Proof Technology in Mathematics Research and Teaching: Mathematics Education in the Digital Era, cartea 14
Editat de Gila Hanna, David A. Reid, Michael de Villiersen Limba Engleză Hardback – 18 oct 2019
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.
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Specificații
ISBN-13: 9783030284824
ISBN-10: 3030284824
Pagini: 379
Ilustrații: VIII, 379 p. 137 illus., 83 illus. in color.
Dimensiuni: 155 x 235 mm
Ediția:1st ed. 2019
Editura: Springer International Publishing
Colecția Springer
Seria Mathematics Education in the Digital Era
Locul publicării:Cham, Switzerland
ISBN-10: 3030284824
Pagini: 379
Ilustrații: VIII, 379 p. 137 illus., 83 illus. in color.
Dimensiuni: 155 x 235 mm
Ediția:1st ed. 2019
Editura: Springer International Publishing
Colecția Springer
Seria Mathematics Education in the Digital Era
Locul publicării:Cham, Switzerland
Cuprins
Chapter 1. Proof technology: Implications for teaching.- Chapter 2. A fully automatic theorem prover with human-style output.- Chapter 3. A common type of rigorous proof that resists Hilbert's programme.- Chapter 4. SMTCoq: Mixing automatic and interactive proof technologies.- Chapter 5. Studying algebraic structures using Prover9 and Mace4.- Chapter 6. Didactical issues at the interface of mathematics and computer science.- Chapter 7. Issues and challenges in instrumental proof.- Chapter 8. Reasoning by equivalence: the potential contribution of an automatic proof checker.- Chapter 9. Virtual manipulatives and students’ counterexamples during proving.- Chapter 10. Proof technology and learning in mathematics: Common issues and perspectives.
Recenzii
“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)
Textul de pe ultima copertă
This book presents chapters exploring the most recent developments in the role of technology in proving. The full range of topics related to this theme are explored, including computer proving, digital collaboration among mathematicians, mathematics teaching in schools and universities, and the use of the internet as a site of proof learning.
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 astandard 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.
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.
Caracteristici
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