Teaching Mathematical Reasoning in Secondary School Classrooms
For too many students, mathematics consists of facts in a vacuum, to be memorized because the instructor says so, and to be forgotten when the course of study is completed. In this all-too-common scenario, young learners often miss the chance to develop s
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Karin Brodie
Teaching Mathematical Reasoning in Secondary School Classrooms With Contributions by Kurt Coetzee Lorraine Lauf Stephen Modau Nico Molefe Romulus O’Brien
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Karin Brodie School of Education University of the Witwatersrand Johannesburg South Africa [email protected]
ISBN 978-0-387-09741-1 e-ISBN 978-0-387-09742-8 DOI 10.1007/978-0-387-09742-8 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2009935695 © Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Foreword
The Road to Reasoning The teachers in this book share a worthy and courageous mission. They have all set out to provide children with one of the most important educational experiences it is possible to have – a form of mathematics teaching that is based upon sense making and discussion, rather than submission and silence. Mathematical “reasoning” is what mathematicians do – it involves forming and communicating a path between one idea or concept and the next. When students form these paths they come to enjoy mathematics, understand the reasons why ideas work, and develop a connected and powerful form of knowledge. When students do not engage in reasoning, they often do not know that there are paths between different ideas in mathematics and they come to believe, dangerously, that mathematics is a set of isolated facts and methods that need to be remembered. I have visited hundreds of classrooms across the world in which students have been required to work in silence on maths questions, never talking about the ideas or forming links and connections between ideas; most of these students come to dislike mathematics and drop the subject as soon as they can. Such students are not only being denied the opportunity to learn in the most helpful way, but they are denied access to real, living mathematics. The teachers in this book, through their work with Karin Brodie, the author, learned about the value of mathematical reasoning and set out to teach students to engage in this valuable act. This book shares their important journey and provides the world with new lenses for considering the teaching acts that were involved, as well as the challenges and obstacles that stood in their way. For whilst we know
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