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

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.

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

"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