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: 814

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Turtle Geometry presents an innovative program of mathematical discovery thatdemonstrates how the effective use of personal computers can profoundly change the nature of astudent's contact with mathematics. Using this book and a few simple computer programs, students canexplore the properties of space by following an imaginary turtle across the screen.The concept ofturtle 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 universityundergraduates. Harold Abelson is an associate professor in the Department of Electrical Engineeringand Computer Science at MIT. Andrea diSessa is an associate professor in the Graduate School ofEducation, University of California, Berkeley.

Exploring Geometry, Second Edition

Author: Michael Hvidsten
Publisher: CRC Press
ISBN: 1498760988
Category: Mathematics
Page: 558
View: 9003

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This text promotes student engagement with the beautiful ideas of geometry. Every major concept is introduced in its historical context and connects the idea with real-life. A system of experimentation followed by rigorous explanation and proof is central. Exploratory projects play an integral role in this text. Students develop a better sense of how to prove a result and visualize connections between statements, making these connections real. They develop the intuition needed to conjecture a theorem and devise a proof of what they have observed.

Geometry Turned On

Dynamic Software in Learning, Teaching, and Research
Author: James King,Doris Schattschneider
Publisher: Cambridge University Press
ISBN: 9780883850992
Category: Mathematics
Page: 206
View: 3869

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Articles about the uses of active, exploratory geometry carried out with interactive computer software.

An Integrated Introduction to Computer Graphics and Geometric Modeling

Author: Ronald Goldman
Publisher: CRC Press
ISBN: 1439803358
Category: Computers
Page: 574
View: 1352

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Taking a novel, more appealing approach than current texts, An Integrated Introduction to Computer Graphics and Geometric Modeling focuses on graphics, modeling, and mathematical methods, including ray tracing, polygon shading, radiosity, fractals, freeform curves and surfaces, vector methods, and transformation techniques. The author begins with fractals, rather than the typical line-drawing algorithms found in many standard texts. He also brings the turtle back from obscurity to introduce several major concepts in computer graphics. Supplying the mathematical foundations, the book covers linear algebra topics, such as vector geometry and algebra, affine and projective spaces, affine maps, projective transformations, matrices, and quaternions. The main graphics areas explored include reflection and refraction, recursive ray tracing, radiosity, illumination models, polygon shading, and hidden surface procedures. The book also discusses geometric modeling, including planes, polygons, spheres, quadrics, algebraic and parametric curves and surfaces, constructive solid geometry, boundary files, octrees, interpolation, approximation, Bezier and B-spline methods, fractal algorithms, and subdivision techniques. Making the material accessible and relevant for years to come, the text avoids descriptions of current graphics hardware and special programming languages. Instead, it presents graphics algorithms based on well-established physical models of light and cogent mathematical methods.


A Retrospective
Author: D Lamont Johnson,Cleborne D Maddux
Publisher: CRC Press
ISBN: 9780789003744
Category: Computers
Page: 212
View: 5015

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In Logo: A Retrospective, you?ll look back and see why attempts to teach Logo in American schools failed the first time it was introduced, and you?ll learn what you can do so educators don?t make the same mistake again. You?ll explore how teachers can sidestep the all-too-familiar cycle of zealous overselling, eventual disappointment, backlash, and abandonment that undermined Logo?s first appearance in American school curricula. Of particular interest to teachers, parents, computer programmers, and members of the general public, Logo: A Retrospective, thoroughly and more accurately outlines Logo?s philosophical and theoretical framework and shows you how you can play a part in the current Logo renaissance already thriving in Australia, Latin America, and Europe. Specifically, this book contains: a decade?s worth of scholarly research on Logo information concerning Logo?s future and evolution strategies for handling student autonomy and teacher intervention recent software design data and feedback for learning Logo new research on computer programming?s effects on children?s cognitive development Without a doubt, computers and other electronic media will be a vital source of learning in the classrooms of the future. The development of powerful new versions of the Logo language, such as MicroWorlds, is welcome evidence that Logo?s popularity is on the rise. So put the past behind you. Read Logo: A Retrospective, and see what?s presently giving schoolchildren all over the world a fresh headstart at their classroom computer terminals.

Paris--a Musical Gazetteer

Author: Nigel Simeone
Publisher: Yale University Press
ISBN: 9780300080544
Category: History
Page: 299
View: 8522

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This essential guidebook is designed for all travelers interested in exploring the historic musical sites of Paris - in person or from an armchair. Paris is a uniquely rich music capital, its streets echoing with centuries of great music that has been created and performed there. Virtually every neighborhood boasts a concert hall, church, museum, or home that has played a significant role in the extraordinary musical tradition of the city. This gazetteer will guide you to the important musical landmarks in Paris and explain why each is noteworthy.

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: 9790

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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.

Advanced Logo

A Language for Learning
Author: Michael Friendly
Publisher: Psychology Press
ISBN: 1317766784
Category: Psychology
Page: 676
View: 9921

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Advanced Logo shows how LOGO can be used as a vehicle to promote problem solving skills among secondary students, college students, and instructors. The book demonstrates the wide range of educational domains that can be explored through LOGO including generative grammars, physical laws of motion and mechanics, artificial intelligence, robotics, and calculus.

Perspectives on the Teaching of Geometry for the 21st Century

An ICMI Study
Author: C. Mammana,V. Villani
Publisher: Springer Science & Business Media
ISBN: 9401152268
Category: Education
Page: 353
View: 2938

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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.

Computers and mathematics

the use of computers in undergraduate instruction : a project of the Committee on Computers in Mathematics Education of the Mathematical Association of America
Author: David Alexander Smith,Mathematical Association of America. Committee on Computers in Mathematics Education
Publisher: Mathematical Assn of Amer
ISBN: 9780883850596
Category: Mathematics
Page: 147
View: 1227

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MAA Notes

Author: N.A
Publisher: The Mathematical Association of America
Category: Education
Page: N.A
View: 3276

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Visualization in Human-Computer Interaction

7th Interdisciplinary Workshop on Informatics and Psychology, Schärding, Austria, May 24-27, 1988. Selected Contributions
Author: Peter Gorny,Michael J. Tauber
Publisher: Springer Science & Business Media
ISBN: 9783540526988
Category: Computers
Page: 274
View: 3448

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This volume presents a selection of the contributions to the 7th Workshop on Informatics and Psychology, held in May 1988 in Austria. The theme of the workshop was visualization in human-computer interaction.

Gaia Matrix

Arkhom and the Geometries of Destiny in the North American Landscape
Author: Peter William Champoux,William Stuart Buehler
Publisher: Gaia Matrix
ISBN: 0967232805
Category: Gaia hypothesis
Page: 249
View: 7584

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