Uncovering Student Thinking About Mathematics in the Common Core, Grades 3-5

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. Emily R. Fagan is a senior curriculum design associate at Education Development Center (EDC) in Massachusetts where she has developed print and online curricula as well as professional development and assessment materials in mathematics for fourteen years. She was Director of the MathScape Curriculum Center, a project funded by the National Science Foundation (NSF) to support schools, districts, and teachers in curriculum implementation, and she directed the revision of MathScape: Seeing and Thinking Mathematically (McGraw-Hill, 2005). She was a developer and facilitator of three NSF-funded projects, Addressing Accessibility in Mathematics and Differentiated Professional Development: Building Mathematics Knowledge for Teaching Struggling Students (DPD) aimed at supporting struggling math learners, particularly those with learning disabilities, and Formative Assessment in the Mathematics Classroom: Engaging Teachers and Students (FACETS) the inspiration for this book. Fagan is the co-author of two books: Uncovering Student Thinking About Mathematics in the Common Core, Grades K-2 (2013) and its companion for grades 3-5, as well as book chapters and articles about curriculum implementation and instruction. Prior to joining EDC, Emily taught high school and middle school mathematics in Philadelphia and in Salem and Brookline, Massachusetts. She was a mentor teacher, math coach and member of the Massachusetts faculty of the Coalition of Essential Schools. She has long been interested in accessibility in mathematics education and improving opportunities for all students to learn and love math. While mathematics has been her focus for the last two decades, she has also taught science, social studies, and Spanish. Fagan holds an AB cum laude from Harvard University. She lives in Sudbury, Massachusetts, with her husband and their two children.

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. Operations and Algebraic Thinking Probes Completing Number Sentences Multiplication and Division Sentences (Number Models) Classifying Numbers Card Sort Which Answer Makes Sense? (Working With Remainders) Evaluating Expressions Chapter 3. Number and Operations: Base-Ten Probes Rounding Whole Numbers Subtracting Whole Numbers Are They Equivalent? Rounding Decimals Adding Decimals Decimal Division Estimates Chapter 4. Number and Operations: Fractions Probes Locating a Fraction on a Number Line Equivalent Fractions Card Sort Representing Decimals Comparing to 1/2 Fraction Estimates: Addition Chapter 5. Measurement and Data Probes What Does the Graph Say? Comparing Lengths Estimating Measures Comparing Metric Measures Chapter 6. Geometry and Geometric Measurement Probes Finding Area Naming the Perimeter Volume of the Box Classifying Angles Card Sort Names of the Shape 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