Enabling Students in Mathematics A Three-Dimensional Perspective for
This book addresses the cognitive, social, and psychological dimensions that shape students’ mathematics experience to help students become more capable, cooperative, and confident in the process of engaging mathematics. In these ways they can have a
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Marshall Gordon
Enabling Students in Mathematics A Three-Dimensional Perspective for Teaching Mathematics in Grades 6–12
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Marshall Gordon The Park School Baltimore, Maryland, USA
ISBN 978-3-319-25404-3 ISBN 978-3-319-25406-7 (eBook) DOI 10.1007/978-3-319-25406-7 Library of Congress Control Number: 2015953839 Springer © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com)
To my wife, Paddy, and our children, Ian, Sara, and Eva, who inspire me every day.
Acknowledgments
I wish to thank my colleagues at the Park School of Baltimore who I had the pleasure of working with in writing the first iteration of the Habits of Mind mathematics curriculum—Tony Asdourian, Arnaldo Cohen, Mimi Cukier, Rina Foygel, Tim Howell, Bill Tabrisky, and Anand Thakker. Their dedication, creativity, and thoughtfulness made it happen. And also, F. Parvin Sharpless whose creation of the summer endowment program for faculty made the Habits of Mind curriculum effort possible. I also want to thank Bill Tabrisky for the graphics work that is included in this book. And Stephen I. Brown who read the manuscript and understood what it needed for its more complete expression. I wish to also acknowledge folks at Springer Publishers, Rishi Pal Gupta who shepherded the manuscript to its publication, and Melissa James, Vivian Roberson, and Bill Tucker for getting things going. August 2015
Marshall Gordon
Overview
Teaching is an extraordinary adventure. Looking at the front covers of physics books where there is an illustration of subatomic particles flying in this direction and that as a result of heightened interaction, it is evident how complicated things are beneath the surface. Mathematics teachers know all about that. Exploding into and out of existence in our students’ minds are concerns related and not, qu
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