Thinking Geometrically
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Thinking Geometrically
Author: Thomas Q. Sibley
language: en
Publisher: The Mathematical Association of America
Release Date: 2015-08-14
Thinking Geometrically: A Survey of Geometries is a well written and comprehensive survey of college geometry that would serve a wide variety of courses for both mathematics majors and mathematics education majors. Great care and attention is spent on developing visual insights and geometric intuition while stressing the logical structure, historical development, and deep interconnectedness of the ideas. Students with less mathematical preparation than upper-division mathematics majors can successfully study the topics needed for the preparation of high school teachers. There is a multitude of exercises and projects in those chapters developing all aspects of geometric thinking for these students as well as for more advanced students. These chapters include Euclidean Geometry, Axiomatic Systems and Models, Analytic Geometry, Transformational Geometry, and Symmetry. Topics in the other chapters, including Non-Euclidean Geometry, Projective Geometry, Finite Geometry, Differential Geometry, and Discrete Geometry, provide a broader view of geometry. The different chapters are as independent as possible, while the text still manages to highlight the many connections between topics. The text is self-contained, including appendices with the material in Euclid’s first book and a high school axiomatic system as well as Hilbert’s axioms. Appendices give brief summaries of the parts of linear algebra and multivariable calculus needed for certain chapters. While some chapters use the language of groups, no prior experience with abstract algebra is presumed. The text will support an approach emphasizing dynamical geometry software without being tied to any particular software.
Thinking Geometrically
Author: John T. Waisanen
language: en
Publisher: Peter Lang Incorporated, International Academic Publishers
Release Date: 2002
What skills do we need to negotiate the changing technological circumstances of our lives? How should we respond to the changing space of the visual, the technological? We are bombarded with answers to these questions: by media, by government, and by education. For the most part we are told that what we need to do is utilize the latest technologies and develop the newest skills (computer literacy prominent among them). Here, with keen interdisciplinary insight, historical sensitivity, and corporate design experience, John T. Waisanen offers a different kind of argument. He looks to particular skills we might be losing (and might have for some time been losing): drawing in particular; and to the «art» of integrating complex vision, thought and practice, what he calls design - or geometrical thinking. This points to the importance of the arts as a physical practice and to the cultivation of complex vision and thought gained in and through an education where geometry and literature are equally important, where physical intelligence (not just dexterity) and philosophical intelligence are equally important.
Developing Thinking in Geometry
'Geometry is often given less time in the teaching timetable than other aspects of mathematics. This book encourages practitioners to think about and raise its profile, indeed achieving what its title suggest' - Primary Practice `This creative, innovative and fascinating book/CD package is one you "MUST BUY". All prospective, new and experienced teachers of mathematics can use it to transform their teaching. All readers can use it to reignite their fascination with mathematics' - Professor Sylvia Johnson, Sheffield Hallam University 'This book exudes activity and interactivity. Moreover, it provides challenge in the context of a significant pedagogy, one that is not just present but actually made explicit. It is undoubtedly a book to learn geometry with, but also one to learn to think more deeply about geometry, about its nature and essence, and also about its teaching and learning' - David Pimm Developing Thinking in Geometry enables teachers and their support staff to experience and teach geometric thinking. As well as discussing key teaching principles, the book and accompanying interactive CD include many activities that encourage readers to extend their own learning, and consequently their teaching practices. The book is constructed around the following key themes: - invariance; - language and points of view; - reasoning using invariance; - visualising and representing. These themes draw on teaching principles developed by the team at the Open University's Centre for Mathematics Education which has a 20-year track record of innovative approaches to teaching and learning geometry. This is a 'must have' text for all primary mathematics specialists, secondary and Further Education mathematics teachers and their support staff. Anyone who wishes to create an understanding and enthusiasm for geometry based upon firm research and effective practice, will enjoy this book. This is the course reader for the Open University Course ME627 Developing Geometric Thinking
