The Notion of Mathematical Proof: Key Rules and Considerations

"The Notion Of Mathematical Proof: Key Rules And Considerations" is an edited book consisting of 16 contemporaneous open-access articles that aim to cover the different aspects of learning and teaching mathematical proof. The first part of this book aims at summing up factors that influence the cognitive development required to successfully understand and solve mathematical proofs. The second part of the book aims to overview implementations of learning methods for constructing and evaluating the validity of mathematical proof, as well as to provide strategies for overcoming possible difficulties in mathematical proof processing. It also includes other studies related to mathematical proof and a motion-based program for improving mathematical reasoning through action. This book is intended to reach out to an academic audience ranging from undergraduate students to junior researchers. Cover Title Page Copyright DECLARATION ABOUT THE EDITOR TABLE OF CONTENTS List of Contributors List of Abbreviations Preface Chapter 1 Venues for Analytical Reasoning Problems: How Children Produce Deductive Reasoning Abstract Introduction Theoretical Background Methodology Results And Findings Discussion Conclusions Author Contributions References Chapter 2 Relations between Generalization, Reasoning and Combinatorial Thinking in Solving Mathematical Open-Ended Problems within Mathematical Contest Abstract Introduction Materials and Methods Results Discussion Conclusions Author Contributions References Chapter 3 Counteracting Destructive Student Misconceptions of Mathematics Abstract Introduction and Background Theoretical Constructs Related to Student Beliefs Methodological Aspects First Case: Mathematics as Disconnected Procedures Second Case: Everyday Conceptions in Mathematics Third Case: Long-Standing Training of Procedures Analysis of the Three Students’ Beliefs Discussion of the Efficacy of the Interventions Conclusions Acknowledgments Author Contributions References Chapter 4 Adversity Quotient and Resilience in Mathematical Proof Problem-Solving Ability Abstract Introduction Research Method Results and Discussion Conclusion References Chapter 5 Profile of Students’ Errors in Mathematical Proof Process Viewed from Adversity Quotient (AQ) Abstract Introduction Theoretical Support Method Result and Discussion Conclusion References Chapter 6 Introducing a Measure of Perceived Self-efficacy for Proof (PSEP): Evidence of Validity Abstract Introduction Research Methods Results and Discussion Conclusion Acknowledgment References Chapter 7 Deductive or Inductive? Prospective Teachers’ Preference of Proof Method on an Intermediate Proof Task Method Results and Discussion Conclusion References Chapter 8 Flaws in Proof Constructions of Postgraduate Mathematics Education Student Teachers Abstract Method Result and Discussion Conclusion References Chapter 9 Mathematical Understanding and Proving Abilities: Experiment With Undergraduate Student By Using Modified Moore Learning Approach Abstract Introduction Methodolgy Findings and Discussion Conclussion and Recommendation References Chapter 10 Understanding on Strategies of Teaching Mathematical Proof for Undergraduate Students Abstract Introduction Research Method Results and Analysis Conclusion References Chapter 11 Application of Discovery Learning Method in Mathematical Proof of Students in Trigonometry Abstract Introduction Research Methods Results and Discussion Conclusion and Suggestion References Chapter 12 Organizing the Mathematical Proof Process with the Help of Basic Components in Teaching Proof: Abstract Algebra Example Abstract Introduction Literature Review Method Findings Results and Discussion Acknowledgements References Chapter 13 The Implementation of Self-explanation Strategy to Develop Understanding Proof in Geometry Abstract Introduction Research Methods Results and Discussion Conclusion Acknowledgement Bibliography Chapter 14 Mathematical Proof: The Learning Obstacles of Pre-Service Mathematics Teachers on Transformation Geometry Abstract Method Results and Discussion Conclusion Acknowledgments References Chapter 15 Students’ Mathematical Problem-Solving Ability Based on Teaching Models Intervention and Cognitive Style Abstract Method Result and Discussion Conclusion Acknowledgments References Chapter 16 Grounded and Embodied Mathematical Cognition: Promoting Mathematical Insight and Proof using Action and Language Abstract Significance Background A GEMC Theory of Proof-With-Insight Research to Practice Via Learning Environment Design Conclusions References Index Back Cover