'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.