Reason to Believe in Mathematics
This chapter provides a theoretical discussion of how we understand mathematical knowledge. The theory presents rationality and belief as mutually formative dimensions of mathematics, where each term is more politically and socially embedded than sometime
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A Contemporary Theory of Mathematics Education Research
A Contemporary Theory of Mathematics Education Research
Tony Brown
A Contemporary Theory of Mathematics Education Research
Tony Brown Manchester Metropolitan University Manchester, UK
ISBN 978-3-030-55099-8 ISBN 978-3-030-55100-1 (eBook) https://doi.org/10.1007/978-3-030-55100-1 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are solely and exclusively licensed 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, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
This book addresses the domain, purpose and functioning of research in mathematics education. What is mathematics teaching? How do we improve mathematics teaching? Why do we want to improve mathematics teaching? What do we understand by improvement? Mathematics education research addresses many such questions. And although research and the scientific theories it produces may never reveal the truth, theories have proved very useful in guiding us around an infinite landscape, even if ultimately each scientific model or theory reveals the limits of its own functionality, style or endurance. But more generally, any story we tell about what mathematics is, or what a learner is, or what we are trying to do, will eventually become out of kilter with the times. New demands on “people” and new demands on “mathematics” change what both of them are and how they respond to each other. Research has as much to do with working out where we could go as it is with assessing where we are now. The current state of affairs can be depicted in many ways, where alternative mappings of our pasts and presents open alternative trajectories into the future. This provokes a more general
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