Multifaceted Nature of Creativity in the Teach Geometry

Table of Contents
Acknowledgment
Prolog
Section I: The World of Creativity
	Chapter 1 The many faces of creativity
		Introduction
		Milestones in the Development of the Concept “Creativity”
			Creativity in the Modern Period
		General Creativity versus Domain-Specific Creativity
		Perception of Creativity from the Product and Process Aspects
			Creativity from the product aspect
			Creativity from the process aspect
			Absolute creativity versus relative creativity
		References
	Chapter 2 Nurturing mathematical creativity at school
		Introduction
		Creativity and Instruction
			Learning environments designed for developing pupils’ creativity
			Teachers’ perceptions of creativity and development of pupils’ creativity
		Creativity in Teaching Mathematics at School
			Nurturing mathematical creativity by encouraging pupils to pose problems and questions
		References
Section II: Creative Approaches to the Teaching of Geometry
	Chapter 3 Creative view of internal and external angles of convex polygons
		Introduction
		The Visual Representation in Geometry Teaching
		Drawing and cutting for the purpose of illustration and fostering pupils’ creativity
			Calculating the sum of polygon angles by paper and scissors
				Sum of triangle angles
				Sum of angles of any quadrilateral
				Sum of angles of any pentagon
				Sum of angles of any hexagon
				Sum of a convex polygon angles
				Sum of convex polygon angles – using another way
				Complete the drawing – to an n-sided polygon
				Sum of exterior angles in convex polygons.
		Recommendation for further activity
			Difficulties and anticipated errors
		Summary
		References
	Chapter 4 On areas, perimeters and creativity
		Activity 1:
		Activity 2:
		Activity 3:
		Activity 4:
		Solutions of Activity 1
		Solutions of activity 2
		Solutions of activity 3
		Solutions of activity 4
		Summary
		References
	Chapter 5 Analytic geometry and logic as promoters of graphical Literacy
		Introduction
		Theoretical Background
		Visual literacy and creative thinking development in mathematics lessons
		Graphical representations as part of visual literacy and the teaching thereof
		Acquaintance with René Descartes as an Introduction to the Teaching of the Cartesian Coordinates
		Examples of Activities Based on Reading Information from a Graph
		Preliminary activity
		Suggestions for teaching the subject in class
		Activity No. 1
		Activity No. 2:
		Integration of the Foundations of Geometry and Analytic Geometry
		Summary
		References
	Chapter 6 Building geometric understanding – Identifying and refuting false claims
		Introduction
		Inductive Reasoning, Deductive Reasoning, and Mathematical Proofs
		Proof and Refutation of Claims
		Pre-service Teachers’ Knowledge of Geometry
		Recommended Activities for Teaching False Claims as a Tool for Better Understanding
		Discussion, Conclusions, and Recommendations
		References
		Appendix A
	Chapter 7 Developing mathematical creativity through geometric problem posing
		Introduction
		‘What If Not?’ – Posing Problems Strategy
		The Given Problem
		Problem 1
		Problem 2
		Problem 3
		Problem 4
		Problem 5
		Summary
		References
Section III: Geometry and the Creative Brain
	Chapter 8 From peeling a tangerine to image processing: The beauty of geometry and its relevance to everyday life
		Introduction
		Theoretical Background
			Curvature and its geometric meaning
			A short introduction to image processing
		Main Problems in the Field of Image Processing
			Image denoising
			Sharpening blurry areas
			Segmentation
		Solutions of the Problems Presented in Part 2
			Classic solutions
			New direction – Geometric approach to image processing
			Image denoising
			Sharpening blurry areas
			Segmentation
			Facing the future
		From Theory to Practice: Proposal for Teaching Non-Euclidean Geometry
			Non-planar surfaces
			Curvature
		Summary from a Personal Perspective
		References
	Chapter 9 The concept of invariance in geometry: A long-term history and present-day implications for learning
		Introduction: Concepts of Invariance and Change
		The History of Geometry through the Lens of Invariance and Change
			Pre-Euclidean period
			Euclid’s Elements: The deductive structure of geometry from the aspect of invariance and change
			Invariance as an instrument for classifying geometric objects
			Invariance as a characteristic of various geometries
		Theorems in Geometry as “a Game” of Seeking the Invariance and Effect of the Change
			The invariance of area and its application: Euclid’s proof of the Pythagorean Theorem
			Invariance of orthogonality
			Invariance of parallelism
			Invariance of a shape
		The Concept of Invariance and Change as a Didactic Instrument
			Understanding the effect of possible change as a means of solving problems
			Discovering the invariance as a way of solving a problem
			Constructing the change as a means of solution
		Summary
		References
	Chapter 10 Assessing creativity and its development using a psychometric model: The case of problem posing
		Introduction
		Description of the Model
		Guidelines for scoring the four indices of creativity
			Fluency scoring
			Flexibility scoring
			Originality scoring
			Organization (or generalization) scoring
			An overall total score for creativity
		Demonstrating the Scoring Process
		Arranging the Data
			Scoring fluency, flexibility, originality, organization, and creativity
			Scoring total and relative fluency
			Scoring total and relative flexibility
			Scoring total and relative originality
			Scoring total and relative organization
			Scoring overall creativity
		Assessing the Development of Creativity
			Graphical display of data
			Evaluating the development of creativity
				Mean relative scores
				Standard deviations
		Self-Assessment of the Development of Creativity
		Summary
		References
Epilog
	1. A five-pointed star
	2. Good neighborhood
	3. Drawing medians in a triangle
	4. A rhombus-shaped swimming pool
	5. Water lily in the pond
	6. Dana’s golden ring
	7. Moving boats
About the editors and the writers
	About the writers
Name Index
Subject Index