Designing Learning Environments for Developing Understanding of Geometry and Space PDF Download

Author: Richard Lehrer
Publisher: Routledge
ISBN: 1136490582
Category : Education
Languages : en
Pages : 520

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Book Description
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.

Author: Richard Lehrer
Publisher: Taylor & Francis
ISBN: 1000839257
Category : Education
Languages : en
Pages : 256

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Book Description
Measuring and Visualizing Space in Elementary Mathematics Learning explores the development of elementary students’ understanding of the mathematics of measure, and demonstrates how measurement can serve as an anchor for supporting a deeper understanding of number operations and rational numbers. The concept of measurement is centrally implicated in a number of mathematical operations, yet is not often given the placement it deserves in the elementary mathematics curriculum. By drawing on K-5 classroom research, authors Lehrer and Schauble have been able to articulate a learning progression that describes benchmarks of student learning about measure in length, angle, area, volume, and rational number, exploring related concepts, classroom experiences, and instructional practices at each stage. Offering a unique, research driven resource for helping students develop a deep understanding of measurement to further enhance mathematical understanding, as well as further learning in other STEM disciplines; the book will be relevant for scholars, teacher educators, and specialists in math education. The book is accompanied by online resources developed for practitioners, including instructional guides, examples of student thinking, and other teacher-focused materials, helping clarify how to bring concepts of measure and rational number to life in classrooms.

Author: K.P Gravemeijer
Publisher: Springer Science & Business Media
ISBN: 9401731942
Category : Education
Languages : en
Pages : 304

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Book Description
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.

Author: Lyn D. English
Publisher: Routledge
ISBN: 1135665796
Category : Education
Languages : en
Pages : 848

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Book Description
This state-of-the-art Handbook brings together important mathematics education research that makes a difference in both theory and practice--research that: anticipates problems and needed knowledge before they become impediments to progress; interprets future-oriented problems into researchable issues; presents the implications of research and theory development in forms that are useful to practitioners and policymakers; and facilitates the development of research communities to focus on neglected priorities or strategic opportunities. The volume represents a genuine attempt by contributors from around the world to advance the discipline, rather than simply review what has been done and what exists. The Handbook was developed in response to a number of major global catalysts for change, including the impact of national and international mathematics comparative assessment studies; the social, cultural, economic, and political influences on mathematics education and research; the influence of progressively sophisticated and available technology; and the increasing globalization of mathematics education and research. From these catalysts have emerged specific priority themes and issues for mathematics education research in the 21st century. Three key themes were identified for attention in this volume: life-long democratic access to powerful mathematical ideas; advances in research methodologies; and influences of advanced technologies. Each of these themes is examined in terms of learners, teachers, and learning contexts, with theory development as an important component of all these aspects. Dynamic and forward looking, the Handbook of International Research in Mathematics Education is distinguished by its focus on new and emerging theoretical models, perspectives, and research methodologies; its uniformly high standard of scholarship; and its emphasis on the international nature of mathematics education research. It is an essential volume for all researchers, professionals, and students interested in mathematics education research in particular and, more generally, in international developments and future directions in the broad field of educational research.

Author: Irving B. Weiner
Publisher: John Wiley & Sons
ISBN: 9780471384069
Category : Education
Languages : en
Pages : 696

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Book Description
Includes established theories and cutting-edge developments. Presents the work of an international group of experts. Presents the nature, origin, implications, an future course of major unresolved issues in the area.

Author: Douglas H. Clements
Publisher: Routledge
ISBN: 1135843805
Category : Education
Languages : en
Pages : 342

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Book Description
In this important new book for pre- and in-service teachers, early math experts Douglas Clements and Julie Sarama show how "learning trajectories" help teachers become more effective professionals. By opening up new windows to seeing young children and the inherent delight and curiosity behind their mathematical reasoning, learning trajectories ultimately make teaching more joyous. They help teachers understand the varying level of knowledge and thinking of their classes and the individuals within them as key in serving the needs of all children. In straightforward, no-nonsense language, this book summarizes what is known about how children learn mathematics, and how to build on what they know to realize more effective teaching practice. It will help teachers understand the learning trajectories of early mathematics and become quintessential professionals.

Author: Pat Herbst
Publisher: Taylor & Francis
ISBN: 1351973533
Category : Education
Languages : en
Pages : 240

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Book Description
IMPACT (Interweaving Mathematics Pedagogy and Content for Teaching) is an exciting new series of texts for teacher education which aims to advance the learning and teaching of mathematics by integrating mathematics content with the broader research and theoretical base of mathematics education. The Learning and Teaching of Geometry in Secondary Schools reviews past and present research on the teaching and learning of geometry in secondary schools and proposes an approach for design research on secondary geometry instruction. Areas covered include: teaching and learning secondary geometry through history; the representations of geometric figures; students’ cognition in geometry; teacher knowledge, practice and, beliefs; teaching strategies, instructional improvement, and classroom interventions; research designs and problems for secondary geometry. Drawing on a team of international authors, this new text will be essential reading for experienced teachers of mathematics, graduate students, curriculum developers, researchers, and all those interested in exploring students’ study of geometry in secondary schools.

Author: Kevin Crowley
Publisher: Psychology Press
ISBN: 1135662223
Category : Psychology
Languages : en
Pages : 461

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Book Description
This volume explores the integration of recent research on everyday, classroom, and professional scientific thinking. It brings together an international group of researchers to present core findings from each context; discuss connections between contexts, and explore structures; technologies, and environments to facilitate the development and practice of scientific thinking. The chapters focus on: * situations from young children visiting museums, * middle-school students collaborating in classrooms, * undergraduates learning about research methods, and * professional scientists engaged in cutting-edge research. A diverse set of approaches are represented, including sociocultural description of situated cognition, cognitive enthnography, educational design experiments, laboratory studies, and artificial intelligence. This unique mix of work from the three contexts deepens our understanding of each subfield while at the same time broadening our understanding of how each subfield articulates with broader issues of scientific thinking. To provide a common focus for exploring connections between everyday, instructional, and professional scientific thinking, the book uses a "practical implications" subtheme. In particular, each chapter has direct implications for the design of learning environments to facilitate scientific thinking.

Author: Robert Glaser
Publisher: Routledge
ISBN: 1134803745
Category : Education
Languages : en
Pages : 421

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Book Description
Investigators have moved back and forth between design efforts and basic studies in cognition to improve both application and fundamental knowledge. This volume's theme is this interaction between practice and science with the opportunity for reflecting on findings in order to understand them and suggesting improved forms of application and their underlying explanation. This is seen in various arenas including theory-based computer-assisted instruction for teaching mathematics, the design of communities of learning in elementary schools, teaching in the context of problem-solving situations and reasoning with models, self-explanation as a highly effective learning activity, conceptual change in medical training and health education, and workplace training in electronic troubleshooting. The results of extensive long-term experience and analysis in each of these areas are insightfully reported by the well-known contributors to this volume. Special features of this fifth edition include: * The work of eminent cognitive scientists in the design and evaluation of educational and training environments to increase current understanding of learning and development, as this understanding is applied to innovative instructional programs and teaching methods. * A description of learning theory and principles as well as implications and examples on research and development on educational application. * A presentation on the 10-year change in perspective on research and development in problem solving environments that invite inquiry about academic information and skills in the context of instruction of elementary school children. * An innovative approach to math and science instruction in which teaching is oriented around constructing, evaluating, and revising models. * An examination of the process of self-explaining, which involves explaining to one's self in an attempt to make sense of a new situation. * A description of a long-term program of cognitive task analysis and instructional design on problem solving in the operation of complex equipment. * An investigation on the acquisition of clinical reasoning skills and the understanding of biomedical concepts in both professional medicine and the health practices of the lay population.

Author: James J. Kaput
Publisher: Routledge
ISBN: 1351577093
Category : Education
Languages : en
Pages : 552

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Book Description
This volume is the first to offer a comprehensive, research-based, multi-faceted look at issues in early algebra. In recent years, the National Council for Teachers of Mathematics has recommended that algebra become a strand flowing throughout the K-12 curriculum, and the 2003 RAND Mathematics Study Panel has recommended that algebra be “the initial topical choice for focused and coordinated research and development [in K-12 mathematics].” This book provides a rationale for a stronger and more sustained approach to algebra in school, as well as concrete examples of how algebraic reasoning may be developed in the early grades. It is organized around three themes: The Nature of Early Algebra Students’ Capacity for Algebraic Thinking Issues of Implementation: Taking Early Algebra to the Classrooms. The contributors to this landmark volume have been at the forefront of an effort to integrate algebra into the existing early grades mathematics curriculum. They include scholars who have been developing the conceptual foundations for such changes as well as researchers and developers who have led empirical investigations in school settings. Algebra in the Early Grades aims to bridge the worlds of research, practice, design, and theory for educators, researchers, students, policy makers, and curriculum developers in mathematics education.