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The starting point for this study stems from an interest in how gestures contribute to learning processes in social interaction. By investigating this issue, I aim to provide a theoretical basis from which can be hypothesized on the potential of gestures
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Christina M. Krause
The Mathematics in Our Hands How Gestures Contribute to Constructing Mathematical Knowledge With a foreword by Angelika Bikner-Ahsbahs and Ferdinando Arzarello
Christina M. Krause University of Duisburg-Essen Germany Dissertation University of Bremen, 2015 Date of thesis defense: April 21st, 2015 Assessors: Prof. Dr. Angelika Bikner-Ahsbahs (Doctoral supervisor) (University of Bremen, Germany) Prof. Dr. Ferdinando Arzarello (University of Turin, Italy)
ISBN 978-3-658-11947-8 ISBN 978-3-658-11948-5 (eBook) DOI 10.1007/978-3-658-11948-5 Library of Congress Control Number: 2015956041 Springer Spektrum © Springer Fachmedien Wiesbaden 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 Spektrum is a brand of Springer Fachmedien Wiesbaden Springer Fachmedien Wiesbaden is part of Springer Science+Business Media (www.springer.com)
Foreword “anyway the exponential function would ,wouldn't go up again' because one but it would flatten further that would than haven u-h ,as its asymptote” is Tim’s commentary as he watches the computer screen in front of him. On the computer screen we find a coordinate system. Starting from the first quadrant, a parabola is swept out, crossing the y-axis in the curve’s lowest point. However, Tim does not directly refer to the parabola but to the graph of an exponential function, that is not visible on the screen. In his commentary, Tim wants to say that the visual piece of the curve on the screen cannot represent an exponential function, “… because one but it would flatten further that would than haven u-h ,as its asymptote”. The last part of his utterance is accompanied by a gesture: directly in front of the computer screen, Tim’s finger draws the graph of an exponential function in the air, passing from the right top downwards, a bit up again before going to the left and approximating the x-axis. Such situations often happen in mathematical learning situations. Even when unobserved, studen
