The Mathematics Teacher in the Digital

Mathematics Education in the Digital Era Alison Clark-Wilson Ornella Robutti Nathalie Sinclair Editors The Mathematics Teacher in the Digital Era An International Perspective on Technology Focused Professional Development The Mathematics Teacher in the Digital Era MATHEMATICS EDUCATION IN THE DIGITAL ERA Volume 2 Series Editors: Dragana Martinovic, University of Windsor, ON, Canada Viktor Freiman, Université de Moncton, NB, Canada Editorial Board: Marcelo Borba, State University of São Paulo, São Paulo, Brazil Rosa Maria Bottino, CNR – Istituto Tecnologie Didattiche, Genoa, Italy Paul Drijvers, Utrecht University, The Netherlands Celia Hoyles, University of London, London, UK Zekeriya Karadag, Bayburt University, Turkey Stephen Lerman, London South Bank University, London, UK Richard Lesh, Indiana University, Bloomington, USA Allen Leung, Hong Kong Baptist University, Hong Kong John Mason, Open University, UK John Olive, The University of Georgia, Athens, USA Sergey Pozdnyakov, Saint-Petersburg State Electro Technical University, Saint-Petersburg, Russia Ornella Robutti, Università di Torino, Turin, Italy Anna Sfard, Michigan State University, USA & University of Haifa, Haifa, Israel Bharath Sriraman, The University of Montana, Missoula, USA Anne Watson, University of Oxford, Oxford, UK For further volumes: http://www.springer.com/series/10170 Alison Clark-Wilson • Ornella Robutti Nathalie Sinclair Editors The Mathematics Teacher in the Digital Era An International Perspective on Technology Focused Professional Development Editors Alison Clark-Wilson Ornella Robutti London Knowledge Lab Dipartimento di Matematica Institute of Education Università di Torino University of London Turin, Italy London , UK Nathalie Sinclair Faculty of Education Simon Fraser University Burnaby, BC, Canada Additional material can be downloaded from http://extras.springer.com ISSN 2211-8136 ISSN 2211-8144 (electronic) ISBN 978-94-007-4637-4 ISBN 978-94-007-4638-1 (eBook) DOI 10.1007/978-94-007-4638-1 Springer Dordrecht Heidelberg New York London Library of Congress Control Number: 2013955236 © Springer Science+Business Media Dordrecht 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifi cally the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfi lms 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifi cally for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specifi c statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) Foreword Integrated Circuits David Pimm It is 1982. I am 28 years old and two-and-a-half years into paid work as a neophyte researcher in mathematics education in the UK. I sit in a secondary mathematics classroom, armed with a coding sheet, watching a lesson based on a piece of software on a Research Machines 380Z, the whole class attending to a small monitor. My aim is to see what difference the computer’s presence makes to the lesson, particularly to the teacher’s practice. I learn many things over the course of a term, including but not limited to: • How restrictive coding sheets can be, how they serve to determine what can actually be documented as occurring; • How the need to write a code every 10 s (an early form of digital sampling) fragments a lesson and, more subtly, how coding is not a real-time activity – for instance, in order to ascertain whether a teacher question has been asked is not simply a matter of the grammatical form of an utterance, it involves waiting to see how it is taken by the students; • How looking for altered patterns of interaction requires a strong grounding in prior norms; and, • How hard it can be to see the really new. Reading across the chapters in this volume brought back these earlier memories, not least because of the intertwined discussions of classroom structures and teacher ‘orchestrations’, as well as both the regularities and distinctions among them that occur in different settings. A staggering amount has changed in the past 30 years, with regard to the richness, range and sophistication of the mathematical devices and their encodings that are available for school use in the teaching and learning of mathematics. How far we have come from ‘Computer-Aided Learning (CAL)’ as it was then known. What is much more complicated to address, and problematic in a D. Pimm Simon Fraser University v vi Foreword variety of senses, is the scope and depth of actual use of this plethora of electronic possibilities in actual school classrooms and other learning contexts. In a chapter of a book for teachers on ICT (information and communication technology) and mathematics, Sinclair and Jackiw (2005) attempt to look to the future: in a prognosticating vein, they identify three waves in technology-for- mathematics- education. The fi rst focuses on the individual student (the site of the ‘L’ in CAL), the second develops the context of classroom learning (including the teacher and the curriculum), and the third looks outward to the world (wide web) . Issues they explore include the relation between curricular specifi city and mathematical expressivity with any particular instance of technology-and-software. I mention their piece here in part as an introduction to my thinking across the various chapters of this collection, given the latter’s more or less common focus on and concern with the teacher in a mathematics classroom and the use of pertinent digital technology. In Sinclair and Jackiw’s terms, then, this book is primarily second wave. But also in terms of research on technologised mathematics classrooms, this feels to me a second-wave collection. Many early studies in this area focused on what teachers did with the technology (for more on the broader study mentioned above, see, for example, Ridgway et al. 1984) and were largely descriptive and untheorised (cer- tainly the one I was involved in was: in an important sense the coding scheme both summarised and operationalised the extent of theorisation of the act of mathematics teaching – and it was not technology specifi c). “What is it like teaching mathematics with technology present?” such studies asked. We and many others learnt how hard it is (but not much about why). Others also learnt, among other things, about the potential for the ‘worksheetifi cation’ of expressive technology, as well as the ten- sion between programming and small program use [1]. But even given such commonality, this book is still quite plural. There is no one single focus, neither in terms of object of attention, phenomenon of interest, nor method of examination. Actual classrooms are looked at, often; teachers (present in various incarnations, novice and expert, experienced with technology or not, etc.) are considerably more in focus than students (computer-aided teaching?) and are repre- sented by their views via questionnaires and interviews and by their reported classroom actions. We are told about what is and also about what might be. Mathematics is the presumed common concern of all authors, but this book is only cursorily about technology’s effect on or interaction with mathematics. Technological devices are widespread across the chapters, but even they are not in continuous view. In terms of foreground, I fi nd a marked concern with exploring the complexity of being the teacher in a technologised classroom, as well as beginning to address the intricate ‘teacher education’ question about what manner and nature of support to offer teachers in their work (whether beginning or ongoing) in such settings. Some chapters report on more narrowly delineated research studies (some attempt to doc- ument the state of play while others opt for case studies, then, both in terms of the closeness of focus to a very few teachers and necessarily I feel in terms of examining specifi c forms of technology). Others still attempt to propose or harness a far more theorised frame and then look at some teaching settings through it. And some do both and some look across a range of studies. In terms of method and manner of exploration, there is again appreciable diversity. At times, for me, I felt a sense of Foreword vii struggle to fi nd a suitably helpful grip size that is suffi ciently specifi c to offer traction on the particular while rising suffi ciently above it to improve the view before disappearing into the clouds. Returning briefl y to my opening personal vignette, we are far, far along the road from that naïve encounter. Mathematics education has produced much more informed and sophisticated classroom watchers. But despite this enhanced attention, there are still some fundamental and signifi cant questions about operating as a teacher in a technologised classroom that do not seem to have gone away.

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