Geiger Vince - Teaching secondary school mathematics: research and practice for the 21st century

First published in 2017

Copyright Merrilyn Goos, Colleen Vale, Gloria Stillman, Katie Makar, Sandra Herbert and Vince Geiger 2017

All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without prior permission in writing from the publisher. The Australian Copyright Act 1968 (the Act) allows a maximum of one chapter or 10 per cent of this book, whichever is the greater, to be photocopied by any educational institution for its educational purposes provided that the educational institution (or body that administers it) has given a remuneration notice to the Copyright Agency (Australia) under the Act.

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ISBN 978 1 74331 593 4

eBook ISBN 978 1 95253 549 9

Index by Puddingburn

Figures

Tables

Our goal in writing this book was to provide prospective and practising secondary mathematics teachers and university-based mathematics teacher educators with a research-based text that is also rich in practical teaching ideas. In this second edition we have updated each of the chapters in line with changes to the secondary mathematics curriculum in Australia and recent research on the teaching and learning of mathematics. We invited colleagues with particular expertise to assist with revising chapters in the text and have acknowledged their contribution as authors: Katie Makar, who wrote the original chapter on Teaching and Learning Chance and Data and revised this chapter for the second edition, Sandra Herbert, who revised the chapters on Teaching and Learning Algebra and Teaching and Learning Calculus, and Vince Geiger, who revised the chapter on Effective Use of Technologies in Mathematics Education.

We are grateful to the following for permission to reproduce material: Computers in the Schools; Educational Studies in Mathematics; Journal for Research in Mathematics Education; Journal of Mathematics Teacher Education; Journal of Teacher Education; Mathematics Education Research Journal; Procedia Social and Behavioural Sciences; Teaching Mathematics and its Applications; American Mathematical Society; Australian Association of Mathematics Teachers; Australian Bureau of Statistics; Australian Council for Educational Research; Australian Curriculum, Assessment and Reporting Authority; Australian Institute for Teaching and School Leadership; Department of Education and Training Victoria; Department of Education NSW; International Association for the Evaluation of Educational Achievement; Mathematical Association of Victoria; Mathematics Education Research Group of Australasia; National Council of Teachers of Mathematics; NSW Board of Studies, Teaching and Educational Standards; Sense Publishers; Taylor and Francis Group; Wolfram Alpha; Monica Baker; Helen Chick; Doug Clarke; Kaye Stacey; and Mike Thomas.

Merrilyn Goos is Professor and Head of the School of Education at The University of Queensland, where for ten years she coordinated mathematics curriculum studies for prospective secondary school teachers in the Schools Graduate Diploma in Education and Bachelor of Education programs. She is an internationally recognised mathematics educator whose research is well known for its strong focus on classroom practice. She has led projects that investigated students mathematical thinking, the impact of digital technologies on mathematics learning and teaching, the professional learning of mathematics teachers, and numeracy across the curriculum. She has served her professional and research communities as Chair of the Queensland Studies Authoritys Mathematics Syllabus Advisory Committee, Vice-President of the Queensland Association of Mathematics Teachers, and President of the Mathematics Education Research Group of Australasia. In 2004 she won an Australian Award for University Teaching for her work as a mathematics teacher educator.

Colleen Vale is Associate Professor of Mathematics Education at Deakin University where she teaches in primary and secondary pre-service and associate teacher education programs. She works closely with schools and teachers to provide further teaching experiences for secondary pre-service teachers of mathematics and to provide professional learning for primary and secondary teachers. She has an international reputation for her research on gender equity and social justice in mathematics education. Her current research projects concern the identities and teaching practices of out-of-field and beginning secondary mathematics teachers, instructional leadership and professional learning for mathematical reasoning and inquiry-based teaching and learning. Colleen has been an active participant in the mathematics education and research field as a co-writer of the original VCE Mathematics course and held positions as the President of the Mathematics Association of Victoria, Vice-President of Mathematics Education Research Group of Australasia and editor of Mathematics Teacher Education and Development.

Gloria Stillman is an Associate Professor at the Australian Catholic University of Melbourne. She has had an extensive career as a lecturer teaching secondary mathematics methods at the University of Melbourne and in tertiary institutions in Queensland, where she was on the state panel for Mathematics C then A for the Board of Senior Secondary School Studies. Previously she was a secondary mathematics teacher in a Brisbane school. Glorias research interests focus on mathematics education and, in particular, the teaching, learning and assessing of real-world applications and modelling. Significant projects of international regard include RITEMATHS, an Australian Research Council-funded Linkage project, and CCiSM, an ongoing research project into curriculum change in secondary mathematics in mathematical modelling. She has recently co-edited two books on international research about the teaching and learning of mathematical modelling and is President of ICTMA (International Community of Teachers of Mathematical Modelling and Applications). Gloria is a member of the Editorial Board of