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Author: Barbara E. Reynolds
Publisher: John Wiley & Sons
ISBN: 1119718112
Category : Education
Languages : en
Pages : 371
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Book Description
From two authors who embrace technology in the classroom and value the role of collaborative learning comes College Geometry Using GeoGebra, a book that is ideal for geometry courses for both mathematics and math education majors. The book's discovery-based approach guides students to explore geometric worlds through computer-based activities, enabling students to make observations, develop conjectures, and write mathematical proofs. This unique textbook helps students understand the underlying concepts of geometry while learning to use GeoGebra software—constructing various geometric figures and investigating their properties, relationships, and interactions. The text allows students to gradually build upon their knowledge as they move from fundamental concepts of circle and triangle geometry to more advanced topics such as isometries and matrices, symmetry in the plane, and hyperbolic and projective geometry. Emphasizing active collaborative learning, the text contains numerous fully-integrated computer lab activities that visualize difficult geometric concepts and facilitate both small-group and whole-class discussions. Each chapter begins with engaging activities that draw students into the subject matter, followed by detailed discussions that solidify the student conjectures made in the activities and exercises that test comprehension of the material. Written to support students and instructors in active-learning classrooms that incorporate computer technology, College Geometry with GeoGebra is an ideal resource for geometry courses for both mathematics and math education majors.
Author: Barbara E. Reynolds
Publisher: John Wiley & Sons
ISBN: 1119718112
Category : Education
Languages : en
Pages : 371
Get Book Here
Book Description
From two authors who embrace technology in the classroom and value the role of collaborative learning comes College Geometry Using GeoGebra, a book that is ideal for geometry courses for both mathematics and math education majors. The book's discovery-based approach guides students to explore geometric worlds through computer-based activities, enabling students to make observations, develop conjectures, and write mathematical proofs. This unique textbook helps students understand the underlying concepts of geometry while learning to use GeoGebra software—constructing various geometric figures and investigating their properties, relationships, and interactions. The text allows students to gradually build upon their knowledge as they move from fundamental concepts of circle and triangle geometry to more advanced topics such as isometries and matrices, symmetry in the plane, and hyperbolic and projective geometry. Emphasizing active collaborative learning, the text contains numerous fully-integrated computer lab activities that visualize difficult geometric concepts and facilitate both small-group and whole-class discussions. Each chapter begins with engaging activities that draw students into the subject matter, followed by detailed discussions that solidify the student conjectures made in the activities and exercises that test comprehension of the material. Written to support students and instructors in active-learning classrooms that incorporate computer technology, College Geometry with GeoGebra is an ideal resource for geometry courses for both mathematics and math education majors.
Author: Barbara E Reynolds
Publisher:
ISBN: 9781119718086
Category :
Languages : en
Pages :
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Book Description
"Several years ago, we co-authored the text College Geometry using The Geometer's Sketchpada. In the time since then, friends and colleagues have expressed substantial interest in using our course materials with an alternative software package, GeoGebraa. Indeed, some reported to us that they have used the Sketchpad book with GeoGebra and have experienced good success. Spurred on by those reports, we began experimenting ourselves with this other option for geometry software. This new text is the result of our course experiences with GeoGebra. Of course, there are differences in commands and tools between the two software packages. Those differences imposed frequent re-wording and revising of the computer investigations. Further, the algebraic presentation used by GeoGebra required us to re-think many of the investigations to encourage students to grapple with the geometric content. The activities have been re-written to match GeoGebra, as have the portions of the text that discuss the specific software. However, the geometric content remains the same as our earlier text. We hope this new version of College Geometry will support students and instructors who desire a pedagogy that incorporates technology in an active, exploratory classroom"--
Author: Gerard A. Venema
Publisher: American Mathematical Soc.
ISBN: 0883857847
Category : Mathematics
Languages : en
Pages : 147
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Book Description
This book provides an inquiry-based introduction to advanced Euclidean geometry. It utilizes dynamic geometry software, specifically GeoGebra, to explore the statements and proofs of many of the most interesting theorems in the subject. Topics covered include triangle centers, inscribed, circumscribed, and escribed circles, medial and orthic triangles, the nine-point circle, duality, and the theorems of Ceva and Menelaus, as well as numerous applications of those theorems. The final chapter explores constructions in the Poincare disk model for hyperbolic geometry. The book can be used either as a computer laboratory manual to supplement an undergraduate course in geometry or as a stand-alone introduction to advanced topics in Euclidean geometry. The text consists almost entirely of exercises (with hints) that guide students as they discover the geometric relationships for themselves. First the ideas are explored at the computer and then those ideas are assembled into a proof of the result under investigation. The goals are for the reader to experience the joy of discovering geometric relationships, to develop a deeper understanding of geometry, and to encourage an appreciation for the beauty of Euclidean geometry.
Author: Barbara E. Reynolds
Publisher: Wiley Global Education
ISBN: 1118213408
Category : Mathematics
Languages : en
Pages : 376
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Book Description
From two authors who embrace technology in the classroom and value the role of collaborative learning comes College Geometry Using The Geometer's Sketchpad, a book that is ideal for geometry courses for both mathematics and math education majors. The book's truly discovery-based approach guides students to learn geometry through explorations of topics ranging from triangles and circles to transformational, taxicab, and hyperbolic geometries. In the process, students hone their understanding of geometry and their ability to write rigorous mathematical proofs.
Author: Barbara E. Reynolds
Publisher:
ISBN: 9781119718123
Category : Geometry
Languages : en
Pages : 311
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Book Description
"Several years ago, we co-authored the text College Geometry using The Geometer's Sketchpad®. In the time since then, friends and colleagues have expressed substantial interest in using our course materials with an alternative software package, GeoGebra®. Indeed, some reported to us that they have used the Sketchpad book with GeoGebra and have experienced good success. Spurred on by those reports, we began experimenting ourselves with this other option for geometry software. This new text is the result of our course experiences with GeoGebra. Of course, there are differences in commands and tools between the two software packages. Those differences imposed frequent re-wording and revising of the computer investigations. Further, the algebraic presentation used by GeoGebra required us to re-think many of the investigations to encourage students to grapple with the geometric content. The activities have been re-written to match GeoGebra, as have the portions of the text that discuss the specific software. However, the geometric content remains the same as our earlier text. We hope this new version of College Geometry will support students and instructors who desire a pedagogy that incorporates technology in an active, exploratory classroom"--
Author: Maureen T. Carroll
Publisher: American Mathematical Soc.
ISBN: 1470448432
Category : Mathematics
Languages : en
Pages : 502
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Book Description
Geometry: The Line and the Circle is an undergraduate text with a strong narrative that is written at the appropriate level of rigor for an upper-level survey or axiomatic course in geometry. Starting with Euclid's Elements, the book connects topics in Euclidean and non-Euclidean geometry in an intentional and meaningful way, with historical context. The line and the circle are the principal characters driving the narrative. In every geometry considered—which include spherical, hyperbolic, and taxicab, as well as finite affine and projective geometries—these two objects are analyzed and highlighted. Along the way, the reader contemplates fundamental questions such as: What is a straight line? What does parallel mean? What is distance? What is area? There is a strong focus on axiomatic structures throughout the text. While Euclid is a constant inspiration and the Elements is repeatedly revisited with substantial coverage of Books I, II, III, IV, and VI, non-Euclidean geometries are introduced very early to give the reader perspective on questions of axiomatics. Rounding out the thorough coverage of axiomatics are concluding chapters on transformations and constructibility. The book is compulsively readable with great attention paid to the historical narrative and hundreds of attractive problems.
Author: Annalisa Crannell
Publisher: Princeton University Press
ISBN: 0691197385
Category : Mathematics
Languages : en
Pages : 291
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Book Description
Through a unique approach combining art and mathematics, Perspective and Projective Geometry introduces students to the ways that projective geometry applies to perspective art. Geometry, like mathematics as a whole, offers a useful and meaningful lens for understanding the visual world. Exploring pencil-and-paper drawings, photographs, Renaissance paintings, and GeoGebra constructions, this textbook equips students with the geometric tools for projecting a three-dimensional scene onto two dimensions. Organized as a series of exercise modules, this book teaches students through hands-on inquiry and participation. Each lesson begins with a visual puzzle that can be investigated through geometry, followed by exercises that reinforce new concepts and hone students’ analytical abilities. An electronic instructor’s manual available to teachers contains sample syllabi and advice, including suggestions for pacing and grading rubrics for art projects. Drawing vital interdisciplinary connections between art and mathematics, Perspective and Projective Geometry is ideally suited for undergraduate students interested in mathematics or computer graphics, as well as for mathematically inclined students of architecture or art. · Features computer-based GeoGebra modules and hands-on exercises · Contains ample visual examples, math and art puzzles, and proofs with real-world applications · Suitable for college students majoring in mathematics, computer science, and art · Electronic instructor’s manual (available only to teachers)
Author: Miltiadis D. Lytras
Publisher: Springer Science & Business Media
ISBN: 3642131654
Category : Computers
Languages : en
Pages : 724
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Book Description
It is a great pleasure to share with you the Springer CCIS proceedings of the First International Conference on Reforming Education, Quality of Teaching and Technology-Enhanced Learning: Learning Technologies, Quality of Education, Educational Systems, Evaluation, Pedagogies––TECH-EDUCATION 2010, Which was a part of the World Summit on the Knowledge Society Conference Series. TECH-EDUCATION 2010 was a bold effort aiming to foster a debate on the global need in our times to invest in education. The topics of the conference dealt with six general pillars: Track 1. Quality of Education––A new Vision Track 2. Technology-Enhanced Learning––Learning Technologies––Personalization-E-learning Track 3. Educational Strategies Track 4. Collaborative/ Constructive/ Pedagogical/ Didactical Approaches Track 5. Formal/ Informal/ and Life–Long Learning Perspectives Track 6. Contribution of Education to Sustainable Development Within this general context the Program Committee of the conference invited contributions that fall in to the following list of topics. Track 1: Quality of the Education––A new Vision • Teaching Methodologies and Case Studies • Reforms in Degrees • The European Educational Space • Academic Curricula Designs • Quality of Teaching and Learning • Quality and Academic Assessment • The School / University of the Future • Challenges for Higher Education in the 21st Century • New Managerial Models for Education • Financing the New Model for Education of the 21st Century • The Quality Milestones for Education of the 21st Century • Evaluation in Academia • The Role of Teachers • International Collaborations for Joint Programs/Degrees • Industry–Academia Synergies • Research Laboratories Management
Author: H.S.M. Coxeter
Publisher: Springer Science & Business Media
ISBN: 9780387406237
Category : Mathematics
Languages : en
Pages : 180
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Book Description
In Euclidean geometry, constructions are made with ruler and compass. Projective geometry is simpler: its constructions require only a ruler. In projective geometry one never measures anything, instead, one relates one set of points to another by a projectivity. The first two chapters of this book introduce the important concepts of the subject and provide the logical foundations. The third and fourth chapters introduce the famous theorems of Desargues and Pappus. Chapters 5 and 6 make use of projectivities on a line and plane, respectively. The next three chapters develop a self-contained account of von Staudt's approach to the theory of conics. The modern approach used in that development is exploited in Chapter 10, which deals with the simplest finite geometry that is rich enough to illustrate all the theorems nontrivially. The concluding chapters show the connections among projective, Euclidean, and analytic geometry.
Author: Gerard Venema
Publisher:
ISBN: 9780136020585
Category : Geometry
Languages : en
Pages : 0
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Book Description
Normal 0 false false false Foundations of Geometry, Second Edition is written to help enrich the education of all mathematics majors and facilitate a smooth transition into more advanced mathematics courses. The text also implements the latest national standards and recommendations regarding geometry for the preparation of high school mathematics teachers--and encourages students to make connections between their college courses and classes they will later teach. This text's coverage begins with Euclid's Elements, lays out a system of axioms for geometry, and then moves on to neutral geometry, Euclidian and hyperbolic geometries from an axiomatic point of view, and then non-Euclidean geometry. Good proof-writing skills are emphasized, along with a historical development of geometry. The Second Edition streamlines and reorganizes material in order to reach coverage of neutral geometry as early as possible, adds more exercises throughout, and facilitates use of the open-source software Geogebra. This text is ideal for an undergraduate course in axiomatic geometry for future high school geometry teachers, or for any student who has not yet encountered upper-level math, such as real analysis or abstract algebra. It assumes calculus and linear algebra as prerequisites.
