Mine the Gap for Mathematical Understanding, Grades 3-5: 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 students’ 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 180 high-quality tasks aligned to the standards and big ideas of Grades 3-5 mathematics, including addition and subtraction of multi-digit whole numbers, multiplication and division of single and multi-digit whole numbers, foundational fraction concepts, foundational decimal concepts, and operations with fractions and decimals. 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 task what 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. MINE THE GAP FOR MATHEMATICAL UNDERSTANDING- FRONT COVER MINE THE GAP FOR MATHEMATICAL UNDERSTANDING COPYRIGHT 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- ADDITION AND SUBTRACTION WITHIN 1,000 CHAPTER 3- MULTIPLICATION AND DIVISION CHAPTER 4- FOUNDATIONAL FRACTION CONCEPTS CHAPTER 5- DECIMAL CONCEPTS CHAPTER 6- ADDITION AND SUBTRACTION WITH FRACTIONS CHAPTER 7- MULTIPLICATION AND DIVISION WITH FRACTIONS AND DECIMALS CHAPTER 8- WHAT DO WE DO NEXT? REFERENCES AND ADDITIONAL RESOURCES In this remarkable book, John SanGiovanni reminds us that mathematical mistakes are not random, and when we take the time to "mine the gap," we can dispel misunderstandings before they take root. Discover the reasons behind elementary mathematics students' errors, including those in grades 3 through 5, to lead them to correct mathematics.-- Source other than Library of Congress