"Finally, a book to help teachers differentiate math instruction using their own individualized, current data! The practical, simple-to-use formative assessments allow teachers to identify areas of difficulty, correct misconceptions, and guide learning." —Renee Peoples, Fourth Grade Teacher and K–5 District Math Facilitator Swain County Schools, NC "This book offers ways for teachers to gain more insight into what their students know and don′t know." —Carol Amos, Teacher Leader/Mathematics Coordinator Twinfield Union School, VT 25 targeted probes that gauge students′ mathematics comprehension in Grades K–5 Quickly identify each child′s level of understanding with these easy-to-use assessment tools! This sequel to the bestseller Uncovering Student Thinking in Mathematics answers teachers′ requests for more strategies to monitor classroom learning in real time. The authors provide 25 field-tested probes—brief, easily administered assessments—that can pinpoint students′ areas of struggle in mathematics. Aligned with NCTM standards, these grade-appropriate probes are easy to implement immediately and help teachers: Build on children′s current understandings while addressing their identified difficulties Quickly and objectively evaluate specific math skills Determine students′ common mistakes and obstacles to learning math Measure learners′ abilities and compare them to performance objectives Tobey and Minton include their proprietary QUEST cycle model, which provides teachers with the necessary tools to make sound instructional choices and improve all students′ mathematical knowledge.

"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.

Make formative assessment work for you—and your math students! Finally, formative assessment that adds up! Bringing Math Students Into the Formative Assessment Equation is the ultimate resource for helping teachers implement formative assessment in the middle school mathematics classroom. And it’s much more than that. With this research-based, teacher-tested guide, you won’t just learn effective teaching strategies—you’ll turn your students into self-regulated learners. They’ll monitor and assess their own progress—and communicate to you about it! Features include: A clear and manageable six-aspect instructional model Detailed strategies for helping students own their successes Real-life examples from middle school mathematics teachers Useful resources and a companion website to help you implement formative assessment in your classroom Formative assessment isn’t just for teachers anymore. With the help of this essential resource, you’ll work together with your students toward a common goal of math success. "This book is outstanding. I would recommend it to any math educator. The depth of research integrated into practice is extensive and, as a result, it is the most practical book I have come across related to formative assessment and mathematics The self-regulation aspects, as well as the ownership and involvement emphasized in the book, went beyond the traditional cognitive strategies endorsed in most books." Marc Simmons, Principal Ilwaco Middle School, Ocean Beach School District, Long Beach, WA "The ideas in this book are brought to life with examples of teachers and students in the classroom. The teacher voices, comments, and quotes lend credibility and are a big component of the book’s strengths as well as the visuals and graphics." Rita Tellez, Math Coordinator Ysleta Independent School District, El Paso, TX

"Finally, a book to help teachers differentiate math instruction using their own individualized, current data! The practical, simple-to-use formative assessments allow teachers to identify areas of difficulty, correct misconceptions, and guide learning."--Renee Peoples, Fourth Grade Teacher and K-5 District Math FacilitatorSwain County Schools, NC "This book offers ways for teachers to gain more insight into what their students know and don′t know."--Carol Amos, Teacher Leader/Mathematics CoordinatorTwinfield Union School, VT 25 targeted probes that gauge students′ mathematics comprehension in Grades K-5 Quickly identify each child′s level of understanding with these easy-to-use assessment tools! This sequel to the bestseller Uncovering Student Thinking in Mathematics answers teachers′ requests for more strategies to monitor classroom learning in real time. The authors provide 25 field-tested probes--brief, easily administered assessments--that can pinpoint students′ areas of struggle in mathematics. Aligned with NCTM standards, these grade-appropriate probes are easy to implement immediately and help teachers: Build on children′s current understandings while addressing their identified difficulties Quickly and objectively evaluate specific math skills Determine students′ common mistakes and obstacles to learning math Measure learners′ abilities and compare them to performance objectives Tobey and Minton include their proprietary QUEST cycle model, which provides teachers with the necessary tools to make sound instructional choices and improve all students′ mathematical knowledge.

Get to the core of your students’ understanding of math! Back by popular demand, Cheryl Tobey and new coauthor Emily Fagan bring you 25 entirely new formative assessment probes—this time specifically for Grades K–2 and directly aligned to the Common Core. Thousands of teachers have already discovered that using probes may be the single-best way to identify students’ understandings and misunderstandings of key math concepts and then follow-up with the most appropriate instructional choices. Organized by strand, the probes will enable you to: Objectively evaluate each child’s prior basic numeracy and math knowledge Systematically address common mistakes and obstacles before they become long-term problems Help students integrate new mathematical ideas and immediately pinpoint areas of struggle Plan targeted instruction that builds on students’ current understandings while addressing their identified difficulties With the help of these probes, K–2 teachers will eliminate once and for all the perception "some kids just aren’t good at math" and put all students on the path of lifelong proficiency. "Tobey and Fagan provide both a roadmap and GPS for navigating the Common Core Standards for Mathematics. In a time when teachers are asked to do more and more, this is a fabulous resource to guide instruction that will meet the needs of individual students. I was so impressed with the content, I found myself taking copious notes as I read." —Roxie R. Ahlbrecht, Math Intervention Specialist Lowell MST, Sioux Falls, SD "These probes get to the heart of the Common Core Standards. The Teacher Notes provide valuable guidance on interpreting student results and using the information to inform instruction." —Donna Boucher, K–5 Math Instructional Coach Morton Ranch Elementary School, Katy ISD, Katy, TX

Formative assessment informs the design of learning opportunities that take students from their existing ideas of science to the scientific ideas and practices that support conceptual understanding. Science Formative Assessment shows K-12 educators how to weave formative assessment into daily instruction. Discover 75 assessment techniques linked to the Next Generation Science Standards and give classroom practices a boost with: Descriptions of how each technique promotes learning Charts linking core concepts at each grade level to scientific practices Implementation guidance, such as required materials and student grouping Modifications for different learning styles Ideas for adapting techniques to other content areas

Being an effective math educator is one part based on the quality of the tasks we give, one part how we diagnose what we see, and one part what we do with what we find. Yet with so many students and big concepts to cover, it can be hard to slow down enough to look for those moments when students’ responses tell us what we need to know about next best steps. In this remarkable book, John SanGiovanni and Jennifer Rose Novak help us value our students’ misconceptions and incomplete understandings as much as their correct ones—because it’s the gap in their understanding today that holds the secrets to planning tomorrow’s best teaching. The authors lay out 180 high-quality tasks aligned to the standards and big ideas of Grades 6–8 mathematics, including number systems, integers, ratio and proportion, equations and expressions, geometry, and statistics and probability. The tasks are all downloadable so you can use or modify them for instruction and assessment. Each big idea offers a starting task followed by: what makes it a high-quality task what you might anticipate before students work with the task four student examples of the completed task showcasing a distinct "gap" commentary on what precisely counts for mathematical understanding and the next instructional steps commentary on the misconception or incomplete understanding so you learn why the student veered off course three additional tasks aligned to the mathematics topic and ideas about what students might do with these additional tasks It’s time to break our habit of rushing into re-teaching for correctness and instead get curious about the space between right and wrong answers. Mine the Gap for Mathematical Understanding is a book you will return to again and again to get better at selecting tasks that will uncover students’ reasoning, better at discerning the quality and clarity of students’ understanding, and better at planning teaching based on the gaps you see.

Transform mathematics learning from “doing” to “thinking” American students are losing ground in the global mathematical environment. What many of them lack is numeracy—the ability to think through the math and apply it outside of the classroom. Referencing the new common core and NCTM standards, the authors outline nine critical thinking habits that foster numeracy and show you how to: Monitor and repair students’ understanding Guide students to recognize patterns Encourage questioning for understanding Develop students’ mathematics vocabulary Included are several numeracy-rich lesson plans, complete with clear directions and student handouts.

Take a deep dive into the five practices for facilitating productive mathematical discussions Enhance your fluency in the five practices—anticipating, monitoring, selecting, sequencing, and connecting—to bring powerful discussions of mathematical concepts to life in your elementary classroom. This book unpacks the five practices for deeper understanding and empowers you to use each practice effectively. • Video excerpts vividly illustrate the five practices in action in real elementary classrooms • Key questions help you set learning goals, identify high-level tasks, and jumpstart discussion • Prompts guide you to be prepared for and overcome common challenges Includes planning templates, sample lesson plans and completed monitoring tools, and mathematical tasks.

Uncovering Student Thinking About Mathematics in the Common Core, High School: 25 Formative Assessment Probes Cheryl Rose Tobey, Carolyn B. Arline "Not only does this book make strong connections to the CCSS, it provides a framework for teachers to improve their craft. Identifying student misconceptions is an extremely important aspect of assessment and this book provides a solid format to aid teachers." —Randy Wormald, Math Teacher Kearsarge Regional High School, Sutton, NH Take the guesswork out of high school math instruction! Helping your students master high school mathematics just got a whole lot easier! Bestselling authors Cheryl Rose Tobey and Carolyn B. Arline provide 25 detailed and grade-level specific assessment probes that promote deep learning and expert math instruction. Learn to ask the right questions to uncover where and how students commonly get confused. Focused on subconcepts within the new Common Core State Standards for Mathematics and organized by strand, the probes will help you foster new and accurate skills--while learning is underway. You’ll learn how to Quickly diagnose students’ common misconceptions and procedural mistakes Help students pinpoint areas of struggle Plan targeted instruction that builds on students’ current understandings while addressing difficulties with Algebra, Geometry,Functions, Logarithms, Statistics and Probability, Trigonometric Ratios, and more Elicit the skills and processes related to the Standards for Mathematical Practices You’ll find sample student responses, extensive Teacher Notes, and research-based tips and resources to help you instill new mathematical ideas. Includes the QUEST Cycle for effective, hands-on implementation. Now you can eliminate the guesswork once and for all and join thousands of busy high school teachers who’ve used these easy-to-implement tools to build solid math proficiency! Other Books From Corwin: 1. Tobey: Uncovering Student Thinking About Mathematics in the Common Core, Grades K–2, 978-1-4522-3003-0 2. Tobey: Uncovering Student Thinking About Mathematics in the Common Core, Grades 3-5, 978-1-4522-7024-1 3. Tobey: Uncovering Student Thinking About Mathematics in the Common Core, Grades 6-8, 978-1-4522-3088-7 Cheryl Rose Tobey is a Senior Mathematics Associate at Education Development Center (EDC). She is the implementation director for the Pathways to Mathematics Achievement Study and a mathematics specialist for the NSF-funded Formative Assessment in the Mathematics Classroom: Engaging Teachers and Students (FACETS) and Differentiated Professional Development: Building Mathematics Knowledge for Teaching Struggling Students (DPD) projects. She also serves as a project director for an Institute for Educational Science (IES) project, Eliciting Mathematics Misconceptions (EM2). Carolyn B. Arline is a secondary mathematics educator, currently teaching high school students in Maine. She 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.