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

Being an effective math educator is one part based on the quality of the tasks we give, one part how we diagnose what we see, and one part what we do with what we find. Yet with so many students and big concepts to cover, it can be hard to slow down enough to look for those moments when students’ responses tell us what we need to know about next best steps. In this remarkable book, John SanGiovanni helps us value our young learners’ misconceptions and incomplete understandings as much as their correct ones—because it’s the gap in their understanding today that holds the secrets to planning tomorrow’s best teaching. SanGiovanni lays out 160 high-quality tasks aligned to the standards and big ideas of grades K-2 mathematics, including  counting and representing numbers, number relationships and comparison, addition and subtraction within 100 and 1000, money and time,  and multiplication and division. The tasks are all downloadable so you can use or modify them for instruction and assessment. Each big idea offers a starting task followed by: what makes it a high-quality taskwhat you might anticipate before students work with the task 4 student examples of the completed task showcasing a distinct "gap" commentary on what precisely counts for mathematical understanding and the next instructional steps commentary on the misconception or incomplete understanding so you learn why the student veered off course  three additional tasks aligned to the mathematics topic and ideas about what students might do with these additional tasks. It’s time to break our habit of rushing into re-teaching for correctness and instead get curious about the space between right and wrong answers. Mine the Gap for Mathematical Understanding is a book you will return to again and again to get better at selecting tasks that will uncover students’ reasoning—better at discerning the quality and clarity of students’ understanding—and better at planning teaching based on the gaps you see. 

Table of Contents:
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

About the Author :
John J. SanGiovanni is a mathematics coordinator in Howard County, Maryland. There, he leads mathematics curriculum development, digital learning, assessment, and professional development. John is passionate about growing new mathematics leaders in the district and through McDaniel College. In addition to the Figuring Out Fluency series, some of his many Corwin books include Daily Routines to Jump-Start Problem Solving, Grades K–8; Answers to Your Biggest Questions About Teaching Elementary Math; the Daily Routines to Jump-Start Math series; and Productive Math Struggle: A 6-Point Action Plan for Fostering Perseverance. John is a national mathematics curriculum and professional learning consultant who also speaks frequently at national conferences and institutes. He is active in state and national professional organizations, recently serving on the board of directors for the National Council of Teachers of Mathematics (NCTM) and on the board of directors for NCSM.

Review :
"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." "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!" "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." "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." "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." "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." "John SanGiovanni continues to provide teacher-friendly, must-have books. They empower teachers by deepening their understanding of content and teaching."