Mathematical Creativity: A Developmental Perspective

Description

This book is important and makes a unique contribution in the field of mathematics education and creativity. The book comprises the most recent research by renowned international experts and scholars, as well as a comprehensive up to date literature review. The developmental lens applied to the research presented makes it unique in the field. Also, this book provides a discussion of future directions for research to complement what is already known in the field of mathematical creativity. Finally, a critical discussion of the importance of the literature in relation to development of learners and accordingly pragmatic applications for educators is provided.  Many books provide the former (2) foci, but omit the final discussion of the research in relation to developmental needs of learners in the domain of mathematics. Currently, educators are expected to implement best practices and illustrate how their adopted approaches are supported by research.  The authors and editors of this book have invested significant effort in merging theory with practice to further this field and develop it for future generations of mathematics learners, teachers and researchers. Foreword Contents About the Author Part I: History and Background of Mathematical Creativity Chapter 1: Creativity and Mathematics: A Beginning Look 1.1 What Is Creativity? 1.1.1 What Creativity Is Not 1.1.1.1 Creativity Does Not Occur in the Right Brain 1.1.1.2 Creativity Is Not the Same as Intelligence or Expertise 1.1.1.3 Creativity Is Not Just for a Lucky Few 1.1.1.4 Creativity Is Not Just a Phenomenon in the Arts 1.1.2 Mathematical Creativity 1.2 How Does Creativity Develop? 1.2.1 Creativity Across Time 1.2.2 Talent Development in Mathematics 1.3 About This Section References Chapter 2: Creativity in Mathematics: An Overview of More Than 100 Years of Research 2.1 Research on Creativity Originating in (Mathematical) Problem-Solving 2.2 Quantitative Approaches to Measuring (Mathematical) Creativity (from Psychology) 2.3 Sorting the Field References Chapter 3: Mathematical Creativity and Society 3.1 A History of Mathematical Creativity 3.2 Overview of Creativity Research 3.3 An In-Depth Look at Mathematical Creativity 3.4 Value of Mathematical Creativity 3.5 Organizational Framework of the Book 3.5.1 Mathematical Creativity Is Dynamic 3.5.2 Mathematical Creativity Is Influenced by Affect, Intelligence, and Other Constructs 3.5.3 Final Factors That Influence Mathematical Creativity 3.6 Conclusion References Chapter 4: Organizational Framework for Book and Conceptions of Mathematical Creativity 4.1 Organizational Framework of Book 4.2 Development and Mathematical Creativity in Relation to Creativity Models 4.2.1 The Four C’s 4.2.2 Person, Process, and Product: Portions of the Four P Model 4.3 Barriers to Eliciting Creative Process and Product 4.4 Additional Factors in the Relationship Between Mathematical Creativity and Development 4.4.1 Empirical Evidence of Affect/Conation Relationship to Mathematical Creativity 4.4.2 Five Legs Theory 4.5 Conclusion References Chapter 5: Commentary on Section 5.1 Mathematical Creativity Research in the Elementary Grades 5.2 Empirical Findings on Creative in Mathematics Among Secondary School Students 5.3 Mathematical Creativity at the Tertiary Level: A Systematic Review of the Literature 5.4 Themes 5.5 Mathematical Creativity: A Complex Topic 5.6 Mathematical Creativity: Where It Lives and How It Is Understood 5.7 Mathematical Creativity in the Classroom 5.8 Concluding Thoughts References Part II: Synthesis of Literature on Mathematical Creativity Chapter 6: Mathematical Creativity Research in the Elementary Grades 6.1 Mathematical Creativity Research in the Elementary Grades 6.2 Mathematical Creativity Research: Academic-Oriented and Practice-Oriented 6.3 Academic-Oriented Research on Mathematical Creativity: Impacting Future Research 6.3.1 Psychology and Cognitive Science Research 6.3.2 Mathematics Education and Psychology Research 6.4 Practice-Oriented Research on Mathematical Creativity: Impacting Future Practice 6.4.1 Instructional Tasks 6.4.1.1 Open-Ended and Multiple Solution Tasks 6.4.1.2 Technological Integrations to Support MC 6.4.2 Environmental Aspects That Relate to MC 6.4.2.1 The Didactic Contract of Mathematics Teaching 6.4.2.2 Classroom Affective Development 6.5 Next Steps: Answering Some of the Field’s Most Immediate Questions 6.5.1 Promising Directions for Academic-Oriented Research on MC for Elementary Students 6.5.2 Promising Directions for Practice-Oriented Research on MC for Elementary Students References Chapter 7: Literature Review on Empirical Findings on Creativity in Mathematics Among Secondary School Students 7.1 Theoretical Background 7.2 Methods 7.3 Data Analysis 7.4 Results 7.4.1 Perspective I: Understanding Creativity and Validation of Creativity Models 7.4.2 Perspective II: Relation and Correlation to Other Constructs 7.4.3 Perspective III: Reflecting on Instructions and Interventions 7.4.4 Perspective IV: Articles That Do Not Fit Perspectives I–III 7.4.5 Perspective V: Problems and Tasks for Assessment 7.5 Discussion and Outlook References Chapter 8: Mathematical Creativity at the Tertiary Level: A Systematic Review of the Literature 8.1 Introduction 8.2 Method 8.3 Results 8.4 Discussion and Future Research Directions 8.5 Conclusion Appendix A: Table of all 29 Articles/Book Chapters Listed by Alphabetical Last Name References Chapter 9: Mathematical Creativity from an Educational Perspective: Reflecting on Recent Empirical Studies 9.1 To Comment Is to Reflect 9.2 Creative Processes: What Are They? 9.3 Creative Processes: How Can We Foster Them? 9.4 Some Pre-reading Suggestions References Part III: New Empirical Research on Mathematical Creativity Chapter 10: Now You See It, Now You Don’t: Why The Choice of Theoretical Lens Matters When Exploring Children’s Creative Mathematical Thinking 10.1 Introduction 10.2 On Seeing and Not Seeing Mathematical Creativity 10.3 Children’s Mathematical Thinking in a Fractions Lesson 10.4 A Human-/Language-Centric Lens on Children’s Creative Thinking 10.4.1 Agentivity 10.4.2 Language 10.4.3 Materials 10.5 A Materialist Posthuman Lens on Children’s Creative Mathematical Thinking 10.5.1 Agentivity 10.5.2 Language 10.5.3 Materials 10.6 Further Thoughts: Dialogue Between Analytic Lenses References Chapter 11: The Creative Mathematical Thinking Process 11.1 Introduction 11.1.1 Divergent and Convergent Thinking 11.1.2 The Creative Mathematical Thinking Process 11.1.3 The Current Study 11.2 Method 11.2.1 Participants 11.2.2 Mathematical Tasks 11.2.3 Procedure 11.2.4 Data Analysis 11.3 Findings 11.3.1 Number of Creative Ideas 11.3.2 The Use of Divergent Thinking 11.3.3 The Use of Convergent Thinking and Combinations of Divergent and Convergent Thinking 11.3.4 Differences Between Children and Tasks 11.4 Discussion 11.4.1 The Use of Divergent and Convergent Thinking 11.4.2 The Role of Mathematical Achievement and Task Type 11.4.3 Future Studies and Limitations 11.5 Conclusion and Implications Appendix References Chapter 12: Group Creativity 12.1 Introduction 12.2 Building Thinking Classrooms 12.3 Burstiness 12.4 Method 12.4.1 Course and Participants 12.4.2 The Lesson 12.4.3 The Data 12.4.4 The Episode 12.5 Analysis I: Burstiness 12.5.1 Burst 1: Lines 9–17 12.5.2 Burst 2: Lines 18–20 12.5.3 Burst 3: Lines 23–27 12.5.4 Burst 4: Lines 31–32 12.5.5 Burst 5: Lines 33–37 12.6 Analysis II: Environment 12.6.1 Some Structure 12.6.2 Diversity 12.6.3 Psychological Safety 12.6.4 Welcome Criticism 12.6.5 Freedom to Shift Attention 12.6.6 Focus 12.6.7 Opportunity for Nonverbal Communication 12.7 Conclusions References Chapter 13: “Creativity Is Contagious” and “Collective”: Progressions of Undergraduate Students’ Perspectives on Mathematical Creativity 13.1 Introduction 13.2 Background Literature 13.3 Theoretical Perspective and Methodology 13.4 Method 13.4.1 Setting 13.4.2 Participants 13.4.3 Data Collection and Analysis 13.5 Results 13.5.1 Progression of Alice’s Perspective 13.5.2 Progression of Stephanie’s Perspective 13.5.3 Progression of Peyton’s Perspective 13.5.4 Progression of Olivia’s Perspective 13.6 Uniqueness and Similarities in Progressions Across Participants 13.7 Conclusion Appendix 1 References Chapter 14: The Role of Creativity in Teaching Mathematics Online 14.1 Introduction 14.2 Related Literature 14.3 Methods 14.4 Data Collection and Analysis 14.4.1 Interviews 14.4.2 Surveys 14.5 Findings 14.6 How Traits of Creativity Were Called Upon in the Transition 14.7 Constraints Leading to Creativity 14.8 Affordances of the Online Environment: More Higher-Level Thinking Allowed 14.9 Redefining What It Means to Learn Mathematics 14.10 The Need to Be Creative in Assessments 14.11 Supporting the Creative Process 14.12 More Time to “Stew” 14.13 Features of the Course that Played a Role in the Transition 14.14 Discussion 14.15 Conclusion Appendix A Interview Protocol Appendix B Pre-semester Survey Appendix C Post-semester Survey References Part IV: Research Application, Implications, and Future Directions Chapter 15: Concluding Thoughts on Research: Application, Implications, and Future Directions 15.1 Introduction 15.2 General Overview of the Book 15.3 Needed Research 15.4 Application of Research 15.4.1 Application of Research to Scholars 15.4.2 Application of Research to Practitioners References Index