Transformation: A Fundamental Idea of Mathematics Education

Hardcover, xxii + 409 pages, NOT ex-library. Book is clean and bright with unmarked text, free of inscriptions and stamps, firmly bound. Boards show gentle handling wear. Issued without a dust jacket. -- Contents: Part I Transformations at Transitions in Mathematics Education: 1 How 18th-Century Mathematics was Transformed into 19th-Century School Curricula [Double Discontinuity; Euler's Algebraic Analysis; Combinatorial Approach and Its Cultural Impact; Adaptical Conception of Algebraic Analysis; Algebraic Analysis as a "Complete Paradigm"; Decline of Algebra Analysis and the Meran Reform; Coexistence of Paradigms]; 2 Framework for Examining the Transformation of Mathematics and Mathematics Learning in the Transition from School to University: An Analysis of German Textbooks from Upper Secondary School and the First Semester; 3 Knowledge Transformation between Secondary School and University Mathematics; 4 Student Transition to University Mathematics Education: Transformations of People, Tools and Practices; 5 Overcoming the Gap between University and School Mathematics: The Impact of an Innovative Programme in Mathematics Teacher Education at the Justus-Liebig-University in Giessen [Theoretical Framework and Study Design of the TEDS-Telekom Study; Development of Cognitive Dispositions of Achievement; Development of Performance in Cognitive Domains; Learning Opportunities; First Results on the Evaluation of the Influence of Institutional Conditions; Conclusions and Further Prospects]; 6 Mathematical Moments in a Human Life: Narratives on Transformation; Discussion of Part I: Transitions in Learning Mathematics as a Challenge for People and Institutions; Part II Transformations Related to Representations of Mathematics: 7 Constructing Knowledge by Transformation: Diagrammatic Reasoning in Practice [Reading and Writing; Semiotics and Mathematics Education; Diagrams as Means for Thinking; the Text: Transforming Diagrams Into Diagrams]; 8 Transforming Images in a DGS: The Semiotic Potential of the Dragging Tool for Introducing the Notion of Conditional Statement [Theory of Semiotic Mediation; Transforming Figures in a DGS: Dragging and Invariants; Dragging to Produce a Conditional Statement; Teaching Experiment; Unfolding of the Semiotic Potential]; 9 Dynamic Representations of Complex Numbers: Opportunities to Learn in Teacher Training [High Hopes, Slow Pace; Course Contents; Course Arrangements and Opportunities to Learn; Dynamic Representations of Complex Numbers; Functional Relations; Impressions of Student's Work]; 10 Dynamic and Tangible Representations in Mathematics Education; 11 Role of Social Aspects of Teaching and Learning in Transforming Mathematical Activity: Tools, Tasks, Individuals and Learning Communities [Technological Tools in Mathematics Education; Sociocultural Perspective on Teaching and Learning with Technology; Episodes of Resource Use in Social Contexts; Peer-Based Interactions in Small-Group and Whole-Group Social Settings]; 12 Designing a Simulator in Building Trades to Transform Vocational Education; Discussion I of Part II: Representing and Meaning-Making: The Transformation of Transformation; Discussion II of Part II: Digital Technologies and Transformation in Mathematics Education; Part III Transformation Related to Concepts and Ideas: 13 From Proof Image to Formal Proof: A Transformation; 14 Elementary Stochastic Seeing in Primary Mathematics Classrooms: Epistemological Foundation and Empirical Evaluation of a Theoretical Construct; 15 Understanding Geometric Work through its Development and its Transformations; 16 Small Steps to Promote "Mathematical Literacy"; 17 Transformation as a Fundamental Concept in Arithmetical Competence Modelling: An Example of Informatical Educational Science; Discussion of Part III: Fundamental Ideas of Didactics: Reactions to the Suggested Meta-Theoretical Construct for Reflecting and Connecting Theories; Epilogue; Index.…