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

© 2014 | 232 pages | Corwin

Pinpoint and reverse math misconceptions with laser-like accuracy

Here’s the middle-grades math resource you’ve been waiting for! Bestselling authors Cheryl Tobey and Carolyn Arline are back with 25 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!

"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
RIMLE President, PARCC/CCSS ELC Cadre for Rhode Island, and Adjunct Professor

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

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ISBN: 9781452230887

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