Understanding the mathematical way of thinking : the registers of semiotic representations /: the registers of semiotic representations. ([2017])

• Record Type: Book
• Other Titles: Registers of semiotic representations
• Further Information: Note: Raymond Duval ; edited by Tânia M. M. Campos.
• Authors: Duval, Raymond
• Editors: Campos, Tânia M. M
• Contents: Foreword; Preface; Acknowledgments; Contents; List of Figures ; Chapter 1: Representation and Knowledge: The Semiotic Revolution; 1.1 The Fundamental Epistemological Distinction and the First Knowledge Analysis Scheme; 1.1.1 The Cognitive Issue of Access to the Objects Themselves and Role of Representations; 1.1.2 Sign and Representation: The Cognitive Divide; 1.2 The Semiotic Revolution: Towards a New Knowledge Analysis Scheme; 1.3 The Three Models of Sign Analysis That Have Founded Semiotics: Contributions and Limits; 1.3.1 Saussure: Structural Analysis of Semiotic Systems. 1.3.2 Peirce: The Classification of Kinds of Representations1.3.3 Frege: Semiotic Substitution and Production of New Knowledge in Mathematics; 1.4 Conclusion: The Semiotic Representations; Annex; Chapter 2: Mathematical Activity and the Transformations of Semiotic Representations; 2.1 Two Epistemological Situations, One Irreducible to the Other, in the Access to Objects of Knowledge; 2.1.1 The Juxtaposition Test with a Material Object: The Photo Montage of Kosuth; 2.1.2 The Juxtaposition Test with the Natural Numbers; 2.1.3 How to Recognize the Same Object in Different Representations? 2.1.4 A Fundamental Cognitive Operation in Mathematics: One-to-One Mapping2.2 The Transformation of Semiotic Representations at the Heart of the Mathematical Way of Working; 2.2.1 Description of an Elementary Mathematical Activity: The Development of Polygonal Unit Marks Configuration; 2.2.2 Representational Transformations Specific to each Kind of Semiotic Representation: The Case of Representation of Numbers; 2.2.2.1 Operations with Small Natural Numbers; 2.2.2.2 Operations with Relative Integers; 2.2.2.3 The Operations with Rational Numbers. 2.3 Conclusion: The Cognitive Analysis of the Mathematical Activity and the Functioning of the Mathematical ThinkingChapter 3: Registers of Semiotic Representations and Analysis of the Cognitive Functioning of Mathematical Thinking; 3.1 Semiotic Registers and Cognitive Functioning of Thought; 3.1.1 Two Heterogeneous Kinds of Semiotic Systems: The Codes and Registers; 3.1.2 The Three Types of Discursive Operations and the Cognitive Functions of Natural Languages; 3.1.3 The Relationship Between Thought and Language: Discursive Operations and Linguistic Expression. 3.1.4 Conclusion: What Characterizes a Register of Semiotic Representation3.2 Do the Various Forms of Representation Used in Mathematics Depend on Registers?; 3.2.1 How do We see a Figure?; 3.2.2 The Two Types of Figural Operations Proper to the Geometrical Figures; 3.2.3 Concealment of the Register of Figures in the Teaching of Geometry and Didactic Analyses; 3.2.4 Geometric Visualization and Problems from Reality: Direct Passage or Need for Intermediary Representations?; 3.3 Conclusions; Chapter 4: The Registers: Method of Analysis and Identification of Cognitive Variables.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2017
• Extent: 1 online resource
• Subjects: 510.71; Education; Mathematics -- Study and teaching; Mathematics; EDUCATION -- Essays; EDUCATION -- Organizations & Institutions; EDUCATION -- Reference; Mathematics -- Study and teaching; Education -- Professional Development; Education -- Educational Psychology; Teacher training; Teaching skills & techniques; Education -- Teaching Methods & Materials -- Mathematics; Teaching of a specific subject; Education; Mathematics Education; Teaching and Teacher Education; Learning & Instruction; Electronic books; Electronic books
• Languages: English
• ISBNs: 9783319569109; 3319569104
• Related ISBNs: 9783319569093; 3319569090
• Notes: Note: Includes bibliographical references (pages viii-ix) and index.; Note: Description based on online resource, title from PDF title page (Springer, viewed December 28, 2017).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.