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Developing Fractions Knowledge

Developing Fractions Knowledge Author Amy J. Hackenberg
ISBN-10 9781473987616
Release 2016-07-21
Pages 224
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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.



Developing Number Knowledge

Developing Number Knowledge Author Robert J Wright
ISBN-10 9781446253687
Release 2011-11-04
Pages 312
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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; " an accompanying CD with extensive instructional resources. 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.



Early Numeracy

Early Numeracy Author Robert J Wright
ISBN-10 9781446227145
Release 2006-01-05
Pages 224
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'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.



Teaching Number in the Classroom with 4 8 Year Olds

Teaching Number in the Classroom with 4 8 Year Olds Author Robert J Wright
ISBN-10 9781473908758
Release 2014-10-17
Pages 256
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Bring the principles and practice of the acclaimed Mathematics Recovery Programme to whole-class teaching! WHY INVEST IN THE NEW EDITION? In full-colour with a revised layout for clearer navigation More up-to-date tasks, activities and real classroom examples Learning trajectories for guiding instruction and tracking progress on key topics Extra resources online on the companion website Part of the best-selling Maths Recovery series, this practical, step-by-step guide to classroom instruction takes an inquiry-based approach to assess children's knowledge and build on this to develop a firm foundation of understanding and confidence in mathematics. Topics covered range from beginning number and early counting strategies to multi-digit addition and subtraction right through to multiplication and division. An invaluable resource for use on pre-service teacher training courses and for all primary classroom teachers and assistants, including experienced Mathematics Recovery instructors, as well as learning support personnel, primary mathematics advisors, numeracy consultants and educational psychologists. WHAT EXTRAS ARE ON THE COMPANION WEBSITE? Downloadable extra chapter resources like print-out grids, worksheets, cards and much more A Facilitator’s Guide that can be used either individually or in group study to help you get the most out of the material In-class video demonstrations to clearly show how the instructional activities in the book are used in the classroom Webinar discussing the key points in the book and how it supports your teaching Visit the companion website at https://study.sagepub.com/wrighttnc "Research informs practice in this easy to access resource. Each chapter gives educators practical, bite-sized assessments, linked to a host of activities that helps them target teaching and develop the firm foundations which are so vital for confident and competent mathematicians." - Jill Piotrowski, Numeracy Consultant, Wigan Local Authority, UK "'The Classroom Instructional Framework in Early Number is research-based and provides a roadmap of not only the what, but the when and the how to teach all aspects of early number." - Vicki Nally, Mathematics Consultant at Catholic Education Office, Melbourne "The structured approach offers a wealth of rich and easily implemented classroom-based activities that work - thousands of teachers in Ireland attest to this!" - Noreen O'Loughlin, Director Maths Recovery and Maths Education Lecturer, Mary Immaculate College, Limerick, Ireland



The Learning Framework in Number

The Learning Framework in Number Author Robert J Wright
ISBN-10 9781526415424
Release 2018-03-31
Pages 184
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This book is borne out of a collaborative research project (2004-8) between Math Recovery and CEM (Catholic Education Melbourne) funded by the Australian Research Council focusing on intervention in the number learning of low-attaining students in the first five years of school. This has involved developing new pedagogical tools (PTs) for assessment, instruction and intervention including a coherent, research-based framework for understanding the key aspects of students’ developing number knowledge. It also offers guidance on innovative video-based assessment and an overview of principles of intervention instruction. This book will be a useful guide for all primary and elementary school classroom teachers and assistants, and specialist teachers, including experienced Mathematics Recovery instructors. It will also be of significant interest to teacher educators and researchers.



Teaching Number

Teaching Number Author Robert J Wright
ISBN-10 1446237575
Release 2006-08-30
Pages 264
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The book lets teachers identify where their students are in terms of number skills, and sets out a strategy for developing their knowledge. The authors show how to advance children's learning across five stages of early arithmetical learning - emergent, perceptual, figurative, initial number, and facile number. This provides for increasingly sophisticated number strategies across addition, subtraction, multiplication and division, as well as developing children's number word and numeral knowledge, and their ability to structure number and have grouping strategies. The approach used nine guiding principles for teaching. Each chapter has clearly defined teaching procedures which show how to take the children onto the next more sophisticated stage. The teaching procedures are organized into key teaching topics, and each includes: o a clearly defined purpose o detailed instructions, activities, learning tasks and reinforcing games o lists of responses which children may make o application in whole class, small group and individualised settings o a link to the Learning Framework in Number (see Early Numeracy- second edition, 2005) o how the guiding principles for teaching can be used to allow teachers to evaluate and reflect upon their practice Primary practitioners in Australia, the United States, the United Kingdom and Canada have tested the teaching procedures which can be used in conjunction with each country's numeracy strategy. Primary teachers, especially of the early years, mathematics co-ordinators, heads of school, mathematics advisers, special educationalists, learning support personnel, teacher assistants, lecturers in initial teacher training and educational psychologists will all find this book invaluable.



Adding It Up

Adding It Up Author National Research Council
ISBN-10 0309132843
Release 2001-11-13
Pages 480
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Adding It Up explores how students in pre-K through 8th grade learn mathematics and recommends how teaching, curricula, and teacher education should change to improve mathematics learning during these critical years. The committee identifies five interdependent components of mathematical proficiency and describes how students develop this proficiency. With examples and illustrations, the book presents a portrait of mathematics learning: Research findings on what children know about numbers by the time they arrive in pre-K and the implications for mathematics instruction. Details on the processes by which students acquire mathematical proficiency with whole numbers, rational numbers, and integers, as well as beginning algebra, geometry, measurement, and probability and statistics. The committee discusses what is known from research about teaching for mathematics proficiency, focusing on the interactions between teachers and students around educational materials and how teachers develop proficiency in teaching mathematics.



Teaching Numeracy

Teaching Numeracy Author Margie Pearse
ISBN-10 9781452238852
Release 2011-03-23
Pages 240
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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.



A Focus on Fractions

A Focus on Fractions Author Marjorie M. Petit
ISBN-10 9781317597308
Release 2015-07-24
Pages 194
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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.



Young mathematicians at work

Young mathematicians at work Author Catherine Twomey Fosnot
ISBN-10 032500353X
Release 2001-04-09
Pages 193
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The first in a three-volume set, Young Mathematicians at Work focuses on young children between the ages of four and eight as they construct a deep understanding of number and the operations of addition and subtraction.



Knowing and Teaching Elementary Mathematics

Knowing and Teaching Elementary Mathematics Author Liping Ma
ISBN-10 9781135149499
Release 2010-03-26
Pages 232
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Studies of teachers in the U.S. often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education. Knowing and Teaching Elementary Mathematics describes the nature and development of the knowledge that elementary teachers need to become accomplished mathematics teachers, and suggests why such knowledge seems more common in China than in the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts. The anniversary edition of this bestselling volume includes the original studies that compare U.S and Chinese elementary school teachers’ mathematical understanding and offers a powerful framework for grasping the mathematical content necessary to understand and develop the thinking of school children. Highlighting notable changes in the field and the author’s work, this new edition includes an updated preface, introduction, and key journal articles that frame and contextualize this seminal work.



Becoming Batman

Becoming Batman Author E. Paul Zehr
ISBN-10 9780801896217
Release 2009-11-17
Pages 320
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A fun foray of escapism grounded in sound science, Becoming Batman provides the background for attaining the realizable—though extreme—level of human performance that would allow you to be a superhero.



How Students Learn

How Students Learn Author Committee on How People Learn: A Targeted Report for Teachers
ISBN-10 9780309089500
Release 2004-12-28
Pages 264
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How Students Learn: Science in the Classroom builds on the discoveries detailed in the best-selling How People Learn. Now these findings are presented in a way that teachers can use immediately, to revitalize their work in the classroom for even greater effectiveness. Organized for utility, the book explores how the principles of learning can be applied in science at three levels: elementary, middle, and high school. Leading educators explain in detail how they developed successful curricula and teaching approaches, presenting strategies that serve as models for curriculum development and classroom instruction. Their recounting of personal teaching experiences lends strength and warmth to this volume. This book discusses how to build straightforward science experiments into true understanding of scientific principles. It also features illustrated suggestions for classroom activities.



Fraction Action

Fraction Action Author Loreen Leedy
ISBN-10 0613972074
Release 1996-03-01
Pages
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Miss Prime and her animal students explore fractions by finding many examples in the world around them.



Gender Differences in Mathematics

Gender Differences in Mathematics Author Ann M. Gallagher
ISBN-10 1139443755
Release 2004-12-27
Pages
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Females consistently score lower than males on standardized tests of mathematics - yet no such differences exist in the classroom. These differences are not trivial, nor are they insignificant. Test scores help determine entrance to college and graduate school and therefore, by extension, a person's job and future success. If females receive lower test scores then they also receive fewer opportunities. Why does this discrepancy exist? This book presents a series of papers that address these issues by integrating the latest research findings and theories. Authors such as Diane Halpern, Jacquelynne Eccles, Beth Casey, Ronald Nuttal, James Byrnes, and Frank Pajares tackle these questions from a variety of perspectives. Many different branches of psychology are represented, including cognitive, social, personality/self-oriented, and psychobiological. The editors then present an integrative chapter that discusses the ideas presented and other areas that the field should explore.



Mindfulness and the 12 Steps

Mindfulness and the 12 Steps Author ThŽrse Jacobs-Stewart
ISBN-10 1592859879
Release 2010-05-20
Pages 208
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With the artistry of a memoirist, Thérèse Jacobs-Stewart draws on her personal story and an impressive range of knowledge in psychology, spirituality, and the Twelve Steps to show us the way out of the morass of pain and confusion that addiction creates. Mindfulness and the 12 Steps is moving and inspiring, full of practical guidance. --KEVIN GRIFFIN, author of One Breath at a Time: Buddhism and the Twelve Steps and A Burning Desire: Dharma God and the Path of Recovery FOR THOSE OF US IN RECOVERY, Mindfulness and the 12 Steps offers a fresh approach to developing our own spiritual path through the Buddhist practice of mindfulness, or bringing one's awareness to focus on the present moment. We can revisit each of the Twelve Steps, exploring the interplay of ideas between mindfulness and Twelve Step traditions--from the idea of living "one day at a time" to the emphasis on prayer and meditation--and learn to incorporate mindfulness into our path toward lifelong sobriety. Through reflections, questions for inquiry, and stories from Buddhist teachers and others who practice mindfulness in recovery, Mindfulness and the 12 Steps will help us awaken new thinking and insights into what it means to live fully--body, mind, and spirit--in the here and now.



Visible Learning for Mathematics Grades K 12

Visible Learning for Mathematics  Grades K 12 Author John Hattie
ISBN-10 9781506362977
Release 2016-09-16
Pages 304
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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.