Curriculum in focus:Research guided practice

Proceedings of the 37th Annual Conference of the Mathematics Education Research Group of Australasia

Edited by Judy Anderson, Michael Cavanagh & Anne Prescott

Curriculum in Focus: Research Guided Practice

Proceedings of the 37th annual conference of the Mathematics Education Research Group of Australasia

Edited by Judy Anderson, Michael Cavanagh & Anne Prescott

Mathematics Education Research Group of Australasia Inc., 2014

ISBN: 978-1-920846-27-5

Published by the Mathematics Education Research Group of Australasia (MERGA) Inc.

MERGA Inc. GPO Box 2747 Adelaide, SA 5001 www.merga.net.au

The 37th annual conference of the Mathematics Education Research Group of Australasia was held at the Aerial Centre, the University of Technology, Sydney, NSW, Australia, from 29 June to 3 July 2014

Local Organising Committee and Conference Convenors:

Judy Anderson, The University of Sydney Michael Cavanagh, Macquarie University Mary Coupland, University of Technology, Sydney Anne Prescott, University of Technology, Sydney Paul White, Australian Catholic University, Strathfield

Administrative Assistance:

Annie Muir Nikky Vanderhout

Proceedings Cover Design: Toby Spencer

Conference Logo Design: Mary Coupland and Toby Spencer

Conference Sponsors:

Australian Catholic University Macquarie University University of Technology, Sydney The University of Sydney

PREFACE The Proceedings of the 37th annual conference of the Mathematics Education Research

Group of Australasia (MERGA 2014) was compiled into one volume and published on the conference USB and on the MERGA website at (www.merga.edu.au). The 2014 Conference was held at the University of Technology, Sydney (UTS) in collaboration with colleagues from four Sydney-based universities Assoc. Prof. Judy Anderson (the University of Sydney), Dr Michael Cavanagh (Macquarie University), Dr Mary Coupland (UTS), Dr Anne Prescott (UTS), and Assoc. Prof. Paul White (Australian Catholic University, Strathfield).

The theme of the conference was Curriculum in Focus: Research Guided Practice. This was chosen to acknowledge the development of the first Australian Curriculum: Mathematics F-10, to provide an opportunity to consider national curriculum development in other countries, to share what is occurring in the Australian context, and to encourage research into mathematics curriculum development and evaluation. To that end, the keynote presentations address this theme by exploring curriculum development in the Singaporean context, by questioning the role of mathematics education research in curriculum development, and by exploring our historical journey through mathematics education research. At the conference, a panel discussion session sought advice about the development and implementation of national curricula internationally and included Prof. Barbara Jaworkski (UK), Prof. Berinderjeet Kaur (Singapore), Prof. Glenda Anthony (NZ) and Prof. Merrilyn Goos (Australia). This panel session was held on the Teachers Day on Wednesday 2nd June along with a selection of research papers applicable to school contexts and of interest to teachers.

During the conference, MERGA presentations comprised research papers, symposia, round tables, short communications and posters, and covered a wide variety of topics relevant to mathematics education across all countries, with a particular focus on the Australasian region. Research into mathematics education in early childhood settings, primary and secondary schools, or in tertiary institutions was covered. In accordance with the established MERGA procedures, all research papers and symposium papers were blind peer reviewed, as were the abstracts for short communications, round tables and posters. Research papers were accepted for both publication and presentation, or for presentation only. The published proceedings include the keynote papers, the research papers followed by the symposia papers, the abstracts for round tables, short communications and posters.

The Editorial Team would like to acknowledge and thank the Reviewing Panel Chairs and all of the reviewers for their efforts to read and provide constructive feedback in a short timeframe. Ensuring the published papers meet high academic standards is an important and shared responsibility of the MERGA community. We would also like to thank the authors for taking the time and necessary care to use the MERGA conference paper template and guidelines before submitting their papers.

The Conference Organising Committee welcomed participants from all states and territories of Australia, as well as from many countries including Brunei Darussalam, France, Japan, Mauritius, New Zealand, Norway, Papua New Guinea, Singapore, Sweden and the United Kingdom. We hope you enjoyed your time at the conference, making new connections and new friends, and that you had a chance to enjoy the city of Sydney and the many wonderful places to visit. We would also like to thank our Sydney-based colleagues who helped us to welcome you and show you around. We certainly enjoyed meeting you and hosting this conference. Editors: Judy Anderson, Michael Cavanagh and Anne Prescott

MERGA 37 REVIEWERS Kim Allan Megan Anakin Dayle Anderson Glenda Anthony Robin Averill Judy Bailey Anne Bennison Brenda Bicknell Trevor Bills Trevor Black Leicha Bragg Kathy Brady Fiona Budgen Tim Burgess Nigel Calder Ban Heng Choy Julie Clark * Audrey Cooke Mary Coupland Lisa Darragh Lorraine Day Jaguthsing Dindyal Ann Downton Michael Drake Michael Easey Fiona Ell Sarah Ferguson Nicholas Flegg Jill Fox Linda Galligan * Ann Gervasoni Rose Golds Merrilyn Goos Peter Grootenboer Kevin Hannah

Ngrewa Hawera Ann Heirdsfield Kate Highfield Kai Fai Ho Leong Yew Hoong Marj Horne Bobbie Hunter Jodie Hunter * Derek Hurrell Chris Hurst * Romina Jamieson-Proctor Jyoti Jhagroo Harry Kanasa Berinderjeet Kaur * Marian Kemp Barry Kissane Mun Ye Lai Toh Tin Lam Janeen Lamb * Kevin Larkin Generosa Leach Shiree Lee Chris Linsell Gregor Lomas Karen Major Katie Makar Margaret Marshman * Jennie Marston Jane McChesney * Christine McDonald Susan McDonald Andrea McDonough * Robert McDougall Colleen McMurchy-Pilkington Paula Mildenhall

Jodie Miller Judith Mills Eric Chan Chun Ming Joanne Mulligan Carol Murphy Dawn Ng Christine Ormond Virginia Pattingale Pam Perger Cheng Lu Pien Glorianne Porter Theodosia Prodromou Peter Rawlins Anne Roche Matt Sexton Sashi Sharma Grace Skrzypiec Cathy Solomon Merilyn Taylor Zain Thompson Stephen Thornton Colleen Vale Margaret Walshaw Jennifer Way Wanty Widjaja John West Brian Westbrooke Bruce White Paul White Sue Wilson * Tiffany Winn Monica Wong Vince Wright Oleksiy Yevdokimov Wong Khoon Yoong

*Review panel chair

TABLE OF CONTENTS

Preface iii MERGA 37 Reviewers iv

Keynote Papers

Mathematics Education Development: Research in Teaching Learning in Practice

2

Barbara Jaworski Evolution of Singapores School Mathematics Curriculum 24

Berinderjeet Kaur The Annual Clements Foyster Lecture Custodians of Quality: Mathematics Education in Australasia Where from? Where at? Where to?

38

Peter Galbraith

Research Papers

Item Context Factors Affecting Students Performance on Mathematics Items 55 Felipe Almuna Salgado & Kaye Stacey

From Arithmetic to Algebra: Sequences and Patterns as an Introductory Lesson in Seventh Grade Mathematics

63

Diana Grace Aniban, Von Christopher Chua, Jellen Garcia & Levi Esteban Elipane

Early Career Teachers, Mathematics and Technology: Device Conflict and Emerging Mathematical Knowledge

71

Catherine Attard & Joanne Orlando Linking Geogebra to Explorations of Linear Relationships 79

Belinda Aventi, Penelope Serrow & Steve Tobias Undergraduate Mathematics Students Pronumeral Misconceptions 87

Caroline Bardini, Jill Vincent, Robyn Pierce & Deborah King Teacher Identity and Numeracy: Evaluating a Conceptual Framework for Identity as a Teacher of Numeracy

95

Anne Bennison Towards a Fresh Understanding of the Relationship Between Teacher Beliefs about Mathematics and their Classroom Practices

103

Kathy Brady Affordances: Ten Years On 111

Jill P. Brown & Gloria Stillman

RESEARCH PAPERS

2014. In J. Anderson, M. Cavanagh & A. Prescott (Eds.). Curriculum in focus: Research guided practice (Proceedings of the 37th annual conference of the Mathematics Education Research Group of Australasia) pp. . Sydney: MERGA.

De La Salle University Manila De La Salle University Manila

De La Salle University Manila University of the Philippines Diliman De La Salle University - Manila

a posteriori

a prioria posteriori

A Priori Analysis

Data Gathering Through Microteaching

A Posteriori Analysis

Microteaching

Figure 1.

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Post-Lesson Discussion

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PrefaceReviewersTable of contentsKeynote papersJaworskiKaurpreambleGalbraith

Research papersAlmuna SalgadoAnibanAttardAventiBardiniBennisonBradyBrownCarmichaelChanCheeseman ChoyCookeD'AgostinDalitzDarraghDimarakisDragesetEbaeguinEdmonds-WathenEnglishFermeGanesanGeigerGoodwinGouldGreenleesGrootenboerHunterHurstHurstJazbyJorgensenKargasKestelKinnearKnightLadeleLambLambLarkinLeachLederLeeLimLivyLongLowrieMaherMcDonoughMcGregorMillerMojica-CaseyMorleyMuirMulliganNguParishPricePrietoRamfulRumiatiRumiatiSawatzkiSeahSemlerSextonSkillingSullivanSullivanThorntonTranWalkerWilkieWilsonWilsonWongYoung-LoveridgeZmoodZoanetti

SymposiaWidjajaBraggHerbertLoongMajorLinsellIngramAnakinOwensKraviaBinoBino

Round table discussionsAlkhatibGoosHigginsHunterHurstJenningsMcDiarmid

Short communicationsAbdullahBartonBeswickBobisBradyChengChongElizarGetenetGoldsGoosGrothrusHillHodgsonIngramJhagrooKusznirczukLeeLimLindwall EhrnlundLomasMarshmanMarstonMcDonaldMokMonteleoneOatesOzasaPatahuddinPearnPerkinsSymonsTrenholmWilliamsWoolcottWoolcottYoon

Poster presentationsKanasaLindwall EhrnlundRumiatiTan