Integrating Metacognition into Math: A Practical Guidebook to Enhancing Mathematics Education
Edition: 1
Copyright: 2024
Pages: 318
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This book is designed for pre-service and in-service educators of students in mathematics at any level: elementary, secondary, and post-secondary. It demystifies ‘metacognition’ and turns a complicated subject into one that is practical and seamless to integrate into math instruction. Created as an add-on to existing teaching practices for direct infusion into instruction, this text is designed to both model and teach the process of integrating metacognition into mathematics instruction. It is intended to be used as an introduction, guide, and resource-OnDemand when building this key skill into instruction. Educators will learn how to teach their students to think with more advanced strategies, make full use of their
resources, and be able to transfer these skills into any area of learning. The Integration of Metacognition into Mathematics bridges the gap between research and practice for educators. It includes both research and results from a lifetime of study and teaching in the field. It features a summary of the core theory and includes practical examples as well as elite resources, strategies, and processes to support learning in mathematics. It is specifically engineered to facilitate the transfer mathematics learning and metacognition into life beyond the classroom. It is not only intended to help educators learn metacognition, but to have accessible guides and strategies for integrating it into instruction with ease.
Chapter 1: Introduction to Metacognition
Basic Terminology and Theoretical Foundation
Chapter 2: Identifying
Building Metacognitive Strategic Knowledge
Chapter 3: Organizing
Categorizing and Recognizing Thoughts
Chapter 4: Evaluating
Training and Calibrating Instinct
Chapter 5: Planning
Constructing and Maintaining Focus
Chapter 6: Debugging
Troubleshooting the Complex, Unknown, and Unfamiliar
Chapter 7: Monitoring
Mindfully Thinking with Focus
Chapter 8: Transfer
Applying Metacognition and Mathematics Learning Beyond the Classroom
The book is designed to model the instructional order when scaffolding metacognition (see Chapter 1 and Chapter 2). It begins with an overview of metacognition, followed by identifying metacognition (i.e., metacognitive strategic knowledge), organizing, evaluating, planning, debugging, monitoring, and concluding with transfer. There is a symmetry to the book: each chapter focuses on a predictable pattern to holistically learn, understand, and instruct the topic:
- Foundational Theory. Chapters begin with a summary of the key concepts required to understand the cognitive, emotional, and related capacities of a learner when using the component.
- Development and Instruction. How the component develops with recommendations for instruction is included.
- Function. The purpose and capacities of the component is articulated.
- Advantages, Challenges, and Strategies. Each of the components have their strengths highlighted, with challenges identified and strategies for overcoming them.
- Suggested Uses and Examples. Three top recommendations are provided for suggested uses followed by real-life and mathematics examples. The real-life examples are provided first to ground the understanding in practical ways before developing an understanding of its application in mathematics.
- Strategies. Math-specific strategies are included with each chapter. These strategies are corresponding companions to the metacognitive component identified, and their inclusion is paired to strengthen their relevance and use.
- Daily Practice. A three-day set of prompts, which include both questions and reflections, are given to engage in developing the use of the targeted metacognitive component.
- Math Practice. A dedicated set of math practice is provided, with sample problems and answers aimed for Grades 3, 6, and 8. These problems could be used as examples with students, and are intended for educators to select based on comfort and area of focus.
- Transfer Activity. A set of reflective questions are provided, which are intended to be used after a week of practicing the use of the targeted metacognitive component.
- References. Relevant references are included for each chapter.
- Worksheets. Each chapter comes with a complementary set of worksheets which may be used with permission to instruct students as an owner of this book. These worksheets are designed to be used with any age of student, particularly grades 3+. The worksheets include handouts, exercises, and teaching guides, to support learning and development in students as exemplars of directly applying the process given in this book. The above process is designed to focus on examples, practical application, and direct instruction for the purpose of transferring knowledge.
When you are reading this book, I recommend the following process:
- Review the theory. It doesn’t need to be memorized, but the knowledge in there is fun to learn – it reveals so many important aspects of teaching that can be transferrable into other areas.
- Consult the advantages, challenges, and strategies. When you’re stuck, this will be a great area to return to for insight.
- Enjoy the suggested uses and examples. These practical guides are intentionally designed, with deep analysis included, to show you how powerful these tools are – and recognize that these are only scratching the surface of what is possible. If you are looking for an expert tip: try to develop examples of your own to show your students!
- Teach the strategies. These strategies reduce wasted classroom time – they include many of the most comment conceptual difficulties with proven techniques to help students master their understanding and use.
- Use the practice. It will take discipline and external prompts, but the fastest way to both experience and teach these processes is to learn by doing it. Even just seeing these prompts, and thinking about your reactions to them, can have a profound impact on the resulting use.
- Be open to using it everywhere. The more you (and your students) practice looking for areas to use what is contained in this text, the more frequently you will find other useful aspects!
- Invest in including this in your teaching. The worksheets are designed to be used for any math topic, or grade level. Taking time out of your ‘regular’ instruction to integrate this for even eight weeks will have a notable impact in your class. The beautiful part: you can take what you are teaching and include it right into the process. The best part: if you continue to cycle through this process, you will see even more results.
Finally, revisit this work when you need. It is not designed to be memorized, but used – it is an encyclopedia, lesson planner, and troubleshooting guide. Keep it handy, and revisit it when you are stuck or need help – and join our community online for continued support!
Justin Teeuwen is an international motivational speaker, author, educator, business coach, and performance coach. He completed his Doctor of Philosophy in Education with a focus on Cognition and Learning in 2019. Previously, he completed a Master of Science Degree in Physics in 2010 and a Bachelor of Education Degree in 2012. Justin has taught in Canada, England, Tanzania, China, and the United States at every level of education. Justin has been researching, developing, and practicing as an educator for more than 15 years. For the past five years Justin has continued to focus his practice by infusing metacognition into his instruction across several domains including mathematics, physics, science, and dance. He has also continued to publish his research, with areas of focus in metacognition and metawellness. Justin also applies his research into a coaching practice as one of the founders of the Meta Excellence program. Combining the four Meta Tools (metacognition, metaemotion, metawellness, and metacharacter), the MetaExcellence program enhances performance in thinking, feeling, doing, and being.
This book is designed for pre-service and in-service educators of students in mathematics at any level: elementary, secondary, and post-secondary. It demystifies ‘metacognition’ and turns a complicated subject into one that is practical and seamless to integrate into math instruction. Created as an add-on to existing teaching practices for direct infusion into instruction, this text is designed to both model and teach the process of integrating metacognition into mathematics instruction. It is intended to be used as an introduction, guide, and resource-OnDemand when building this key skill into instruction. Educators will learn how to teach their students to think with more advanced strategies, make full use of their
resources, and be able to transfer these skills into any area of learning. The Integration of Metacognition into Mathematics bridges the gap between research and practice for educators. It includes both research and results from a lifetime of study and teaching in the field. It features a summary of the core theory and includes practical examples as well as elite resources, strategies, and processes to support learning in mathematics. It is specifically engineered to facilitate the transfer mathematics learning and metacognition into life beyond the classroom. It is not only intended to help educators learn metacognition, but to have accessible guides and strategies for integrating it into instruction with ease.
Chapter 1: Introduction to Metacognition
Basic Terminology and Theoretical Foundation
Chapter 2: Identifying
Building Metacognitive Strategic Knowledge
Chapter 3: Organizing
Categorizing and Recognizing Thoughts
Chapter 4: Evaluating
Training and Calibrating Instinct
Chapter 5: Planning
Constructing and Maintaining Focus
Chapter 6: Debugging
Troubleshooting the Complex, Unknown, and Unfamiliar
Chapter 7: Monitoring
Mindfully Thinking with Focus
Chapter 8: Transfer
Applying Metacognition and Mathematics Learning Beyond the Classroom
The book is designed to model the instructional order when scaffolding metacognition (see Chapter 1 and Chapter 2). It begins with an overview of metacognition, followed by identifying metacognition (i.e., metacognitive strategic knowledge), organizing, evaluating, planning, debugging, monitoring, and concluding with transfer. There is a symmetry to the book: each chapter focuses on a predictable pattern to holistically learn, understand, and instruct the topic:
- Foundational Theory. Chapters begin with a summary of the key concepts required to understand the cognitive, emotional, and related capacities of a learner when using the component.
- Development and Instruction. How the component develops with recommendations for instruction is included.
- Function. The purpose and capacities of the component is articulated.
- Advantages, Challenges, and Strategies. Each of the components have their strengths highlighted, with challenges identified and strategies for overcoming them.
- Suggested Uses and Examples. Three top recommendations are provided for suggested uses followed by real-life and mathematics examples. The real-life examples are provided first to ground the understanding in practical ways before developing an understanding of its application in mathematics.
- Strategies. Math-specific strategies are included with each chapter. These strategies are corresponding companions to the metacognitive component identified, and their inclusion is paired to strengthen their relevance and use.
- Daily Practice. A three-day set of prompts, which include both questions and reflections, are given to engage in developing the use of the targeted metacognitive component.
- Math Practice. A dedicated set of math practice is provided, with sample problems and answers aimed for Grades 3, 6, and 8. These problems could be used as examples with students, and are intended for educators to select based on comfort and area of focus.
- Transfer Activity. A set of reflective questions are provided, which are intended to be used after a week of practicing the use of the targeted metacognitive component.
- References. Relevant references are included for each chapter.
- Worksheets. Each chapter comes with a complementary set of worksheets which may be used with permission to instruct students as an owner of this book. These worksheets are designed to be used with any age of student, particularly grades 3+. The worksheets include handouts, exercises, and teaching guides, to support learning and development in students as exemplars of directly applying the process given in this book. The above process is designed to focus on examples, practical application, and direct instruction for the purpose of transferring knowledge.
When you are reading this book, I recommend the following process:
- Review the theory. It doesn’t need to be memorized, but the knowledge in there is fun to learn – it reveals so many important aspects of teaching that can be transferrable into other areas.
- Consult the advantages, challenges, and strategies. When you’re stuck, this will be a great area to return to for insight.
- Enjoy the suggested uses and examples. These practical guides are intentionally designed, with deep analysis included, to show you how powerful these tools are – and recognize that these are only scratching the surface of what is possible. If you are looking for an expert tip: try to develop examples of your own to show your students!
- Teach the strategies. These strategies reduce wasted classroom time – they include many of the most comment conceptual difficulties with proven techniques to help students master their understanding and use.
- Use the practice. It will take discipline and external prompts, but the fastest way to both experience and teach these processes is to learn by doing it. Even just seeing these prompts, and thinking about your reactions to them, can have a profound impact on the resulting use.
- Be open to using it everywhere. The more you (and your students) practice looking for areas to use what is contained in this text, the more frequently you will find other useful aspects!
- Invest in including this in your teaching. The worksheets are designed to be used for any math topic, or grade level. Taking time out of your ‘regular’ instruction to integrate this for even eight weeks will have a notable impact in your class. The beautiful part: you can take what you are teaching and include it right into the process. The best part: if you continue to cycle through this process, you will see even more results.
Finally, revisit this work when you need. It is not designed to be memorized, but used – it is an encyclopedia, lesson planner, and troubleshooting guide. Keep it handy, and revisit it when you are stuck or need help – and join our community online for continued support!
Justin Teeuwen is an international motivational speaker, author, educator, business coach, and performance coach. He completed his Doctor of Philosophy in Education with a focus on Cognition and Learning in 2019. Previously, he completed a Master of Science Degree in Physics in 2010 and a Bachelor of Education Degree in 2012. Justin has taught in Canada, England, Tanzania, China, and the United States at every level of education. Justin has been researching, developing, and practicing as an educator for more than 15 years. For the past five years Justin has continued to focus his practice by infusing metacognition into his instruction across several domains including mathematics, physics, science, and dance. He has also continued to publish his research, with areas of focus in metacognition and metawellness. Justin also applies his research into a coaching practice as one of the founders of the Meta Excellence program. Combining the four Meta Tools (metacognition, metaemotion, metawellness, and metacharacter), the MetaExcellence program enhances performance in thinking, feeling, doing, and being.