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Author : Michael D. De Villiers
Publisher :
ISBN 13 : 9781559536462
Total Pages : 214 pages
Book Rating : 4.5/5 (364 download)
Download or read book Rethinking Proof With the Geometer's Sketchpad written by Michael D. De Villiers and published by . This book was released on 2006 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michael D. De Villiers
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (133 download)
Download or read book Rethinking Proof with Geometer's Sketchpad written by Michael D. De Villiers and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michael D. De Villiers
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (135 download)
Download or read book Rethinking Proof written by Michael D. De Villiers and published by . This book was released on 2003 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : KEY CURRICULUM
Publisher : McGraw-Hill Education
ISBN 13 : 9781604402797
Total Pages : 224 pages
Book Rating : 4.4/5 (27 download)
Download or read book The Geometer's Sketchpad, Rethinking Proof written by KEY CURRICULUM and published by McGraw-Hill Education. This book was released on 2012-09-01 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: These activities use the power of dynamic geometry to support students in making conjectures, then developing explanations of why they must be true.
Author : Gila Hanna
Publisher : Springer Science & Business Media
ISBN 13 : 9400721293
Total Pages : 468 pages
Book Rating : 4.4/5 (7 download)
Download or read book Proof and Proving in Mathematics Education written by Gila Hanna and published by Springer Science & Business Media. This book was released on 2012-06-14 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: *THIS BOOK IS AVAILABLE AS OPEN ACCESS BOOK ON SPRINGERLINK* One of the most significant tasks facing mathematics educators is to understand the role of mathematical reasoning and proving in mathematics teaching, so that its presence in instruction can be enhanced. This challenge has been given even greater importance by the assignment to proof of a more prominent place in the mathematics curriculum at all levels. Along with this renewed emphasis, there has been an upsurge in research on the teaching and learning of proof at all grade levels, leading to a re-examination of the role of proof in the curriculum and of its relation to other forms of explanation, illustration and justification. This book, resulting from the 19th ICMI Study, brings together a variety of viewpoints on issues such as: The potential role of reasoning and proof in deepening mathematical understanding in the classroom as it does in mathematical practice. The developmental nature of mathematical reasoning and proof in teaching and learning from the earliest grades. The development of suitable curriculum materials and teacher education programs to support the teaching of proof and proving. The book considers proof and proving as complex but foundational in mathematics. Through the systematic examination of recent research this volume offers new ideas aimed at enhancing the place of proof and proving in our classrooms.
Author : Andreas J. Stylianides
Publisher : Oxford University Press
ISBN 13 : 0191034738
Total Pages : 256 pages
Book Rating : 4.1/5 (91 download)
Download or read book Proving in the Elementary Mathematics Classroom written by Andreas J. Stylianides and published by Oxford University Press. This book was released on 2016-07-14 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although proving is core to mathematics as a sense-making activity, it currently has a marginal place in elementary classrooms internationally. Blending research with practical perspectives, this book addresses what it would take to elevate the place of proving at elementary school. The book uses classroom episodes from two countries to examine different kinds of proving tasks and the proving activity they can generate in the elementary classroom. It examines further the role of teachers in mediating the relationship between proving tasks and proving activity, including major mathematical and pedagogical issues that arise for teachers as they implement each kind of proving task. In addition to its contribution to research knowledge, the book has important implications for teaching, curricular resources, and teacher education.
Author : Dieter Probst
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 150150262X
Total Pages : 384 pages
Book Rating : 4.5/5 (15 download)
Download or read book Concepts of Proof in Mathematics, Philosophy, and Computer Science written by Dieter Probst and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-07-25 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: A proof is a successful demonstration that a conclusion necessarily follows by logical reasoning from axioms which are considered evident for the given context and agreed upon by the community. It is this concept that sets mathematics apart from other disciplines and distinguishes it as the prototype of a deductive science. Proofs thus are utterly relevant for research, teaching and communication in mathematics and of particular interest for the philosophy of mathematics. In computer science, moreover, proofs have proved to be a rich source for already certified algorithms. This book provides the reader with a collection of articles covering relevant current research topics circled around the concept 'proof'. It tries to give due consideration to the depth and breadth of the subject by discussing its philosophical and methodological aspects, addressing foundational issues induced by Hilbert's Programme and the benefits of the arising formal notions of proof, without neglecting reasoning in natural language proofs and applications in computer science such as program extraction.
Author : Barbara E. Reynolds
Publisher : John Wiley & Sons
ISBN 13 : 1119718112
Total Pages : 371 pages
Book Rating : 4.1/5 (197 download)
Download or read book College Geometry with GeoGebra written by Barbara E. Reynolds and published by John Wiley & Sons. This book was released on 2021-01-20 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Ronald N. Umble
Publisher : CRC Press
ISBN 13 : 1482234726
Total Pages : 235 pages
Book Rating : 4.4/5 (822 download)
Download or read book Transformational Plane Geometry written by Ronald N. Umble and published by CRC Press. This book was released on 2014-12-01 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for a one-semester course at the junior undergraduate level, Transformational Plane Geometry takes a hands-on, interactive approach to teaching plane geometry. The book is self-contained, defining basic concepts from linear and abstract algebra gradually as needed. The text adheres to the National Council of Teachers of Mathematics Principles and Standards for School Mathematics and the Common Core State Standards Initiative Standards for Mathematical Practice. Future teachers will acquire the skills needed to effectively apply these standards in their classrooms. Following Felix Klein's Erlangen Program, the book provides students in pure mathematics and students in teacher training programs with a concrete visual alternative to Euclid's purely axiomatic approach to plane geometry. It enables geometrical visualization in three ways: Key concepts are motivated with exploratory activities using software specifically designed for performing geometrical constructions, such as Geometer's Sketchpad. Each concept is introduced synthetically (without coordinates) and analytically (with coordinates). Exercises include numerous geometric constructions that use a reflecting instrument, such as a MIRA. After reviewing the essential principles of classical Euclidean geometry, the book covers general transformations of the plane with particular attention to translations, rotations, reflections, stretches, and their compositions. The authors apply these transformations to study congruence, similarity, and symmetry of plane figures and to classify the isometries and similarities of the plane.
Author : Robert E. Mason
Publisher : Trillium Press
ISBN 13 : 9780898245455
Total Pages : 93 pages
Book Rating : 4.2/5 (454 download)
Download or read book An Introduction to Geometer's Sketchpad written by Robert E. Mason and published by Trillium Press. This book was released on 1998-07 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Despina A. Stylianou
Publisher : Routledge
ISBN 13 : 1135856745
Total Pages : 515 pages
Book Rating : 4.1/5 (358 download)
Download or read book Teaching and Learning Proof Across the Grades written by Despina A. Stylianou and published by Routledge. This book was released on 2010-09-23 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Co-Publication of Routledge for the National Council of Teachers of Mathematics (NCTM) In recent years there has been increased interest in the nature and role of proof in mathematics education; with many mathematics educators advocating that proof should be a central part of the mathematics education of students at all grade levels. This important new collection provides that much-needed forum for mathematics educators to articulate a connected K-16 "story" of proof. Such a story includes understanding how the forms of proof, including the nature of argumentation and justification as well as what counts as proof, evolve chronologically and cognitively and how curricula and instruction can support the development of students’ understanding of proof. Collectively these essays inform educators and researchers at different grade levels about the teaching and learning of proof at each level and, thus, help advance the design of further empirical and theoretical work in this area. By building and extending on existing research and by allowing a variety of voices from the field to be heard, Teaching and Learning Proof Across the Grades not only highlights the main ideas that have recently emerged on proof research, but also defines an agenda for future study.
Author : Celia Hoyles
Publisher : Springer Science & Business Media
ISBN 13 : 1441901469
Total Pages : 489 pages
Book Rating : 4.4/5 (419 download)
Download or read book Mathematics Education and Technology-Rethinking the Terrain written by Celia Hoyles and published by Springer Science & Business Media. This book was released on 2009-10-09 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics Education and Technology-Rethinking the Terrain revisits the important 1985 ICMI Study on the influence of computers and informatics on mathematics and its teaching. The focus of this book, resulting from the seventeenth Study led by ICMI, is the use of digital technologies in mathematics teaching and learning in countries across the world. Specifically, it focuses on cultural diversity and how this diversity impinges on the use of digital technologies in mathematics teaching and learning. Within this focus, themes such as mathematics and mathematical practices; learning and assessing mathematics with and through digital technologies; teachers and teaching; design of learning environments and curricula; implementation of curricula and classroom practice; access, equity and socio-cultural issues; and connectivity and virtual networks for learning, serve to organize the study and bring it coherence. Providing a state-of-the-art view of the domain with regards to research, innovating practices and technological development, Mathematics Education and Technology-Rethinking the Terrain is of interest to researchers and all those interested in the role that digital technology plays in mathematics education.
Author : Sue Johnston-Wilder
Publisher : McGraw-Hill Education (UK)
ISBN 13 : 0335225969
Total Pages : 273 pages
Book Rating : 4.3/5 (352 download)
Download or read book EBOOK: Teaching Secondary Mathematics with ICT written by Sue Johnston-Wilder and published by McGraw-Hill Education (UK). This book was released on 2004-10-16 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: “This is a book all mathematics teachers and teacher educators should read! It brings together a wealth of insights from a range of authors… The major issues confronting teachers of mathematics who wish to use ICT in different domains of mathematics are addressed in a clear and accessible way.” Professor Celia Hoyles OBE, Dean of Research and Consultancy, Institute of Education, University of London Teaching Secondary Mathematics with ICT shows the reader how to use Information and Communication Technology (ICT) effectively to enhance the teaching of mathematics in the secondary school. The book explains which forms of technology can be used to improve mathematics teaching and learning, how to get started and where to go for further information. The first two chapters provide a useful introduction for those new to teaching mathematics with ICT. Further chapters cover topics including: ICT and the curriculum: number, algebra, geometry and statistics Making use of interactive whiteboards in the classroom Using the internet and video-conferencing to enhance teaching The book includes practical classroom scenarios and case studies (for example, the government-funded MathsAlive! Initiative), as well as discussions of general issues, such as the role of feedback and the use of ICT in whole-class teaching. It draws on current research and is supplemented by a linked web site, which provides access to demonstration copies of software and sample files. It also includes a directory of resources with lists of organisations, web sites, projects and further reading. Key reading for Education students specialising in Mathematics and all those teaching secondary mathematics, including non-specialists and those on professional development courses. Visit the text-supporting website: www.openup.co.uk/jwp
Author : David A. Reid
Publisher : BRILL
ISBN 13 : 946091246X
Total Pages : 265 pages
Book Rating : 4.4/5 (69 download)
Download or read book Proof in Mathematics Education written by David A. Reid and published by BRILL. This book was released on 2010-01-01 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research on teaching and learning proof and proving has expanded in recent decades. This reflects the growth of mathematics education research in general, but also an increased emphasis on proof in mathematics education.
Author : Doug French
Publisher : A&C Black
ISBN 13 : 0826473628
Total Pages : 176 pages
Book Rating : 4.8/5 (264 download)
Download or read book Teaching and Learning Geometry written by Doug French and published by A&C Black. This book was released on 2004-01-01 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This fascinating title reviews the teaching and learning of school geometry from the perspective of both the new teacher and the more experienced teacher. It is designed to extend and deepen subject knowledge and to offer practical advice and ideas for the classroom in the context of current practice and research. Particular emphasis is given to the following elements: Understanding the key ideas of the geometry curriculum. Learning geometry effectively: lessons from research and current practice. Misconceptions and errors. Geometry reasoning: problem solving and proving. The role of technology in learning geometry.
Author :
Publisher :
ISBN 13 :
Total Pages : 1240 pages
Book Rating : 4.F/5 ( download)
Download or read book ENC Focus written by and published by . This book was released on 2000 with total page 1240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Claudi Alsina
Publisher : MAA
ISBN 13 : 9780883857465
Total Pages : 202 pages
Book Rating : 4.8/5 (574 download)
Download or read book Math Made Visual written by Claudi Alsina and published by MAA. This book was released on 2006-07-06 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: The object of this book is to show how visualization techniques may be employed to produce pictures that have interest for the creation, communication and teaching of mathematics. Mathematical drawings related to proofs have been produced since antiquity in China, Arabia, Greece and India but only in the last thirty years has there been a growing interest in so-called 'proofs without words.' In this book the authors show that behind most of the pictures 'proving' mathematical relations are some well-understood methods. The first part of the book consists of twenty short chapters, each one describing a method to visualize some mathematical idea (a proof, a concept, an operation,...) and several applications to concrete cases. Following this the book examines general pedagogical considerations concerning the development of visual thinking, practical approaches for making visualizations in the classroom and a discussion of the role that hands-on material plays in this process.
