Uncovering Student Thinking About Mathematics in the Common Core, High S

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 and Quantity Probes Complex Numbers Rational Exponents Operating With Matrices Chapter 3. Algebra Probes Equivalent Expressions Simplifying Rational Expressions Solving for a Variable Solving Quadratic Equations Systems of Linear Equations Matrix Equations Chapter 4. Functions Probes Jogging: Graphical Representation Interpreting Functions Transformation of Functions Circular Measurement Direct and Inverse Variation Equation of the Function Logarithms Chapter 5. Geometry Probes Properties of Angles Is It a Parallelogram? Names of the Shape Circles and Angles Trigonometric Ratios Geometry Formulas Card Sort Chapter 6. Statistics and Probability Probes Modeling With Linear Graphs Comparing Data in Box Plots Probability Chapter 7. Additional Considerations Establishing Learning Targets Individual Metacognition and Reflection (The 4Cs) Giving Student Interviews Addressing Individual Needs Promoting Mathematical Discourse 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

"High school mathematics can be one of the most difficult subjects for students to learn. This book provides the teacher with tools to help the student get to the root of their thinking in order to correct the underlying misconceptions that students amass during their school years." -- Lyneille Meza, Coordinator of Data & Assessment "Not only does this book make strong connections to the CCSS, it provides a framework for teachers to improve their craft. Identifying student misconceptions is an extremely important aspect of assessment and this book provides a solid format to aide teachers." -- Randy Wormald, Math Teacher