Uncovering Student Thinking in Mathematics: 25 Formative Assessment Probes

"Uncovering Student Thinking in Mathematics shows us ways to listen and observe children and their mathematical understandings so we can find better ways to help them take their next learning steps. This book is a gift to educators who ′seek to understand before being understood.′"
―From the Foreword by Anne Davies

"A fresh and unique resource for mathematics teachers who recognize the importance of carefully establishing the starting points of instruction in terms of what students already know. The collection of assessment probes is inventive, engaging for students, and invaluable for teachers."
―Richard H. Audet, Associate Professor, Roger Williams University

Use formative assessment probes to take the guesswork out of mathematics instruction and improve learning!

Students learn at varying rates, and if a misconception in mathematics develops early, it may be carried from year to year and obstruct a student′s progress. To identify fallacies in students′ preconceived ideas, Uncovering Student Thinking in Mathematics offers educators a powerful diagnostic technique in the form of field-tested assessment probes―brief, easily administered activities to determine students′ thinking on core mathematical concepts.

Designed to question students′ conceptual knowledge and reveal common understandings and misunderstandings, the probes generate targeted information for modifying mathematics instruction, allowing teachers to build on students′ existing knowledge and individually address their identified difficulties.

Linked to National Council of Teachers of Mathematics standards, this invaluable handbook assists educators with:

• 25 ready-to-use mathematical probes
• Teacher guides for implementing each probe at any grade level
• Examples of typical obstacles and faulty thinking demonstrated by students

This rich resource combines standards, educational research findings, and practical craft knowledge to help teachers deliver informed instruction that strengthens all students′ learning and achievement in mathematics.

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.

Leslie Minton is currently a mathematics consultant for Math Matters 2, Portland, Maine. She is currently providing individualized mathematics professional development to area schools and districts PK-8, as well as, teaching Math Methods courses at the University of Southern Maine. Previously, Leslie was a Project Director for the Maine Mathematics and Science Alliance, Augusta, Maine. She provided technical assistance to schools as well as designed a professional development course and diagnostic materials designed to support numeracy understanding. She is a fellow of the second cohort group of Governor’s Academy for Science and Mathematics Educators. She has taught regular and special education for grades 4-12. Leslie receive her B.S. in elementary and special education from the University of Maine at Farmington and her M.Ed in curriculum, instruction and assessment from Walden University. Currently she is completing a M.Ed program, Educational Design and Media Technology, Full Sail University.

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.