Conference Proceedings 2010


MERGA33 - 2010 Shaping the Future of Mathematics Education Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia held at John Curtin College of the Arts, Fremantle, 3-7 July 2010
Editors: Len Sparrow, Barry Kissane, Chris Hurst
Len Sparrow, for the Conference Organising Committee
Using Primary-School Learning Environments to Teach Maths at University
David Butler
List of Reviewers
Keynote Address
Reform under attack - Forty Years of Working on Better Mathematics Education thrown on the Scrapheap? No Way!
Marja van den Heuvel-Panhuizen
Structured Failing: Reshaping a Mathematical Future for Marginalised Learners
Robyn Jorgensen (Zevenbergen)
Technology, Research and Practice in Mathematics Education
Barry Kissane
Practical Implication Award
Maths in the Kimberley Project: Evaluating the Pedagogical Model
Robyn Jorgensen (Zevenbergen) & Peter Grootenboer & Peter Sullivan & Richard Niesche
Playing with Mathematics: Play in Early Childhood as a Context for Mathematical Learning.
Janette Bobis & Eva deVries & Kate Highfield & Robert P. Hunting & Shiree Lee & Bob Perry & Louise Thomas & Elizabeth Warren
Problem Solving in the School Curriculum from a Design Perspective
Toh Tin Lam & Leong Yew Hoong & Jaguthsing Dindyal & Quek Khiok Seng
Research Paper
Making Sense of Critical Mathematics Teaching
Annica Andersson
Perceived Professional Learning Needs of Numeracy Coaches
Leonie Anstey & Barbara Clarke
Students' Experiences of Mathematics During the Transition from Primary to Secondary School
Catherine Attard
Percentages: The Effect of Problem Structure, Number Complexity and Calculation Format
Wendy Baratta & Beth Price & Kaye Stacey & Vicki Steinle & Eugene Gvozdenko
Why do Disadvantaged Filipino Children Find Word Problems in English Difficult?
Debbie Bautista & Joanne Mulligan
Two Test Items to Explore High School Students' Beliefs of Sample Size when Sampling from Large Populations
Anthony Bill & Sally Henderson & John Penman
The Impact of a Developmental Framework in Number on Primary Teachers' Classroom Practice
Janette Bobis
Language Negotiation In a Multilingual Mathematics Classroom: An Analysis
Arindam Bose & Manojendu Choudhury
The "Number Proficiency Index": Establishing the Starting Point for Mathematical Instruction in High School
Phil Brockbank
Scratching Below the Surface: Mathematics through an Alternative Digital Lens?
Nigel Calder & Merilyn Taylor
Using Developmental Frameworks to Support Curriculum Outcomes
Rosemary Callingham & John Pegg
Students' Frames of Reference and Their Assessments of Interest for Statistical Literacy
Colin Carmichael
Aspects of Teachers' Knowledge for Helping Students Learn About Ratio
Helen Chick
Teachers' Extent of the Use of Particular Task Types in Mathematics and Choices Behind That Use
Doug Clarke & Anne Roche
Students as Decoders of Graphics in Mathematics
Carmel M. Diezmann & Tom Lowrie
Challenging Multiplicative Problems Can Elicit Sophisticated Strategies
Ann Downton
The Impact of Two Teachers' Use of Specific Scaffolding Practices on Low-attaining Upper Primary Students
Sarah Ferguson & Andrea McDonough
The Predominance of Procedural Knowledge in Fractions
Tricia Forrester & Mohan Chinnappan
Becoming More Numerate: The Journey of Tania
Linda Galligan
Bridging the Numeracy Gap for Students in Low SES Communities: The Power of a Whole School Approach
Ann Gervasoni & Linda Parish with Cait Upton, Teresa Hadden, Kathie Turkenburg, Kate Bevan, Carole Livesey, Deirdre Thompson, Melissa Croswell and Julie Southwell
Auditing the Numeracy Demands of the Middle Years Curriculum
Merrilyn Goos & Vince Geiger & Shelley Dole
The Terminology of Mathematics Assessment
Jane Greenlees
Mathematics Teachers: Negotiating Professional and Discipline Identities
Peter Grootenboer & Julie Ballantyne
A Network Analysis of Concept Maps of Triangle Concepts
Jin Haiyue & Wong Khoon Yoong
Impact of Context and Representation on Year 10 Students' Expression of Conceptions of Rate
Sandra Herbert
Year 11 Advanced Mathematics: Hearing from Students who Buck the Trend
Kai Fai Ho
'You might say you're 9 years old but you're actually B years old because you're always getting older': Facilitating Young Students' Understanding of Variables
Jodie Hunter
Coming to 'Know' Mathematics through 'Acting, Talking and Doing' Mathematics
Roberta Hunter
The Mathematical Needs of Urban Indigenous Primary Children: A Western Australian Snapshot
Chris Hurst & Len Sparrow
Student Attitude, Student Understanding and Mathematics Anxiety
Michelle Jennison & Kim Beswick
Dispersing Mathematics Curriculum Leadership in Remote Aboriginal Communities
Robyn Jorgensen (Zevenbergen) & Richard Niesche
Upper Primary School Students' Algebraic Thinking
Natcha Kamol & Yeap Ban Har
Learning Mathematical Concepts Through Authentic Learning
Koh Noi Keng & Low Hwee Kian
A Teacher Pair Approach to Adopting Effective Numeracy Teaching Practice
Janeen Lamb & Vince Geiger
Assessment for Learning Tasks and the Peer Assessment Process
Lorraine Lauf & Shelley Dole
I liked it till Pythagoras: The Public's Views of Mathematics
Gilah C. Leder & Helen J. Forgasz
Examinations in the Final Year of Transition to Mathematical Methods Computer Algebra System (CAS)
David Leigh-Lancaster & Magdalena Les & Michael Evans
Mathematics Attitudes and Achievement of Junior College Students in Singapore
Lim Siew Yee
A 'knowledge quartet' Used to Identify a Second-Year Pre-service Teacher's Primary Mathematical Content Knowledge.
Sharyn Livy
Beyond the Curriculum: The Mathematical Beliefs of Pre-service Primary Teachers in Hong Kong
Wing Yee Lo & Judy Anderson
Web-based Mathematics: Student Perspectives
Esther Yook-Kin Loong
The Relationship between the Number Sense and Problem Solving Abilities of Year 7 Students
Jemmy Louange & Jack Bana
Teachers' Perceptions of Geometry Instruction and the Learning Environment in Years 9-10 ESL Classrooms
Rinna K. Ly & John A. Malone
Young Children's Measurement Knowledge: Understandings about Comparison at the Commencement of Schooling
Amy MacDonald
Developing a Framework for the Selection of Picture Books to Promote Early Mathematical Development
Jennifer Marston
Professional Standards and Professional Learning: A Position Paper
Karen McDaid
Co-Constructing New Classroom Practices: Professional Development Based upon the Principles of Lesson Study
Sue McDonald
Teacher Change in Response to a Professional Learning Project
Andrea McDonough & Philip Clarkson & Anne Scott
Pre-service Students' Responses to Being Tested on their Primary School Mathematical Knowledge
Tamsin Meaney & Troels Lange
Computational Estimation in the Primary School: A Single Case Study of One Teacher's Involvement in a Professional Learning Intervention
Paula Mildenhall & Mark Hackling & Paul Swan
Gap Thinking in Fraction Pair Comparisons is not Whole Number Thinking: Is This What Early Equivalence Thinking Sounds Like?
Annie Mitchell & Marj Horne
Connecting the Points: Cognitive Conflict and Decimal Magnitude
Bruce Moody
A Decade of MERGA Theses
Judith A. Mousley
Using Video-Stimulated Recall as a Tool for Reflecting on the Teaching of Mathematics
Tracey Muir
Implementing a Pattern and Structure Mathematics Awareness Program (PASMAP) in Kindergarten
Joanne T. Mulligan & Lyn D. English & Michael C. Mitchelmore & Greg Robertson
Partial Metacognitive Blindness in Collaborative Problem Solving
Kit Ee Dawn Ng
Changing our Perspective on Space: Place Mathematics as a Human Endeavour
Kay Owens
Experiences of Learning and Teaching Mathematics: Using Activity Theory to Understand Tensions in Practice
Shaileigh Page & Julie Clarke
Facilitating the Development of Proportional Reasoning through Teaching Ratio
Linda Parish
An Ethnographic Intervention using the Five Characteristics of Effective Teacher Professional Development
Sitti Maesuri Patahuddin
Exploring the Relationship between Mathematical Modelling and Classroom Discourse
Trevor Redmond & Joanne Sheehy & Raymond Brown
Assessing the Number Knowledge of Children in the First and Second Grade of an Indonesian School
Rumi Rumiati & Robert (Bob) Wright
Enactivism and Figural Apprehension in the Context of Pattern Generalisation
Duncan Samson
Mathematics Registers in Indigenous Languages: Experiences from South Africa
Marc Schafer
Using Concept Cartoons to Access Student Beliefs about Preferred Approaches to Mathematics Learning and Teaching
Matthew Sexton
How to Build Powerful Learning Trajectories for Relational Thinking in the Primary School Years
Max Stephens & Dian Armanto
Students' Opinions about Characteristics of Their Desired Mathematics Lessons
Peter Sullivan & Doug Clarke & Helen O'Shea
The Multifaceted Variable Approach: Selection of Method in Solving Simple Linear Equations
Salma Tahir & Michael Cavanagh
Interactive Whiteboards and all that Jazz: Analysing Classroom Activity with Interactive Technologies
Howard Tanner & Sonia Jones & Gary Beauchamp & Steve Kennewell
One on One Numeracy Intervention: A Pilot Project in Low SES Communities
Steve Thornton & Gina Galluzzo & Mary Quinane & Debbie Taylor
Critical Moments in Learning Mathematics: First Year Pre-service Primary Teachers' Perspectives
Stephen Tobias & Penelope Serow & Martin Schmude
Now I'm teaching the children: Changing from Assessment of Learning to Assessment for Learning in Fiji
Kaye Treacy & Poniparte Tiko Fiji & Sarita Harish & Prabha Nairn
Student Centred Approaches: Teachers' Learning and Practice
Colleen Vale & Mary Weaven & Anne Davies & Neil Hooley
Utilising Year Three NAPLAN Results to Improve Queensland Teachers' Mathematical Pedagogical Content Knowledge
Eduarda van Klinken
Documenting the Learning of Teacher Communities Across Changes in their Membership
Jana Visnovska
The Researcher's Self in Research: Confronting Issues about Knowing and Understanding Others
Margaret Walshaw
Indigenous Children's Ability to Pattern as They Enter Kindergarten/Pre-prep Settings: An Exploratory Study
Elizabeth Warren & Jodie Miller
Biased Sampling and PCK: The Case of the Marijuana Problem
Jane M. Watson & Erica L. Nathan
Student Change Associated with Professional Learning in Mathematics
Jane Watson & Natalie Brown & Kim Beswick & Rosemary Callingham & Suzie Wright
Counting On in the Middle Years
Allan Leslie White
Modelling the Cooling of Coffee: Insights From a Preliminary Study in Indonesia
Wanty Widjaja
Abstracting by Constructing and Revising a 'Partially Correct Construct': A Case Study
Gaye Williams
Pre-service Teachers Constructing Positive Mathematical Identities: Positing a Grounded Theory Approach
Sue Wilson
'I always feel more confident when I know where things are going': How do Pre-service Teachers Engage with Mathematics Curriculum Documentation?
Sue Wilson & Jane McChesney
Algebraic Thinking: A Problem Solving Approach
Will Windsor
Equivalent Fractions: Developing a Pathway of Students' Acquisition of Knowledge and Understanding
Monica Wong
Three Primary School Students' Cognition about 3D Rotation in a Virtual Reality Learning Environment
Andy Yeh
Socio-economic Background, Senior Secondary Mathematics, and Post-secondary Pathways
Eng Yeoh & David Leigh-Lancaster
Two Decades of Mathematics Education Reform in New Zealand: What Impact on the Attitudes of Teacher Education Students?
Jenny Young-Loveridge
The influence of the mathematics class on middle school students' interest for statistical literacy.
Colin Carmichael
Walking the Talk: Translation of Mathematical Content Knowledge to Practice
Short Communication (abstract only)
A Survey of Instructional Leaders in Primary Schools: Emerging Patterns in Numeracy Leadership
Joanna Higgins & Linda Bonne

One component of an ongoing New Zealand study investigating instructional leadership in numeracy, an online survey, was completed by 44 primary school leaders - numeracy lead teachers, principals, deputy and assistant principals, and syndicate/team leaders. Patterns identified in an analysis of the responses showed that numeracy lead teachers often had a multiplicity of roles, and suggested that numeracy lead teachers who were also a member of the management team had greater influence than those who were not. Implications for the future leadership of numeracy will be discussed.

Aboriginal Independent Community Schools Numeracy Strategy
Daniel Pinchas & Renae Small & Rebecca Youdale & Shirley Riley & Kaye Treacy

The Aboriginal Independent Community Schools (AICS) Numeracy Strategy is a DEEWR funded action research project providing support to independent Indigenous community schools in Western Australia. Over the next two years, the Strategy will work towards making significant improvements in Indigenous students' understanding and skills in numeracy. The project uses a cycle of discovering what students know, focusing on the mathematics they need to learn and implementing effective pedagogy. Consultants will make regular visits to the schools, working shoulder to shoulder with teachers, Aboriginal Education Workers, and principals. Professional development workshops will be run within schools and at conferences, with resources being developed to support the implementation of the Strategy. Progress will be monitored using standardised assessment and classroom based assessment tasks.

An Alternative Pathway to University Mathematics
Nicholas Crouch

The University of Adelaide's Maths Learning Service offers a bridging course as an alternative pathway to university. This self-paced course is for some students a form of distance education. The course appears to be unique in Australia because of the self-paced nature, with students able to take as much or little time as they require, and the fact that students are not graded but rather only progress once a certain level of understanding is achieved. This communication will discuss the experience of teaching in this mode and the effectiveness of the individual feedback on learning.

Calculator Technologies and Females' Mathematics Learning: A Pilot Study
Janelle Hill

The relationship between females' attitudes to calculator technology and their achievement and participation in higher-level secondary school mathematics was investigated in this small pilot study. The sample comprised nine females who had recently completed secondary schooling. Most believed that technologies such as graphics and Computer Algebra System calculators were obstacles to higher-level mathematics learning and did not enable them to gain a better understanding of mathematical concepts. Several indicated that mathematics was not particularly useful or relevant for them except as a vehicle to university entry. More research is needed to determine the representativeness and significance of these findings.

Elementary Students' Understanding of Variable: The Role of Problem Type and Representation
J. Matt Switzer

Research has found marked differences in student performance with various algebraic problems (e.g., word problems, word equations, equations) (Koedinger & Nathan, 2004). In addition, research has shown that students' understanding of variable is fragile (Booth, 1984; Carraher, Schielmann, & Brizuela, 2001; Stacey, 1989). Often, the teacher/researcher's introduction of literal symbols assumes that students make connections between their informal symbolisations and formal conventional symbolisations (Kaput, 2008). This cross-sectional research project explores the influence of problem type and variable representation for United States Grade 4 & 6 students as they transition from informal representations of variables to formal conventional representations.

Lesson Study as Research and Professional Development for Practitioners
Jodie Hunter

Lesson study is a professional development process whereupon teachers collectively and systematically examine their own practice in order to improve their teaching (Fernandez & Yoshida, 2004; Stigler & Hiebert, 1999). The focus of this report is on how involvement in a lesson study cycle focused on primary mathematics lessons supported teachers to develop reflective practice. It will outline teacher perspectives of their experiences in the project and examine how their reflective skills and investigation into their classroom practices developed. Conclusions will be drawn of the factors which facilitate or inhibit lesson study as a process of professional development and research.

Pre-service Primary Teachers' Ability to Communicate Mathematics Concepts Effectively
Chua Kwee Gek

Process, one of the important components to attain the aim of the Singapore Mathematics curriculum, is often given less emphasis as its mastery seem less tangible in an assessment context. This paper describes a preliminary study to determine Singapore pre-service teachers' ability to articulate mathematics concepts succinctly. The findings show that they were not able to communicate their teaching ideas and concepts effectively. Effective mathematics communication skills using accurate mathematics language and various strategies were then integrated into their pedagogy module so as to equip them better with the necessary repertoire of knowledge and skills for effective mathematics teaching.

Preparing a New Generation of High School Mathematics Teachers
Joanne E. Goodell

In 2005, the National Academy of Sciences and National Academy of Engineering together commissioned the report "Rising Above the Gathering Storm" (Committee on Prospering in the Global Economy of the 21st Century, 2007). The report recommended the UTeach teacher preparation program at the University of Texas at Austin as one that should be scaled up across the nation to address the declining population of high school mathematics teachers. Cleveland State University is now one of 20 universities replicating UTeach, and will accept first year students in August 2010. In this session, I will outline the major differences between this program and traditional programs, and discuss issues I have dealt with during the pre-implementation phase.

Primary Students' Theories of Intelligence, Mathematics Self-Efficacy and Achievement: Analysis of the Initial Data
Linda Bonne

In preparation for the collection of baseline data for doctoral research, two assessment instruments  - one for students, the other for teachers -  were trialled in 2009. At the start of 2010, the final student questionnaire was completed by Year 3 to 6 students in seven schools to gauge their implicit theories of intelligence and their mathematics self-efficacy. Data from a separate assessment of the students'mathematics achievement were also collected (n = 364). The students' teachers (n = 24) completed a questionnaire to identify their theories of intelligence and self-efficacy for teaching mathematics. Initial findings will be presented.

Singaporean Senior Secondary Students' Ways of Using Graphics Calculators
Hazel Tan

This presentation provides some preliminary findings from a large scale survey of 964 Singaporean Senior Secondary mathematics students regarding the use of graphics calculators. Based on Geiger's (2005) framework of four metaphors for technology use – Master, Servant, Partner and Extension of Self – an instrument was developed (Tan, 2009). It was administered as part of a PhD study on students' learning preferences and their ways of learning and using graphics calculators. The findings are compared to those in the pilot study presented at MERGA 32 (Tan, 2009). The relationship between students' use of calculators and their mathematics self ratings are discussed.

Teaching and Learning in an Interactive Multimedia E-Learning Environment
Sharon London & Mike Mitchelmore & Michael Cavanagh &

This project investigated how teachers used the HOTmaths learning system in laptop learning environments. It took place in 8 Year 9 classes at three Catholic secondary metropolitan NSW schools. Each school used laptops in a different configuration, and selected teachers in two schools were provided with extensive professional development. Data on the implementation were collected via classroom observations, interviews with teachers, and pre- and post-testing using the ACER PATMaths test. The results indicated significant improvements in student performance of the intervention groups as compared with the non-intervention groups.

The Effectiveness of a Dynamic Professional Development Model Using an Online Mathematics Learning System
Sharon London & Joanne Mulligan & Michael Cavanagh & Matthew Bower

This study will evaluate the effectiveness of an online professional development model using communication pathways developed for a web-based mathematics learning system. Upper primary teachers from Catholic and government schools in NSW and Victoria will engage in a four-stage online professional development program employing web-conferencing software (Adobe Connect). Professional development will focus on new pedagogies using technology, and promote collaborative reflection and analysis of teaching and learning. Data sources will include digital recordings of a representative sample of lessons, transcripts of PD sessions, data generated by the online mathematics learning system, online surveys completed by students and teachers, and online interviews with teachers.

Values Operating in Effective Mathematics Lessons in Singapore: Reflections from Classroom Observations
Ho Siew Yin

This presentation reports on a study that investigated the professional and pedagogical beliefs of effective mathematics lessons that were co-valued by the teacher and students. This study contributed data to an international pilot study that investigated how different interpretations of effectiveness incorporate traditional, cultural or indigenous views of mathematics education. The conceptualisation of this study was stimulated by previous research findings which found that students' learning of mathematical ideas appeared to be regulated by the teachers' valuing of professional and pedagogical beliefs (Seah, 2007; Seah & Ho, 2009). Data from photos of "effective learning moments" taken by students during the lesson observations in one primary school will also be presented.

Poster (abstract only)
Round Table (abstract only)
K-10 National Mathematics Curriculum Implementation: Implications for Research and Teacher Education
Merrilyn Goos & Robyn Jorgensen & Christelle Plummer & Glenys Reid & Peter Sullivan & Gaye Williams &

The session started will start a few minutes' reflection from panel members about issues associated with the implementation of the K-10 National Curriculum. This will be followed by input of ideas from participants. Gaye Williams will highlight aspects of MERGA Feedback on the Draft K-10 National Curriculum as they become pertinent to the conversations arising. The purpose of the session is to raise awareness of issues associated with National Curriculum implementation, and invite contributions from participants about future directions for research and teacher education in the light of this.

Magnifying Misalignment of Student Data Across a Range of Assessment Tools to Inform Future Learning Goals
Marie Hirst & Anuja Singh
The round table discussion will begin by presenting the findings from a small study investigating possible misalignment of student data from three different assessment tools. It will also look at how any misalignments impact on making overall teacher judgements about student achievement. The three tools used in this case study were AsTTle (Assessment Tool for Teaching and Learning), GloSS (Global Strategy Stage Assessment) and IKAN (Knowledge Assessment for Numeracy) some of which are widely used across New Zealand schools. With the introduction of National Standards in New Zealand, teachers will become more accountable when making overall teacher judgements (OTJ). An essential aspect of OTJ is that teachers effectively select, use and analyse different assessment tools such as those mentioned above. The small study focuses on helping teachers understand the misalignments within the assessment tools thus helping teachers to use data effectively in order to set clear learning goals. In the Round Table we hope to stimulate discussion with Australian, New Zealand and other international colleagues about: ·           How do other countries address misalignments of various assessment tools? ·           Challenges when selecting appropriate assessment tools. ·           Feedback and advice on how to extend this small case study further by formulating a research question. ·           How to best utilise overall teacher judgement with a range of assessment tools?




Make it Count: An Evidence Base to support Numeracy, Mathematics and Indigenous Learners
Will Morony & Caty Morris

Make it count: Numeracy, mathematics and Indigenous learners is a national, four year project that is developing whole school, evidence based, sustainable practices to enhance Indigenous students’ learning. Community engagement is key to the project's success and various communities of practice are being built to support the work of the project. Eight clusters of schools across Australia are working together to build their evidence base so teachers will know whether they are doing things better or not; so they have certainty around what they believe, and clarity about why things have worked (or not). Contributing to this is the emerging role of the clusters ·          Critical Friends' ·          mathematics and/or Indigenous education academics ·          who are working in collaboration with the schools in their particular focus. Adding to the evidence base is the overall project evaluation which includes both quantitative and qualitative longitudinal data about change. The project staff is also identifying direct and indirect evidence. Our challenge is to provide an evidence base of "stuff" that works. How do we marshall the different layers of this "stuff" into the evidence base and, at the same time, evolve the various roles of those contributing? Do we need something more? The aim of this round table presentation is to open up discussions about participants' experiences and knowledge that can maximise the evidence base from a layered, school-based project like this and to inform the work of the project with new thinking, learning and knowledge.

Online Professional Development for Mathematics Teachers
Brooke Evans & Patricia McKenna & Don Gilmore & James Loats

Using collaborative problem solving to develop a "learning community" among mathematics teachers is an established approach to professional development within the field (Lachance & Confrey, 2003; Ryve, 2007). However, the question of whether an online environment adequately facilitates the development of a learning community among teacher-learners remains unanswered (Kim & Bonk, 2006). Any answer to that question will be partial and temporary for two reasons. First, teacher-educators can currently choose from an array of web-based conferencing software of variable quality and capabilities. Second, the rapid pace of innovation of educational technology creates both opportunities and challenges for teacher educators: what some technologies constrain today, other technologies enable tomorrow. Despite these conditions, this roundtable discussion will focus on how one online approach to professional development used by the faculty of Metropolitan State College of Denver (Metro) both promoted and impeded community building and collaborative problem-solving among a group of elementary mathematics teachers in rural Colorado and how other schools may be working through these issues. The growth of online mathematics education and the need for teachers in rural schools to obtain certification in mathematics suggest that mathematics teacher-educators can use Metro's study and the discussions at this roundtable to structure and conduct online professional development courses in ways that conform to the principles of reform-based instruction.

Targeted Learning: A Successful Approach
Linda Cheeseman & Bina Kachwalla & Marilyn Holmes

In 2007 “Targeted Learning Groups were set up in Otago and Southland, New Zealand to support students with their development of knowledge about numbers and to help students become numerate flexible thinkers (Holmes & Tait-McCutcheon, 2009). Since then many schools in New Zealand have trialled the intervention and adapted, where appropriate, to suit the audience in their areas. The purpose of this round table is to outline how the mathematical intervention has been implemented in some of the low socio-economic schools in Auckland, New Zealand. The discussion will focus on the impact of this intervention on student mathematical knowledge and problem solving skills. Data collated from sample schools have indicated that if there is a delay in strategy learning, it is often due to a deficit in one or all of the four knowledge domains: numeral identification, number sequence, place value, and basic facts. In order to bridge the knowledge deficit this intervention provides teachers, parents and teacher aides with a structured and sequential framework of knowledge teaching. The repetition of any learning enables students to master and retain new knowledge (Nuthall 2002) and the consistent nature of the intervention knowledge lessons provide a foundation for students to develop confidence to problem solve. This round table forum will afford an opportunity for international colleagues to share their experiences of mathematical interventions that have effectively raised student achievement. The discussion will be open to support, critique and/or add to the existing intervention and to seek further research ideas.

Teaching Mathematics for an Ethical Citizenry
Helen J Forgasz

At a recent professional development session where I spoke, the principal, a former high school head of mathematics, welcomed participants and reflected on the importance of mathematics for children's futures. He spoke of the relevance of mathematics and its power to model reality. The following exemplar was proposed: “Imagine you are the general of three army divisions. The first is winning handsomely, the second is holding its ground, and the third is suffering huge losses. You have sufficient support troops for only one division. Where would you deploy them?” The answer, he said, was simple, and based on mathematical modeling, “To the winning division, naturally”. He provided a second example: “Imagine you are charged with placing landmines for maximum effect. How would you arrange them?” Again, he claimed, mathematical modeling would enable this decision to be easily made. I left the session disturbed and perplexed. Both examples used to epitomise the power of mathematics were in military contexts, and enabling deaths (collateral damage) was not considered problematic. The principal seemed insensitive to any conceivable wrong in what he had put forward. Contemporary mathematics curricula urge teachers to ensure that students are exposed to “real world” mathematics. I have no argument with this. But, do teachers reflect on the implications of the contexts in which the examples are set? Do they consider if there are covert messages that reinforce stereotypes, or have moral, ethical, or political implications? At this round table, these issues and the research opportunities offered will be explored.