegrating spatial reasoning into the mathematical mainstream--indeed, placing it at the core of K-12 mathematics environments that promote learning with understanding--will mean increased attention to problems in modeling, structure, and design and reinvigoration of traditional topics such as measure, dimension, and form. Further, the editors' position is that the teaching of geometry and spatial visualization in school should not be compressed into a characterization of Greek geometry, but should include attention to contributions to the mathematics of space that developed subsequent to those of the Greeks. This volume is essential reading for those involved in mathematics education at all levels, including university faculty, researchers, and graduate students.
Teachers and students examine different aspects of size, develop facility in composing and decomposing shapes, and examine different sizes to develop sense of volume.
Whether you are just starting out with watercolor painting or want to expand your skills and raise your art to the next level, this book has all the inspiration and practical know-how you'll need. Starting from the very basics, such as choosing the right brushes and practicing color mixes, this book proceeds to tackle every conceivable watercolor technique—from applying a flat wash to experimenting with texture. Techniques and inspiration are then combined in a wide-ranging section on subject matter—from landscapes to botanical illustration, urban scenes, portraiture, and abstraction—which examines the practical considerations of each topic and showcases numerous different approaches to try, with tutorials on achieving particular effects. Each technique and stylistic approach is demonstrated by a professional artist working on an original painting, which is photographed at different stages of development to give rare insights into the artistic process. Also featuring content dedicated to the use of watercolor in graphic illustration, as well as how to combine it with other painting and drawing media, Artist's Watercolor Techniques will help you challenge yourself, try new things, and grow as an artist.
Schools are complex social settings where students, teachers, administrators, and parents interact to shape a child's educational experience. Any effort to improve educational outcomes for America's children requires a dynamic understanding of the environments in which children learn. In The Social Organization of Schooling, editors Larry Hedges and Barbara Schneider assemble researchers from the fields of education, organizational theory, and sociology to provide a new framework for understanding and analyzing America's schools and the many challenges they face. The Social Organization of Schooling closely examines the varied components that make up a school's social environment. Contributors Adam Gamoran, Ramona Gunter, and Tona Williams focus on the social organization of teaching. Using intensive case studies, they show how positive professional relations among teachers contribute to greater collaboration, the dissemination of effective teaching practices, and ultimately, a better learning environment for children. Children learn more from better teachers, but those best equipped to teach often opt for professions with higher social stature, such as law or medicine. In his chapter, Robert Dreeben calls for the establishment of universal principles and practices to define good teaching, arguing that such standards are necessary to legitimize teaching as a high status profession. The Social Organization of Schooling also looks at how social norms in schools are shaped and reinforced by interactions among teachers and students. Sociologist Maureen Hallinan shows that students who are challenged intellectually and accepted socially are more likely to embrace school norms and accept responsibility for their own actions. Using classroom observations, surveys, and school records, Daniel McFarland finds that group-based classroom activities are effective tools in promoting both social and scholastic development in adolescents. The Social Organization of Schooling also addresses educational reforms and the way they affect a school's social structures. Examining how testing policies affect children's opportunities to learn, Chandra Muller and Kathryn Schiller find that policies which increased school accountability boosted student enrollment in math courses, reflecting a shift in the school culture towards higher standards. Employing a variety of analytical methods, The Social Organization of Schooling provides a sound understanding of the social mechanisms at work in our educational system. This important volume brings a fresh perspective to the many ongoing debates in education policy and is essential reading for anyone concerned with the future of America's children.