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The Mav 51St Annual Conference MAV ANNUAL ANNUAL MAV C ONFERENCE 2014 ONFERENCE THE MAV 51ST ANNUAL CONFERENCE 4 & 5 December 2014, La Trobe University, Bundoora Editors: Jill Vincent, Gail FitzSimons and Joanna Steinle Reviewers: Caroline Bardini Sandra Herbert Robyn Pierce Leicha Bragg Marj Horne Wee Tiong Seah Jill Brown Derek Hurrell Kaye Stacey Jill Cheeseman Ian Lowe Max Stephens Helen Chick Andrea McDonough Gloria Stillman Philip Clarkson Rob Money Wanty Widjaja Ann Downton Ray Peck Gaye Williams MAV 2014 MAV_ProceedingBookCover-2014_01.indd 1 20/11/2014 3:26 pm Maths Rocks Editors Jill Vincent, Gail FitzSimons and Joanna Steinle Reviewers Caroline Bardini Andrea McDonough Leicha Bragg Rob Money Jill Brown Ray Peck Jill Cheeseman Robyn Pierce Helen Chick Wee Tiong Seah Philip Clarkson Kaye Stacey Ann Downton Max Stephens Sandra Herbert Gloria Stillman Marj Horne Wanty Widjaja Derek Hurrell Gaye Williams Ian Lowe Published by: THE MATHEMATICAL ASSOCIATION OF VICTORIA FOR THE FIFTY FIRST ANNUAL CONFERENCE 4–5 December 2014 2014-MAV-Conference-Book.indb 1 20/11/2014 3:13 pm Maths Rocks Published December 2014 by The Mathematical Association of Victoria “Cliveden” 61 Blyth Street Brunswick VIC 3056 Designed by Idaho Design & Communication Produced by Printhouse Group National Library of Australia Cataloguing-in-Publication Data: ISBN: 978-1-876949-57-0 © Copyright 2014 Permission to reproduce material from this publication must be sought from the owner of copyright, and due acknowledgement be given to Mathematical Association of Victoria as publisher. While every care has been taken to trace and acknowledge copyright, the publishers tender their apologies for any accidental infringement where copyright has proved untraceable. The MAV would be pleased to come to a suitable arrangement with the rightful owner in each case. Should readers wish to contact any of the authors, full addresses are available from the Professional Officer, the Mathematical Association of Victoria. The opinions expressed in this publication do not necessarily reflect the position or endorsement of the Editors or of the Mathematical Association of Victoria. ii 2014-MAV-Conference-Book.indb 2 20/11/2014 3:13 pm Mathematical Association of Victoria’s Annual 2014 Conference FOREWORD The 51st conference of the Mathematical Association of Victoria has the theme Maths Rocks — a theme that is intended to inspire teachers and to encourage them to pass on their enthusiasm for mathematics to their students. Several authors have used the theme in the titles of their papers. The theme is open to numerous interpretations, including having fun with mathematics, and this comes through in several contributions. Another interpretation is of teachers forging closer relations with their students, trying to optimise student engagement and understanding, making a difference in students’ current lives and encouraging them to continue their studies in mathematics. Regardless of how authors have chosen to interpret the theme, all papers portray a sense of purpose in teaching mathematics. As editors we have enjoyed reading the many submissions to the proceedings. The papers cover diverse interest areas, ranging from effective methods for teaching topics that students traditionally find difficult to enriching the mathematical experiences of able students through mathematics competitions. Although not all of us will have the opportunity to visit the Museum of Mathematics in New York, we are treated to some fascinating examples of the mathematically rich displays. Papers submitted for Double blind review and Peer review have undergone a rigorous review process. Summary submissions have accommodated those presenters who wish to share key points related to their presentation in a shortened format. We hope that readers will find the papers enjoyable and valuable. We also thank the reviewers of the blind and peer reviewed papers for their willingness to review and for their carefully considered constructive comments. Their contribution to the continued success of the MAV conference proceedings is greatly appreciated. We close by thanking the MAV conference staff for their professionalism and for the support provided to us in our role as editors. Jill Vincent, Gail FitzSimons and Joanna Steinle, The University of Melbourne (Editors) iii 2014-MAV-Conference-Book.indb 3 20/11/2014 3:13 pm Maths Rocks The Review Process for the Mathematical Association of Victoria 51st Annual Conference Proceedings Papers were submitted for double-blind review, peer review or as summaries. The Editors received 11 full papers for the double blind review process, for which the identities of author and reviewer were concealed from each other. Details in the papers that identified the authors were removed to protect the review process from any potential bias, and the reviewers’ reports were anonymous. Two reviewers reviewed each of the 11 blind review papers and if they had a differing outcome a third reviewer was required. Ten of the 11 papers were accepted for publication. In addition, we received 14 full papers for the peer review process, where the names of the authors were identified to reviewers; 11 were accepted for publication as peer-reviewed papers and two were accepted as summary papers. Eight papers submitted as summary papers were reviewed by a combination of external reviewers and the editorial team. Seven of these were accepted for publication (one as a peer reviewed paper). In the Conference Proceedings, double-blind and peer reviewed papers are grouped together and arranged in alphabetical order of author names. Double-blind reviewed papers and peer reviewed papers are indicated by ** and * respectively following the paper title. Summary papers follow the double blind and peer reviewed papers. Of the total of 33 papers received, 30 papers are published: ten double-blind reviewed papers, twelve peer reviewed papers and eight summary papers. Altogether, 21 reviewers assisted in the review process, all of whom provided thoughtful feedback and were outstanding in responding quickly to our invitations. iv 2014-MAV-Conference-Book.indb 4 20/11/2014 3:13 pm Mathematical Association of Victoria’s Annual 2014 Conference CONTENTS ** Double blind reviewed paper * Peer reviewed paper Foreword .............................................................................................................................................iii DEVELOPING ALGEBRAIC THINKING: PROVIDING NEW TOOLS TO UNDERSTAND MATHEMATICAL RELATIONSHIPS * ..................9 George Booker WHEN ARE WE GOING TO USE THIS? * .......................................................................14 Mike Clapper IMPLEMENTING PROBLEM-SOLVING AT EAGLE POINT PRIMARY SCHOOL: A WHOLE SCHOOL APPROACH * .......................................20 Natalie Clarke and Anna Duncan Gaye Williams SMORGASBORD OF MATHS – WHAT’S ON THE MENU TODAY? DIFFERENTIATION IN THE PRIMARY CLASSROOM * ...................29 Cathy Davidson and June Penney Jenny Dockeary TEACHER QUESTIONING IN MATHEMATICS CLASSES IN CHINA AND AUSTRALIA: A CASE STUDY ** .............................................................37 Lianchun Dong and Wee Tiong Seah David Clarke ASSESSMENT FOR LEARNING IN SECONDARY MATHEMATICS * .............47 Heather Ernst VALUES ALIGNMENT STRATEGIES FOR MATHEMATICS TEACHERS ** ......54 Darren Fitzpatrick THE MATHS ONLINE INTERVIEW STILL ROCKS! * .............................................60 Pam Hammond THE IMPORTANCE OF FRACTIONS IN BEING A SUCCESSFUL MATHEMATICS STUDENT ** ............................................................................................67 Derek Hurrell and Lorraine Day v 00TableOfContents2014.indd 5 20/11/2014 3:38 pm Maths Rocks NURTURING NUMBER SENSE ** ......................................................................................76 Derek Hurrell Paul Swan ENRICHING THE MATHEMATICS CLASSROOM: A VISIT TO THE VIRTUAL ISLAND ** ......................................................................................................84 Minh Huynh and James Baglin MAGIC TRICKS IN THE TEACHING OF THE ARITHMETIC MEAN ** .........94 Pearlyn Lim Fu Siqiang Pamela Foong Hui Shan BIGGEST LOSER PROJECT *............................................................................................... 102 Robert Money and Donald Smith Ian Lowe IMPLEMENTING A SELF-DIRECTED LEARNING APPROACH TO MATHEMATICS IN A PRIMARY SETTING * ....................................................111 Stephanie Nitschke TRISECTING AN ANGLE * ................................................................................................ 120 Karim Noura EFFECTIVE DIFFERENTIATION: WHERE A GROWTH MINDSET MEETS THE ZPD * ........................................................................................... 128 Yvonne Reilly and Jodie Parsons DEVELOPING GEOMETRIC REASONING ABILITIES THROUGH VISUALISATION ** ................................................................................................................. 136 Rebecca Seah ALIGNING VALUES, ENERGISING MATHEMATICS LEARNING ** ..........145 Wee Tiong Seah FUN WITH DYNAMIC GEOMETRY IN PRE-SCHOOLS AND PRIMARY SCHOOLS ** ..........................................................................................................154 Pumadevi Sivasubramaniam DOUBLE DIVISION ** ........................................................................................................... 164 Pumadevi Sivasubramaniam and Mohd Ariff Jasmi vi 00TableOfContents2014.indd 6 20/11/2014 3:38 pm Mathematical Association of Victoria’s
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