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Foreword; The Digital Revolution in Society and in School ; The Cyber Youngsters ; The Immigrant Teachers, Innovation and Comfort Zone ; Are Mobile Technologies the Future? ; Preface; Contents; Chapter 1: Mathematical Problem-Solving with Technology: An Overview of the Problem@Web Project; 1.1 Introduction; 1.2 Young People with Technology; 1.3 Young People's Mathematical Problem-Solving with Technology; 1.4 The Research Focus; 1.5 The SUB12 and SUB14 Mathematics Competitions; 1.6 Methodological Issues; 1.7 Concluding Comments; References
Chapter 2: Youngsters Solving Mathematical Problems with Technology: Their Experiences and Productions2.1 Introduction; 2.2 The Participants in the Mathematical Competitions SUB12 and SUB14; 2.3 The Participants and the Use of Digital Technologies; 2.4 The Participants' Productions with Digital Technologies; 2.4.1 From the Use of Paper and Pencil to Writing with Word and Excel; 2.4.2 The Use of Tables; 2.4.3 The Use of Images and Diagrams; 2.4.4 The Use of Numerical Software; 2.4.5 The Use of Geometrical Software; 2.5 Concluding Comments; References
Chapter 3: Perspectives of Teachers on Youngsters Solving Mathematical Problems with Technology3.1 Introduction; 3.2 The Role of the Teachers in the Mathematical Competitions; 3.2.1 The Support of the Teachers: From the First Round to the Final; 3.2.2 The Social Part of the Competitions: The Meeting at the Final; 3.3 Perspectives of Teachers About the Mathematical Competitions SUB 12 and SUB14; 3.4 Mathematical Communication: An Additional Challenge; 3.5 The Use of Technology: The Sharing of Experiences Between Teachers and Students; 3.6 Overview and Conclusion; References
Chapter 4: Theoretical Perspectives on Youngsters Solving Mathematical Problems with Technology4.1 The Theoretical Stance; 4.2 Problem-Solving as Mathematisation; 4.3 Problem-Solving as Expressing Thinking; 4.3.1 Expository Discourse in Problem-Solving; 4.3.2 Technology Used for Expressing Thinking in Problem-Solving; 4.4 Multiple External Representations; 4.5 Humans-with-Media and Co-action with Digital Tools; 4.6 An Outlook; References; Chapter 5: Digitally Expressing Conceptual Models of Geometrical Invariance; 5.1 Main Theoretical Ideas; 5.1.1 Perceiving Affordances of Digital Tools
5.1.2 The Indivisibility Between the Subject and the Context5.1.3 Humans-with-Media Mathematising; 5.1.4 Mathematisation with Dynamic Geometry Software; 5.2 Context and Method; 5.3 Data Analysis; 5.3.1 The Problem: Building a Flowerbed; 5.3.2 Zooming in: The Participants' Productions; 5.3.2.1 Exhibit A: The Solution of Marta and Miguel; 5.3.2.2 Exhibit B: The Solution of Andreia, Lucas and José; 5.3.2.3 Exhibit C: The Solution of Sara; 5.3.2.4 Exhibit D: The Solution of Jessica; 5.3.3 Zooming Out: Comparing and Contrasting; 5.4 Discussion and Conclusion; References
Chapter 2: Youngsters Solving Mathematical Problems with Technology: Their Experiences and Productions2.1 Introduction; 2.2 The Participants in the Mathematical Competitions SUB12 and SUB14; 2.3 The Participants and the Use of Digital Technologies; 2.4 The Participants' Productions with Digital Technologies; 2.4.1 From the Use of Paper and Pencil to Writing with Word and Excel; 2.4.2 The Use of Tables; 2.4.3 The Use of Images and Diagrams; 2.4.4 The Use of Numerical Software; 2.4.5 The Use of Geometrical Software; 2.5 Concluding Comments; References
Chapter 3: Perspectives of Teachers on Youngsters Solving Mathematical Problems with Technology3.1 Introduction; 3.2 The Role of the Teachers in the Mathematical Competitions; 3.2.1 The Support of the Teachers: From the First Round to the Final; 3.2.2 The Social Part of the Competitions: The Meeting at the Final; 3.3 Perspectives of Teachers About the Mathematical Competitions SUB 12 and SUB14; 3.4 Mathematical Communication: An Additional Challenge; 3.5 The Use of Technology: The Sharing of Experiences Between Teachers and Students; 3.6 Overview and Conclusion; References
Chapter 4: Theoretical Perspectives on Youngsters Solving Mathematical Problems with Technology4.1 The Theoretical Stance; 4.2 Problem-Solving as Mathematisation; 4.3 Problem-Solving as Expressing Thinking; 4.3.1 Expository Discourse in Problem-Solving; 4.3.2 Technology Used for Expressing Thinking in Problem-Solving; 4.4 Multiple External Representations; 4.5 Humans-with-Media and Co-action with Digital Tools; 4.6 An Outlook; References; Chapter 5: Digitally Expressing Conceptual Models of Geometrical Invariance; 5.1 Main Theoretical Ideas; 5.1.1 Perceiving Affordances of Digital Tools
5.1.2 The Indivisibility Between the Subject and the Context5.1.3 Humans-with-Media Mathematising; 5.1.4 Mathematisation with Dynamic Geometry Software; 5.2 Context and Method; 5.3 Data Analysis; 5.3.1 The Problem: Building a Flowerbed; 5.3.2 Zooming in: The Participants' Productions; 5.3.2.1 Exhibit A: The Solution of Marta and Miguel; 5.3.2.2 Exhibit B: The Solution of Andreia, Lucas and José; 5.3.2.3 Exhibit C: The Solution of Sara; 5.3.2.4 Exhibit D: The Solution of Jessica; 5.3.3 Zooming Out: Comparing and Contrasting; 5.4 Discussion and Conclusion; References