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.
Author(s): Scott A. Chamberlin, Peter Liljedahl, Miloš Savić
Series: Research in Mathematics Education
Publisher: Springer
Year: 2022
Language: English
Pages: 251
City: Cham
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
