Concept-based mathematics
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Description
Book Introduction
"Concept-Based Mathematics," a book that integrates a concept-based curriculum into math classes, has been translated and published!
A new learning concept that breaks away from the traditional curriculum that emphasizes only knowledge and skills and explores concepts and ideas!
This book expands and develops the work of Lynn Erickson and Lois Lanning into the mathematics domain in a concept-based curriculum.
Although primarily focused on secondary mathematics classrooms, the strategies presented by the author transfer across elementary, middle, and high school classrooms.
Even teachers of other subjects can refer to this book for its many strategies, making it a valuable resource for sharing.
Special sections include sample lessons, sample student assignments, vignettes from international educators, and discussion questions that can be used during book readings with colleagues or in teacher training settings.
Traditional curricula focus on rules and procedures rather than understanding the conceptual relationships in mathematics.
Concept-based curricula, on the other hand, feature a three-dimensional design model that links factual content, skills, and processes into subject concepts, generalizations, and principles.
In his book, Worsall presents several design strategies that can help you design lessons that elicit deep and sophisticated thinking.
This book allows teachers to focus their teaching on deeper conceptual understanding and prepare students for future success.
Develop a concept-based approach to curriculum and instruction through practical examples of concept-based lessons, unit meshes, unit plans, and various assessment tools.
This text provides a set of sample lesson modules and free online resources (including templates) with activity sheets that promote deeper conceptual understanding of specific math topics.
Additional elementary, middle, and high school math class examples can be explored on the online platforms listed in the text.
A new learning concept that breaks away from the traditional curriculum that emphasizes only knowledge and skills and explores concepts and ideas!
This book expands and develops the work of Lynn Erickson and Lois Lanning into the mathematics domain in a concept-based curriculum.
Although primarily focused on secondary mathematics classrooms, the strategies presented by the author transfer across elementary, middle, and high school classrooms.
Even teachers of other subjects can refer to this book for its many strategies, making it a valuable resource for sharing.
Special sections include sample lessons, sample student assignments, vignettes from international educators, and discussion questions that can be used during book readings with colleagues or in teacher training settings.
Traditional curricula focus on rules and procedures rather than understanding the conceptual relationships in mathematics.
Concept-based curricula, on the other hand, feature a three-dimensional design model that links factual content, skills, and processes into subject concepts, generalizations, and principles.
In his book, Worsall presents several design strategies that can help you design lessons that elicit deep and sophisticated thinking.
This book allows teachers to focus their teaching on deeper conceptual understanding and prepare students for future success.
Develop a concept-based approach to curriculum and instruction through practical examples of concept-based lessons, unit meshes, unit plans, and various assessment tools.
This text provides a set of sample lesson modules and free online resources (including templates) with activity sheets that promote deeper conceptual understanding of specific math topics.
Additional elementary, middle, and high school math class examples can be explored on the online platforms listed in the text.
- You can preview some of the book's contents.
Preview
index
I recommend 『Concept-Based Mathematics』 / iv
Translator's Note / viii
List of Figures / xiv
Recommendation / xviii
Preface / xx
Acknowledgments / xxvi
About the Author xxviii
Author's Note xxix
Part I: What is Concept-Based Curriculum and Instruction in Mathematics?
Chapter 1: Why is it important for students to learn conceptually? / 3
Why should we develop curricula and lessons to include conceptual levels? / 3
Structure of Knowledge and Structure of Process / 5
Chapter 1: A Glance / 25
Discussion Questions / 26
Chapter 2: What are the elements that make up the structure of knowledge and the structure of processes in mathematics? / 27
Layers of Knowledge Structure / 28
Layers of Process Structure / 32
Macro, Meso, and Micro Concepts in Mathematics /55
Combining the Structure of Knowledge and the Structure of Process / 56
Chapter 2: A Glance / 62
Discussion Questions / 63
Part II: Writing Generalizations and Unit Design for Deep Conceptual Understanding
Chapter 3: What is Generalization in Mathematics? / 67
What is the difference between generalizations and principles in mathematics? / 68
How to elicit conceptual understanding from students? / 81
Chapter 3: A Glance / 89
Discussion Questions / 90
Chapter 4: How to Design Units for a Concept-Based Mathematics Curriculum / 91
Unit Net / 93
Unit Design / 95
Guiding Questions / 97
Designing a Unit on Functions / 98
Designing a Circle Unit / 107
Designing Calculus Units: Differentiation and Integration / 107
Chapter 4: A Glance / 137
Discussion Questions / 138
Part III How do we implement classes that promote student participation?
About the strategy of engaging, evaluating and diagnosing
Chapter 5: How to Capture Students' Hearts / 141
Eight Strategies to Encourage Students to Engage with Their Feelings and Thoughts / 141
Strategy 1: Create a Collaborative Learning Environment / 142
Strategy 2: Provide an open and safe environment that allows mistakes to be made as part of the learning process / 144
Strategy 3: Developing Conceptual Understanding with Appropriate Levels of Inquiry and Inductive Approaches / 146
Strategy 4: Reduce Teacher Speaking Time in Whole Class / 152
Strategy 5: Supporting All Students in the Class; Using Differentiation Strategies / 153
Strategy 6: Evaluation Strategies / 161
Strategy 7: Be intentional when asking students to answer questions; there's safety in numbers / 163
Strategy 8: The Classroom Without a Pedestrian: Reimagining Collaborative Spaces / 163
Chapter 5: A Glance / 166
Discussion Questions / 167
Chapter 6 How do we know that students understand the concept?
Evaluation Strategies / 169
Evaluation with Conceptual Depth / 170
Open-Ended Inquiry Tasks and Open Questions / 171
Visible Thinking Routine / 173
Performance Assessment Task / 177
Freire Model / 185
Concept Acquisition Card / 185
For, Against, Hold / 189
0, 1, 2, 3 / 190
Assessment and Development of Cross-Curricular Core Skills / 191
Assessing Concept-Based Learner Development / 193
Self-Assessment / 194
Chapter 6: A Glance / 199
Discussion Questions / 200
Chapter 7: How to Integrate Technology to Facilitate Conceptual Understanding / 201
Math Graphing Software and Graphical Display Calculators / 205
Flipped Classroom / 206
Multimedia Project / 213
Collaboration Tools: Google Apps / 216
Apps on your phone / 217
When Not to Use Technology / 219
Chapter 7: A Glance / 229
Discussion Questions / 230
Chapter 8: What Does an Ideal Concept-Based Mathematics Classroom Look Like? / 231
Cultivate a Growth Mindset / 232
Pedagogical Principles for the Ideal Classroom / 232
Developing Ideal Concept-Based Math Lessons / 234
Designing a Teaching and Learning Plan for an Ideal Mathematics Class / 240
Common Concerns and Misconceptions About Concept-Based Curriculum and Instruction / 240
Chapter 8 at a Glance / 250
Conclusion / 251
Discussion Questions / 252
Glossary / 253
[Concept-Based Mathematics: Designing Lessons that Develop Thinking Skills] Readings / 259
References and Additional Reading / 271
Search / 277
Translator's Note / viii
List of Figures / xiv
Recommendation / xviii
Preface / xx
Acknowledgments / xxvi
About the Author xxviii
Author's Note xxix
Part I: What is Concept-Based Curriculum and Instruction in Mathematics?
Chapter 1: Why is it important for students to learn conceptually? / 3
Why should we develop curricula and lessons to include conceptual levels? / 3
Structure of Knowledge and Structure of Process / 5
Chapter 1: A Glance / 25
Discussion Questions / 26
Chapter 2: What are the elements that make up the structure of knowledge and the structure of processes in mathematics? / 27
Layers of Knowledge Structure / 28
Layers of Process Structure / 32
Macro, Meso, and Micro Concepts in Mathematics /55
Combining the Structure of Knowledge and the Structure of Process / 56
Chapter 2: A Glance / 62
Discussion Questions / 63
Part II: Writing Generalizations and Unit Design for Deep Conceptual Understanding
Chapter 3: What is Generalization in Mathematics? / 67
What is the difference between generalizations and principles in mathematics? / 68
How to elicit conceptual understanding from students? / 81
Chapter 3: A Glance / 89
Discussion Questions / 90
Chapter 4: How to Design Units for a Concept-Based Mathematics Curriculum / 91
Unit Net / 93
Unit Design / 95
Guiding Questions / 97
Designing a Unit on Functions / 98
Designing a Circle Unit / 107
Designing Calculus Units: Differentiation and Integration / 107
Chapter 4: A Glance / 137
Discussion Questions / 138
Part III How do we implement classes that promote student participation?
About the strategy of engaging, evaluating and diagnosing
Chapter 5: How to Capture Students' Hearts / 141
Eight Strategies to Encourage Students to Engage with Their Feelings and Thoughts / 141
Strategy 1: Create a Collaborative Learning Environment / 142
Strategy 2: Provide an open and safe environment that allows mistakes to be made as part of the learning process / 144
Strategy 3: Developing Conceptual Understanding with Appropriate Levels of Inquiry and Inductive Approaches / 146
Strategy 4: Reduce Teacher Speaking Time in Whole Class / 152
Strategy 5: Supporting All Students in the Class; Using Differentiation Strategies / 153
Strategy 6: Evaluation Strategies / 161
Strategy 7: Be intentional when asking students to answer questions; there's safety in numbers / 163
Strategy 8: The Classroom Without a Pedestrian: Reimagining Collaborative Spaces / 163
Chapter 5: A Glance / 166
Discussion Questions / 167
Chapter 6 How do we know that students understand the concept?
Evaluation Strategies / 169
Evaluation with Conceptual Depth / 170
Open-Ended Inquiry Tasks and Open Questions / 171
Visible Thinking Routine / 173
Performance Assessment Task / 177
Freire Model / 185
Concept Acquisition Card / 185
For, Against, Hold / 189
0, 1, 2, 3 / 190
Assessment and Development of Cross-Curricular Core Skills / 191
Assessing Concept-Based Learner Development / 193
Self-Assessment / 194
Chapter 6: A Glance / 199
Discussion Questions / 200
Chapter 7: How to Integrate Technology to Facilitate Conceptual Understanding / 201
Math Graphing Software and Graphical Display Calculators / 205
Flipped Classroom / 206
Multimedia Project / 213
Collaboration Tools: Google Apps / 216
Apps on your phone / 217
When Not to Use Technology / 219
Chapter 7: A Glance / 229
Discussion Questions / 230
Chapter 8: What Does an Ideal Concept-Based Mathematics Classroom Look Like? / 231
Cultivate a Growth Mindset / 232
Pedagogical Principles for the Ideal Classroom / 232
Developing Ideal Concept-Based Math Lessons / 234
Designing a Teaching and Learning Plan for an Ideal Mathematics Class / 240
Common Concerns and Misconceptions About Concept-Based Curriculum and Instruction / 240
Chapter 8 at a Glance / 250
Conclusion / 251
Discussion Questions / 252
Glossary / 253
[Concept-Based Mathematics: Designing Lessons that Develop Thinking Skills] Readings / 259
References and Additional Reading / 271
Search / 277
GOODS SPECIFICS
- Publication date: September 6, 2022
- Page count, weight, size: 320 pages | 188*257*30mm
- ISBN13: 9791160735345
- ISBN10: 1160735344
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