| cognitively guided instruction math: Children's Mathematics Thomas P. Carpenter, Elizabeth Fennema, Megan Loef Franke, Linda Levi, Susan B. Empson, 2015 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. |
| cognitively guided instruction math: Children's Mathematics Thomas P. Carpenter, 1999 Accompanying CD-ROMs provide examples of children's strategies and classroom examples of the concepts covered in the text. |
| cognitively guided instruction math: Extending Children's Mathematics Susan B. Empson, Linda Levi, 2011 With the collaboration of a number of dedicated teachers and their students, Susan Empson and Linda Levi have produced a volume that is faithful to the basic principles of CGI while at the same time covering new ground with insight and innovation. -Thomas P. Carpenter This highly anticipated follow-up volume to the landmark Children's Mathematics: Cognitively Guided Instruction addresses the urgent need to help teachers understand and teach fraction concepts. Fractions remain one of the key stumbling blocks in math education, and here Empson and Levi lay a foundation for understanding fractions and decimals in ways that build conceptual learning. They show how the same kinds of intuitive knowledge and sense making that provides the basis for children's learning of whole number arithmetic can be extended to fractions and decimals. Just as they did in Children's Mathematics and Thinking Mathematically, Empson and Levi provide important insights into children's thinking and alternative approaches to solving problems. Three themes appear throughout the book: building meaning for fractions and decimals through discussing and solving word problems the progression of children's strategies for solving fraction word problems and equations from direct modeling through relational thinking designing instruction that capitalizes on students' relational thinking strategies to integrate algebra into teaching and learning fractions. With illuminating examples of student work, classroom vignettes, Teacher Commentaries from the field, sample problems and instructional guides provided in each chapter, you'll have all the tools you need to teach fractions and decimals with understanding and confidence. |
| cognitively guided instruction math: Children's Mathematics Thomas P. Carpenter, 2000 |
| cognitively guided instruction math: Children's Mathematics Elizabeth Fennema, 1999 |
| cognitively guided instruction math: Thinking Mathematically Thomas P. Carpenter, Megan Loef Franke, Linda Levi, 2003 In this book the authors reveal how children's developing knowledge of the powerful unifying ideas of mathematics can deepen their understanding of arithmetic |
| cognitively guided instruction math: Making Sense James Hiebert, 1997 This book presents several key principles for teaching mathematics for understanding that you can use to reflect on your own teaching, make more informed decisions, and develop more effective systems of instruction. |
| cognitively guided instruction math: Good Questions for Math Teaching Peter Sullivan, Pat Lilburn, 2002 Open-ended questions, coined ï¿1⁄2good questionsï¿1⁄2 by the authors, can prompt children to think creatively and critically. This useful book helps teachers define ï¿1⁄2good questions,ï¿1⁄2 offers teachers tips on how to create their own good questions, and presents a wide variety of sample questions that span 16 mathematical topics, including number, measurement, geometry, probability, and data. |
| cognitively guided instruction math: Choral Counting & Counting Collections Megan L Franke, Elham Kazemi, Angela Chan Turrou, 2023-10-10 In this influential book from collaborative authors Megan L Franke, Elham Kazemi, and Angela Chan Turrou, Choral Counting & Counting Collections: Transforming the PreK – 5 Math Classroom, explores ways in which two routines -- Choral Counting and Counting Collections -- can transform your elementary math classroom, your students' math understanding, and your partnerships with families. It paints a vision for how deeply and creatively children can engage with ideas of number and operations and mathematical reasoning through counting. Created with real educators' needs in mind and organized by grade-level band (preschool, K-2, and 3-5), inside this book you'll find: Easy-to-use planning templates to guide teachers in implementing these powerful routines A variety of student recording sheets for Counting Collections that allow teachers to enact different variations of this activity across the grades Guides for selecting Choral Counts that support grade-level standards and mathematical goals Goal charts that provide specific guidance on teacher language and moves Advice on supporting both students' mathematical and social goals through Choral Counting and Counting Collections The authors have collected the wisdom of math teachers and researchers across the country who explore activities that are both playful and intentional, simple and sophisticated. If you're looking for ways to bring new energy into your math instruction, Choral Counting & Counting Collections: Transforming the PreK - 5 Math Classroom is the perfect book for you and your students. |
| cognitively guided instruction math: Reggio-Inspired Mathematics Richmond School District, 2015-09-03 This booklet documents our school district's collaborative inquiry project looking at how Reggio-inspired practices can inform and enhance primary mathematics teaching and learning. |
| cognitively guided instruction math: How I Wish I'd Taught Maths Craig Barton, 2018 Brought to an American audience for the first time, How I Wish I'd Taught Maths is the story of an experienced and successful math teacher's journey into the world of research, and how it has entirely transformed his classroom. |
| cognitively guided instruction math: Visible Learning for Mathematics, Grades K-12 John Hattie, Douglas Fisher, Nancy Frey, Linda M. Gojak, Sara Delano Moore, William Mellman, 2016-09-15 Selected as the Michigan Council of Teachers of Mathematics winter book club book! Rich tasks, collaborative work, number talks, problem-based learning, direct instruction...with so many possible approaches, how do we know which ones work the best? In Visible Learning for Mathematics, six acclaimed educators assert it’s not about which one—it’s about when—and show you how to design high-impact instruction so all students demonstrate more than a year’s worth of mathematics learning for a year spent in school. That’s a high bar, but with the amazing K-12 framework here, you choose the right approach at the right time, depending upon where learners are within three phases of learning: surface, deep, and transfer. This results in visible learning because the effect is tangible. The framework is forged out of current research in mathematics combined with John Hattie’s synthesis of more than 15 years of education research involving 300 million students. Chapter by chapter, and equipped with video clips, planning tools, rubrics, and templates, you get the inside track on which instructional strategies to use at each phase of the learning cycle: Surface learning phase: When—through carefully constructed experiences—students explore new concepts and make connections to procedural skills and vocabulary that give shape to developing conceptual understandings. Deep learning phase: When—through the solving of rich high-cognitive tasks and rigorous discussion—students make connections among conceptual ideas, form mathematical generalizations, and apply and practice procedural skills with fluency. Transfer phase: When students can independently think through more complex mathematics, and can plan, investigate, and elaborate as they apply what they know to new mathematical situations. To equip students for higher-level mathematics learning, we have to be clear about where students are, where they need to go, and what it looks like when they get there. Visible Learning for Math brings about powerful, precision teaching for K-12 through intentionally designed guided, collaborative, and independent learning. |
| cognitively guided instruction math: Integrating Research on Teaching and Learning Mathematics Elizabeth Fennema, Thomas P. Carpenter, Susan J. Lamon, 1991-01-01 During the last decade there were significant advances in the study of students' learning and problem solving in mathematics, and in the study of classroom instruction. Because these two research programs usually have been conducted individually, it is generally agreed now that there is an increasing need for an integrated research program. This book represents initial discussions and development of a unified paradigm for studying teaching in mathematics that builds upon both cognitive as well as instructional research. |
| cognitively guided instruction math: A Teacher's Guide to Mentor Texts, 6-12 Allison Marchetti, Rebekah O'Dell, 2021 This book is a practical guide to using mentor texts in the teaching of writing in middle and high school classrooms-- |
| cognitively guided instruction math: Lost and Found and Found Again Gerald R Fast, 2021-03-21 Lost and Found and Found Again: A Math Mystery is a unique child's story that seamlessly weaves primary level mathematics into a fantasy adventure. Ideal as a classroom read-aloud, for homeschool math instruction, or pleasure reading. Mathematics that focuses on solving word problems and developing number sense is carefully sequenced to correspond with the developmental stages of children's thinking as outlined by Cognitively Guided Instruction. |
| cognitively guided instruction math: A Fresh Look at Formative Assessment in Mathematics Teaching Edward A. Silver, Valerie L. Mills, 2018 |
| cognitively guided instruction math: The Young Child and Mathematics, Third Edition Angela Chan Turrou, Nicholas C. Johnson, Megan L. Franke, 2021-10 Tap into the Power of Child-Led Math Teaching and Learning Everything a child does has mathematical value--these words are at the heart of this completely revised and updated third edition of The Young Child and Mathematics. Grounded in current research, this classic book focuses on how teachers working with children ages 3 to 6 can find and build on the math inherent in children's ideas in ways that are playful and intentional. This resource - Illustrates through detailed vignettes how math concepts can be explored in planned learning experiences as well as informal spaces - Highlights in-the-moment instructional decision-making and child-teacher interactions that meaningfully and dynamically support children in making math connections - Provides an overview of what children know about counting and operations, spatial relations, measurement and data, and patterns and algebra - Offers examples of informal documentation and assessment approaches that are embedded within classroom practice Deepen your understanding of how math is an integral part of your classroom all day, every day. Includes online video! |
| cognitively guided instruction math: Young Children's Mathematics Thomas P. Carpenter, Megan Loef Franke, Nicholas C. Johnson, Angela Chan Turrou, Anita A. Wager, 2017 This book is for pre-K to 1st grade and shows how teachers can promote math development in ways that honor children's thinking.-- |
| cognitively guided instruction math: Mathematics Teachers in Transition Elizabeth Fennema, Barbara Scott Nelson, 1997 This book addresses the need of professional development leaders and policymakers for scholarly knowledge about influencing teachers to modify mathematical instruction to bring it more in alignment with the recommendations of the current reform movement initiated by the National Council of Teachers of Mathematics. The book presents: * theoretical perspectives for studying, analyzing, and understanding teacher change; * descriptions of contextual variables to be considered as one studies and attempts to understand teacher change; and * descriptions of professional development programs that resulted in teacher change. One chapter builds a rationale for looking to developmental psychology for guidance in constructing models of reconstructing new forms of mathematical instruction. Another highlights the relevance to mathematics teacher development of research-based knowledge about how children construct mathematical ideas. Other chapters explore the relationships between the various contexts of schooling and instructional change. Included also are chapters that describe and analyze major reform efforts designed to assist teachers in modifying their instructional practices (Cognitively Guided Instruction, Math-Cubed, Project Impact, Mathematics in Context, and the Case-Based Project). Finally, the current state of knowledge about encouraging teachers to modify their instruction is discussed, the implications of major research and implementation findings are suggested, and some of the major questions that need to be addressed are identified, such as what we have learned about teacher change. |
| cognitively guided instruction math: Five Practices for Orchestrating Productive Mathematics Discussions Margaret Schwan Smith, Mary Kay Stein, 2011 Describes five practices for productive mathematics discussions, including anticipating, monitoring, selecting, sequencing, and connecting. |
| cognitively guided instruction math: Math Exchanges Kassia Omohundro Wedekind, 2011 Traditionally, small-group math instruction has been used as a format for reaching children who struggle to understand. Math coach Kassia Omohundro Wedekind uses small-group instruction as the centerpiece of her math workshop approach, engaging all students in rigorous math exchanges. The key characteristics of these mathematical conversations are that they are: 1) short, focused sessions that bring all mathematical minds together, 2) responsive to the needs of the specific group of mathematicians, and 3) designed for meaningful, guided reflection. As in reading and writing workshop, students in math workshop become self-directed and independent while participating in a classroom community of learners. Through the math exchanges, students focus on number sense and the big ideas of mathematics. Teachers guide the conversations with small groups of students, mediating talk and thinking as students share problem-solving strategies, discuss how math works, and move toward more effective and efficient approaches and greater mathematical understanding. Although grounded in theory and research, Math Exchanges: Guiding Young Mathematicians in Small Group Meetings is written for practicing teachers and answers such questions as the following: How can I use a math workshop approach and follow a certain textbook or set of standards? How should I form small groups? How often should I meet with small groups? What should I focus on in small groups? How can I tell if my groups are making progress? What do small-group math exchanges look like, sound like, and feel like? |
| cognitively guided instruction math: Helping Children Learn Mathematics National Research Council, Division of Behavioral and Social Sciences and Education, Center for Education, Mathematics Learning Study Committee, 2002-07-31 Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society. |
| cognitively guided instruction math: How People Learn National Research Council, Division of Behavioral and Social Sciences and Education, Board on Behavioral, Cognitive, and Sensory Sciences, Committee on Developments in the Science of Learning with additional material from the Committee on Learning Research and Educational Practice, 2000-08-11 First released in the Spring of 1999, How People Learn has been expanded to show how the theories and insights from the original book can translate into actions and practice, now making a real connection between classroom activities and learning behavior. This edition includes far-reaching suggestions for research that could increase the impact that classroom teaching has on actual learning. Like the original edition, this book offers exciting new research about the mind and the brain that provides answers to a number of compelling questions. When do infants begin to learn? How do experts learn and how is this different from non-experts? What can teachers and schools do-with curricula, classroom settings, and teaching methodsâ€to help children learn most effectively? New evidence from many branches of science has significantly added to our understanding of what it means to know, from the neural processes that occur during learning to the influence of culture on what people see and absorb. How People Learn examines these findings and their implications for what we teach, how we teach it, and how we assess what our children learn. The book uses exemplary teaching to illustrate how approaches based on what we now know result in in-depth learning. This new knowledge calls into question concepts and practices firmly entrenched in our current education system. Topics include: How learning actually changes the physical structure of the brain. How existing knowledge affects what people notice and how they learn. What the thought processes of experts tell us about how to teach. The amazing learning potential of infants. The relationship of classroom learning and everyday settings of community and workplace. Learning needs and opportunities for teachers. A realistic look at the role of technology in education. |
| cognitively guided instruction math: Number Talks Sherry Parrish, 2010 A multimedia professional learning resource--Cover. |
| cognitively guided instruction math: Tomags-2 - Examiner's Manual Gail R Ryser, 2021-02 This manual contains specific instructions for administering and scoring the TOMAGS-2. |
| cognitively guided instruction math: Teaching Mathematics Meaningfully David H. Allsopp, David Allsopp (Ph. D.), Maggie M. Kyger, LouAnn H. Lovin, 2007 Making mathematics concepts understandable is a challenge for any teacher--a challenge that's more complex when a classroom includes students with learning difficulties. With this highly practical resource, educators will have just what they need to teach mathematics with confidence: research-based strategies that really work with students who have learning disabilities, ADHD, or mild cognitive disabilities. This urgently needed guidebook helps teachers Understand why students struggle.Teachers will discover how the common learning characteristics of students with learning difficulties create barriers to understanding mathematics. Review the Big Ideas. Are teachers focusing on the right things? A helpful primer on major NCTM-endorsed mathematical concepts and processes helps them be sure. Directly address students' learning barriers. With the lesson plans, practical strategies, photocopiable information-gathering forms, and online strategies in action, teachers will have concrete ways to help students grasp mathematical concepts, improve their proficiency, and generalize knowledge in multiple contexts. Check their own strengths and needs. Educators will reflect critically on their current practices with a thought-provoking questionnaire. With this timely book--filled with invaluable ideas and strategies adaptable for grades K-12--educators will know just what to teach and how to teach it to students with learning difficulties. |
| cognitively guided instruction math: Principles to Actions National Council of Teachers of Mathematics, 2014-02 This text offers guidance to teachers, mathematics coaches, administrators, parents, and policymakers. This book: provides a research-based description of eight essential mathematics teaching practices ; describes the conditions, structures, and policies that must support the teaching practices ; builds on NCTM's Principles and Standards for School Mathematics and supports implementation of the Common Core State Standards for Mathematics to attain much higher levels of mathematics achievement for all students ; identifies obstacles, unproductive and productive beliefs, and key actions that must be understood, acknowledged, and addressed by all stakeholders ; encourages teachers of mathematics to engage students in mathematical thinking, reasoning, and sense making to significantly strengthen teaching and learning. |
| cognitively guided instruction math: Equity-Centered Trauma-Informed Education Alex Shevrin Venet, 2023-09-01 Educators must both respond to the impact of trauma, and prevent trauma at school. Trauma-informed initiatives tend to focus on the challenging behaviors of students and ascribe them to circumstances that students are facing outside of school. This approach ignores the reality that inequity itself causes trauma, and that schools often heighten inequities when implementing trauma-informed practices that are not based in educational equity. In this fresh look at trauma-informed practice, Alex Shevrin Venet urges educators to shift equity to the center as they consider policies and professional development. Using a framework of six principles for equity-centered trauma-informed education, Venet offers practical action steps that teachers and school leaders can take from any starting point, using the resources and influence at their disposal to make shifts in practice, pedagogy, and policy. Overthrowing inequitable systems is a process, not an overnight change. But transformation is possible when educators work together, and teachers can do more than they realize from within their own classrooms. |
| cognitively guided instruction math: Becoming the Math Teacher You Wish You'd Had Tracy Johnston Zager, 2023-10-10 Ask mathematicians to describe mathematics and they' ll use words like playful, beautiful, and creative. Pose the same question to students and many will use words like boring, useless, and even humiliating. Becoming the Math Teacher You Wish You' d Had, author Tracy Zager helps teachers close this gap by making math class more like mathematics. Zager has spent years working with highly skilled math teachers in a diverse range of settings and grades and has compiled those' ideas from these vibrant classrooms into' this game-changing book. Inside you' ll find: ' How to Teach Student-Centered Mathematics:' Zager outlines a problem-solving approach to mathematics for elementary and middle school educators looking for new ways to inspire student learning Big Ideas, Practical Application:' This math book contains dozens of practical and accessible teaching techniques that focus on fundamental math concepts, including strategies that simulate connection of big ideas; rich tasks that encourage students to wonder, generalize, hypothesize, and persevere; and routines to teach students how to collaborate Key Topics for Elementary and Middle School Teachers:' Becoming the Math Teacher You Wish You' d Had' offers fresh perspectives on common challenges, from formative assessment to classroom management for elementary and middle school teachers No matter what level of math class you teach, Zager will coach you along chapter by chapter. All teachers can move towards increasingly authentic and delightful mathematics teaching and learning. This important book helps develop instructional techniques that will make the math classes we teach so much better than the math classes we took. |
| cognitively guided instruction math: Open Middle Math Robert Kaplinsky, 2023-10-10 This book is an amazing resource for teachers who are struggling to help students develop both procedural fluency and conceptual understanding.. --Dr. Margaret (Peg) Smith, co-author of5 Practices for Orchestrating Productive Mathematical Discussions Robert Kaplinsky, the co-creator of Open Middle math problems, brings hisnew class of tasks designed to stimulate deeper thinking and lively discussion among middle and high school students in Open Middle Math: Problems That Unlock Student Thinking, Grades 6-12. The problems are characterized by a closed beginning,- meaning all students start with the same initial problem, and a closed end,- meaning there is only one correct or optimal answer. The key is that the middle is open- in the sense that there are multiple ways to approach and ultimately solve the problem. These tasks have proven enormously popular with teachers looking to assess and deepen student understanding, build student stamina, and energize their classrooms. Professional Learning Resource for Teachers: Open Middle Math is an indispensable resource for educators interested in teaching student-centered mathematics in middle and high schools consistent with the national and state standards. Sample Problems at Each Grade: The book demonstrates the Open Middle concept with sample problems ranging from dividing fractions at 6th grade to algebra, trigonometry, and calculus. Teaching Tips for Student-Centered Math Classrooms: Kaplinsky shares guidance on choosing problems, designing your own math problems, and teaching for multiple purposes, including formative assessment, identifying misconceptions, procedural fluency, and conceptual understanding. Adaptable and Accessible Math: The tasks can be solved using various strategies at different levels of sophistication, which means all students can access the problems and participate in the conversation. Open Middle Math will help math teachers transform the 6th -12th grade classroom into an environment focused on problem solving, student dialogue, and critical thinking. |
| cognitively guided instruction math: Teaching Mathematics for Social Justice Anita A. Wager, David W. Stinson, 2012 This collection of original articles is the start of a compelling conversation among some of the leading figures in critical and social justice mathematics, a number of teachers and educators who have been inspired by them-and who have inspiring stories of their own to tell - and any reader interested in the intersection of education and social justice. An important read for every educator, this book shows how to teach mathematics so that all students are given the tools they need to confront issues of social justice today and in the years ahead--page [4] of cover. |
| cognitively guided instruction math: Guided Math: A Framework for Mathematics Instruction Sammons, Laney, 2017-03-01 Use a practical approach to teaching mathematics that integrates proven literacy strategies for effective instruction. This professional resource will help to maximize the impact of instruction through the use of whole-class instruction, small-group instruction, and Math Workshop. Incorporate ideas for using ongoing assessment to guide your instruction and increase student learning, and use hands-on, problem-solving experiences with small groups to encourage mathematical communication and discussion. Guided Math supports the College and Career Readiness and other state standards. |
| cognitively guided instruction math: The Tapping Solution Nick Ortner, 2013-04-02 In the New York Times best-selling book The Tapping Solution, Nick Ortner, founder of the Tapping World Summit and best-selling filmmaker of The Tapping Solution, is at the forefront of a new healing movement. In this book, he gives readers everything they need to successfully start using the powerful practice of tapping—or Emotional Freedom Techniques (EFT).Tapping is one of the fastest and easiest ways to address both the emotional and physical problems that tend to hamper our lives. Using the energy meridians of the body, practitioners tap on specific points while focusing on particular negative emotions or physical sensations. The tapping helps calm the nervous system to restore the balance of energy in the body, and in turn rewire the brain to respond in healthy ways. This kind of conditioning can help rid practitioners of everything from chronic pain to phobias to addictions. Because of tapping’s proven success in healing such a variety of problems, Ortner recommends to try it on any challenging issue. In The Tapping Solution, Ortner describes not only the history and science of tapping but also the practical applications. In a friendly voice, he lays out easy-to-use practices, diagrams, and worksheets that will teach readers, step-by-step, how to tap on a variety of issues. With chapters covering everything from the alleviation of pain to the encouragement of weight loss to fostering better relationships, Ortner opens readers’ eyes to just how powerful this practice can be. Throughout the book, readers will see real-life stories of healing ranging from easing the pain of fibromyalgia to overcoming a fear of flying.The simple strategies Ortner outlines will help readers release their fears and clear the limiting beliefs that hold them back from creating the life they want. |
| cognitively guided instruction math: Deep Learning for Coders with fastai and PyTorch Jeremy Howard, Sylvain Gugger, 2020-06-29 Deep learning is often viewed as the exclusive domain of math PhDs and big tech companies. But as this hands-on guide demonstrates, programmers comfortable with Python can achieve impressive results in deep learning with little math background, small amounts of data, and minimal code. How? With fastai, the first library to provide a consistent interface to the most frequently used deep learning applications. Authors Jeremy Howard and Sylvain Gugger, the creators of fastai, show you how to train a model on a wide range of tasks using fastai and PyTorch. You’ll also dive progressively further into deep learning theory to gain a complete understanding of the algorithms behind the scenes. Train models in computer vision, natural language processing, tabular data, and collaborative filtering Learn the latest deep learning techniques that matter most in practice Improve accuracy, speed, and reliability by understanding how deep learning models work Discover how to turn your models into web applications Implement deep learning algorithms from scratch Consider the ethical implications of your work Gain insight from the foreword by PyTorch cofounder, Soumith Chintala |
| cognitively guided instruction math: Thinking Together Rozlynn Dance, Tessa Kaplan, 2018 Want students to understand-really understand-and retain the math they're learning? Focus on building your classroom community first. In Thinking Together, veteran teachers Rozlynn Dance and Tessa Kaplan explore nine beliefs that lead to a powerful community of learners. When students are part of a classroom where they feel valued and included, they are more likely to take risks, ask questions, and grow exponentially as mathematicians. Rozlynn and Tessa tell us, We must create a kind, caring, trusting community of learners who feel comfortable tackling the unknown, taking risks, and making mistakes. This book doesn't pretend teaching is simple-instead, it celebrates the potential in the everyday messiness of learning together. Each chapter includes: opportunities to reflect on your practice through an exploration of beliefs such as Mistakes are great! and It's not just about the answer practical guidance for building your classroom community through student-centered strategies and classroom examples When Things Don't Seem to be Working sections for troubleshooting common challenges and adapting to teaching that doesn't go as planned. An environment fine-tuned for learning creates conditions in which your students can thrive as mathematical thinkers. Thinking Together will help shape your beliefs about what it means to be a learning community and provide support for building those beliefs into your classroom. |
| cognitively guided instruction math: The Great Mental Models, Volume 1 Shane Parrish, Rhiannon Beaubien, 2024-10-15 Discover the essential thinking tools you’ve been missing with The Great Mental Models series by Shane Parrish, New York Times bestselling author and the mind behind the acclaimed Farnam Street blog and “The Knowledge Project” podcast. This first book in the series is your guide to learning the crucial thinking tools nobody ever taught you. Time and time again, great thinkers such as Charlie Munger and Warren Buffett have credited their success to mental models–representations of how something works that can scale onto other fields. Mastering a small number of mental models enables you to rapidly grasp new information, identify patterns others miss, and avoid the common mistakes that hold people back. The Great Mental Models: Volume 1, General Thinking Concepts shows you how making a few tiny changes in the way you think can deliver big results. Drawing on examples from history, business, art, and science, this book details nine of the most versatile, all-purpose mental models you can use right away to improve your decision making and productivity. This book will teach you how to: Avoid blind spots when looking at problems. Find non-obvious solutions. Anticipate and achieve desired outcomes. Play to your strengths, avoid your weaknesses, … and more. The Great Mental Models series demystifies once elusive concepts and illuminates rich knowledge that traditional education overlooks. This series is the most comprehensive and accessible guide on using mental models to better understand our world, solve problems, and gain an advantage. |
| cognitively guided instruction math: The Development of Arithmetic Concepts and Skills Arthur J. Baroody, Ann Dowker, 2013-06-17 This volume focuses on two related questions that are central to both the psychology of mathematical thinking and learning and to the improvement of mathematics education: What is the nature of arithmetic expertise? How can instruction best promote it? Contributors from a variety of specialities, including cognitive, developmental, educational, and neurological psychology; mathematics education; and special education offer theoretical perspectives and much needed empirical evidence about these issues. As reported in this volume, both theory and research indicate that the nature of arithmetic expertise and how to best promote it are far more complex than conventional wisdom and many scholars, past and present, have suggested. The results of psychological, educational, and clinical studies using a wide range of arithmetic tasks and populations (including normally and atypically developing children, non-injured and brain-injured adults, and savants) all point to the same conclusion: The heart of arithmetic fluency, in general, and the flexible and creative use of strategies, in particular, is what is termed adaptive expertise (meaningful or conceptually based knowledge). The construction of adaptive expertise in mathematics is, for the first time, examined across various arithmetic topics and age groups. This book will be an invaluable resource for researchers and graduate students interested in mathematical cognition and learning (including mathematics educators, developmental and educational psychologists, and neuropsychologists), educators (including teachers, curriculum supervisors, and school administrators), and others interested in improving arithmetic instruction (including officials in national and local education departments, the media, and parents). |
| cognitively guided instruction math: Learning and Instruction National Research Council, Division of Behavioral and Social Sciences and Education, PANEL ON LEARNING AND INSTRUCTION., Strategic Education Research Partnership, 2003-12-04 The Strategic Education Research Partnership (SERP) is a bold, ambitious plan that proposes a revolutionary program of education research and development. Its purpose is to construct a powerful knowledge base, derived from both research and practice, that will support the efforts of teachers, school administrators, colleges of education, and policy officialsâ with the ultimate goal of significantly improving student learning. The proposals in this book have the potential to substantially improve the knowledge base that supports teaching and learning by pursuing answers to questions at the core of teaching practices. It calls for the linking of research and development, including instructional programs, assessment tools, teacher education programs, and materials. Best of all, the book provides a solid framework for a program of research and development that will be genuinely useful to classroom teachers. |
| cognitively guided instruction math: Native American Pedagogy and Cognitive-Based Mathematics Instruction Judith T. Hankes, 2019-05-20 Native American Pedagogydetails a study that investigated the teaching of mathematics to Oneida Indian kindergartners. This study proves that Native American children who are taught with culturally sensitive methods will perform more successfully on mathematical problem solving tasks, and that Cognitively Guided Instruction, an approach that provides teachers with research-based knowledge of how children learn mathematics, enables such culturally sensitive teaching methods. |
| cognitively guided instruction math: What's Math Got to Do with It? Jo Boaler, 2015-04-28 “Highly accessible and enjoyable for readers who love and loathe math.” —Booklist A critical read for teachers and parents who want to improve children’s mathematics learning, What’s Math Got to Do with It? is “an inspiring resource” (Publishers Weekly). Featuring all the important advice and suggestions in the original edition of What’s Math Got to Do with It?, this revised edition is now updated with new research on the brain and mathematics that is revolutionizing scientists’ understanding of learning and potential. As always Jo Boaler presents research findings through practical ideas that can be used in classrooms and homes. The new What’s Math Got to Do with It? prepares teachers and parents for the Common Core, shares Boaler’s work on ways to teach mathematics for a “growth mindset,” and includes a range of advice to inspire teachers and parents to give their students the best mathematical experience possible. |
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research program, Cognitively Guided Instruction (CGI), which investigates the impact of providing primary teachers with access to a structured, coherent body of knowledge about …
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This study focused on the teaching technique known as cognitively guided instruction (CGI), through which teachers explore the individual learning styles of their students and use the …
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This 1-credit online course provides an introduction to Cognitively Guided Instruction (CGI) and how to integrate it into teaching mathematics in PreK-12. “This course provided me with a more …
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What is CGI? • Cognitively Guided Instruction (CGI) is an approach to teaching mathematics that uses students’ own mathematical thinking, through questioning techniques, as the foundation …
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This introductory course on CGI (Cognitively Guided Instruction) defines this research-based approach in teaching mathematics while also applying these principles to other content areas …
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Cognitively Guided Instruction (CGI) is an approach to teaching and learning mathematics in which knowledge of children’s thinking is central to instructional decision making. Teachers use …
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Cognitively Guided Instruction (CGI) is a research-based approach to teaching number operations. It focuses on problem contexts and children’s thinking. The research base on …
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It explores the philosophy of Cognitively Guided Instruction (CGI) for helping students to solve problems like those discussed in Children's Mathematics. Research team goal.
Professional Development Programs: Cognitively Guided …
professional development in the following essay. The first is Cognitively Guided Instruction (CGI) and the second is Math As Text (MAT). I will begin by briefly outlining how the program is …
Impact of Cognitively Guided Instruction on Elementary …
Mathematics teacher professional development (PD) programs based on Cognitively Guided Instruction (CGI) have been the subject of dozens of studies using qualitative, quantitative, and …
Cognitively Guided Instruction (CGI) - Under the Dome
•Learn what Cognitively Guided Instruction (CGI) is and how it can be used to understand student strategies and mathematical understanding. •Explore the different problem-types and engage …
An implementation analysis of a Cognitively Guided …
In this article, we describe the conceptualization and measurement of implementation fidelity for an evidence-based mathematics teacher professional development program called Cognitively …
CHAPTER TWO Cognitively Guided Instruction: …
Carpenter and Franke emphasize the idea that the scale-up of cognitively guided instruction (CGI), a distinctive approach to teaching mathematics in elementary schools, has come about …
Examining How Cognitively Guided Instruction (CGI) …
Abstract: When students solve complex mathematical problems by themselves, many will experience and encounter difficulties, struggles, and tensions. Existing research provides little …
ED 372 929 AUTHOR TITLE Cognitively Guided Instruction. …
research program, Cognitively Guided Instruction (CGI), which investigates the impact of providing primary teachers with access to a structured, coherent body of knowledge about …
Cognitively Guided Instruction in Elementary Mathematics: …
This study focused on the teaching technique known as cognitively guided instruction (CGI), through which teachers explore the individual learning styles of their students and use the …
Instruction Math Cognitively Guided - education4equity.com
This 1-credit online course provides an introduction to Cognitively Guided Instruction (CGI) and how to integrate it into teaching mathematics in PreK-12. “This course provided me with a …
Cognitively Guided Instruction
What is CGI? • Cognitively Guided Instruction (CGI) is an approach to teaching mathematics that uses students’ own mathematical thinking, through questioning techniques, as the foundation …
HOW THE KNOWLEDGE OF COGNITIVELY GUIDED …
Cognitively Guided Instruction, a constructivist-based approach for teaching primary level mathematics (Carpenter, et al., 1998). Besides affirming compatibility, the study also …
18.05.06: Developing World Problem Solving Skills through …
My unit will address the need for problem-solving skill-building when it comes to mathematical reasoning, using cognitively guided instruction. It will cover 2 of the 4 critical areas for 2nd …
CGI Math: Cognitively Guided Math Instruction
This introductory course on CGI (Cognitively Guided Instruction) defines this research-based approach in teaching mathematics while also applying these principles to other content areas …
What is CGI? Cognitively Guided Instruction (CGI) is an …
Cognitively Guided Instruction (CGI) is an approach to teaching and learning mathematics in which knowledge of children’s thinking is central to instructional decision making. Teachers …
Cognitively Guided Instruction - blogs.sd38.bc.ca
Cognitively Guided Instruction (CGI) is a research-based approach to teaching number operations. It focuses on problem contexts and children’s thinking. The research base on …
CGI Problem Types - Idaho State Department of Education
book Children’s Mathematics: Cognitively Guided Instruction, (Heinemann, 1999). The Idaho Content Standards for Mathematics (2022) refers to these problem types in standards for …
Cognitive Guided Instruction
Using CGI, teachers start with what children already know about math and build on it to move them toward deeper levels of understanding. Children solve problems in ways that make …
Building Synergy: Cognitively Guided Instruction and
The course curriculum featured cognitively guided instruction (CGI) as the exemplar for understanding and implementing problem-based, cognitively oriented pedagogy. Our ˜ ndings …
Legends manual replacement - University of …
Cognitively Guided Instruction is an inquiry-based approach to teaching mathematics that was developed at the Wisconsin Center for Education Research (Carpenter et al, 1999). This …
Cognitively Guided Instruction Math Problem Types
It explores the philosophy of Cognitively Guided Instruction (CGI) for helping students to solve problems like those discussed in Children's Mathematics. Research team goal.
Professional Development Programs: Cognitively Guided …
professional development in the following essay. The first is Cognitively Guided Instruction (CGI) and the second is Math As Text (MAT). I will begin by briefly outlining how the program is …
Impact of Cognitively Guided Instruction on Elementary …
Mathematics teacher professional development (PD) programs based on Cognitively Guided Instruction (CGI) have been the subject of dozens of studies using qualitative, quantitative, …
Cognitively Guided Instruction (CGI) - Under the Dome
•Learn what Cognitively Guided Instruction (CGI) is and how it can be used to understand student strategies and mathematical understanding. •Explore the different problem-types and engage …
An implementation analysis of a Cognitively Guided …
In this article, we describe the conceptualization and measurement of implementation fidelity for an evidence-based mathematics teacher professional development program called Cognitively …
CHAPTER TWO Cognitively Guided Instruction: …
Carpenter and Franke emphasize the idea that the scale-up of cognitively guided instruction (CGI), a distinctive approach to teaching mathematics in elementary schools, has come about …
Examining How Cognitively Guided Instruction (CGI) …
Abstract: When students solve complex mathematical problems by themselves, many will experience and encounter difficulties, struggles, and tensions. Existing research provides little …
