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 handbook assists educators with: (1) 25 ready-to-use mathematical probes; (2) Teacher guides for implementing each probe at any grade level; and (3) Examples of typical obstacles and faulty thinking demonstrated by students. This 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. Following a foreword by Anne Davies and a preface, this book contains five chapters: (1) Mathematics Assessment Probes; (2) Instructional Implications; (3) Number and Operation Assessment Probes; (4) Algebra, Data Analysis, and Probability Assessment Probes; and (5) Geometry and Measurement Assessment Probes. This book is concluded with Resource A: Template for QUEST Cycle, a list of references and an index.