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Uncovering Student Thinking about Mathematics in the Common Core, Grades K-2


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Table of Contents

Preface: Mathematics Assessment Probes Acknowledgments About the Authors Chapter 1. Mathematics Assessment Probes Chapter 2. Counting and Cardinality Probes Chapter 3. Number and Operations in Base Ten Probes Chapter 4. Operations and Algebraic Thinking Probes Chapter 5. Measurement and Data Probes Chapter 6. Geometry Probes Chapter 7. Additional Considerations Appendix A. Information on the Standards for Mathematical Practice Appendix B. Developing Assessment Probes Appendix C. Action Research Reflection Template: QUEST Cycle References Index

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. 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.


"It provides both a roadmap and GPS for navigating the Common Core Mathematics Standards. In a time when teachers are being asked to do more and more, this is a fabulous resource to guide instruction that will meet the needs of individual students. I was so impressed with the content, I found myself taking copious notes as I read." -- Roxie R. Ahlbrecht, NBCT, Math Intervention Specialist
"These probes get to the heart of the Common Core Standards. The teacher notes provide valuable guidance on interpreting student results and using the information to inform instruction." -- Donna Boucher, K-5 Math Instructional Coach
"The material presented in the book is useful and practical for immediate use and implementation. The book clearly provides processes that support a plan to monitor and diagnose student understanding in an authentic manner. The Quest Cycle is a means for placing a framework around each chapter's content along with the alignment to the CCSS for mathematics and NCTM as a critical piece to provide a layer of integrity to the work presented in the book." -- Lenisera Barnes-Bodison, K-12 Mathematics Coordinator

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