1st Edition
Unlocking Creativity in Solving Novel Mathematics Problems Cognitive and Non-Cognitive Perspectives and Approaches
Unlocking Creativity in Solving Novel Mathematics Problems delivers a fascinating insight into thinking and feeling approaches used in creative problem solving and explores whether attending to ‘feeling’ makes any difference to solving novel problems successfully.
With a focus on research throughout, this book reveals ways of identifying, describing and measuring ‘feeling’ (or ‘intuition’) in problem-solving processes. It details construction of a new creative problem-solving conceptual framework using cognitive and non-cognitive elements, including the brain’s visuo-spatial and linguistic circuits, conscious and non-conscious mental activity, and the generation of feeling in listening to the self, identified from verbal data. This framework becomes the process model for developing a comprehensive quantitative model of creative problem solving incorporating the Person, Product, Process and Environment dimensions of creativity.
In a world constantly seeking new ideas and new approaches to solving complex problems, the application of this book’s findings will revolutionize the way students, teachers, businesses and industries approach novel problem solving, and mathematics learning and teaching.
Contents
List of Figures
List of Tables
About the Author
Preface
Acknowledgements
Terminology
Reading Map
Introduction
Section 1: Defining Creativity in Problem Solving: Cognitive and Non-Cognitive Approaches to Reasoning
Chapter 1 Why Study Creativity in Problem Solving?
Chapter 2 Macroscopic and Microscopic Models of Creativity
Section 2: Constructing and Testing a Conceptual Framework of Creative Problem Solving
Chapter 3 Constructing the Framework: The Particular Case
Chapter 4 Constructing the Framework: The General Case Part 1 – Forming the Scales
Chapter 5 Constructing the Framework: The General Case Part 2 – Confirming the Scales
Section 3: Constructing and Testing a Comprehensive Model of Creative Problem Solving in Mathematics
Chapter 6 Causal Modelling: Toward a Comprehensive Model of Creative Problem Solving
Chapter 7 Testing the Cute Numbers Model of Creative Problem Solving
Chapter 8 Testing the Birthday Cake Model of Creative Problem Solving
Section 4: A New Approach to Problem Solving
Chapter 9 Refining the Comprehensive Model of Creative Problem Solving
Chapter 10 No Model of Solutions without the Involvement of Feeling
Appendix
Biography
Carol R. Aldous, BSc (Hons) developmental genetics, PhD (mathematics education and creative problem solving) is a senior lecturer in science and mathematics education at Flinders University, Adelaide, Australia. She leads a South Australian government-funded STEM industry engagement project and passionately researches the role of creativity in problem solving.
