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Mine the Gap for Mathematical Understanding, Grades K-2: Common Holes and Misconceptions and What To Do About Them

John J. SanGiovanni

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Corwin Press Inc
02 December 2016
Curriculum planning & development; Primary & middle schools; Teaching skills & techniques; Educational material
Misconceptions and incomplete mathematical thinking often go undetected, as teachers are rarely trained to consider why or how an answer was generated. They often respond to incorrect answers by re-teaching the correct processes, and the underlying problem persists. Unrecognized misconceptions then become permanent ways of thinking; each new layer of mathematics knowledge builds upon on flawed foundations. This book addresses that problem head on. By covering the essential content or big ideas of K-2 mathematics, it turns elementary teachers into experts in diagnosis, intervention, and evaluation, and delivers the tasks and tools to use in the classroom day-to-day.
By:   John J. SanGiovanni
Imprint:   Corwin Press Inc
Country of Publication:   United States
Dimensions:   Height: 279mm,  Width: 215mm,  Spine: 13mm
Weight:   800g
ISBN:   9781506337685
ISBN 10:   1506337686
Series:   Corwin Mathematics Series
Pages:   384
Publication Date:   02 December 2016
Audience:   Professional and scholarly ,  Undergraduate
Format:   Paperback
Publisher's Status:   Active
Big Ideas & Tasks at a Glance Acknowledgments Publisher's Acknowledgments About the Author Introduction CHAPTER 1. RICH MATHEMATICS TASKS, STUDENT MISCONCEPTIONS, USING TASKS CHAPTER 2. COUNTING AND REPRESENTING NUMBERS BIG IDEAS 1. Counting on From Any Number (0-120) 2. Counting on a Number Line 3. Skip-Counting 4. Representing Numbers 5. Representing Numbers to 1,000 With Models 6. Understanding Relationships Between Numbers CHAPTER 3. NUMBER RELATIONSHIPS AND COMPARISON BIG IDEAS 7. Comparing Numbers Within 100 8. Comparing Numbers Within 1,000 9. Comparing Numbers Within 1,000 10. Number Relationships Through Number Lines 11. Decomposing Numbers Less Than 100 12. More Decomposing Numbers CHAPTER 4. ADDITION AND SUBTRACTION BIG IDEAS 13. Representing Addition 14. Properties of Addition 15. Reasoning About Addition 16. Representing Subtraction 17. Connecting Addition and Subtraction 18. Reasoning About Subtraction 19. The Meaning of the Equal Sign 20. Problem Solving With Addition and Subtraction CHAPTER 5. ADDITION AND SUBTRACTION WITHIN 100 BIG IDEAS 21. Addition Within 100 22. More With Addition Within 100 23. Reasoning About Addition Within 100 24. Subtraction Within 100 25. Reasoning About Subtraction Within 100 26. Problem Solving Using Addition and Subtraction Within 100 CHAPTER 6. ADDITION AND SUBTRACTION WITHIN 1,000 BIG IDEAS 27. Adding Within 1,000 28. Reasoning About Addition Within 1,000 29. Subtraction Within 1,000 30. Reasoning About Subtraction Within 1,000 31. Problem Solving Within 1,000 CHAPTER 7. MEASUREMENT WITH MONEY AND TIME BIG IDEAS 32. Working and Problem Solving With Money 33. Working and Problem Solving With Money 34. Telling Time 35. Elapsed Time CHAPTER 8. MULTIPLICATION AND DIVISION BIG IDEAS 36. Representing Multiplication and Division 37. Reasoning About Multiplication 38. Properties of Multiplication 39. Representing Division 40. Problem Solving With Multiplication and Division CHAPTER 9. WHAT DO WE DO NEXT? References and Additional Resources

John SanGiovanni is a mathematics supervisor in Howard County, Maryland. There he leads mathematics curriculum development, digital learning, assessment, and professional development for 41 elementary schools and more than 1,500 teachers. John is an adjunct professor and coordinator of the Elementary Mathematics Instructional Leader graduate program at McDaniel College. He is an author and national mathematics curriculum and professional learning consultant. John is a frequent speaker at national conferences and institutes. He is active in state and national professional organizations and currently serves on the Board of Directors for the National Council of Teachers of Mathematics.

Reviews for Mine the Gap for Mathematical Understanding, Grades K-2: Common Holes and Misconceptions and What To Do About Them

John SanGiovanni continues to provide teacher-friendly, must-have books. They empower teachers by deepening their understanding of content and teaching. -- Megan Dooley More than just a nice collection of problems, this book shares a road map for teachers looking to enhance the quality of the math tasks they use with students. Teachers will appreciate the examples of actual student work paired with tips for analysis and instruction. -- Delise Andrews Mine the Gap is a great tool for teachers to use to grow their own understanding of student misconceptions and incomplete understandings and how to address them. This is an indispensable resource for all involved in supporting students' growth in mathematics. -- Nathan Rosin Mine the Gap for Mathematical Understanding is a much-needed and anticipated resource for teachers, mathematics coaches, mathematics specialists, administrators, and other stakeholders. The easy to follow, teacher-friendly format, the accompanying commentary for each student work sample, along with the thoughtful reflection questions will quickly make this resource a `go-to' professional development tool. -- Latrenda Knighten This work does what other books only attempt to do. It combines instruction, assessment, and practice with open-ended and rich tasks that allow for teachers to not only immediately implement the ideas but also understand the content and pedagogy behind them. The tasks, which are immediately implementable and customizable, engage each and every learner. They are based on cutting edge and research-based instructional frameworks and provide countless learning opportunities for students. -- Zachary Champagne Too often students (and parents and teachers) have the notion that the goal in math should be to get the right answer. Yet insight into misconceptions and students' thinking can tell us much more about what students know (and don't know) beyond simply a correct or incorrect answer. SanGiovanni offers teachers a treasure trove of rich tasks and student work on those tasks. Examples of how to analyze student thinking and next instructional steps make this a volume that should be on every K-2 math teacher's desk! -- Linda Gojak Wow! Mine the Gap for grades K-2 teachers really unpacks! Not only does the book provide dozens of great mathematical tasks, but-perhaps more important-it gives teachers the chance to consider each task; anticipate student responses-a critical first step in formative assessment; analyze actual student responses; and then consider what they would do in the classroom. Thoughts about modifying each task provide another option for each task. At a time when teachers are encouraged to regularly provide students with tasks that promote reasoning and problem solving, this book will help teachers dig deeper as they mine for understandings. -- Francis (Skip) Fennell


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