Editors:
- Provides a much needed update on new developments on proof in the digital era
- Brings new ideas on teaching proof and proving in mathematics education
- Emphasizes interdisciplinary approaches on education, philosophy and technology
Part of the book series: Mathematics Education in the Digital Era (MEDE, volume 14)
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Table of contents (17 chapters)
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Front Matter
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Introduction
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Front Matter
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Theoretical Perspectives on Computer-Assisted Proving
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Front Matter
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Suggestions for the Use of Proof Software in the Classroom
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Front Matter
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Classroom Experience with Proof Software
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Front Matter
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About this book
Proving is sometimes thought to be the aspect of mathematical activity most resistant to the influence of technological change. While computational methods are well known to have a huge importance in applied mathematics, there is a perception that mathematicians seeking to derive new mathematical results are unaffected by the digital era. The reality is quite different. Digital technologies have transformed how mathematicians work together, how proof is taught in schools and universities, and even the nature of proof itself. Checking billions of cases in extremely large but finite sets, impossible a few decades ago, has now become a standard method of proof. Distributed proving, by teams of mathematicians working independently on sections of a problem, has become very much easier as digital communication facilitates the sharing and comparison of results. Proof assistants and dynamic proof environments have influenced the verification or refutation of conjectures, and ultimately how and why proof is taught in schools. And techniques from computer science for checking the validity of programs are being used to verify mathematical proofs.
Chapters in this book include not only research reports and case studies, but also theoretical essays, reviews of the state of the art in selected areas, and historical studies. The authors are experts in the field.
Reviews
“This book is intended for specialists in mathematics education with an interest in computer science advances as well as for researchers in the field of automated reasoning with an interest in the pedagogical and didactic implications of their work. It provides a valuable contribution to mathematics education by initiating a process of in-depth reflection on the educational value of new technological tools such as automatic theorem provers and dynamic geometric environments.” (Frédéric Morneau-Guérin, MAA Reviews, May 24, 2020)
Editors and Affiliations
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Ontario Institute for Studies in Education, University of Toronto, Toronto, Canada
Gila Hanna
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AG Didaktik, Fachbereich 3, Universität Bremen, Bremen, Germany
David A. Reid
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Faculty of Education, Stellenbosch University, Stellenbosch, South Africa
Michael de Villiers
Bibliographic Information
Book Title: Proof Technology in Mathematics Research and Teaching
Editors: Gila Hanna, David A. Reid, Michael de Villiers
Series Title: Mathematics Education in the Digital Era
DOI: https://doi.org/10.1007/978-3-030-28483-1
Publisher: Springer Cham
eBook Packages: Education, Education (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Hardcover ISBN: 978-3-030-28482-4Published: 18 October 2019
Softcover ISBN: 978-3-030-28485-5Published: 18 October 2020
eBook ISBN: 978-3-030-28483-1Published: 02 October 2019
Series ISSN: 2211-8136
Series E-ISSN: 2211-8144
Edition Number: 1
Number of Pages: VIII, 379
Number of Illustrations: 54 b/w illustrations, 83 illustrations in colour
Topics: Mathematics Education, Technology and Digital Education, Structures and Proofs, Critical Thinking, Teaching and Teacher Education