Developing Fractions Knowledge
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Developing Fractions Knowledge
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Author : Amy J. Hackenberg
language : en
Publisher: SAGE
Release Date : 2016-07-21
Developing Fractions Knowledge written by Amy J. Hackenberg and has been published by SAGE this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-21 with Education categories.
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 Fractions Knowledge
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Author : Amy J. Hackenberg
language : en
Publisher: SAGE
Release Date : 2016-07-21
Developing Fractions Knowledge written by Amy J. Hackenberg and has been published by SAGE this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-21 with Education categories.
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.
Children S Fractional Knowledge
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Author : Leslie P. Steffe
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-02
Children S Fractional Knowledge written by Leslie P. Steffe and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-02 with Education categories.
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.
The Cambridge Handbook Of Cognition And Education
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Author : John Dunlosky
language : en
Publisher: Cambridge University Press
Release Date : 2019-02-07
The Cambridge Handbook Of Cognition And Education written by John Dunlosky and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-07 with Psychology categories.
This Handbook reviews a wealth of research in cognitive and educational psychology that investigates how to enhance learning and instruction to aid students struggling to learn and to advise teachers on how best to support student learning. The Handbook includes features that inform readers about how to improve instruction and student achievement based on scientific evidence across different domains, including science, mathematics, reading and writing. Each chapter supplies a description of the learning goal, a balanced presentation of the current evidence about the efficacy of various approaches to obtaining that learning goal, and a discussion of important future directions for research in this area. It is the ideal resource for researchers continuing their study of this field or for those only now beginning to explore how to improve student achievement.
Developing Mathematical Reasoning
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Author : Pamela Weber Harris
language : en
Publisher: Corwin Press
Release Date : 2025-02-13
Developing Mathematical Reasoning written by Pamela Weber Harris and has been published by Corwin Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-13 with Education categories.
Math is not rote-memorizable. Math is not random-guessable. Math is figure-out-able. Author Pam Harris argues that teaching real math—math that is free of distortions–will reach more students more effectively and result in deeper understanding and longer retention. This book is about teaching undistorted math using the kinds of mental reasoning that mathematicians do. Memorization tricks and algorithms meant to make math "easier" are full of traps that sacrifice long-term student growth for short-lived gains. Students and teachers alike have been led to believe that they’ve learned more and more math, but in reality their brains never get any stronger. Using these tricks may make facts easier to memorize in isolation, but that very disconnect distorts the reality of math. The mountain of trivia piles up until students hit a breaking point. Humanity′s most powerful system of understanding, organizing, and making an impact on the world becomes a soul-draining exercise in confusion, chaos, and lost opportunities. Developing Mathematical Reasoning: Avoiding the Trap of Algorithms emphasizes the importance of teaching students increasingly sophisticated mathematical reasoning and understanding underlying concepts rather than relying on a set rule for solving problems. This book illuminates a hierarchy of mathematical reasoning to help teachers guide students through various domains of math development, from basic counting and adding to more complex proportional and functional reasoning. Everyone is capable of understanding and doing real math. This book: Highlights the important mathematical relationships, strategies, and models for students to develop Offers personal stories, reflection sections, and extensive practical exercises for easy implementation Includes real math—a lot of it—to provide teachers with examples they can put to use in their classrooms immediately This book is a valuable resource for educators looking to reach more students by building a strong foundation of mathematical thinking in their students. By addressing common misconceptions about math and providing practical strategies for teaching real math, this book shows that everyone can use the mathematical relationships they already know to reason about new relationships. In other words, everyone can math.
Strategies For Teaching Fractions
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Author : David B. Spangler
language : en
Publisher: Corwin Press
Release Date : 2011-08-17
Strategies For Teaching Fractions written by David B. Spangler and has been published by Corwin Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-17 with Education categories.
"Analyzing student work for error patterns (such as on a diagnostic test) and then providing timely, specific, and meaningful intervention will decrease the probability that the errors will be repeated in the future. Taking into account academic research on how students learn, Spangler provides a practical intervention model and specific hands-on materials for teachers to use when working with the many students who struggle with fractions. The step-by-step intervention strategies illustrated in this book will result in improved student performance and improved student dispositions towards mathematics. It will contain the following elements: reproducibles for fully functional diagnostic tests practice pages for exercises keyed to the diagnostic tests and error patterns, and pages to practice alternative algorithms and estimation teacher resources for hands-on activities, game sheets and pieces, and more"--Provided by publisher.
The Learning Framework In Number
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Author : Robert J Wright
language : en
Publisher: SAGE
Release Date : 2018-03-12
The Learning Framework In Number written by Robert J Wright and has been published by SAGE this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-12 with Education categories.
This latest book in the bestselling Mathematics Recovery® series gives mathematics educators a complete research-based framework for assessment, instruction and intervention in whole number arithmetic across grades K to 5. The integrated set of classroom tools includes: Nine carefully designed schedules of assessment tasks Nine models of learning progressions Ten teaching maps that guide the instructional progressions across key topics The book offers guidance on innovative video-based assessment, and an overview of principles of intervention instruction, giving you an integrated resource for supporting the children you teach. The Learning Framework in Number will be a useful guide for all primary and elementary school classroom teachers and assistants, and specialist teachers, including experienced Mathematics Recovery® instructors. The book will also be of significant interest to teacher educators and researchers.
Development Of Mathematical Cognition
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Author : Daniel B. Berch
language : en
Publisher: Academic Press
Release Date : 2015-10-03
Development Of Mathematical Cognition written by Daniel B. Berch and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-03 with Psychology categories.
Development of Mathematical Cognition: Neural Substrates and Genetic Influences reviews advances in extant imaging modalities and the application of brain stimulation techniques for improving mathematical learning. It goes on to explore the role genetics and environmental influences have in the development of math abilities and disabilities. Focusing on the neural substrates and genetic factors associated with both the typical and atypical development of mathematical thinking and learning, this second volume in the Mathematical Cognition and Learning series integrates the latest in innovative measures and methodological advances from the top researchers in the field. - Provides details about new progress made in the study of neural correlates of numerical and arithmetic cognition - Addresses recent work in quantitative and molecular genetics - Works to improve instruction in numerical, arithmetical, and algebraic thinking and learning - Informs policy to help increase the level of mathematical proficiency among the general public
The Development Of Children S Fraction Thinking In A First Grade Classroom
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Author : Susan Carol Baker
language : en
Publisher:
Release Date : 1994
The Development Of Children S Fraction Thinking In A First Grade Classroom written by Susan Carol Baker and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.
Early Fraction Learning
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Author : Robert P. Hunting
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Early Fraction Learning written by Robert P. Hunting and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Education categories.
Early Fraction learning is centrally of interest to students and researchersin mathematics education, tackling as it does one of that discipline's most vexing problems: why are fractions so difficult to learn and to teach?