Advertisement
| cra model in math: Making Mathematics Accessible for Elementary Students who Struggle Margaret Flores, Megan Burton, Vanessa Hinton, 2018 Making Mathematics Accessible for Elementary Students Who Struggle: Using CRA/CSA for Interventions provides educators with focused methods for students who struggle in elementary mathematics. The methods and procedures revolve around the CRA/CSA (concrete-representational/semi-concrete-abstract) instructional sequence. These strategies are intended for small group intensive instruction, one that addresses students' need for increased repetition and explicitness that cannot be provided within a large group of students with diverse learning needs. Current research on the CRA/CSA instructional sequence is scattered across multiple resources. This book provides comprehensive coverage of the most up-to-date research in one user-friendly resource. The sequence is included in every chapter and addresses instruction related to number sense, counting, basic operations, complex operations, basic fraction concepts, and operations with fractions. This resource is written by experienced professors spanning the fields of special education and curriculum and teaching. Its professional insight, aligned with current mathematical teaching standards and CRA/CSA research, makes this text invaluable to upcoming or current teachers in elementary mathematics. Features: Explicit and hands-on examples of CRA/CSA's use aligned with current mathematics standards and practices, Suggestions and tips for various classroom situations, Application questions for every chapter, Drawings and diagrams associated with steps of the teaching process, Classroom-tested strategies Book jacket. |
| cra model in math: Guided Math Workshop Laney Sammons, Donna Boucher, 2017-03-01 This must-have resource helps teachers successfully plan, organize, implement, and manage Guided Math Workshop. It provides practical strategies for structure and implementation to allow time for teachers to conduct small-group lessons and math conferences to target student needs. The tested resources and strategies for organization and management help to promote student independence and provide opportunities for ongoing practice of previously mastered concepts and skills. With sample workstations and mathematical tasks and problems for a variety of grade levels, this guide is sure to provide the information that teachers need to minimize preparation time and meet the needs of all students. |
| cra model in math: Symbolizing, Modeling and Tool Use in Mathematics Education K.P Gravemeijer, R. Lehrer, H.J. van Oers, Lieven Verschaffel, 2013-03-09 This book explores the option of building on symbolizing, modeling and tool use as personally meaningful activities of students. It discusses the dimension of setting: varying from the study of informal, spontaneous activity of students, to an explicit focus on instructional design, and goals and effects of instruction; and the dimension of the theoretical framework of the researcher: varying from constructivism, to activity theory, cognitive psychology and instructional-design theory. |
| cra model in math: Response to Intervention in Math Paul J. Riccomini, Bradley S. Witzel, 2010 Provides educators with instructions on applying response-to-intervention (RTI) while teaching and planning curriculum for students with learning disabilities. |
| cra model in math: Solving for Why John Tapper, 2022-10-25 Solving for Why offers educators the tools and guidance essential for successfully solving for why students struggle with mathematics. The step-by-step, RTI (Response to Intervention) - like approaches, focused on assessment and communication with students, help teachers gain insight into student understanding in a remarkably different way that recipe-type approaches that assume the same solution applies to learners with similar struggles. With Solving for Why you'll learn how to: identify a struggling math learner; develop theories for why a learner may be struggling; facilitate a Concrete-Representational-Abstract (CRA) Assessment; implement an insightful Collaborative Study; conduct powerful student interviews; support learners who struggle with memory challenges, attention deficit disorder, and affective difficulties (math anxiety); differentiate instruction through a main lesson-menu lesson plan; and more. Each chapter includes reproducible templates for ease in carrying out the assessments. A final section offers resources for supporting students who struggle with additive reasoning, multiplicative reasoning, fractions, and proportional reasoning. The reproducibles are also available in a downloadable, printable format. |
| cra model in math: Pictorial Mathematics Guillermo Mendieta, 2006-02 Pictorial Mathematics is a comprehensive and engaging resource for teaching and learning second through algebra level mathematics. It uses multiple representations and effective visuals to help learners with a wide variety of learning styles to develop a strong conceptual understanding of each concept. Pictorial Mathematics provides the perfect bridge between the abstract and the concrete. Its 400 pages are packed with invaluable tools to help teachers, parents and the learner develop meaning, connections and a deeper conceptual understanding of key mathematical concepts. Inside, you?ll find such resources as:More than 1,000 engaging visual exercises, Powerful and engaging models for the development of conceptual understanding of place value, fractions, ratios, geometry, the four operations and algebra concepts, Energizing tasks -- for small groups, large classrooms, or individuals alike, Master guides to create personalized pictorial problems, Tools to differentiate instruction, A complete set of 38 pictorial templates: from printable manipulatives to graphing paper with suggested activities for these. For previews of the book go to www.pictorialmath.com. |
| cra model in math: The Teaching of Fractions Edward Wildeman, 1923 |
| cra model in math: Contexts for Learning Mathematics Catherine Twomey Fosnot, Pearson Education, Fosnot, 2007-05 Contexts for Learning consists of: Investigations and Resource Guides - workshop structure involves students in inquiring, investigating, discussing, and constructing mathematical solutions and strategies - investigations encourage emergent learning and highlight the developmental landmarks in mathematical thinking - strings of related problems develop students' deep number sense and expand their strategies for mental arithmetic Read-Aloud Books and Posters - create rich, imaginable contexts--realistic and fictional--for mathematics investigations - are carefully crafted to support the development of the big ideas, strategies, and models - encourage children to explore and generate patterns, generalize, and develop the ability to mathematize their worlds Resources for Contexts for Learning CD-ROM - author videos describe the series' philosophy and organization - video overviews show classroom footage of a math workshop, including minilessons, investigations, and a math congress - print resources include research base, posters, and templates |
| cra model in math: Concrete Mathematics Ronald L. Graham, Donald E. Knuth, Oren Patashnik, 1994-02-28 This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline. Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. More concretely, the authors explain, it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems. The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study. Major topics include: Sums Recurrences Integer functions Elementary number theory Binomial coefficients Generating functions Discrete probability Asymptotic methods This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them. |
| cra model in math: Number Sense Routines Jessica F. Shumway, 2011 Just as athletes stretch their muscles before every game and musicians play scales to keep their technique in tune, mathematical thinkers and problem solvers can benefit from daily warm-up exercises. Jessica Shumway has developed a series of routines designed to help young students internalize and deepen their facility with numbers. The daily use of these quick five-, ten-, or fifteen-minute experiences at the beginning of math class will help build students' number sense. Students with strong number sense understand numbers, ways to represent numbers, relationships among numbers, and number systems. They make reasonable estimates, compute fluently, use reasoning strategies (e.g., relate operations, such as addition and subtraction, to each other), and use visual models based on their number sense to solve problems. Students who never develop strong number sense will struggle with nearly all mathematical strands, from measurement and geometry to data and equations. In Number Sense Routines, Jessica shows that number sense can be taught to all students. Dozens of classroom examples -- including conversations among students engaging in number sense routines -- illustrate how the routines work, how children's number sense develops, and how to implement responsive routines. Additionally, teachers will gain a deeper understanding of the underlying math -- the big ideas, skills, and strategies children learn as they develop numerical literacy. |
| cra model in math: Educational Assessment of Students Anthony J. Nitko, Susan M. Brookhart, 2013-11-01 For a wide variety of courses in classroom assessment. This highly respected text offers the most comprehensive discussion of traditional and alternative assessments of any classroom assessment text-explaining, giving examples, discussing pros and cons, and showing how to construct virtually all of the traditional and alternative assessments teachers use in the classroom. The author explores assessment theories and research findings as they affect teaching and learning, and examines why, when, and how teachers should use assessment in the classroom. To the text's hundreds of practical examples are added checklists to aid in evaluating assessment vehicles and scores of strategies for assessing higher-order thinking, critical-thinking, and problem-solving skills. |
| cra model in math: Teaching Numeracy Margie Pearse, K. M. Walton, 2011-03-23 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. |
| cra model in math: Liberating Leadership Capacity Linda Lambert, Diane P. Zimmerman, Mary E. Gardner, 2016-04-01 During the past quarter century, conceptions of leadership have evolved in concert with breakthrough discoveries in science and generative learning. This book captures these new ideas through the integration of the authors' earlier works in constructivist leadership and leadership capacity. What emerges is a pathway through which educators can become the primary designers of their own learning and that of their students, thus creating sustainable systems of high leadership capacity. This vision of leadership reframes professional learning designs and knowledge creation, describing how these ideas are richly manifested in local, national, and international programs. The context is democratic communities; the learning is constructivist; the leadership is shared. The result is wise schools, organizations, and socieities. This book speaks to all adult learners who are engaged in educational improvement. |
| cra model in math: Number Talks Sherry Parrish, 2010 A multimedia professional learning resource--Cover. |
| cra model in math: Mathematical Mindsets Jo Boaler, 2015-10-12 Banish math anxiety and give students of all ages a clear roadmap to success Mathematical Mindsets provides practical strategies and activities to help teachers and parents show all children, even those who are convinced that they are bad at math, that they can enjoy and succeed in math. Jo Boaler—Stanford researcher, professor of math education, and expert on math learning—has studied why students don't like math and often fail in math classes. She's followed thousands of students through middle and high schools to study how they learn and to find the most effective ways to unleash the math potential in all students. There is a clear gap between what research has shown to work in teaching math and what happens in schools and at home. This book bridges that gap by turning research findings into practical activities and advice. Boaler translates Carol Dweck's concept of 'mindset' into math teaching and parenting strategies, showing how students can go from self-doubt to strong self-confidence, which is so important to math learning. Boaler reveals the steps that must be taken by schools and parents to improve math education for all. Mathematical Mindsets: Explains how the brain processes mathematics learning Reveals how to turn mistakes and struggles into valuable learning experiences Provides examples of rich mathematical activities to replace rote learning Explains ways to give students a positive math mindset Gives examples of how assessment and grading policies need to change to support real understanding Scores of students hate and fear math, so they end up leaving school without an understanding of basic mathematical concepts. Their evasion and departure hinders math-related pathways and STEM career opportunities. Research has shown very clear methods to change this phenomena, but the information has been confined to research journals—until now. Mathematical Mindsets provides a proven, practical roadmap to mathematics success for any student at any age. |
| cra model in math: Key Ideas in Teaching Mathematics Anne Watson, Keith Jones, Dave Pratt, 2013-02-21 International research is used to inform teachers and others about how students learn key ideas in higher school mathematics, what the common problems are, and the strengths and pitfalls of different teaching approaches. An associated website, hosted by the Nuffield Foundation, gives summaries of main ideas and access to sample classroom tasks. |
| cra model in math: Teaching Students to Communicate Mathematically Laney Sammons, 2018-04-04 Students learning math are expected to do more than just solve problems; they must also be able to demonstrate their thinking and share their ideas, both orally and in writing. As many classroom teachers have discovered, these can be challenging tasks for students. The good news is, mathematical communication can be taught and mastered. In Teaching Students to Communicate Mathematically, Laney Sammons provides practical assistance for K–8 classroom teachers. Drawing on her vast knowledge and experience as a classroom teacher, she covers the basics of effective mathematical communication and offers specific strategies for teaching students how to speak and write about math. Sammons also presents useful suggestions for helping students incorporate correct vocabulary and appropriate representations when presenting their mathematical ideas. This must-have resource will help you help your students improve their understanding of and their skill and confidence in mathematical communication. |
| cra model in math: Rigor for Students with Special Needs Barbara R. Blackburn, Bradley S. Witzel, 2013-10-08 This practical, easy-to-read guide explains how to raise the rigor for students with special needs so they can achieve higher levels of learning. Learn how to set clear goals and expectations establish a climate of success scaffold and model lessons use graphic organizers and think-alouds apply modifications and accommodations use rigorous questioning strategies differentiate instruction increase family involvement Get even more out of this book by discussing it with others! It’s ideal for study groups and the appendix features a detailed guide on how to make it work for your group! Bonus! You get a great variety of handy black line masters for use in your own classroom. |
| cra model in math: Book of Proof Richard H. Hammack, 2016-01-01 This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. |
| cra model in 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. |
| cra model in math: Math Running Records in Action Nicki Newton, 2016-06-17 In this new book from popular consultant and bestselling author Dr. Nicki Newton, you’ll discover how to use Math Running Records to assess students’ basic fact fluency and increase student achievement. Like a GPS, Math Running Records pinpoint exactly where students are in their understanding of basic math facts and then outline the next steps toward comprehensive fluency. This practical book introduces a research-based framework to assess students’ thinking and move them toward becoming confident, proficient, flexible mathematicians with a robust sense of numbers. Topics include: Learning how often to administer Math Running Records and how to strategically introduce them into your existing curriculum; Analyzing, and interpreting Math Running Records for addition, subtraction, multiplication, and division; Using the data gathered from Math Running Records to implement evidence-based, research-driven instruction. Evaluating students’ speed, accuracy, flexibility, and efficiency to help them attain computational fluency; Each chapter offers a variety of charts and tools that you can use in the classroom immediately, and the strategies can easily be adapted for students at all levels of math fluency across grades K-8. Videos of sample running records are also available for download at https://guidedmath.wordpress.com/math-running-records-videos. Blackline masters are available on the Running Records Dropbox at https://bit.ly/3gnggIq |
| cra model in math: Mathematics Framework for California Public Schools California. Curriculum Development and Supplemental Materials Commission, 1999 |
| cra model in math: Everyone Can Learn Math Alice Aspinall, 2018-10-16 How do you approach a math problem that challenges you? Do you keep trying until you reach a solution? Or are you like Amy, who gets frustrated easily and gives up? Amy is usually a happy and enthusiastic student in grade five who loves to dance, but she is struggling with a tough math assignment. She doesn’t think she is good at math because her classmates always get the answers faster than she does and sometimes she uses her fingers to help her count. Even though her mom tries to help her, Amy is convinced she just cannot do math. She decides not to do the assignment at all since she thinks she wouldn’t do well anyway. As Amy goes about her day, her experiences at ballet class, the playground, and gym class have her thinking back to how she gave up on her math assignment. She starts to notice that hard-work, practice, and dedication lead to success, thanks to her friends and teachers. She soon comes to understand that learning math is no different than learning any other skill in life. With some extra encouragement from her math teacher, a little help from her mom, and a new attitude, Amy realizes that she can do math! |
| cra model in math: Creating Literacy Instruction for All Students Thomas G. Gunning, 2013 The Eighth Edition of this authoritative, best-selling resource from distinguished author Tom Gunning gives aspiring and practicing teachers the help they need to become highly effective teachers--so that their students become proficient readers and writers well on their way to preparing for college and careers. Drawing on landmark research that focuses on highly effective practices, such as setting goals, monitoring progress, and teaching strategies, Gunning's Teaching Literacy Strategies for All Students is packed with step-by-step guidance for teaching reading and writing, including 30 sample lessons that cover virtually every major literacy skill and strategy, incorporating the key elements of effective assessment and instruction. The book emphasizes how to adapt instruction for struggling readers and writers, English language learners, and special needs students; stresses effective steps teachers can use to implement Response to Intervention; and familiarizes teachers with the reading and writing requirements stemming from the widely-adopted Common Core State Standards. |
| cra model in 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. |
| cra model in math: Computation of Integers Paul J. Riccomini, Bradley S. Witzel, 2009 This practical new text will empower those educators responsible for math instruction to successfully teach students in grades six through eight, as well as other students, to master computation of integers. Integration of picture-led, step-by-step instruction with accompanying dialogue will aid educators to deliver the exact vocabulary and stepwise procedures necessary for success--that of their students learning the mathematical process to computing integers. Written for math educators including elementary, middle school, special education teachers, tutors and home school teachers, this accessible guide will improve instructors' ability to teach integers, and the confidence in their students to master the subject matter. Special pedagogical features include: Student Work Pages for every lesson! Scripted, step-by-step examples outline how to teach each stage using hands-on, pictorial and abstract approaches. Concrete to Representational to Abstract sequence of instruction (CRA) in each section of the book and materials. Instructional lessons with assessment matching inform both the student and the teacher what learning occurred and where to start in order to master the skill. Cumulative reviews to help eachstudent successfully retain information. |
| cra model in math: RtI in Math Linda Forbringer, Wendy Weber, 2014-01-03 Learn how to help K–8 students who struggle in math. This book provides a variety of clear, practical strategies that can be implemented right away to boost student achievement. You will find out how to design lessons that work with struggling learners, implement the recommendations for math intervention from the What Works Clearinghouse, use praise and self-motivation more effectively, develop number sense and computational fluency, teach whole numbers and fractions, increase students’ problem-solving abilities, and more! Extensive examples are provided for each strategy, as well as lesson plans, games, and resources. |
| cra model in math: Proofs from THE BOOK Martin Aigner, Günter M. Ziegler, 2013-06-29 According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such perfect proofs, those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics. |
| cra model in math: Computation of Fractions Bradley S. Witzel, Paul J. Riccomini, 2009 In response to the lack of intervention resources available to middle school teachers to help their struggling students, the authors present this collection of easy-to-implement, research-based lesson plans to help those who struggle with mathematical fractions. |
| cra model in math: High Leverage Practices for Inclusive Classrooms James McLeskey, Lawrence Maheady, Bonnie Billingsley, Mary T. Brownell, Timothy J. Lewis, 2022-03-30 High Leverage Practices for Inclusive Classrooms, Second Edition offers a set of practices that are integral to the support of student learning, and that can be systematically taught, learned, and implemented by those entering the teaching profession. In this second edition, chapters have been fully updated to reflect changes in the field since its original publication, and feature all new examples illustrating the use of HLPs and incorporating culturally responsive practices. Focused primarily on Tiers 1 and 2—or work that mostly occurs with students with mild to moderate disabilities in general education classrooms—this powerful, research-based resource provides rich, practical information highly suitable for teachers, and additionally useful for teacher educators and teacher preparation programs. |
| cra model in math: Why Evolution is True Jerry A. Coyne, 2010-01-14 For all the discussion in the media about creationism and 'Intelligent Design', virtually nothing has been said about the evidence in question - the evidence for evolution by natural selection. Yet, as this succinct and important book shows, that evidence is vast, varied, and magnificent, and drawn from many disparate fields of science. The very latest research is uncovering a stream of evidence revealing evolution in action - from the actual observation of a species splitting into two, to new fossil discoveries, to the deciphering of the evidence stored in our genome. Why Evolution is True weaves together the many threads of modern work in genetics, palaeontology, geology, molecular biology, anatomy, and development to demonstrate the 'indelible stamp' of the processes first proposed by Darwin. It is a crisp, lucid, and accessible statement that will leave no one with an open mind in any doubt about the truth of evolution. |
| cra model in math: The Very Hungry Caterpillar Eric Carle, 2016-11-22 The all-time classic picture book, from generation to generation, sold somewhere in the world every 30 seconds! Have you shared it with a child or grandchild in your life? For the first time, Eric Carle’s The Very Hungry Caterpillar is now available in e-book format, perfect for storytime anywhere. As an added bonus, it includes read-aloud audio of Eric Carle reading his classic story. This fine audio production pairs perfectly with the classic story, and it makes for a fantastic new way to encounter this famous, famished caterpillar. |
| cra model in math: Teaching Student-Centered Mathematics Access Code John a Van De Walle, 2017-01-28 NOTE: Used books, rentals, and purchases made outside of Pearson If purchasing or renting from companies other than Pearson, the access codes for the Enhanced Pearson eText may not be included, may be incorrect, or may be previously redeemed. Check with the seller before completing your purchase. This access code card provides access to the Enhanced Pearson eText. For courses in Elementary Mathematics Methods and for classroom teachers. A practical, comprehensive, student-centered approach to effective mathematical instruction for grades Pre-K-2. Helping students make connections between mathematics and their worlds-and helping them feel empowered to use math in their lives-is the focus of this widely popular guide. Designed for classroom teachers, the book focuses on specific grade bands and includes information on creating an effective classroom environment, aligning teaching to various standards and practices, such as the Common Core State Standards and NCTM's teaching practices, and engaging families. The first portion of the book addresses how to build a student-centered environment in which children can become mathematically proficient, while the second portion focuses on practical ways to teach important concepts in a student-centered fashion. The new edition features a corresponding Enhanced Pearson eText version with links to embedded videos, blackline masters, downloadable teacher resource and activity pages, lesson plans, activities correlated to the CCSS, and tables of common errors and misconceptions. This book is part of the Student-Centered Mathematics Series, which is designed with three objectives: to illustrate what it means to teach student-centered, problem-based mathematics, to serve as a reference for the mathematics content and research-based instructional strategies suggested for the specific grade levels, and to present a large collection of high quality tasks and activities that can engage students in the mathematics that is important for them to learn. Improve mastery and retention with the Enhanced Pearson eText* This access code card provides access to the new Enhanced Pearson eText, a rich, interactive learning environment designed to improve student mastery of content. The Enhanced Pearson eText is: Engaging. The new interactive, multimedia learning features were developed by the authors and other subject-matter experts to deepen and enrich the learning experience. Convenient. Enjoy instant online access from your computer or download the Pearson eText App to read on or offline on your iPad(R) and Android(R) tablet.* Affordable. Experience the advantages of the Enhanced Pearson eText along with all the benefits of print for 40% to 50% less than a print bound book. *The Enhanced eText features are only available in the Pearson eText format. They are not available in third-party eTexts or downloads. *The Pearson eText App is available on Google Play and in the App Store. It requires Android OS 3.1-4, a 7- or 10- tablet, or iPad iOS 5.0 or later. |
| cra model in math: Introduction to Representation Bonnie H. Ennis, Kimberly S. Witeck, 2007 NCTM's Process Standards were designed to support teaching that helps children develop independent, effective mathematical thinking. The books in the Heinemann Math Process Standards Series give every elementary teacher the opportunity to explore each one of the standards in depth. And with language and examples that don't require prior math training to understand, the series offers friendly, reassuring advice to any teacher preparing to embrace the Process Standards. In Introduction to Representation, Bonnie Ennis and Kimberly Witeck share ways to help students use algorithms, graphs, manipulatives, diagrams, and other written and pictorial forms to express math ideas. They offer an array of entry points for understanding, planning, and teaching, including strategies that help students internalize manipulatives and other models of mathematical thinking so that they can begin documenting their mathematical processes. Full of activities that are modifiable for immediate use with students of all levels and written by veteran teachers for teachers of every level of experience, Introduction to Representation highlights the importance of encouraging children to demonstrate their mathematical thinking techniques through a variety of mathematical means, while also recommending ways to implement representation-based teaching without rewriting your curriculum. Best of all, like all the titles in the Math Process Standards Series, Introduction to Representation comes with two powerful tools to help you get started and plan well: a CD-ROM with activities customizable to match your lessons and a correlation guide that helps you match mathematical content with the processes it utilizes. If you need to better understand how students represent their thinking. Or if you're simply looking for new ways to work the representation standard into your curriculum, read, dog-ear, and teach with Introduction to Representation. And if you'd like to learn about any of NCTM's process standards, or if you're looking for new, classroom-tested ways to address them in your math teaching, look no further than Heinemann's Math Process Standards Series. You'll find them explained in the most understandable and practical way: from one teacher to another. |
| cra model in math: How Children Learn Number Concepts Kathy Richardson, Math Perspectives Teacher Development Center, 2012 This book was written to help Pre-K through 4th educators recognize the complexities of the mathematics young children are expected to learn, and to identify what is required for children to develop an understanding of number concepts. |
| cra model in math: Teaching Students with Learning Problems Cecil D Mercer, Ann R. Mercer, Paige C. Pullen, 2013-09-20 Logically organized, comprehensive, and thoroughly applied, the eighth edition of Teaching Students with Learning Problems contains the resources teachers need to make informed decisions concerning their students with learning or behavior problems. No text on the market offers this many classroom-tested strategies, including activities and games. Unique in its coverage the materials and computer software most appropriate for students with learning problems in every content area, this top-selling text continues to be the most practical and well-researched resource for classroom teachers. |
| cra model in math: Developing Efficient Numeracy Strategies New South Wales. Curriculum Support Directorate, 2003 |
| cra model in math: Young Mathematicians at Work Catherine Twomey Fosnot, Maarten Ludovicus Antonius Marie Dolk, 2001 Explains how children between the ages of four and eight construct a deep understanding of numbers and the operations of addition and subtraction. |
| cra model in 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. |
| cra model in math: Understanding RTI in Mathematics Russell Monroe Gersten, Rebecca Newman-Gonchar, 2011 Response to intervention, it's already improving reading outcomes in reading classrooms across the country, and this approach can be equally effective for K-12 mathematics instruction. This is the definitive volume on RTI in math: what we know about it; why it works, and how to use it to ensure high-quality math instruction and higher student acheivement. With contributions by all of the U.S.'s leading researchers on RTI and math, this cutting-edge text blends the existing evidence base with practical guidelines for RTI implementation. Current and future RTI coordinators, curriculum developers, math specialists, and department heads will get the best, most up-to-date guidance on key facets of RTI in math: conducting valid and reliable universal screening; using evidence-based practices; monitoring students' progress with high-quality tools and measures; teaching students to use an array of visual representations to help them solve math problems; tailoring RTI for every grade level, from kindergarten through high school; and more. Filled with vignettes, accessible summaries of the most recent studies, and best-practice guidelines for making the most of RTI, this comprehensive research volume is ideal for use as a textbook or as a key resource to guide decisions makers. |
Concrete-Representational- Abstract: Instructional Sequence …
mathematical model and use verbalization while using the CRA sequence. What materials do I need to engage in CRA? Concrete manipulatives such as algebra tiles, cups, sticks, or base . …
CRA Approach - Accelerate Learning
The CRA (concrete-representational-abstract) model is a powerful strategy for teaching new math concepts. It is a three-part constructivist process that transitions students from hands-on …
Concrete-Representational-Abstract Instructional Approach
What Is the Concrete-Representational-Abstract (CRA) Instructional Approach? CRA is an intervention for mathematics instruction that research suggests can enhance the mathematics …
Using CRA to Teach Algebra to Students with Math …
The CRA algebra model was used to teach students a series of algebra skills from reducing simple two-statement expressions to solving linear functions with unknowns on both sides of …
Effectiveness of CRA Method Implementation in Secondary and
a model of teaching known as the concrete-representational-abstract (CRA) method. This method uses manipulatives along with pictorial representations and words and numbers in a specific …
Grade 5 Operations and Algebraic Thinking Unit of Instruction
This is a progressive unit of instruction using the Concrete-Representational-Abstract (CRA) Instructional Model. CRA is a three-part instructional model that begins by using concrete …
Applied Problems Intervention Strategy Concrete, …
Model each math concept/skill/problem using “explicit teacher modeling” (see below) with concrete materials (see examples above, depending on the strand in which the student it …
Teaching strategy: Concrete, representational, abstract (CRA)
The Concrete, Representational (Pictorial), Abstract model (CRA) is based on Jerome Brunner’s theory of cognitive development: enactive (action-based), iconic (image-based) and symbolic …
Elementary Math Grades K-5 FRAMEWORK - Roxbury …
The mini lesson is constructed based on the starting point of the grade level Mathematics NJSLS standards, then developed with application of the Concrete-Representational-Abstract (CRA) …
Concrete-Representational-Abstract (CRA) Instructional
What Is the Concrete-Representational-Abstract (CRA) Instructional Approach? CRA is an intervention for mathematics instruction that research suggests can enhance the mathematics …
MODELS AND STRATEGIES LESSON SAMPLE
(CRA) APPROACH The CRA model is a powerful strategy for teaching new math concepts. It is a three-part constructivist process that transitions students from hands-on learning to the math …
Concrete-Pictorial-Abstract: Surveying its Origins and …
Bruner’s model. One such adaptation of Bruner’s model is the Concrete-Representation-Abstract (CRA) sequence. The CRA sequence has been shown to be particularly effective with …
Building Mathematical Understanding: The Power Of CRA …
The Concrete-Representational-Abstract (CRA) approach is a well-established instructional strategy in teaching numeracy that is designed to enhance students' understanding of …
The Extent of Use of Concrete-Representational-Abstract …
CRA approach offers students explicit instruction in Mathematics and assists the learner in constructing his / her knowledge through the use of multiple representations of a concept …
MODEL THE FOUR - info.stemscopes.com
Whether you’re a new or veteran teacher, STEMscopes Math provides everything you need to create a meaningful learning experience. The CRA model is a powerful strategy for teaching …
Grade 3 Fraction Unit of Instruction - Florida Department of …
This is a progressive unit of instruction using the Concrete-Representational-Abstract (CRA) Instructional Model. CRA is a three-part instructional model that begins by using concrete …
Algebra Tiles - Calculate
Concrete, Representational, Abstract (CRA) Model This model is used throughout the lesson sequence. The CRA model is designed to move students from the: Concrete – using …
THE USE CONCRETE-REPRESENTATIONAL-ABSTRACT …
The CRA (concrete-representational-abstract) Approach is a widely recognized teaching method that has been proven to be effective in enhancing students' understanding and mastery of …
Grade 4 Operations and Algebraic Thinking Unit of Instruction
This is a progressive unit of instruction using the Concrete-Representational-Abstract (CRA) Instructional Model. CRA is a three-part instructional model that begins by using concrete …
POSITIVE RATIONAL NUMBER OPERATIONS LESSON …
(CRA) APPROACH The CRA model is a powerful strategy for teaching new math concepts. It is a three-part constructivist process that transitions students from hands-on learning to the math …
Concrete-Representational- Abstract: Instructional Sequence …
mathematical model and use verbalization while using the CRA sequence. What materials do I need to engage in CRA? Concrete manipulatives such as algebra tiles, cups, sticks, or base . …
CRA Approach - Accelerate Learning
The CRA (concrete-representational-abstract) model is a powerful strategy for teaching new math concepts. It is a three-part constructivist process that transitions students from hands-on …
Concrete-Representational-Abstract Instructional Approach
What Is the Concrete-Representational-Abstract (CRA) Instructional Approach? CRA is an intervention for mathematics instruction that research suggests can enhance the mathematics …
Using CRA to Teach Algebra to Students with Math …
The CRA algebra model was used to teach students a series of algebra skills from reducing simple two-statement expressions to solving linear functions with unknowns on both sides of …
Effectiveness of CRA Method Implementation in Secondary and
a model of teaching known as the concrete-representational-abstract (CRA) method. This method uses manipulatives along with pictorial representations and words and numbers in a specific …
Grade 5 Operations and Algebraic Thinking Unit of …
This is a progressive unit of instruction using the Concrete-Representational-Abstract (CRA) Instructional Model. CRA is a three-part instructional model that begins by using concrete …
Applied Problems Intervention Strategy Concrete, …
Model each math concept/skill/problem using “explicit teacher modeling” (see below) with concrete materials (see examples above, depending on the strand in which the student it …
Teaching strategy: Concrete, representational, abstract (CRA)
The Concrete, Representational (Pictorial), Abstract model (CRA) is based on Jerome Brunner’s theory of cognitive development: enactive (action-based), iconic (image-based) and symbolic …
Elementary Math Grades K-5 FRAMEWORK - Roxbury School …
The mini lesson is constructed based on the starting point of the grade level Mathematics NJSLS standards, then developed with application of the Concrete-Representational-Abstract (CRA) …
Concrete-Representational-Abstract (CRA) Instructional
What Is the Concrete-Representational-Abstract (CRA) Instructional Approach? CRA is an intervention for mathematics instruction that research suggests can enhance the mathematics …
MODELS AND STRATEGIES LESSON SAMPLE
(CRA) APPROACH The CRA model is a powerful strategy for teaching new math concepts. It is a three-part constructivist process that transitions students from hands-on learning to the math …
Concrete-Pictorial-Abstract: Surveying its Origins and …
Bruner’s model. One such adaptation of Bruner’s model is the Concrete-Representation-Abstract (CRA) sequence. The CRA sequence has been shown to be particularly effective with …
Building Mathematical Understanding: The Power Of CRA …
The Concrete-Representational-Abstract (CRA) approach is a well-established instructional strategy in teaching numeracy that is designed to enhance students' understanding of …
The Extent of Use of Concrete-Representational-Abstract …
CRA approach offers students explicit instruction in Mathematics and assists the learner in constructing his / her knowledge through the use of multiple representations of a concept …
MODEL THE FOUR - info.stemscopes.com
Whether you’re a new or veteran teacher, STEMscopes Math provides everything you need to create a meaningful learning experience. The CRA model is a powerful strategy for teaching …
Grade 3 Fraction Unit of Instruction - Florida Department of …
This is a progressive unit of instruction using the Concrete-Representational-Abstract (CRA) Instructional Model. CRA is a three-part instructional model that begins by using concrete …
Algebra Tiles - Calculate
Concrete, Representational, Abstract (CRA) Model This model is used throughout the lesson sequence. The CRA model is designed to move students from the: Concrete – using …
THE USE CONCRETE-REPRESENTATIONAL-ABSTRACT …
The CRA (concrete-representational-abstract) Approach is a widely recognized teaching method that has been proven to be effective in enhancing students' understanding and mastery of …
Grade 4 Operations and Algebraic Thinking Unit of …
This is a progressive unit of instruction using the Concrete-Representational-Abstract (CRA) Instructional Model. CRA is a three-part instructional model that begins by using concrete …
POSITIVE RATIONAL NUMBER OPERATIONS LESSON SAMPLE
(CRA) APPROACH The CRA model is a powerful strategy for teaching new math concepts. It is a three-part constructivist process that transitions students from hands-on learning to the math …
