You are here

Uncovering Student Thinking About Mathematics in the Common Core, Grades 6-8

Uncovering Student Thinking About Mathematics in the Common Core, Grades 6-8
25 Formative Assessment Probes

October 2013 | 232 pages | Corwin
Here’s the middle-grades math resource you’ve been waiting for! Bestselling authors Cheryl Tobey and Carolyn Arline are back with 20 entirely new assessment probes that pinpoint subconcepts within the new Common Core Standards for Mathematics to promote deep learning and expert math instruction. Learn to ask the right questions to uncover common student misconceptions. Get practical instructional ideas that build new and accurate skills--while learning is already underway. It’s all here in this detailed and grade-level specific guide.

  • Organized by strand, the probes will enable you to:
  • Quickly and objectively evaluate common misconceptions around fractions and decimals, linear equations, ratios and percents, statistics, and more
  • Systematically address conceptual misunderstandings and procedural mistakes--before they become long-term problems
  • Help students better understand areas of difficulty
  • Plan targeted instruction that builds on students’ current understandings while addressing areas of struggle
  • Master the essential CCSM mathematical processes and proficiencies for Grades 6-8.
You’ll find sample student responses, extensive Teacher Notes, and research-based tips and resources. Eliminate the guesswork and join thousands of busy middle-grades teachers who’ve used these easy-to-implement tools to foster solid math proficiency!
Preface: Mathematics Assessment Probes
About the Authors
Chapter 1. Mathematics Assessment Probes
Questioning Student Understanding: Determine the Key Mathematical Concepts You Want Students to Learn

Uncovering Student Understanding: Use a Probe to Uncover Understandings and Areas of Difficulties

What Is the Structure of a Probe?

QUEST Cycle: Structure of the Supporting Teacher Notes

Beginning to Use the Probes

How to Navigate the Book

Final Chapter 1 Thoughts

Chapter 2. Number System Probes
Estimating Quotients

Division of Fractions

Number Lines

Rational Number Multiplication Estimates

Is It Positive?

Number Card Sort

Chapter 3. Ratio and Proportional Relationship Probes
Best Estimates: Finding Percents

Comparing Measures

Best Estimates: Solving Proportions

Proportional Reasoning Sort

Chapter 4. Expressions and Equations and Functions Probes
Value of the Inequality

Writing Equations

Is It Equivalent?

Linear Equations

Is It a Linear Function?

Chapter 5. Statistics and Probability Probes
Measures of Center and Spread

What's the Chance?


Chapter 6. Geometry Probes
Perimeter and Area

Properties of Angles

Finding Volume


Right Triangles

Heights of Solids


Chapter 7. Additional Considerations
Establishing Learning Targets

Individual Metacognition and Reflection (The 4Cs)

Giving Student Interviews

Addressing Individual Needs

Promoting Math Talk

Supporting the Mathematical Practices

Sharing Experiences and Promoting Professional Collaboration


Appendix A. Information on the Standards for Mathematical Practice
Appendix B. Developing Assessment Probes
Appendix C. Action Research Reflection Template: QUEST Cycle

"The formative assessment probes are the best part of this book. I love that the probes are broken down by concepts and that they are described using the QUEST process – this allows the teachers to really reflect on their teaching and how the students are learning. This book will definitely help mathematics teachers now that the CCSS are becoming such a big part of our teaching."

Debra A. Scarpelli, Middle School Mathematics Teacher
PARCC/CCSS ELC Cadre, Rhode Island

Sample Materials & Chapters

Estimating Quotients

Value of Inequality

Cheryl Rose Tobey

Cheryl Rose Tobey is a senior mathematics associate at Education Development Center (EDC) in Massachusetts. She is the project director for Formative Assessment in the Mathematics Classroom: Engaging Teachers and Students (FACETS) and a mathematics specialist for Differentiated Professional Development: Building Mathematics Knowledge for Teaching Struggling Students (DPD); both projects are funded by the National Science Foundation (NSF). She also serves as a director of development for an Institute for Educational Science (IES) project, Eliciting Mathematics Misconceptions (EM2). Her work is primarily in the areas of formative assessment... More About Author

Carolyn B. Arline

Carolyn B. Arline is a secondary mathematics educator, currently teaching high school students in Maine. Carolyn also works as a teacher leader in the areas of mathematics professional development, learning communities, assessment, systematic school reform, standards-based teaching, learning and grading, student-centered classrooms, and technology.  She has previously worked as a mathematics specialist at the Maine Mathematics and Science Alliance (MMSA) and continues her work with them as a consultant. Carolyn is a fellow of the second cohort group of the Governor’s Academy for Science and Mathematics Educators and serves as a mentor... More About Author

Purchasing options

Please select a format:

ISBN: 9781452230887

SAGE Knowledge is the ultimate social sciences digital library for students, researchers, and faculty. Hosting more than 4,400 titles, it includes an expansive range of SAGE eBook and eReference content, including scholarly monographs, reference works, handbooks, series, professional development titles, and more.

The platform allows researchers to cross-search and seamlessly access a wide breadth of must-have SAGE book and reference content from one source.