From Rod Models to Line Segments
This chapter focuses on number line segment activities taken from one session of the year-long intervention investigating how 4th grade students build fraction ideas (Schmeelk, 2010). The videotapes of the session provide data for a narrative that has bee
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MATHEMATICS TEACHING AND LEARNING Volume 3 Series Editor: Yeping Li, Texas A&M University, College Station, USA International Advisory Board: Marja Van den Heuvel-Panhuizen, Utrecht University, The Netherlands Rongjin Huang, Middle TN State University, USA Eric J. Knuth, University of Wisconsin-Madison, USA Carolyn A. Maher, Rutgers – The State University of New Jersey, USA JeongSuk Pang, Korea National University of Education, South Korea Nathalie Sinclair, Simon Fraser University, Canada Kaye Stacey, University of Melbourne, Australia Günter Törner, Universität Duisburg-Essen, Germany Catherine P. Vistro-Yu, Ateneo de Manila University, The Philippines Anne Watson, University of Oxford, UK Mathematics Teaching and Learning is an international book series that aims to provide an important outlet for sharing the research, policy, and practice of mathematics education to promote the teaching and learning of mathematics at all school levels as well as teacher education around the world. The book series strives to address different aspects, forms, and stages in mathematics teaching and learning both in and out of classrooms, their interactions throughout the process of mathematics instruction and teacher education from various theoretical, historical, policy, psychological, socio-cultural, or cross-cultural perspectives. The series features books that are contributed by researchers, curriculum developers, teacher educators, and practitioners from different education systems.
For further information: https://www.sensepublishers.com/catalogs/bookseries/mathematics-teachingand-learning/
Children’s Reasoning While Building Fraction Ideas
Edited by Carolyn A. Maher Rutgers University, USA and Dina Yankelewitz Pearson Education, USA
A C.I.P. record for this book is available from the Library of Congress.
ISBN: 978-94-6351-006-6 (paperback) ISBN: 978-94-6351-007-3 (hardback) ISBN: 978-94-6351-008-0 (e-book)
Published by: Sense Publishers, P.O. Box 21858, 3001 AW Rotterdam, The Netherlands https://www.sensepublishers.com/
All chapters in this book have undergone peer review.
Printed on acid-free paper
All Rights Reserved © 2017 Sense Publishers No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.
TABLE OF CONTENTS
Forewordvii Judith H. Landis Acknowledgementsxi Introductionxiii Carolyn A. Maher 1. The Experiment Carolyn A. Maher and Dina Yankelewitz
1
2. Establishing a Mathematical Community Miriam Gerstein
13
3. A Problem with No Solution Dina Yankelewitz and Esther Winter
21
4. Designing a New Rod Dina Yankelewitz and Miriam Gerstein
29
5. Reasoning by Cases While Exploring Fractions as Numbers Esther Winter and Dina Yankelewitz
35
6. Developi
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