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Intro; Contents; Introduction; 1 Enhancing Creative Capacities in Mathematically-Promising Students. Challenges and Limits; Abstract; 1.1 Introduction: Setting the Context; 1.2 Frameworks for Studying Students' Creativity and Giftedness in Mathematics; 1.3 Domain Specificity of Creativity; 1.4 Mathematical Creativity; 1.5 Relationships Between Mathematical Giftedness and Creativity-A Mind-and-Brain Perspective; 1.6 Creativity, Giftedness and Social Inclusion; 1.7 Creativity and Innovation; 1.8 Creativity, Giftedness and Expertise; 1.9 Creativity and Metacognition.
1.10 Mathematical Competencies and Teaching Mathematically Promising Students1.11 Brief Overview of This Book; References; Frameworks for Studying Mathematical Creativity and Giftedness; 2 Mathematical Creativity: Product, Person, Process and Press; Abstract; 2.1 Introduction; 2.2 The Components of Creativity; 2.3 Product; 2.4 Person; 2.4.1 Mathematical Ability; 2.4.2 Intelligence; 2.4.3 General Creativity; 2.4.4 Age; 2.4.5 Gender; 2.4.6 Culture; 2.4.7 Personality Traits; 2.5 Process; 2.5.1 Stages of the Creative Process; 2.6 Press; 2.6.1 Teaching Environment and the Teachers' Role.
2.6.2 Activities and Tasks Triggering Mathematical Creativity2.6.3 New Technologies that Support Mathematical Creativity; 2.6.4 Students Interaction/Communication; 2.7 Epilogue; References; 3 Mathematical Giftedness and Creativity in Primary Grades; Abstract; 3.1 Introduction; 3.2 (Mathematical) Giftedness; 3.2.1 Giftedness: Potentials and Achievements; 3.2.2 Mathematical Giftedness and General Intelligence; 3.2.3 Profiles of Mathematical Giftedness; 3.3 Creativity; 3.4 Relations Between (Mathematical) Creativity and (Mathematical) Giftedness.
3.4.1 (Mathematical) Creativity as a Precondition for (Mathematical) Giftedness3.4.2 (Mathematical) Creativity as a Possible Component of Mathematical Giftedness; 3.4.3 (Mathematical) Creativity as a Possible Consequence of Mathematical Giftedness; 3.4.4 Creativity as a (Widely) Independent Area of Giftedness; 3.5 Mathematical Creativity in Primary School Age; 3.6 Creativity as Inventing Mathematical Objects in Primary School; 3.6.1 Inventing Mathematical Operations; 3.6.2 A Purposeful Invention During Problem Solving; 3.7 Conclusion and Outlook; References.
4 Cognitive Variety in Rich-Challenging TasksAbstract; 4.1 Introduction; 4.2 Background; 4.2.1 Problem Posing; 4.2.2 Creativity and Problem Posing; 4.2.3 Problem Validity in Problem Posing; 4.3 Context; 4.3.1 Sample and Method; 4.3.2 The Task; 4.3.3 Some Comments on the Tasks; 4.3.4 A Brief Analysis of the Task; 4.4 Tools for Data Analysis; 4.4.1 Problem Validity; 4.4.2 Problem Complexity; 4.4.3 Topic Variety; 4.5 Data and Results; 4.5.1 Group 1 Proposals-Brief Description; 4.5.1.1 The Case of Diana (4th Grade); 4.5.1.2 The Case of Andrei (4th Grade); 4.5.1.3 The Case of Alexandru (6th Grade).
1.10 Mathematical Competencies and Teaching Mathematically Promising Students1.11 Brief Overview of This Book; References; Frameworks for Studying Mathematical Creativity and Giftedness; 2 Mathematical Creativity: Product, Person, Process and Press; Abstract; 2.1 Introduction; 2.2 The Components of Creativity; 2.3 Product; 2.4 Person; 2.4.1 Mathematical Ability; 2.4.2 Intelligence; 2.4.3 General Creativity; 2.4.4 Age; 2.4.5 Gender; 2.4.6 Culture; 2.4.7 Personality Traits; 2.5 Process; 2.5.1 Stages of the Creative Process; 2.6 Press; 2.6.1 Teaching Environment and the Teachers' Role.
2.6.2 Activities and Tasks Triggering Mathematical Creativity2.6.3 New Technologies that Support Mathematical Creativity; 2.6.4 Students Interaction/Communication; 2.7 Epilogue; References; 3 Mathematical Giftedness and Creativity in Primary Grades; Abstract; 3.1 Introduction; 3.2 (Mathematical) Giftedness; 3.2.1 Giftedness: Potentials and Achievements; 3.2.2 Mathematical Giftedness and General Intelligence; 3.2.3 Profiles of Mathematical Giftedness; 3.3 Creativity; 3.4 Relations Between (Mathematical) Creativity and (Mathematical) Giftedness.
3.4.1 (Mathematical) Creativity as a Precondition for (Mathematical) Giftedness3.4.2 (Mathematical) Creativity as a Possible Component of Mathematical Giftedness; 3.4.3 (Mathematical) Creativity as a Possible Consequence of Mathematical Giftedness; 3.4.4 Creativity as a (Widely) Independent Area of Giftedness; 3.5 Mathematical Creativity in Primary School Age; 3.6 Creativity as Inventing Mathematical Objects in Primary School; 3.6.1 Inventing Mathematical Operations; 3.6.2 A Purposeful Invention During Problem Solving; 3.7 Conclusion and Outlook; References.
4 Cognitive Variety in Rich-Challenging TasksAbstract; 4.1 Introduction; 4.2 Background; 4.2.1 Problem Posing; 4.2.2 Creativity and Problem Posing; 4.2.3 Problem Validity in Problem Posing; 4.3 Context; 4.3.1 Sample and Method; 4.3.2 The Task; 4.3.3 Some Comments on the Tasks; 4.3.4 A Brief Analysis of the Task; 4.4 Tools for Data Analysis; 4.4.1 Problem Validity; 4.4.2 Problem Complexity; 4.4.3 Topic Variety; 4.5 Data and Results; 4.5.1 Group 1 Proposals-Brief Description; 4.5.1.1 The Case of Diana (4th Grade); 4.5.1.2 The Case of Andrei (4th Grade); 4.5.1.3 The Case of Alexandru (6th Grade).