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 and Jennifer Rose Novak help us value our students misconceptions and incomplete understandings as much as their correct onesbecause its the gap in their understanding today that holds the secrets to planning tomorrows best teaching. The authors lay out 180 high-quality tasks aligned to the standards and big ideas of Grades 68 mathematics, including number systems, integers, ratio and proportion, equations and expressions, geometry, and statistics and probability. 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 taskfour student examples of the completed task showcasing a distinct "gap"commentary on what precisely counts for mathematical understanding and the next instructional stepscommentary on the misconception or incomplete understanding so you learn why the student veered off coursethree additional tasks aligned to the mathematics topic and ideas about what students might do with these additional tasks Its 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 Understandingis 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.

 

 

This book is part of a book series called Corwin Mathematics .

There are 408 pages in this book. This book was published in 2017 by SAGE Publications Inc .

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. Dr. Eric Milou is a professor of mathematics at Rowan University in Glassboro, NJ. Dr. Milou has taught at Rowan for the past 20 years and served six terms as the President of the Rowan University Senate from 2007 to 2013. He previously served as President as the Association of Mathematics Teachers of New Jersey, the program chairperson of the 2007 NCTM annual meeting and has extensive speaking experience on standards based reform in mathematics. He is one of the authors of digits, EnVisions 6-8 and EnVisions A|G|A (published by Pearson) and was the recipient of the Max Sobel Outstanding Mathematics Educator Award in 2009.