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Mine the Gap for Mathematical Understanding, Grades 6-8 : Common Holes and Misconceptions and What To Do About Them - John J. SanGiovanni

Mine the Gap for Mathematical Understanding, Grades 6-8

Common Holes and Misconceptions and What To Do About Them

Paperback Published: 20th November 2017
ISBN: 9781506379821
Number Of Pages: 408

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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 ones'because it's the gap in their understanding today that holds the secrets to planning tomorrow's best teaching. The authors lay out 180 high-quality tasks aligned to the standards and big ideas of Grades 6'"8 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 task
    • what you might anticipate before students work with the task
    • four 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.  

Industry Reviews

"Wow! This book is a treasure trove for middle school teachers and those who support middle level mathematics education. The tasks presented are top notch, the student work is illustrative of classrooms, and the suggestions for how to respond are incredible! Each of these three would make a great resource-to have them all blended together is outstanding." -- Kevin Dykema
"Mine the Gap for Mathematical Understanding provides the framework and guidance teachers need to move beyond finding correct answers to dig deeply into the mine of student thinking, to analyze misconceptions and gaps in understanding, and to develop and implement specific strategies to support every student in deep mathematics learning. Every teacher of mathematics needs this amazing resource to learn to mine the gaps for each of their students!" -- Becky M. Walker
"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." -- Zachary Champagne
"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." -- Nathan Rosin
"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." -- Delise Andrews
"This book helps navigate how to use student work to drive instruction with rich engaging tasks, which will help all students become better mathematicians. The authors have done an excellent job of helping teachers to carefully look at student work to identify how students solved math problems, using this evidence to identify those students who understand the targeted skill, along with the misconceptions or misunderstandings of other students, with suggestions of how to move all students forward in their thinking." -- Cynthia Baumann

Big Ideas & Tasks at a Glance
About the Author
Chapter 1: Rich Mathematics Tasks, Student Misconceptions, Using Tasks
Prompts with Purpose: Using High Quality Tasks
Using Quality Tasks
Reflecting on Chapter 1
Chapter 2: Number Systems
Big Idea 1: Addition and Subtraction of Fractions
Big Idea 2. Multiplication and Division of Fractions
Big Idea 3. Reasoning about Addition and Subtraction of Fractions
Big Idea 4. Reasoning about Multiplication and Division of Fractions
Big Idea 5. Problem Solving with Fractions
Big Idea 6. Decimals as Numbers
Big Idea 7. Addition and Subtraction with Decimals
Big Idea 8. Multiplication and Division with Decimals
Chapter 3: Integers
Big Idea 9: Representing Integers
Big Idea 10. Representing Integers on Number Lines
Big Idea 11. More Representing Integers on Number Lines
Big Idea 12. Comparing Integers
Big Idea 13. Addition with Integers
Big Idea 14. Subtraction with Integers
Big Idea 15. Multiplication with Integers
Big Idea 16. Division with Integers
Chapter 4: Ratio, Proportion, and Percent
Big Idea 17. Representing Ratios
Big Idea 18. Equivalent Ratios
Big Idea 19. Unit Rates
Big Idea 20. Using Ratios to Solve Problems
Big Idea 21. Reasoning with Percents
Big Idea 22. Unit Rate as Slope
Chapter 5: Expressions, Equations, and Functions
Big Idea 23. Writing Expressions
Big Idea 24. Evaluating Expressions
Big Idea 25. Equivalent Expressions
Big Idea 26. Writing Equations
Big Idea 27. Solving Equations
Big Idea 28. Inequalities
Big Idea 29. Function Tables
Big Idea 30. Reasoning about Graphing
Big Idea 31. Comparing Functions
Big Idea 32. Systems of Equations
Chapter 6: Geometry
Big Idea 33. Area of Composite Figures
Big Idea 34. Nets and Three-Dimensional Figures
Big Idea 35. Surface Area and Volume
Big Idea 36. Volume of Cylinders and Cones
Big Idea 37. Angle Relationships
Big Idea 38. Transformations, Similarity, and Congruence
Big Idea 39. Distance and Pythagorean Theorem
Chapter 7: Statistics
Big Idea 40. Univariate Categorical Data
Big Idea 41. Univariate Quantitative Data
Big Idea 42. Displays of Univariate Data
Big Idea 43. Deviations from the Mean
Big Idea 44. Bivariate Categorical Data
Big Idea 45. Bivariate Quantitative Data
Chapter 8: References and Additional Resources

ISBN: 9781506379821
ISBN-10: 1506379826
Series: Corwin Mathematics Series
Audience: Professional
For Grades: 6 - 8
Format: Paperback
Language: English
Number Of Pages: 408
Published: 20th November 2017
Publisher: SAGE Publications Inc
Country of Publication: US
Dimensions (cm): 27.9 x 21.5  x 1.3
Weight (kg): 0.8
Edition Number: 1

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John J. SanGiovanni

About the Author

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

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