Concept Mapping in Mathematics Research into Practice
Concept Mapping in Mathematics: Research into Practice is the first comprehensive book on concept mapping in mathematics. It provides the reader with an understanding of how the meta-cognitive tool, namely, hierarchical concept maps, and the process of co
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Karoline Afamasaga-Fuata’i Editor
Concept Mapping in Mathematics Research into Practice
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Editor Karoline Afamasaga-Fuata’i University of New England Australia [email protected]
ISBN 978-0-387-89193-4 DOI 10.1007/978-0-387-89194-1
e-ISBN 978-0-387-89194-1
Library of Congress Control Number: 2008942431 c Springer Science+Business Media, LLC 2009 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.com
Foreword
It is a real pleasure to write a foreword to this first book that seeks to illustrate how concept mapping can be used to facilitate meaningful learning in mathematics. I believe the authors succeed in showing that mathematics can be more than the memorization of procedures to get answers to textbook types of problems. Through all of my elementary and high school studies of mathematics, I thought that what was required was to learn the procedures for getting answers, and I recall thinking that after doing 2 or 3 textbook problems of a given type, mathematics was rather tedious and relatively boring. By contrast, I saw the study of science as the search for understanding of fundamental concepts, such as the nature of matter, energy, and evolution. This I found to be exciting and I was always eager to seek deeper understanding of basic science concepts. It came as a somewhat shocking surprise to me when I was studying calculus at the University of Minnesota that there were fundamental mathematics concepts also, such as limit, slope, proportionality, etc. I recall feeling cheated that none of my teachers had helped me to gain a conceptual understanding of mathematics! Another fact that I pondered during my youth was that there were child prodigies who could do unusually difficult mathematics at ages 10 or 12, but there were very few such prodigies in sciences, literature, or history. With the invention of the concept mapping tool, it became clear to me why the latter was the case in some disciplines. To achieve relative mastery in a field of science, there were many concepts that had to be learned and understood. In contrast, in music or mathematics, if one gains an early understanding of a few dozen fundamental concepts, such as those discussed in the chapters of this book, you can move on to understanding of major domains of mathematics, and perhaps even do some creative mathematics. History has s
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