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Mine the Gap for Mathematical Understanding, Grades K-2

Common Holes and Misconceptions and What To Do About Them
It’s hard to find the time to figure out the ”why” behind students’ math mistakes, so here is a bank of 160 downloadable, standards-aligned math tasks, the common misunderstandings, and next instructional steps.

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A Copy:

How good are you at embracing learners’ mathematical mistakes? In this remarkable book, John SanGiovanni reminds us that mistakes are not random, and when we take the time to “mine the gap,” we can dispel misunderstandings before they take root. Included are 160 downloadable high-quality tasks, aligned to the standards and big ideas grades K-2 mathematics. Each task includes sample student work, commentary on strengths and gaps, and next instructional steps. Whether you use this bank of tasks for instruction or assessment, you will love how it helps you easily identify students’ thinking and then follow-up with instruction that brings clear, complete understanding.

Full description

Product Details
  • Grade Level: PreK-12
  • ISBN: 9781506337685
  • Published By: Corwin
  • Series: Corwin Mathematics Series
  • Year: 2016
  • Page Count: 384
  • Publication date: November 18, 2016

Price: $37.95

Description

Description

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.

Author(s)

Author(s)

John J. SanGiovanni photo

John J. SanGiovanni

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 an adjunct professor and coordinator of the Elementary Mathematics Instructional Leadership graduate program at McDaniel College. In addition to this 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 currently on the board of directors for the National Council of Supervisors of Mathematics (NCSM).

Table of Contents

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


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Related Resources

  • Access to companion resources is available with the purchase of this book.
  • Big Idea 10:  [Lessons and strategies]
  • Big Idea 34:  [Lessons and strategies]