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Developing Fractions Knowledge

First Edition
By: Amy J. Hackenberg, Anderson Norton, Robert J. Wright

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.

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Product Details

Grade Level: PreK-12
ISBN: 9781412962209
Published By: Sage UK
Series: Math Recovery
Year: 2016
Page Count: 224
Publication date: October 18, 2016

Price: $52

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For Instructors

This book is not available as a review copy.

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(s)

Amy J. Hackenberg

Dr. Amy J. Hackenberg taught mathematics to middle and high school students for 9 years in L.A. and Chicago, prior to earning a Ph.D. in mathematics education from the University of Georgia. Amy is currently an associate professor of mathematics education at Indiana University-Bloomington. She conducts research on how middle school students construct fractions knowledge and algebraic reasoning and on how teachers can learn to develop productive student-teacher relationships. In her current project she is investigating how to differentiate instruction for diverse middle school students (see https://idream.sitehost.iu.edu/), studying her own teaching as well as working with practicing teachers. She is the proud co-author of the Math Recovery series book, Developing Fractions Knowledge.

Anderson Norton

Dr. Anderson Norton is a professor in the Department of Mathematics at Virginia Tech. His research focuses on building models of students’ mathematical development. This work has generated interdisciplinary collaborations with psychologists and neuroscientists. Prior to this volume, Norton served as chair of the steering committee for the North American Chapter of the International Group for the Psychology of Mathematics Education, co-editor on a pair of publications bridging psychology and mathematics education, and co-author of the Math Recovery series book, Developing Fractions Knowledge.

Robert J. Wright

Robert Wright earned a Bachelor’s degree in Chemistry from Kutztown University of Pennsylvania in 1966, and began teaching high school science. A few years later in 1969 he earned a Masters degree in school counseling from West Chester University and was employed as a public school counselor, first with high school students and later with middle school students. In 1974 he completed a doctorate (Ph.D.) in Educational Psychology with specializations in child & adolescent development and educational measurement from Temple University. As part of that degree he completed a clinical fellowship in rehabilitation counseling at Moss Hospital, part of the Albert Einstein Medical Center (Philadelphia). Following graduation he completed advanced studies in school psychology at Lehigh University. Professor Wright has taught counseling and supervised counseling interns and has also taught educational measurement, and educational statistics & research for graduate students in counseling. He is a member of the American Counseling Association, the American School Counselor Association, the American Psychological Association (Division 17, counseling psychology), the Association for Counselor Education and Supervision, and the American Educational Research Association. He is professionally licensed to practice in Pennsylvania. During his career Professor Wright chaired 114 doctoral dissertations, published and presented over 120 articles and paper presentations and has had four books published.

Table of Contents

Introduction

Professional Learning and Three Grand Organizers for Arithmetic Instruction

From Whole Numbers to Fractions

Assessing Stages of Units Coordination

Teaching Students at Stage 1: Fragmenting

Transitioning to Stage 2: Part–Whole Reasoning

Teaching Students at Stage 2: Measuring with Unit Fractions

Teaching Students at Stage 2: Reversible Reasoning

Teaching Students at Stage 3: Fractions as Numbers

Teaching Students at Stages 2 and 3: Equal Sharing of Multiple Items

Teaching Students at Stages 2 and 3: Multiplying Fractions

Teaching Students at Stages 2 and 3: Adding and Subtracting Fractions

Teaching Students at Stages 2 and 3: Dividing Fractions

From Fractions to Algebra

Reviews

With its beginnings in whole-number arithmetic understanding, Developing Fractions Knowledge is the most comprehensive look at fractions learning to date. It journeys with the practitioner and learner to view fractions as part-whole concepts, measures, and ultimately as numbers with meaning. The assessment and instructional tasks and practical connections to research and Math Recovery principles make it a must-have resource for educators to use again and again!

Carolyn Olijnek
US Math Recovery® Council

Developing Fractions Knowledge skilfully combines cutting-edge research with practical knowledge of the classroom to provide an essential resource for everyone interested in developing students’ understanding of fractions. I can’t wait to try some of the tasks and activities with students!

Dr Janette Bobis, Professor in Mathematics Education,
University of Sydney

All in, it was an enjoyable book (I have to admit thinking a book on fractions is not one I would choose) and I think would be a worthwhile investment for a department.

N. G. Macleod
Mathematics in Schools

The book includes many example assessment tasks and instructional activities to use with pupils who are learning about fractions for the first time, as well as pupils who are struggling and working to relearn concepts.
This book provides a comprehensive look at fraction knowledge and understanding. It is a great book for anyone teaching primary maths at any age, but would also be appropriate for a longer-term, on-going departmental professional development.

Matthew Reames
SATIPS - Support and Training in Prep, Primary and Senior Schools

Other Titles in: Mathematics | Staff Development & Professional Learning | Teacher Resources

Select Format:

For Instructors

This book is not available as a review copy.