International Perspectives on Teaching and Learning Mathematics with Virtual Manipulatives

Author: Patricia S. Moyer-Packenham

Publisher: Springer

ISBN: 3319327186

Category: Education

Page: 345

View: 1174

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This book explores terminology, frameworks, and research being conducted worldwide on virtual manipulatives. It brings together international authors who provide their perspectives on virtual manipulatives in research and teaching. By defining terminology, explaining conceptual and theoretical frameworks, and reporting research, the authors provide a comprehensive foundation on the study and use of virtual manipulatives for mathematics teaching and learning. This foundation provides a common way for researchers to communicate about virtual manipulatives and build on the major works that have been conducted on this topic. By discussing these big ideas, the book advances knowledge for future research on virtual manipulatives as these dynamic tools move from computer platforms to hand-held, touch-screen, and augmented platforms.

Mathematics and the Body

Material Entanglements in the Classroom

Author: Elizabeth de Freitas,Nathalie Sinclair

Publisher: Cambridge University Press

ISBN: 1107039487

Category: Education

Page: 312

View: 8143

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This book expands the landscape of research in mathematics education by analyzing how the body influences mathematical thinking.

Quaternions and Rotation Sequences

A Primer with Applications to Orbits, Aerospace, and Virtual Reality

Author: Jack B. Kuipers

Publisher: Princeton University Press

ISBN: 9780691102986

Category: Mathematics

Page: 371

View: 7290

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Ever since the Irish mathematician William Rowan Hamilton introduced quaternions in the nineteenth century--a feat he celebrated by carving the founding equations into a stone bridge--mathematicians and engineers have been fascinated by these mathematical objects. Today, they are used in applications as various as describing the geometry of spacetime, guiding the Space Shuttle, and developing computer applications in virtual reality. In this book, J. B. Kuipers introduces quaternions for scientists and engineers who have not encountered them before and shows how they can be used in a variety of practical situations. The book is primarily an exposition of the quaternion, a 4-tuple, and its primary application in a rotation operator. But Kuipers also presents the more conventional and familiar 3 x 3 (9-element) matrix rotation operator. These parallel presentations allow the reader to judge which approaches are preferable for specific applications. The volume is divided into three main parts. The opening chapters present introductory material and establish the book's terminology and notation. The next part presents the mathematical properties of quaternions, including quaternion algebra and geometry. It includes more advanced special topics in spherical trigonometry, along with an introduction to quaternion calculus and perturbation theory, required in many situations involving dynamics and kinematics. In the final section, Kuipers discusses state-of-the-art applications. He presents a six degree-of-freedom electromagnetic position and orientation transducer and concludes by discussing the computer graphics necessary for the development of applications in virtual reality.

Visual Mathematics and Cyberlearning

Author: Dragana Martinovic,Viktor Freiman,Zekeriya Karadag

Publisher: Springer Science & Business Media

ISBN: 9400723210

Category: Education

Page: 250

View: 8992

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This first book in the series will describe the Net Generation as visual learners who thrive when surrounded with new technologies and whose needs can be met with the technological innovations. These new learners seek novel ways of studying, such as collaborating with peers, multitasking, as well as use of multimedia, the Internet, and other Information and Communication Technologies. Here we present mathematics as a contemporary subject that is engaging, exciting and enlightening in new ways. For example, in the distributed environment of cyber space, mathematics learners play games, watch presentations on YouTube, create Java applets of mathematics simulations and exchange thoughts over the Instant Messaging tool. How should mathematics education resonate with these learners and technological novelties that excite them?

New Tertiary Mathematics

Further Applied Mathematics

Author: C. Plumpton,P. S. W. Macliwaine

Publisher: Elsevier

ISBN: 1483147738

Category: Mathematics

Page: 233

View: 8504

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New Tertiary Mathematics, Volume 2, Part 2: Further Applied Mathematics deals with various topics of theoretical mechanics and probability, from statics and the dynamics of a rigid body to the dynamics of a particle with one and two degrees of freedom. Many examples of varying difficulty are worked in the text and exercises are added after each major topic is covered. This book is comprised of five chapters and opens with a discussion on statics, with particular reference to the analysis of systems of forces in three dimensions, along with virtual work, stability, and the catenary. Complicated equilibrium problems are considered. The reader is then introduced to the dynamics of a particle in one and two dimensions, as well as the implications of the Galilean transformation and the general theorems of motion for a system of particles. These theorems are applied to simple cases of the motion of a rigid body. The final chapter on probability examines normal and Poisson distributions, Markov chains, and miscellaneous problems. This monograph will be a useful resource for mathematical pupils and students engaged in private study.

A Course in the Geometry of N Dimensions

Author: Maurice G. Kendall

Publisher: Courier Corporation

ISBN: 0486439275

Category: Mathematics

Page: 63

View: 3523

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This text for undergraduate students provides a foundation for resolving proofs dependent on n-dimensional systems. The two-part treatment begins with simple figures in n dimensions and advances to examinations of the contents of hyperspheres, hyperellipsoids, hyperprisms, etc. The second part explores the mean in rectangular variation, the correlation coefficient in bivariate normal variation, Wishart's distribution, more. 1961 edition.

The Development of Mathematics

Author: E. T. Bell

Publisher: Courier Corporation

ISBN: 0486152286

Category: Mathematics

Page: 656

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Time-honored study by a prominent scholar of mathematics traces decisive epochs from the evolution of mathematical ideas in ancient Egypt and Babylonia to major breakthroughs in the 19th and 20th centuries. 1945 edition.

Mathematics, Ideas and the Physical Real

Author: Albert Lautman

Publisher: A&C Black

ISBN: 1441144331

Category: Philosophy

Page: 352

View: 6009

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Albert Lautman (1908-1944) was a French philosopher of mathematics whose work played a crucial role in the history of contemporary French philosophy. His ideas have had an enormous influence on key contemporary thinkers including Gilles Deleuze and Alain Badiou, for whom he is a major touchstone in the development of their own engagements with mathematics. Mathematics, Ideas and the Physical Real presents the first English translation of Lautman's published works between 1933 and his death in 1944. Rather than being preoccupied with the relation of mathematics to logic or with the problems of foundation, which have dominated philosophical reflection on mathematics, Lautman undertakes to develop an understanding of the broader structure of mathematics and its evolution. The two powerful ideas that are constants throughout his work, and which have dominated subsequent developments in mathematics, are the concept of mathematical structure and the idea of the essential unity underlying the apparent multiplicity of mathematical disciplines. This collection of his major writings offers readers a much-needed insight into his influence on the development of mathematics and philosophy.

Priority of Events

Author: Sean Bowden

Publisher: Edinburgh University Press

ISBN: 0748650776

Category: Philosophy

Page: 304

View: 3973

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This is a radical interpretation of Deleuze's Logic of Sense. It focuses on Deleuze's concept of events and brings Deleuze's work into relation with the traditions of process philosophy and American pragmatism.

Mobile Learning and Mathematics

Foundations, Design, and Case Studies

Author: Helen Crompton,John Traxler

Publisher: Routledge

ISBN: 131780421X

Category: Education

Page: 248

View: 5365

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Mobile Learning and Mathematics provides an overview of current research on how mobile devices are supporting mathematics educators in classrooms across the globe. Through nine case studies, chapter authors investigate the use of mobile technologies over a range of grade levels and mathematical topics, while connecting chapters provide a strong foundational background in mobile learning theories, instructional design, and learner support. For current educators, Mobile Learning and Mathematics provides concrete ideas and strategies for integrating mobile learning into their mathematics instruction—for example, by sharing resources that will help implement Common Core State Standards, or by streamlining the process of selecting from the competing and often confusing technology options currently available. A cutting edge research volume, this collection also provides a springboard for educational researchers to conduct further study.

Parallel Processing and Applied Mathematics

4th International Conference, PPAM 2001 Naleczow, Poland, September 9-12, 2001 Revised Papers

Author: Roman Wyrzykowski

Publisher: Springer Science & Business Media

ISBN: 3540437924

Category: Computers

Page: 915

View: 8667

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This book constitutes the thoroughly refereed post-proceedings of the 4th International Conference on Parallel Processing and Applied Mathematics, PPAM 2002, held in Naleczow, Poland, in September 2001. The 101 papers presented were carefully reviewed and improved during two rounds of reviewing and revision. The book offers topical sections on distributed and grid architectures, scheduling and load balancing, performance analysis and prediction, parallel non-numerical algorithms, parallel programming, tools and environments, parallel numerical algorithms, applications, and evolutionary computing and neural networks.

A Course of Mathematics for Engineers and Scientists

Theoretical Mechanics

Author: Brian H. Chirgwin,Charles Plumpton

Publisher: Elsevier

ISBN: 1483139867

Category: Mathematics

Page: 382

View: 7380

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A Course of Mathematics for Engineers and Scientists, Volume 3: Theoretical Mechanics introduces the concepts of virtual work, generalized coordinates and the derivation of generalized forces from the potential energy function. This book is composed of 10 chapters and begins with the principles of mechanics, plane statistics, virtual work, and continuously distributed forces. The succeeding chapters deal with the motion of a particle and the uniplanar motion of a rigid body, as well as the concept of particle dynamics. These topics are followed by discussions of the motions of interacting particles and the principles of stability. The final chapter describes the impulsive motion of a system of particles and collision between bodies. This book will be of value to mathematics and engineering students.

Mathematics and Plausible Reasoning: Patterns of plausible inference

Author: George Pólya

Publisher: Princeton University Press

ISBN: 9780691025100

Category: Mathematics

Page: 225

View: 4647

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A guide to the practical art of plausible reasoning, this book has relevance in every field of intellectual activity. Professor Polya, a world-famous mathematician from Stanford University, uses mathematics to show how hunches and guesses play an important part in even the most rigorously deductive science. He explains how solutions to problems can be guessed at; good guessing is often more important than rigorous deduction in finding correct solutions. Vol. II, on Patterns of Plausible Inference, attempts to develop a logic of plausibility. What makes some evidence stronger and some weaker? How does one seek evidence that will make a suspected truth more probable? These questions involve philosophy and psychology as well as mathematics.