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Developing Fractions Knowledge
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Developing Fractions Knowledge



© 2016 | 224 pages | SAGE Publications Ltd
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.
 
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

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

I have been waiting with baited breath for this book to be published! It does not disappoint.

Chapters 1 and 2 give a fantastic step by step overview to the development in understanding of fractions which children will go through.

Really like the layout and that each chapter is dedicated to a stage in development as well as having assessment tasks and activities included in each.

We have already started our course but I hope to ensure this is recommended for next year. I will be suggesting this book to my students and will ensure an e-copy is in our library at the very least.

I hope this book will be instrumental in educating our students in how to ensure conceptual fractional development as most other texts simply show students how to teach using pre-partitioned shapes.

Miss Linda Lapere
School of Education, Social Work &, Dundee University
August 29, 2016

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