Mine the Gap for Mathematical Understanding, Grades K-2

  • Title:Mine the Gap for Mathematical Understanding, Grades K-2: Common Holes and Misconceptions and What To Do About Them
  • Author:John SanGiovanni
  • Publication Date:November 2016
  • Grade Level:K-2
  • ISBN:9781506337685
  • Publisher:Corwin Press

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 Bio

John SanGiovanni is a mathematics supervisor in Howard County, Maryland, an adjunct professor and coordinator of the Elementary Mathematics Instructional Leader graduate program at McDaniel College, an author, and a national mathematics curriculum and professional learning consultant. John is a frequent speaker at national conferences and institutes.

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