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

by Cheryl Rose Tobey, Carolyn B. Arline

Overview

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

Product Details

ISBN-13:	9781483340395
Publisher:	SAGE Publications
Publication date:	10/03/2013
Sold by:	Barnes & Noble
Format:	eBook
Pages:	232
File size:	14 MB
Note:	This product may take a few minutes to download.

About the Author

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 and professional development.

Prior to joining EDC, Tobey was the senior program director for mathematics at the Maine Mathematics and Science Alliance (MMSA), where she served as the co–principal investigator of the mathematics section of the NSF-funded Curriculum Topic Study, and principal investigator and project director of two Title IIa state Mathematics and Science Partnership projects. Prior to working on these projects, Tobey was the co–principal investigator and project director for MMSA’s NSF-funded Local Systemic Change Initiative, Broadening Educational Access to Mathematics in Maine (BEAMM), and she was a fellow in Cohort 4 of the National Academy for Science and Mathematics Education Leadership. She is the coauthor of six published Corwin books, including seven books in the Uncovering Student Thinking series (2007, 2009, 2011, 2013, 2014), two Mathematics Curriculum Topic Study resources (2006, 2012), and Mathematics Formative Assessment: 75 Practical Strategies for Linking Assessment, Instruction and Learning (2011). Before joining MMSA in 2001 to begin working with teachers, Tobey was a high school and middle school mathematics educator for ten years. She received her BS in secondary mathematics education from the University of Maine at Farmington and her MEd from City University in Seattle. She currently lives in Maine with her husband and blended family of five children.

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 teacher with the current cohort. She participated as a mathematics mentor in the NSF-funded Northern New England Co-Mentoring Network (NNECN) and continues her role as a mentor teacher. She serves as a board member of the Association of Teachers of Mathematics in Maine (ATOMIM) and on local curriculum committees.  Carolyn received her B.S. in secondary mathematics education from the University of Maine.

Table of Contents

Preface: Mathematics Assessment Probes
Acknowledgments
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?
Scatterplots
Chapter 6. Geometry Probes
Perimeter and Area
Properties of Angles
Finding Volume
Scale
Right Triangles
Heights of Solids
Parallelograms
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
Summary
Appendix A. Information on the Standards for Mathematical Practice
Appendix B. Developing Assessment Probes
Appendix C. Action Research Reflection Template: QUEST Cycle
References
Index

Editorial Reviews

"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