Designed to work with any curriculum, Cognition-Based Assessment and Teaching will enable you to better understand and respond to your students' learning needs and help you choose instructional activities that are best for them. Michael Battista offers a learning-progressions model for maximizing each student's progress&— helping students who are behind catch up, preventing future failures from occurring, and helping students who are ready move quickly ahead. Cognition-Based Assessment and Teaching will help you will all three tiers in RTI. Battista's approach emphasizes three key components that support students' mathematical sense making and proficiency: determining students' levels of sophistication in reasoning; assessing and monitoring the development of students' understanding of core ideas; and, differentiating instruction to meet individual students' learning needs. Using a research-based framework that describes the development of students' thinking and learning in terms of levels of sophistication, a “cognitive terrain” that includes ascents and plateaus, Battista shows how teachers can build on their students' reasoning with instruction that keeps them moving ever upwards.--Publisher.

A Focus on Multiplication and Division is a groundbreaking effort to make mathematics education research readily accessible and understandable to pre- and in-service K–6 mathematics educators. Revealing students’ thought processes with extensive annotated samples of student work and vignettes characteristic of teachers’ experiences, this book is sure to equip educators with the knowledge and tools needed to modify their lessons and to improve student learning of multiplication and division. Special Features: Looking Back Questions at the end of each chapter allow teachers to analyze student thinking and to consider instructional strategies for their own students. Instructional Links help teachers relate concepts from each chapter to their own instructional materials and programs. Big Ideas frame the chapters and provide a platform for meaningful exploration of the teaching of multiplication and division. Answer Key posted online offers extensive explanations of in-chapter questions. Each chapter includes sections on the Common Core State Standards for Mathematics and integrates the Ongoing Assessment Project (OGAP) Multiplicative Reasoning Progression for formative assessment purposes. Centered on the question of how students develop their understanding of mathematical concepts, this innovative book places math teachers in the mode of ongoing action researchers.

""For many students, traditional instruction is so distant from their needs that each day they make little or no learning progress and fall farther and farther behind curriculum demands. In contrast, Cognition-Based Assessment offers a framework to support teaching that enables ALL students to understand, make personal sense of, and become proficient with mathematics." ""-"Michael Battista Designed to work with any curriculum, Cognition-Based Assessment and Teaching will enable you to better understand and respond to your students' learning needs and help you choose instructional activities that are best for them. Michael Battista offers a powerful, learning-progressions model for maximizing each student's progress- helping students who are behind catch up, preventing future failures from occurring, and helping students who are ready move quickly ahead. Cognition-Based Assessment and Teaching will help you will all three tiers in RTI. Battista's approach emphasizes three key components that support students' mathematical sense making and proficiency: Determining students' levels of sophistication in reasoning Assessing and monitoring the development of students' understanding of core ideas Differentiating instruction to meet individual students' learning needs Using a research-based framework that describes the development of students' thinking and learning in terms of levels of sophistication, a "cognitive terrain" that includes ascents and plateaus, Battista shows how teachers can build on their students' reasoning with instruction that keeps them moving ever upwards. Also Available: Addition and Subtraction Multiplication and Division Place Value

Designed to work with any curriculum, Cognition-Based Assessment and Teaching will enable you to better understand and respond to your students' learning needs and help you choose instructional activities that are best for them. Michael Battista offers a learning-progressions model for maximizing each student's progress&— helping students who are behind catch up, preventing future failures from occurring, and helping students who are ready move quickly ahead. Cognition-Based Assessment and Teaching will help you will all three tiers in RTI. Battista's approach emphasizes three key components that support students' mathematical sense making and proficiency: Determining students' levels of sophistication in reasoning Assessing and monitoring the development of students' understanding of core ideas Differentiating instruction to meet individual students' learning needs Using a research-based framework that describes the development of students' thinking and learning in terms of levels of sophistication, a “cognitive terrain” that includes ascents and plateaus, Battista shows how teachers can build on their students' reasoning with instruction that keeps them moving ever upwards.--Publisher.

Designed to work with any curriculum, this title will enable teachers to better understand and respond to their students' learning needs and help readers choose instructional activities that are best for them.

This resource offers a groundbreaking effort to make mathematics education research on ratios and proportions readily accessible and understandable to preservice and in-service teachers of grades 6 to 8. Using extensive annotated samples of student work and based on research gathered in the Ongoing Assessment Project (OGAP), A Focus on Ratios and Proportions teaches readers how students develop understanding and fluency involving ratio and proportion concepts. Special features include: A close focus on student work, including 150+ annotated pieces of student work, to help teachers improve their ability to recognize, assess and monitor their students’ errors and misconceptions, as well as their developing conceptual understanding. A focus on the OGAP Ratios and Proportions Progression, based on research conducted with hundreds of teachers and thousands of pieces of student work. Sections on how Common Core State Standards for Math (CCSSM) are supported by math education research. Student work samples and vignettes to illuminate the research, as well as end of chapter Looking Back questions and Instructional Links, which allow teachers to analyze evidence of student thinking and strategies and consider instructional responses. An accompanying eResource, available online, offers an answer key as well as extensive explanation of the Looking Back questions. Like A Focus on Multiplication and Division and A Focus on Fractions, this book is designed to bridge the gap between what math education researchers know and what teachers need to know in order to better understand evidence in student work and make effective instructional decisions.

Fluency in math doesn’t just happen; it is a well-planned journey. In this book, you’ll find practical strategies and activities for teaching your elementary students basic multiplication and division. The authors lay out the basic framework for building math fluency using a cycle of engagement (concrete, pictorial, abstract) and provide a multitude of examples illustrating the strategies in action. You’ll learn how to help students to model their thinking with a variety of tools; keep students engaged through games, poems, songs, and technology; assess student development to facilitate active and continuous learning; implement distributed practices throughout the year; and boost parental involvement so that students remain encouraged even as material becomes more complex. A final chapter devoted to action plans will help you put these strategies into practice in your classroom right away. Most importantly, you’ll open the door to deep and lasting math fluency.

With a focus on children's mathematical thinking, this second edition adds new material on the mathematical principles underlying children's strategies, a new online video that illustrates student teacher interaction, and examines the relationship between CGI and the Common Core State Standards for Mathematics.

This book addresses the point of intersection between cognition, metacognition, and culture in learning and teaching Science, Technology, Engineering, and Mathematics (STEM). We explore theoretical background and cutting-edge research about how various forms of cognitive and metacognitive instruction may enhance learning and thinking in STEM classrooms from K-12 to university and in different cultures and countries. Over the past several years, STEM education research has witnessed rapid growth, attracting considerable interest among scholars and educators. The book provides an updated collection of studies about cognition, metacognition and culture in the four STEM domains. The field of research, cognition and metacognition in STEM education still suffers from ambiguity in meanings of key concepts that various researchers use. This book is organized according to a unique manner: Each chapter features one of the four STEM domains and one of the three themes—cognition, metacognition, and culture—and defines key concepts. This matrix-type organization opens a new path to knowledge in STEM education and facilitates its understanding. The discussion at the end of the book integrates these definitions for analyzing and mapping the STEM education research. Chapter 4 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com