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Uncovering Student Thinking in Mathematics
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Uncovering Student Thinking in Mathematics
25 Formative Assessment Probes

Edited by:
  • Cheryl M. Rose - Tobey Education Group, LLC, Education Development Center, Newton, MA
  • Leslie Minton - Math Matters, University of Southern Maine, USA
  • Carolyn Arline - Maine Mathematics and Science Alliance


December 2006 | 200 pages | Corwin
'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.

 
Foreword by Anne Davies
 
Preface
 
Acknowledgments
 
About the Authors
 
1. Mathematics Assessment Probes
 
2. Instructional Implications
 
3. Number and Operation Assessment Probes
 
4. Algebra, Data Analysis, and Probability Assessment Probes
 
5. Geometry and Measurement Assessment Probes
 
Resource A: Template for QUEST Cycle
 
References
 
Index

"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

"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

“This resource for K–12 mathematics educators is exactly what the title suggests: It contains 25 formative assessment probes that can be used to drive instruction. This book is easy to read and implement.”

Mathematics Teaching in the Middle School, February 2008, Vol. 13(6)

“The probes in this book give teachers a basis for beginning assessments as well as a guide for assessing manipulatives and activities, not just paper-and-pencil tasks. The guide helps teachers understand student thinking and welcomes deeper understanding and mastery of topics. It is also easy to use with parents to show students’ thinking and to justify grades.”

Teaching Children Mathematics, February 2008, Vol. 14(6)
National Council of Teachers of Mathematics

Preview this book

Cheryl Rose Tobey

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... More About Author

Leslie G. Minton

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... More About Author

Carolyn B. Arline

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... More About Author

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