Primary Mathematics. Capitalising on ICT for today and tomorrow

Transcription

1 Primary Mathematics Capitalising on ICT for today and tomorrow Primary Mathematics provides a comprehensive introduction to teaching and learning mathematics in today s classrooms. Drawing links to the Australian Curriculum, this book covers the core learning areas of measurement, space and geometry, early number concepts, data and statistics, chance and probability, and patterns and algebra. At the centre of this book is the belief that information and communication technology (ICT) can be a powerful tool for enhancing student learning. Although many classrooms have been resourced with computers, interactive whiteboards and mobile technology, teachers need to be able to transform these technological tools into meaningful teaching and learning experiences. This book explores the ways in which technology can be integrated into the mathematics classroom and provides teachers with detailed activities and examples to cater for the mathematical needs of all learners. Each chapter features: definitions of key terms classroom activities pause and reflect points classroom snapshots suggestions for further reading where appropriate. The book also explores issues around student diversity, assessment for, of and as learning, and teaching in rural and remote areas. Grounded in evidence and richly illustrated with examples of student work, online mathematical resources and key concepts, Primary Mathematics is an indispensable resource for preand in-service teachers alike. Penelope (Pep) Serow is a Senior Lecturer in Mathematics Education at the University of New England. She was granted the University of New England Vice Chancellor s Teaching Excellence Award in Rosemary Callingham is Associate Professor and a mathematics educator at the University of Tasmania. She contributed to the success of the University of Tasmania Mathematics Education team that won the Australian Award for Excellence in Teaching in Tracey Muir is a Senior Lecturer in Mathematics Education at the University of Tasmania. She is the recipient of many teaching merit certificates and Vice Chancellor s Awards for Teaching Excellence and Community Engagement, and was part of the University of Tasmania Mathematics Education team that won the Australian Award for Excellence in Teaching in 2012.

2

3 Primary Mathematics Capitalising on ICT for today and tomorrow Penelope Serow Rosemary Callingham Tracey Muir

4 477 Williamstown Road, Port Melbourne, VIC 3207, Australia Published in the United States of America by Cambridge University Press, New York Cambridge University Press is part of the University of Cambridge. It furthers the University s mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence. Information on this title: / Cambridge University Press 2014 This publication is copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2014 Cover designed by Tanya de Silva-McKay Typeset by Newgen Publishing and Data Services Printed in Singapore by C.O.S. Printers Pte Ltd A catalogue record for this publication is available from the British Library A Cataloguing-in-Publication entry is available from the catalogue of the National Library of Australia at ISBN Paperback Reproduction and communication for educational purposes The Australian Copyright Act 1968 (the Act) allows a maximum of one chapter or 10% of the pages of this work, whichever is the greater, to be reproduced and/or communicated by any educational institution for its educational purposes provided that the educational institution (or the body that administers it) has given a remuneration notice to Copyright Agency Limited (CAL) under the Act. For details of the CAL licence for educational institutions contact: Copyright Agency Limited Level 15, 233 Castlereagh Street Sydney NSW 2000 Telephone: (02) Facsimile: (02) info@copyright.com.au Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.

5 Contents CHAPTER 1 TEACHING MATHEMATICS TODAY WITH TOMORROW IN MIND IN THE PRIMARY SETTING 1 The TPACK framework 4 Summary of chapters 7 How to use this book 10 Further reading 10 CHAPTER 2 EXPLORING MEASUREMENT 11 Learning sequence for measurement 12 Measurement topics 14 Estimation 23 Measuring with non-standard units 26 Measurement misconceptions and difficulties 28 Extending measurement concepts into older grades 33 Reflection 39 CHAPTER 3 EXPLORING GEOMETRY 40 Geometrical concepts 41 Theoretical framework 42 Geometry in the primary classroom 48 The van Hiele teaching phases 65 Taking geometry outside the classroom 69 Reflection 72 Further reading 72 CHAPTER 4 EXPLORING EARLY NUMBER CONCEPTS 73 Early number concepts 75 Number frameworks 76 Linking with curriculum documents 77 Early number activities and strategies 79 Extending counting beyond Linking numbers with quantities 83 Subitising 83 Early operations with number 89 Mental computation strategies 90 Drill and practice 92 Alternatives to traditional drill and practice 93 Further reading 100 v

6 Contents CHAPTER 5 EXPLORING COMPUTATION AND PROPORTIONAL REASONING 101 Operations with whole numbers 103 A word about calculators 111 Drill and practice 112 Moving to proportional reasoning 114 Proportional reasoning 124 Reflection 124 Further reading 124 CHAPTER 6 EXPLORING DATA AND STATISTICS 127 Asking questions (problem) 130 Collecting and recording data (plan, data) 131 Analysing and representing data (analyse) 135 Telling a story from the data (conclusions) 142 Using data in social contexts 144 Reflection 145 CHAPTER 7 EXPLORING CHANCE AND PROBABILITY 146 Early primary years 150 Middle primary years 152 Upper primary years 155 Representing probability 161 Reflection 163 Further reading 164 CHAPTER 8 EXPLORING PATTERNS AND ALGEBRA 165 Linking with the Australian Curriculum: Mathematics 166 Pattern and structure 167 Developing an understanding of relationships 173 Equals and equivalence 176 Generalisation in upper primary 183 Reflection 191 CHAPTER 9 CAPITALISING ON ASSESSMENT FOR, OF AND AS LEARNING 192 Assessment 193 Assessment for learning 194 Quality of student responses 198 National testing 205 vi

7 Contents Online assessment item banks 212 Assessment as learning 215 Reflection 215 Further reading 216 CHAPTER 10 CHAPTER 11 CHAPTER 12 CHAPTER 13 CAPITALISING ON ICT IN THE MATHEMATICS CLASSROOM 217 Supporting students learning in technology 220 Considering teacher knowledge 221 Developing an understanding of place value 222 Other suggestions for capitalising on ICT in the classroom 226 Capitalising on ICT through an integrated unit 232 Pedagogical commentary 239 Reflection 242 Further reading 242 DIVERSITY IN THE PRIMARY MATHEMATICS CLASSROOM 243 Teachers beliefs 246 Children with physical disabilities 247 Children with intellectual disabilities 252 Children with social, emotional and behavioural disabilities 255 Children for whom English is an additional language or dialect 257 Children who are gifted and talented 258 Reflection 259 Further reading 260 SURVIVING AS AN OUT OF FIELD TEACHER OF MATHEMATICS 261 Secondary lesson structures 266 Issues to think about in the secondary context within each strand 272 Sample secondary sequence 275 Reflection 278 Further reading 278 TEACHING MATHEMATICS BEYOND THE URBAN AREAS OF AUSTRALIA AND IN PACIFIC ISLANDS SETTINGS 279 Rural and remote areas 280 Being flexible 281 Considering classroom structures 286 National testing 289 vii

8 Contents Resourcing 290 Reflection 297 Further reading 297 CHAPTER 14 PLANNING AND SUSTAINABILITY IN THE MATHEMATICS CLASSROOM 298 The TPACK framework 299 TPACK in the mathematics classroom 301 Planning for teaching mathematics with technology 306 Leading the teaching of ICT within your school 308 Professional reading and viewing 312 Website evaluation 314 Collating resources 315 Involving the community 316 Leadership, ICT and change 317 Reflection 318 References 319 Index 329 viii