“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.
Author(s): Olga Moreira
Publisher: Arcler Press
Year: 2022
Language: English
Pages: 421
City: Boston
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
