Visualization in Teaching and Learning Mathematics PDF Download
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Author: Walter Zimmermann
Publisher: MAA Press
ISBN:
Category : Mathematics
Languages : en
Pages : 242
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Book Description
The twenty papers in the book give an overview of research analysis, practical experience, and informed opinion about the role of visualization in teaching and learning mathematics, especially at the undergraduate level. Visualization, in its broadest level. Visualization, in its broadest sense, is as old as mathematics, but progress in computer graphics has generated a renaissance of interest in visual representations and visual thinking in mathematics.
Author: Walter Zimmermann
Publisher: MAA Press
ISBN:
Category : Mathematics
Languages : en
Pages : 242
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Book Description
The twenty papers in the book give an overview of research analysis, practical experience, and informed opinion about the role of visualization in teaching and learning mathematics, especially at the undergraduate level. Visualization, in its broadest level. Visualization, in its broadest sense, is as old as mathematics, but progress in computer graphics has generated a renaissance of interest in visual representations and visual thinking in mathematics.
Author: Linda M. Phillips
Publisher: Springer Science & Business Media
ISBN: 9048188164
Category : Science
Languages : en
Pages : 112
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Book Description
Science education at school level worldwide faces three perennial problems that have become more pressing of late. These are to a considerable extent interwoven with concerns about the entire school curriculum and its reception by students. The rst problem is the increasing intellectual isolation of science from the other subjects in the school curriculum. Science is too often still taught didactically as a collection of pre-determined truths about which there can be no dispute. As a con- quence, many students do not feel any “ownership” of these ideas. Most other school subjects do somewhat better in these regards. For example, in language classes, s- dents suggest different interpretations of a text and then debate the relative merits of the cases being put forward. Moreover, ideas that are of use in science are presented to students elsewhere and then re-taught, often using different terminology, in s- ence. For example, algebra is taught in terms of “x, y, z” in mathematics classes, but students are later unable to see the relevance of that to the meaning of the universal gas laws in physics, where “p, v, t” are used. The result is that students are c- fused and too often alienated, leading to their failure to achieve that “extraction of an education from a scheme of instruction” which Jerome Bruner thought so highly desirable.
Author: Kelly S. Mix
Publisher: Springer
ISBN: 3319987674
Category : Education
Languages : en
Pages : 382
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Book Description
This unique volume surveys recent research on spatial visualization in mathematics in the fields of cognitive psychology and mathematics education. The general topic of spatial skill and mathematics has a long research tradition, but has been gaining attention in recent years, although much of this research happens in disconnected subfields. This volume aims to promote interaction between researchers, not only to provide a more comprehensive view of spatial visualization and mathematics, but also to stimulate innovative new directions in research based on a more coordinated effort. It features ten chapters authored by leading researchers in cognitive psychology and mathematics education, as well as includes dynamic commentaries by mathematics education researchers on cognitive psychology chapters, and by cognitive psychologists on mathematics education chapters. Among the topics included: From intuitive spatial measurement to understanding of units. Spatial reasoning: a critical problem-solving tool in children’s mathematics strategy tool-kit. What processes underlie the relation between spatial skill and mathematics? Learning with and from drawing in early years geometry. Communication of visual information and complexity of reasoning by mathematically talented students. Visualizing Mathematics makes substantial progress in understanding the role of spatial reasoning in mathematical thought and in connecting various subfields of research. It promises to make an impact among psychologists, education scholars, and mathematics educators in the convergence of psychology and education.
Author: Paolo Mancosu
Publisher: Springer Science & Business Media
ISBN: 9781402033346
Category : Mathematics
Languages : en
Pages : 336
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Book Description
This book contains groundbreaking contributions to the philosophical analysis of mathematical practice. Several philosophers of mathematics have recently called for an approach to philosophy of mathematics that pays more attention to mathematical practice. Questions concerning concept-formation, understanding, heuristics, changes in style of reasoning, the role of analogies and diagrams etc. have become the subject of intense interest. The historians and philosophers in this book agree that there is more to understanding mathematics than a study of its logical structure. How are mathematical objects and concepts generated? How does the process tie up with justification? What role do visual images and diagrams play in mathematical activity? What are the different epistemic virtues (explanatoriness, understanding, visualizability, etc.) which are pursued and cherished by mathematicians in their work? The reader will find here systematic philosophical analyses as well as a wealth of philosophically informed case studies ranging from Babylonian, Greek, and Chinese mathematics to nineteenth century real and complex analysis.
Author: Henry Segerman
Publisher: JHU Press
ISBN: 1421420368
Category : Mathematics
Languages : en
Pages : 201
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Book Description
The first book to explain mathematics using 3D printed models. Winner of the Technical Text of the Washington Publishers Wouldn’t it be great to experience three-dimensional ideas in three dimensions? In this book—the first of its kind—mathematician and mathematical artist Henry Segerman takes readers on a fascinating tour of two-, three-, and four-dimensional mathematics, exploring Euclidean and non-Euclidean geometries, symmetry, knots, tilings, and soap films. Visualizing Mathematics with 3D Printing includes more than 100 color photographs of 3D printed models. Readers can take the book’s insights to a new level by visiting its sister website, 3dprintmath.com, which features virtual three-dimensional versions of the models for readers to explore. These models can also be ordered online or downloaded to print on a 3D printer. Combining the strengths of book and website, this volume pulls higher geometry and topology out of the realm of the abstract and puts it into the hands of anyone fascinated by mathematical relationships of shape. With the book in one hand and a 3D printed model in the other, readers can find deeper meaning while holding a hyperbolic honeycomb, touching the twists of a torus knot, or caressing the curves of a Klein quartic.
Author: Gerald Farin
Publisher: CRC Press
ISBN: 1439865043
Category : Computers
Languages : en
Pages : 286
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Book Description
This non-traditional introduction to the mathematics of scientific computation describes the principles behind the major methods, from statistics, applied mathematics, scientific visualization, and elsewhere, in a way that is accessible to a large part of the scientific community. Introductory material includes computational basics, a review of coo
Author: Claude P. Bruter
Publisher: Springer Science & Business Media
ISBN: 3662049090
Category : Mathematics
Languages : en
Pages : 337
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Book Description
Recent progress in research, teaching and communication has arisen from the use of new tools in visualization. To be fruitful, visualization needs precision and beauty. This book is a source of mathematical illustrations by mathematicians as well as artists. It offers examples in many basic mathematical fields including polyhedra theory, group theory, solving polynomial equations, dynamical systems and differential topology. For a long time, arts, architecture, music and painting have been the source of new developments in mathematics. And vice versa, artists have often found new techniques, themes and inspiration within mathematics. Here, while mathematicians provide mathematical tools for the analysis of musical creations, the contributions from sculptors emphasize the role of mathematics in their work.
Author: H.-C. Hege
Publisher: Springer Science & Business Media
ISBN: 3642591957
Category : Mathematics
Languages : en
Pages : 391
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Book Description
Visualization and mathematics have begun a fruitful relationship, establishing links between problems and solutions of both fields. In some areas of mathematics, like differential geometry and numerical mathematics, visualization techniques are applied with great success. However, visualization methods are relying heavily on mathematical concepts. Applications of visualization in mathematical research and the use of mathematical methods in visualization have been topic of an international workshop in Berlin in June 1995. Selected contributions treat topics of particular interest in current research. Experts are reporting on their latest work, giving an overview on this fascinating new area. The reader will get insight to state-of-the-art techniques for solving visualization problems and mathematical questions.
Author: Alex Bellos
Publisher: Simon and Schuster
ISBN: 1451640129
Category : Mathematics
Languages : en
Pages : 352
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Book Description
From triangles, rotations and power laws, to cones, curves and the dreaded calculus, Alex takes you on a journey of mathematical discovery with his signature wit and limitless enthusiasm. He sifts through over 30,000 survey submissions to uncover the world’s favourite number, and meets a mathematician who looks for universes in his garage. He attends the World Mathematical Congress in India, and visits the engineer who designed the first roller-coaster loop. Get hooked on math as Alex delves deep into humankind’s turbulent relationship with numbers, and reveals how they have shaped the world we live in.
Author: H.-C. Hege
Publisher: Springer Science & Business Media
ISBN: 9783540639916
Category : Mathematics
Languages : en
Pages : 422
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Book Description
Mathematical Visualization is a young new discipline. It offers efficient visualization tools to the classical subjects of mathematics, and applies mathematical techniques to problems in computer graphics and scientific visualization. Originally, it started in the interdisciplinary area of differential geometry, numerical mathematics, and computer graphics. In recent years, the methods developed have found important applications. The current volume is the quintessence of an international workshop in September 1997 in Berlin, focusing on recent developments in this emerging area. Experts present selected research work on new algorithms for visualization problems, describe the application and experiments in geometry, and develop new numerical or computer graphical techniques.
