Turtle Geometry

The Computer as a Medium for Exploring Mathematics

Author: Harold Abelson,Andrea A. DiSessa

Publisher: MIT Press

ISBN: 9780262510370

Category: Computers

Page: 477

View: 3815

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Turtle Geometry presents an innovative program of mathematical discovery that demonstrates how the effective use of personal computers can profoundly change the nature of a student's contact with mathematics. Using this book and a few simple computer programs, students can explore the properties of space by following an imaginary turtle across the screen.The concept of turtle geometry grew out of the Logo Group at MIT. Directed by Seymour Papert, author of Mindstorms, this group has done extensive work with preschool children, high school students and university undergraduates. Harold Abelson is an associate professor in the Department of Electrical Engineering and Computer Science at MIT. Andrea diSessa is an associate professor in the Graduate School of Education, University of California, Berkeley.

Designing Learning Environments for Developing Understanding of Geometry and Space

Author: Richard Lehrer,Daniel Chazan

Publisher: Routledge

ISBN: 1136490582

Category: Education

Page: 518

View: 7523

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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.

Computer Assisted Learning in Physics Education

Author: Alfred Bork

Publisher: Elsevier

ISBN: 1483149005

Category: Science

Page: 90

View: 6575

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Computer Assisted Learning in Physics Education focuses on the use of computers in learning physics. Organized into six chapters, the book begins with an explanation of the CONDUIT series in physics. Subsequent chapters focus on physics education with or without computers; a computer-based course in classical mechanics; physics in the Irvine Educational Technology Center; and an electronics course using an intelligent video format. The last chapter addresses computation as a physical and intellectual environment for learning physics. The book will be useful for physics students as an aid in the use of computers in this field.

Research on e-Learning and ICT in Education

Author: Athanassios Jimoyiannis

Publisher: Springer Science & Business Media

ISBN: 9781461410836

Category: Education

Page: 316

View: 9864

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This book aims to serve as a multidisciplinary forum covering technical, pedagogical, organizational, instructional, as well as policy aspects of ICT in Education and e-Learning. Special emphasis is given to applied research relevant to educational practice guided by the educational realities in schools, colleges, universities and informal learning organizations. In a more generic scope, the volume aims to encompass current trends and issues determining ICT integration in practice, including learning and teaching, curriculum and instructional design, learning media and environments, teacher education and professional development, assessment and evaluation, etc.

Perspectives on the Teaching of Geometry for the 21st Century

An ICMI Study

Author: Carmelo Mammana,V. Villani

Publisher: Springer Science & Business Media

ISBN: 9401152268

Category: Education

Page: 353

View: 2707

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In recent years geometry seems to have lost large parts of its former central position in mathematics teaching in most countries. However, new trends have begun to counteract this tendency. There is an increasing awareness that geometry plays a key role in mathematics and learning mathematics. Although geometry has been eclipsed in the mathematics curriculum, research in geometry has blossomed as new ideas have arisen from inside mathematics and other disciplines, including computer science. Due to reassessment of the role of geometry, mathematics educators and mathematicians face new challenges. In the present ICMI study, the whole spectrum of teaching and learning of geometry is analysed. Experts from all over the world took part in this study, which was conducted on the basis of recent international research, case studies, and reports on actual school practice. This book will be of particular interest to mathematics educators and mathematicians who are involved in the teaching of geometry at all educational levels, as well as to researchers in mathematics education.

Functional Differential Geometry

Author: Gerald Jay Sussman,Jack Wisdom,Will Farr

Publisher: MIT Press

ISBN: 0262019345

Category: Mathematics

Page: 228

View: 9548

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Physics is naturally expressed in mathematical language. Students new to the subject must simultaneously learn an idiomatic mathematical language and the content that is expressed in that language. It is as if they were asked to read Les Misérables while struggling with French grammar. This book offers an innovative way to learn the differential geometry needed as a foundation for a deep understanding of general relativity or quantum field theory as taught at the college level. The approach taken by the authors (and used in their classes at MIT for many years) differs from the conventional one in several ways, including an emphasis on the development of the covariant derivative and an avoidance of the use of traditional index notation for tensors in favor of a semantically richer language of vector fields and differential forms. But the biggest single difference is the authors' integration of computer programming into their explanations. By programming a computer to interpret a formula, the student soon learns whether or not a formula is correct. Students are led to improve their program, and as a result improve their understanding.

Mindstorms

Children, Computers, And Powerful Ideas

Author: Seymour A. Papert

Publisher: Basic Books

ISBN: 9780465046744

Category: Education

Page: 252

View: 9818

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Mindstorms has two central themes: that children can learn to use computers in a masterful way and that learning to use computers can change the way they learn everything else. Even outside the classroom, Papert had a vision that the computer could be used just as casually and as personally for a diversity of purposes throughout a person's entire life. Seymour Papert makes the point that in classrooms saturated with technology there is actually more socialization and that the technology often contributes to greater interaction among students and among students and instructors.

Windows on Mathematical Meanings

Learning Cultures and Computers

Author: Richard Noss,Celia Hoyles

Publisher: Springer Science & Business Media

ISBN: 9400916965

Category: Education

Page: 278

View: 2485

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This book challenges some of the conventional wisdoms on the learning of mathematics. The authors use the computer as a window onto mathematical meaning-making. The pivot of their theory is the idea of webbing, which explains how someone struggling with a new mathematical idea can draw on supportive knowledge, and reconciles the individual's role in mathematical learning with the part played by epistemological, social and cultural forces.

Changing Minds

Computers, Learning, and Literacy

Author: Andrea A. DiSessa

Publisher: MIT Press

ISBN: 9780262541329

Category: Computers

Page: 271

View: 7185

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How computer technology can transform science education for children.

Turtles, Termites, and Traffic Jams

Explorations in Massively Parallel Microworlds

Author: Mitchel Resnick

Publisher: MIT Press

ISBN: 9780262680936

Category: Computers

Page: 163

View: 5655

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How does a bird flock keep its movements so graceful and synchronized? Most people assume that the bird in front leads and the others follow. In fact, bird flocks don't have leaders: they are organized without an organizer, coordinated without a coordinator. And a surprising number of other systems, from termite colonies to traffic jams to economic systems, work the same decentralized way. Turtles, Termites, and Traffic Jams describes innovative new computational tools that can qhelp people (even young children) explore the workings of such systems--and help them move beyond the centralized mindset.

The Age of Spiritual Machines

When Computers Exceed Human Intelligence

Author: Ray Kurzweil

Publisher: Penguin

ISBN: 9781101077887

Category: Computers

Page: 400

View: 7270

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Ray Kurzweil is the inventor of the most innovative and compelling technology of our era, an international authority on artificial intelligence, and one of our greatest living visionaries. Now he offers a framework for envisioning the twenty-first century--an age in which the marriage of human sensitivity and artificial intelligence fundamentally alters and improves the way we live. Kurzweil's prophetic blueprint for the future takes us through the advances that inexorably result in computers exceeding the memory capacity and computational ability of the human brain by the year 2020 (with human-level capabilities not far behind); in relationships with automated personalities who will be our teachers, companions, and lovers; and in information fed straight into our brains along direct neural pathways. Optimistic and challenging, thought-provoking and engaging, The Age of Spiritual Machines is the ultimate guide on our road into the next century. From the Trade Paperback edition.

Unobstructed Shortest Paths in Polyhedral Environments

Author: Varol Akman

Publisher: Springer Science & Business Media

ISBN: 9783540176299

Category: Computers

Page: 106

View: 532

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The first examination of the cervical spine is always made using standard radiographs and, often enough, this suffices as a basis for diagnosis. Malformations, tumours, and more frequently traumas, rheumatism, and even ordinary neck pain require radiological examination of the spine. Interpretation, however, is difficult. Take a cervical vertebra in your hand and you will see that it is complex enough itself. In radiology the overlapping pieces of bone, summation phenomena and the diversity of viewing angles complicate interpretation of the images still further. The book by J.-F. Bonneville and F. Cattin suggests an original method of reading the radiographs, strict but very attractive, which considerably simplifies the interpretation of images of the cervical spine. This book shows that two- or threedimensional computed tomograms accompany standard radiographs as an excellent aid to comprehension. It is as though the reader had access to each part of the bony anatomy shown in the radiographs and from then on everything becomes easy, superimpositions disappear, traps become visible, anatomy triumphs, the image lives.

TUGboat

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Computerized typesetting

Page: N.A

View: 8372

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Perspective design

advanced graphic and mathematical approaches

Author: John H. Mauldin

Publisher: Van Nostrand Reinhold Company

ISBN: N.A

Category: Architecture

Page: 222

View: 680

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