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Advances in Mathematics Education Research on Proof and Proving : an International Perspective

Author: Andreas J Stylianides; Guershon Harel
Publisher: Cham, Switzerland : Springer Nature, 2018.
Series: ICME-13 Monographs.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book explores new trends and developments in mathematics education research related to proof and proving, the implications of these trends and developments for theory and practice, and directions for future research. With contributions from researchers working in twelve different countries, the book brings also an international perspective to the discussion and debate of the state of the art in this important  Read more...
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Genre/Form: Electronic books
Additional Physical Format: (OCoLC)1006452740
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Andreas J Stylianides; Guershon Harel
ISBN: 9783319709963 3319709968
OCLC Number: 1019807159
Description: 1 online resource.
Contents: Intro; Preface; References; Contents; Epistemological Issues Related to Proof and Proving; 1 Reflections on Proof as Explanation; Abstract; Mathematical Explanations; Intra-mathematical Explanations; Pedagogical Explanations; Research by Educators; Philosophical Models of Explanation; Mark Steiner: A Characteristic Property; Philip Kitcher: Theoretical Unification; Marc Lange: Symmetry, Unity, and Salience; Proofs Considered Pedagogically Explanatory; Example 1: Pickâ#x80;#x99;s Theorem; Example 2: The Irrationality of \sqrt 2 Example 3: The Product of Any Three Consecutive Nonzero Natural Numbers Is Divisible by 6Conclusion; Acknowledgements; References; 2 Working on Proofs as Contributing to Conceptualizationâ#x80;#x94;The Case of IR Completeness; Abstract; Introduction; Definition of Real Numbers by Cuts; Creation of Irrational Numbers; Continuity of the Set of Real Numbers; Proofs of the Main Theorems Leaning on Cuts and Completeness; A â#x80;#x98;Set Theoreticâ#x80;#x99; Viewpoint that Mobilizes Actual Infinity; Didactical Implications; Real Numbers as Limit of Fundamental Sequences; Construction of a Totally Ordered Field A Proof, via the Infimum Theorem, that the Field Thus Constructed Is CompleteA Proof, via Cauchy Sequences, that the Set of Real Numbers Is Complete; Didactical Implications; Real Numbers as Decimal Expansions; Didactical Implications; Conclusion; Acknowledgements; References; 3 Types of Epistemological Justifications, with Particular Reference to Complex Numbers; Abstract; Instances of Sentential Epistemological Justification (SEJ); Instances of Apodictic Epistemological Justification (AEJ); Instances of Meta Epistemological Justification (MEJ) Contrast with Current Instructional Treatment of Complex NumbersConcluding Remark; References; 4 Mathematical Argumentation in Elementary Teacher Education: The Key Role of the Cultural Analysis of the Content; Abstract; Introduction; Theoretical Framework; Research for Innovation; Cultural Analysis of the Content (CAC) Competence; Habermasâ#x80;#x99; Construct of Rationality; Argumentation and Toulminâ#x80;#x99;s Model; Other Theoretical Elaborations; The Course; The Design of the Course; The Content; Teaching Method; The Participantsâ#x80;#x99; Assessment; Three Snapshots from the Course; First Snapshot Second SnapshotThird Snapshot; Analysis of Participantsâ#x80;#x99; Self-reflective Reports; Discussion; References; 5 Toward an Evolving Theory of Mathematical Practice Informing Pedagogy: What Standards for this Research Paradigm Should We Adopt?; Abstract; Mathematical Practice Informing Pedagogy; Commonalities in These Book Chapters; Summaries of the Contributed Chapters; Hanna: Criteria for Mathematical Explanations in the Classroom; Durand-Guerrier and Tanguay: Systematizing the Real Line; Harel: Solving Cubics to Produce an Epistemic Justification for Complex Numbers Boero, Fenaroli, and Guala: Contextualizing and Expanding Elementary Preservice Teachersâ#x80;#x99; Conceptions of Proof
Series Title: ICME-13 Monographs.
Responsibility: Andreas J. Stylianides, Guershon Harel, editors.

Abstract:

The book is organized around the following four themes, which reflect the breadth of issues addressed in the book: * Theme 1: Epistemological issues related to proof and proving;  Read more...

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"The contents cover new trends and developments in mathematics education on proof and proving. ... will give readers an idea of what can be found in this volume." (Annie Selden, MAA Reviews, March Read more...

 
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