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

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 ProbesAcknowledgmentsAbout the AuthorsChapter 1. Mathematics Assessment ProbesQuestioning Student Understanding: Determine the Key Mathematical Concepts You Want Students to LearnUncovering Student Understanding: Use a Probe to Uncover Understandings and Areas of DifficultiesWhat Is the Structure of a Probe?QUEST Cycle: Structure of the Supporting Teacher NotesBeginning to Use the ProbesHow to Navigate the BookFinal Chapter 1 ThoughtsChapter 2. Number and Quantity ProbesComplex NumbersRational ExponentsOperating With MatricesChapter 3. Algebra ProbesEquivalent ExpressionsSimplifying Rational ExpressionsSolving for a VariableSolving Quadratic EquationsSystems of Linear EquationsMatrix EquationsChapter 4. Functions ProbesJogging: Graphical RepresentationInterpreting FunctionsTransformation of FunctionsCircular MeasurementDirect and Inverse VariationEquation of the FunctionLogarithmsChapter 5. Geometry ProbesProperties of AnglesIs It a Parallelogram?Names of the ShapeCircles and AnglesTrigonometric RatiosGeometry Formulas Card SortChapter 6. Statistics and Probability ProbesModeling With Linear GraphsComparing Data in Box PlotsProbabilityChapter 7. Additional ConsiderationsEstablishing Learning TargetsIndividual Metacognition and Reflection (The 4Cs)Giving Student InterviewsAddressing Individual NeedsPromoting Mathematical DiscourseSupporting the Mathematical PracticesSharing Experiences and Promoting Professional CollaborationSummaryAppendix A. Information on the Standards for Mathematical PracticeAppendix B. Developing Assessment ProbesAppendix C. Action Research Reflection Template: QUEST CycleReferencesIndex

"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."