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Author: Amy J. Hackenberg
Publisher: SAGE
ISBN: 1473986850
Category : Education
Languages : en
Pages : 225
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Book Description
Supporting and understanding your students’ fractional knowledge is crucial to their overall grasp of numbers and mathematics. By centralizing around three key stages of development, this effective guide will help you to assess your students’ understanding of fractions and modify your teaching accordingly. These key stages are identified as: Stage 1a: Fair Sharing Stage 1b: Part-Whole Stage 2a: Disembedding and IteratingStage 2b: Measuring with Unit Fractions Stage 2c: Reversing Fractions Stage 3a: Fractions as Numbers Stage 3b: Operating with Fractions As the newest addition to the bestselling Maths Recovery Series, this book will be a useful guide for all primary classroom teachers and assistants, including experienced Mathematics Recovery instructors.
Author: Amy J. Hackenberg
Publisher: SAGE
ISBN: 1473986850
Category : Education
Languages : en
Pages : 225
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Book Description
Supporting and understanding your students’ fractional knowledge is crucial to their overall grasp of numbers and mathematics. By centralizing around three key stages of development, this effective guide will help you to assess your students’ understanding of fractions and modify your teaching accordingly. These key stages are identified as: Stage 1a: Fair Sharing Stage 1b: Part-Whole Stage 2a: Disembedding and IteratingStage 2b: Measuring with Unit Fractions Stage 2c: Reversing Fractions Stage 3a: Fractions as Numbers Stage 3b: Operating with Fractions As the newest addition to the bestselling Maths Recovery Series, this book will be a useful guide for all primary classroom teachers and assistants, including experienced Mathematics Recovery instructors.
Author: Robert J Wright
Publisher: SAGE
ISBN: 1446253686
Category : Education
Languages : en
Pages : 313
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Book Description
Following the great success of the earlier books, this fourth book in the Mathematics Recovery series equips teachers with detailed pedagogical knowledge and resources for teaching number to 7 to 11-year olds. Drawing on extensive programs of research, curriculum development, and teacher development, the book offers a coherent, up-to-date approach emphasising computational fluency and the progressive development of students′ mathematical sophistication. The book is organized in key domains of number instruction, including structuring numbers 1 to 20, knowledge of number words and numerals, conceptual place value, mental computation, written computation methods, fractions, and early algebraic reasoning. Features include: fine-grained progressions of instruction within each domain; detailed descriptions of students′ strategies and difficulties; assessment tasks with notes on students′ responses; classroom-ready instructional activities; This book is designed for classroom and intervention teachers, special education teachers and classroom assistants. The book is an invaluable resource for mathematics advisors and coaches, learning support staff, numeracy consultants, curriculum developers, teacher educators and researchers.
Author: Marjorie M. Petit
Publisher: Routledge
ISBN: 1317597303
Category : Education
Languages : en
Pages : 208
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Book Description
A Focus on Fractions is a groundbreaking effort to make the mathematics education research on how students develop their understanding of fraction concepts readily accessible and understandable to pre- and in-service K– 8 mathematics educators. Using extensive annotated samples of student work, as well as vignettes characteristic of classroom teachers’ experiences, this book equips educators with the knowledge and tools to reveal students’ thinking so that they can modify their teaching and improve student learning of fraction concepts. A Focus on Fractions 2nd edition includes sections on the Common Core State Standards for Mathematics and the Ongoing Assessment Project (OGAP) Fraction Framework integrated into each chapter as well as a new chapter on the OGAP Fraction Progression and how it can be used for formative assessment purposes. This updated edition assists teachers in translating research findings into their classroom practice by conveying detailed information about how students develop fraction understandings. Additional images and examples serve to flesh out and supplement the newly-introduced concepts in this updated and expanded edition. Special Features: Looking Back Questions at the end of each chapter provide teachers the opportunity to analyze student thinking and consider instructional strategies for their own students. Instructional Links help teachers relate concepts from the chapter to their own instructional materials and programs. Big Ideas frame the chapters and provide a platform for meaningful exploration of the teaching of fractions. Answer Key posted online offers extensive explanations of in-chapter questions. New sections devoted to the CCSSM and OGAP Fraction Progression are woven throughout the book as well as a new stand alone chapter on the OGAP Fraction Progression. The OGAP Fraction Framework is an all-new eResource, now available as a free download from the book’s website: www.routledge.com/9781138816442.
Author: Kathryn Bouchard Chval
Publisher:
ISBN: 9780873537322
Category : Fractions
Languages : en
Pages : 148
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Book Description
Do your students suppose that 1/3 is greater than 1/2, since 3 is greater than 2? Do they believe that having “halves” means having two, and only two, congruent “pieces” of a whole? What tasks can you offer—what questions can you ask—to determine what your students know or don’t know—and move them forward in their thinking? This book focuses on the specialised pedagogical content knowledge that you need to teach fractions effectively in grades 3–5. The authors demonstrate how to use this multifaceted knowledge to address the big ideas and essential understandings that students must develop for success with fractions—not only in their current work, but also in higher-level mathematics and a myriad of real-world contexts. Explore rich, research-based strategies and tasks that show how students are reasoning about and making sense of fractions. Use the opportunities that these and similar tasks provide to build on their understanding while identifying and correcting misunderstandings that may be keeping them from taking the next steps in learning.
Author: Leslie P. Steffe
Publisher: Springer Science & Business Media
ISBN: 144190591X
Category : Education
Languages : en
Pages : 379
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Book Description
Children’s Fractional Knowledge elegantly tracks the construction of knowledge, both by children learning new methods of reasoning and by the researchers studying their methods. The book challenges the widely held belief that children’s whole number knowledge is a distraction from their learning of fractions by positing that their fractional learning involves reorganizing—not simply using or building upon—their whole number knowledge. This hypothesis is explained in detail using examples of actual grade-schoolers approaching problems in fractions including the schemes they construct to relate parts to a whole, to produce a fraction as a multiple of a unit part, to transform a fraction into a commensurate fraction, or to combine two fractions multiplicatively or additively. These case studies provide a singular journey into children’s mathematics experience, which often varies greatly from that of adults. Moreover, the authors’ descriptive terms reflect children’s quantitative operations, as opposed to adult mathematical phrases rooted in concepts that do not reflect—and which in the classroom may even suppress—youngsters’ learning experiences. Highlights of the coverage: Toward a formulation of a mathematics of living instead of being Operations that produce numerical counting schemes Case studies: children’s part-whole, partitive, iterative, and other fraction schemes Using the generalized number sequence to produce fraction schemes Redefining school mathematics This fresh perspective is of immediate importance to researchers in mathematics education. With the up-close lens onto mathematical development found in Children’s Fractional Knowledge, readers can work toward creating more effective methods for improving young learners’ quantitative reasoning skills.
Author: Pamela D. Tabor
Publisher: SAGE
ISBN: 1529752256
Category : Education
Languages : en
Pages : 225
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Book Description
Numeracy for All Learners is a wide-ranging overview of how Math Recovery® theory, pedagogy, and tools can be applied meaningfully to special education to support learners with a wide range of educational needs. It builds on the first six books in the Math Recovery series and presents knowledge, resources, and examples for teachers working with students with special needs from Pre-K through secondary school. Key topics include: dyscalculia, what contemporary neuroscience tells us about mathematical learning, and differentiating assessment and instruction effectively to meet the needs of all students in an equitable framework.
Author: Monica Neagoy
Publisher: ASCD
ISBN: 1416621237
Category : Education
Languages : en
Pages : 301
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Book Description
For years, the teaching and learning of fractions has been associated with rote memorization. But this mechanical approach to instruction—which strips students of an ability to reason or make sense of math—has resulted in a failure of understanding. Author Monica Neagoy, drawing on decades of research studies, evidence from teacher practice, and 25 years of experience working around the world with teachers, students, and parents, addresses seven big ideas in the teaching and learning of fractions in grades 2–6. Each idea is supported by a vignette from a real classroom, common misconceptions, a thorough unpacking of productive mathematical thinking, and several multistep and thought-provoking problems for teachers to explore. She offers three fundamental reasons why it’s imperative for us to take a closer look at how we teach fractions: 1. Fractions play a key role in students’ feelings about mathematics. 2. Fractions are fundamental to school math and daily life. 3. Fractions are foundational to success in algebra. While a solid grounding in algebra is necessary for a STEM career, the worthy goal of “algebra for all” will not be possible until “fractions for all” is a reality. Unpacking Fractions provides teachers with concrete strategies for achieving that reality—in short, helping all students gain the knowledge they need to feel at ease with fractions.
Author: Robert J Wright
Publisher: SAGE
ISBN: 1446227146
Category : Education
Languages : en
Pages : 226
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Book Description
′Unlike many books based on research work this book doesn′t just let teachers know what is going wrong with children′s learning it actually gives some practical advice about what to do next. The whole book is based upon extensive observation and recording of individual children and their difficulties with mathematics. These children are the most difficult to plan for in a busy classroom and the authors appreciate the small steps and the different learning styles approaches needed for these children. This approach fits well with the NNS wave and springboard materials but takes the analysis of the individual′s difficulties to a more detailed level. The book brings together research carried out across a range of countries and therefore shows the versatility of the approaches taken. This will be a very useful book for trainee teachers as it exemplifies how to use assessment to feed into teaching. It will be helpful for class teachers and mathematics co-ordinators as well as SENCOs to assist in improving the teaching and learning for specific children in our schools′ - Mary Briggs, Primary and Early Years PGCE Co-ordinator, Institute of Education, University of Warwick ′This is a highly practical resource that will be appreciated by classroom and specialist teachers alike. It will provide teachers new to the Math Recovery program with practical help and support to diagnose errors and misconceptions in early numeracy. Practicing Math Recovery Specialists will be thrilled with the addition of four new highly focused assessments and an elaboration of the Learning Framework in Number. Early Numeracy is admirably grounded in international research and well-established theory, characteristics that are much sought after in the current data driven educational environment. Like many others, I was drawn to Math Recovery after reading the first edition of Early Numeracy. This second edition is a treasure - it is exciting to consider the impact it will have on children and teachers, and to the growth of the Math Recovery program′ - Audrey Murray, Lead Teacher, Midwest Math Recovery Training Center, Minneapolis This text has been fully updated to include developments and refinements brought about by widespread international application of the assessment tools in the Mathematics Recovery Programme. The book will help practitioners to identify and provide detailed analyses of all children but especially those who are able and those who underachieve in early numeracy. It will enable teachers, learning support personnel, numeracy consultants and educational psychologists to advise colleagues and parents on children′s number knowledge and strategies for early numeracy. The Mathematics Recovery Programme has been successfully applied in Australia, the United Kingdom and Ireland, the United States and Canada, both in specialist interventions and classroom settings. The revised version shows how familiarisation with, and understanding of, the diagnostic assessment tools has allowed teachers to become more knowledgeable in understanding children′s difficulties and misconceptions, and more skilled and confident in planning programmes of intervention and monitoring the children′s progress. This new edition includes: - Integrated frameworks of useful tasks for assessing children′s number knowledge and strategies; - Four separate and revised diagnostic assessment interviews; - Assessments for addition and subtraction strategies, Base Ten Arithmetical strategies, Early Grouping strategies, and Advanced Grouping strategies in the four operations; - How the assessment process has impacted significantly on teachers′ professional development and contributed to the raising of standards in early numeracy.
Author: Susan J. Lamon
Publisher: Routledge
ISBN: 1135606781
Category : Education
Languages : en
Pages : 254
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Book Description
This popular text addresses the urgent need for curriculum materials that cross traditional boundaries to include many of the elements that are integrated in the teaching/learning enterprise: mathematics content, teacher understanding, student thinking, teaching methods, instructional activities, and assessment. The book pushes readers beyond the limits of their current understanding of rational numbers, challenging them to refine and explain their thinking--without falling back on rules and procedures they have relied on throughout their lives. Written in a conversational and easy to understand style, this is not a textbook as much as it is a resource book. An underlying assumption is that facilitating teacher understanding using the same questions and activities that may be used with children is one way to help teachers build the comfort and confidence they need to begin talking to children about complex ideas. Unlike a textbook that is used to study formal theory and then discarded when it comes to putting ideas into practice, the many problems and activities included to facilitate teacher learning are valuable resources for use in elementary and middle school classrooms. Changes in the second edition include: *even more student work incorporated in every chapter; *discussion of the connectivity between the topics addressed in the book and the elementary and middle school mathematics curricula; *an increased emphasis on measurement; *expansion of some topics, including number sense, percent, scale factors, similarity, and linear graphs; *clarification of the characteristics of ratio and proportions and how to use these to generate discussion with children; and *content-related interview questions for exploring children's thinking. This book is a valuable resource for researchers and curriculum developers in mathematics education, pre-service and in-service teachers of mathematics, those involved in the mathematical and pedagogical preparation of mathematics teachers, and graduate students in mathematics education. The methods and activities it includes have been tested with students in grades 3-8 and with pre-service and in-service teachers and other adults. This text is accompanied by MORE--a supplement that is not merely an answer key but a resource that includes in-depth discussions of all the problems in the text; develops and extends discussion of the issues, teaching problems, and other considerations raised in the chapters; and contains additional problems--with and without solutions--that instructors may find helpful for assessment purposes.
Author: Robert J Wright
Publisher: SAGE
ISBN: 1446203832
Category : Education
Languages : en
Pages : 225
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Book Description
`At last a book is written by teachers for teachers based on sound research that will generate enquiry based learning. It is essential for every classroom with lots of mathematical activities. These will purposefully engage children and allow for differentiation for those who require additional support to understand the number system and the more able children who require to be challenged. Mathematical standards in our schools will improve tremendously following these instructional activities' - Carole Cannon, Development Officer for Mathematics Recovery 'This book ‘Teaching Number in the Classroom with 4-8 year olds’ is an absolute "must have" for all educators involved in early number. Based on sound theoretical foundations, it offers a wealth of down-to-earth, tried and tested, effective approaches to teaching early number concepts and skills. It is a clearly a book written by teachers for teachers. Every single activity in the book is a nugget. Engaging with these activities will change your whole approach to teaching early number' - Noreen O’Loughlin, Associate Vice-President/Lecturer in Maths Education, Mary Immaculate College, University of Limerick, Ireland. 'The authors prove it is possible to write a teacher friendly/teacher useful mathematics book that connects theory and practice. This book may become the primary teacher's "Math Bible"' - Angela Giglio Andrews, Primary Intervention Specialist and Coordinator, and Assistant Professor of Mathematics Education, National Louis University 'Teaching Number in the Classroom translates years of research into a very understandable and comprehensive approach for teaching children how the number system is structured and how to think like a mathematician. For too many years there has been the perception that children who are struggling with mathematics don't know the basic facts. The reality is that these children lack number knowledge and skills. Teaching Number in the Classroom will guide the educational professional through the steps of understanding the development of "number sense", identifying the current levels of knowledge and providing instruction that helps children use the "framework of mathematics" to solve number problems. Teaching Number in the Classroom is a thinking skills approach to mathematics. Children are taught a variety of strategies for solving mathematical problems. The teacher using this book will be able to help all children develop a strong foundation of mathematical understanding' - Carol Meland, K-3rd Grade Principal for the School District of Milton Wisconsin, USA Teaching Number in the Classroom with 4-8 year olds is an absolute "must-have" for all educators involved in early number. Based on sound theoretical foundations, it offers a wealth of down-to-earth, tried and tested, effective approaches to teaching early number concepts and skills. It is a clearly a book written by teachers for teachers. Every single activity in the book is a nugget. Engaging with these activities will change your whole approach to teaching early number' - Noreen O'Loughlin, Associate Vice-President/Lecturer in Maths Education, Mary Immaculate College, University of Limerick Following the success of their previous bestselling titles, Early Numeracy and Teaching Number, the authors of this brand-new text now bring the principles and practice of their acclaimed Mathematics Recovery Programme to whole-class teaching. Central to the book is the concept of an inquiry-based approach to classroom instruction, and topics covered range from beginning number and early counting strategies to multi-digit addition and subtraction right through to multiplication and division. As world leaders in the field of Mathematics Recovery, this book's authors have drawn on their vast experience to create a user-friendly, practical guide focusing on classroom teaching. With its step-by-step approach, the text can be used as a training manual and course reference by teachers everywhere. Key features which make the book such a valuable tool include: - Real-life examples from classroom work - Teaching activities - Assessment tasks - Guidance on classroom organization and teaching specific topics - Activities for parents to do with children An invaluable resource for experienced mathematics recovery teachers, as well as all primary classroom teachers, from kindergarten level to Year three, this text will also be of use to classroom assistants and learning support personnel. Primary mathematics advisors, numeracy consultants and educational psychologists will also find it helpful.
