Advances in Mathematics Education Research on Proof and Proving : an International Perspective /: an International Perspective. (2018)

• Record Type: Book
• Further Information: Note: Andreas J. Stylianides, Guershon Harel, editors.
• Editors: Stylianides, Andreas J; Harel, Guershon, 1952-
• Other Names: Harel, Guershon
• 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
• Publisher Details: Cham, Switzerland : Springer Nature
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 510.71; Education; Mathematics -- Research; Mathematics and physical education; MATHEMATICS / Essays; MATHEMATICS / Pre-Calculus; MATHEMATICS / Reference; Mathematics and physical education; Mathematics -- Research; Education -- Professional Development; Education -- Educational Psychology; Education -- Study Skills; Education -- Comparative; Teacher training; Teaching skills & techniques; Study & learning skills: general; Education; Mathematics; Study Skills; Education -- Teaching Methods & Materials -- Mathematics; Teaching of a specific subject; Electronic books; Electronic books
• Languages: English
• ISBNs: 9783319709963; 3319709968
• Related ISBNs: 9783319709956; 331970995X
• Notes: Note: Includes bibliographical references and index.; Note: Vendor-supplied metadata.
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