Conference Proceedings 2008


Navigating currents and charting directions
Editors: Merrilyn Goos, Ray Brown and Katie Makar
Merrilyn Goos
List of Reviewers
Judges and Reviewers for MERGA 31
Keynote Address
Praxis and Practice Architectures in Mathematics Education
Stephen Kemmis
Stars, Compass, and GPS: Navigating Currents and Charting Directions for Mathematics Education Research on Gender Issues
Helen Forgasz
Practical Implication Award
Facilitating Communities of Mathematical Inquiry
Roberta Hunter
A Longitudinal Study of Student Performance on Items Rich in Graphics
Tom Lowrie
Graphics and the National Numeracy Tests
Carmel Diezmann
Standardised Assessment in Mathematics: The Tale of Two Items
Tracy Logan and Jane Greenlees
The Construction of Knowledge: Theoretical Approaches
Tommy Dreyfus, Michael O. J. Thomas, Jill P. Brown and Gaye Williams
The Role of Information Graphics in Mathematical Proficiency
Carmel Diezmann and Tom Lowrie
Research Paper
Assessing Primary Preservice Teachers’ Mathematical Competence
Karoline Afamasaga-Fuata’i, Paul Meyer and Naomi Falo
The 2007 Common Technology Free Examination for Victorian Certificate of Education (VCE) Mathematical Methods and Mathematical Methods Computer Algebra System (CAS)
David Leigh-Lancaster, Pam Norton, Peter Jones, Magdalena Les, Michael Evans and Margaret Wu
Teachers’ Motivation to Attend Voluntary Professional Development in K-10 Mathematics
Judy Anderson
Using National Numeracy Testing to Benefit Indigenous Students: Case Studies of Teachers Taking Back Control of Outcomes
Annette R. Baturo, Tom J. Cooper, Matthew T. Michaelson and Jessica Stevenson
Recollections of Mathematics Education: Approaching Graduation and 5 Years Later
Kim Beswick and Shelley Dole
Using Paper-Folding in the Primary Years to Promote Student Engagement in Mathematical Learning
Kathy Brady
The Case of Mathematical Proof in Lower Secondary School: Knowledge and Competencies of Pre-service Teachers
Jill Brown, Gloria Stillman, Björn Schwarz and Gabriele Kaiser
Employing Mathematical Modelling to Respond to Indigenous Students’ Needs for Contextualised Mathematics Experiences
Kelli Brown
Reconceptualising Agency Through Teachers Talking About a Sociocultural Approach to Teaching Mathematics in the Classroom
Raymond Brown and Trevor Redmond
Middle School Students’ Interest in Statistical Literacy
Colin Carmichael and Ian Hay
One Secondary Teacher’s Use of Problem-Solving Teaching Approaches
Michael Cavanagh
Does Student Success Motivate Teachers to Sustain Reform-Oriented Pedagogy?
Linda Cheeseman
Year Five Students Solving Mental and Written Problems: What Are They Thinking?
Julie Clark
Mathematics for Engineering Education: What Students Say
Mary Coupland, Anne Gardner and Georgina Carmody
Advancing Research Into Affective Factors in Mathematics Learning: Clarifying Key Factors, Terminology and Measurement
Patricia C. Cretchley
Explorations of Early Childhood – New Entrant Transition in Mathematics
Ngaire M. Davies and Karen Walker
Eliciting Growth in Teachers’ Proportional Reasoning: Measuring the Impact of a Professional Development Program
Shelley Dole, Doug Clarke, Tony Wright, Geoff Hilton and Anne Roche
Links Between Children’s Understanding of Multiplication and Solution Strategies For Division
Ann Downton
Intervention Instruction in Structuring Numbers 1 to 20: The Case of Nate
David Ellemor-Collins and Robert (Bob) Wright
Interdisciplinary Problem Solving: A Focus on Engineering Experiences
Lyn D. English
Addressing Verbal Memory Weaknesses to Assist Students with Mathematical Learning Difficulties
Maureen Finnane
Validation of an Assessment Instrument Developed for Eliciting Student Prior Learning in Graphing and Data Analysis
Noleine Fitzallen
Using Valsiner
Linda Galligan
CAS Enabled Devices as Provocative Agents in the Process of Mathematical Modelling
Vince Geiger, Rhonda Faragher, Trevor Redmond and Jim Lowe
Researcher-Teacher Relationships in Mathematics Education
Merrilyn Goos
Towards a Sociocultural Framework for Understanding the Work of Mathematics Teacher-Educator-Researchers
Merrilyn Goos
Identity as a Lens to Understand Learning Mathematics: Developing a Model
Peter Grootenboer and Robyn Zevenbergen
Capturing Students’ Thinking about Strategies used to Solve Mental Computations by Giving Students Access to a Pedagogical Framework
Judy Hartnett
A Review of Recent Research in Early Mathematics Learning and Technology
Kate Highfield and Kristy Goodwin
The Development of Students’ Use of Justification Strategies
Jodie Hunter and Glenda Anthony
Using Task-Based Interviews to Assess Mathematical Thinking of Primary School Students
Chris Hurst
Who a Student Sits Near to in Maths: Tension between Social and Mathematical Identities
Naomi Ingram
Social Constructivism in the Classroom: From A Community of Learners to A Community of Teachers
Jane Irvin
Primary Teachers’ Beliefs About the Use of Mathematics Textbooks
Romina Jamieson-Proctor and Carmen Byrne
Abstraction in Context, Combining Constructions, Justification and Enlightenment
Ivy Kidron and Tommy Dreyfus
How Humanism Can Foster Mediocrity in Early Years Mathematics Education: A Poststructuralist Comparison
Mary Klein
Preservice Teachers and Numeracy Education: Can Poststructuralism Contribute?
Mary Klein
High Achievers in Mathematics: What Can We Learn From and About Them?
Gilah Leder
Focusing Year 8 Students on Self-Regulating their Learning of Mathematics
Andrea McDonough and Peter Sullivan
Feedback About Professional Growth for Teachers of Mathematics: A Developmental Perspective
Greg McPhan, John Pegg and Stefan Horarik
Fraction Number Line Tasks and the Additivity Concept of Length Measurement
Annie Mitchell and Marj Horne
“Zero is Not a Number”: Teachable Moments and their Role in Effective Teaching of Numeracy
Tracey Muir
Students’ Attitude Towards Using Materials to Learn Algebra: A Year 7 Case Study
Stephen Norton and Will Windsor
Teaching Mathematics and Technology through Design Practice
Stephen Norton and Tom J Cooper
Engaging Mathematics Teachers in Professional Learning by Reflecting on their Pedagogical Practice
Richard O’Donovan
Primary Teachers’ Perceptions of Their Knowledge and Understanding of Measurement
Michelle O’Keefe and Janette Bobis
Use of the Internet for Teacher Professional Development and for Teaching Mathematics: Supports and Inhibitors
Sitti Maesuri Patahuddin
A Situated Perspective on Learning to Teach Secondary Mathematics
Anne Prescott and Michael Cavanagh
The Hospital Problem Revisited. Tertiary Student’s Perceptions of a Problem Involving the Binomial Distribution
Robyn Reaburn
The Identification of Partially Correct Constructs
Gila Ron, Rina Hershkowitz and Tommy Dreyfus
Making Connections: Promoting Connectedness in Early Mathematics Education
Abigail Sawyer
Engagement versus Deep Mathematical Understanding: An Early Career Teacher’s Use of ICT in a Lesson
Anne Scott, Ann Downton, Donna Gronn and Adam Staples
Investigating a Phase Approach to Using Technology as a Teaching Tool
Penelope Serow
The Introduction of Interactive Whiteboard Technology in the Primary Mathematics Classroom: Three Case Studies
Penelope Serow and Rosemary Callingham
School Readiness: What Do Teachers Expect of Children in Mathematics on School Entry?
Brenda Sherley and Megan Clark
Gaining Insight into Alice’s Pedagogy with Respect to Five Dimensions of Numeracy
Jane Skalicky
Modes of Reasoning in Explanations in Year 8 Textbooks
Kaye Stacey and Jill Vincent
What Does Three-quarters Look Like? Students’ Representations of Three-quarters
Vicki Steinle and Beth Price
Some Key Junctures in Relational Thinking
Max Stephens
Chinese Young Children’s Strategies on Basic Addition Facts
Huayu Sun
Self-Efficacy in Mathematics: Affective, Cognitive, and Conative Domains of Functioning
S. L. Tait–McCutcheon
Neuropsychological Evidence for the Role of Graphical and Algebraic Representations in Understanding Function
Michael O. J. Thomas, Anna J. Wilson, Michael C. Corballis and Vanessa K. Lim
Speaking with Different Voices: Knowledge Legitimation Codes of Mathematicians and Mathematics Educators
Steve Thornton
Recognising Different Starting Points in Aboriginal Students’ Learning of Number
Kaye Treacy and Sandra Frid
Deepening the Mathematical Knowledge of Secondary Mathematics Teachers who Lack Tertiary Mathematics Qualifications
Colleen Vale and Alasdair McAndrew
Indigenous Students’ Early Engagement with Numeracy: The Case of Widgy and Caddy
Elizabeth Warren, Janelle Young and Eva De Vries
Building Informal Inference in Grade 7
Jane Watson and Julie Donne
Proportional Reasoning: Student Knowledge and Teachers’ Pedagogical Content Knowledge
Jane Watson, Rosemary Callingham and Julie Donne
Counting On 2007: A Program for Middle Years Students who have Experienced Difficulty with Mathematics
Allan White
How Group Composition Can Influence Opportunities for Spontaneous Learning
Gaye Williams
Success and Consistency in the Use of Heuristics to Solve Mathematics Problems
Khoon Yoong Wong
Fractions as a Measure
Monica Wong and David Evans
Mixing Colours: An ICT Tool Based on a Semiotic Framework for Mathematical Meaning-Making about Ratio and Fractions
Andy Yeh and Rod Nason
Secondary School Students Investigating Mathematics
Joseph Yeo
Teaching Area and Perimeter: Mathematics-Pedagogical-Content Knowledge-in-Action
Kai Kow Joseph Yeo
Problem Solving Activities in a Constructivist Framework: Exploring how Students Approach Difficult Problems
Oleksiy Yevdokimov and Tim Passmore
Creating Equitable Practice in Diverse Classrooms: Developing a Tool to Evaluate Pedagogy
Robyn Zevenbergen, Richard Niesche, Peter Grootenboer and Jo Boaler
Short Communication (abstract only)
Achieving Computational Fluency in Multi-Digit Multiplication and Division
Kristen Tripet

Current teaching practice has been greatly enriched through valuable research into students’ acquisition of deep understanding and skills in early multiplication and division. Research in multi-digit multiplication and division is still relatively undeveloped. This proposed study will explore how students achieve computational fluency in multiplication and division. This paper outlines the background literature and research into multiplication and division. It then proposes questions to be explored and the intended methodology to determine effective pedagogical approaches that encase both mental and written computational methods.

Coaching and Mentoring Numeracy Lead Teachers to Improve Student Learning: The Journey of Two Year Seven and Eight Teachers
Judith Mills

The Numeracy Development Project has been systematically introduced into New Zealand schools since its conception in 2001. For many teachers, successful implementation of this mathematics education reform required a transformation of long held beliefs and practices. This shift involved moving from a view of mathematics learning as individualistic and passive, towards one in which students come to do and understand mathematics through participating in collaborative activity. This change in pedagogy and the required content knowledge has brought a range of challenges for many teachers. The purpose of this short presentation is to share the journey of two lead teachers (coaches) working with a mentor to enhance their understanding of number in the mathematics classroom. The mentor was a school adviser and the coaches came from schools that had previously been involved in the Numeracy Development Project. The process took place over six months and was aimed at improving both pedagogy and content knowledge of the in-school coaches and other teachers within their schools. A particular emphasis was placed on improving student learning in multiplicative and proportional thinking.

Connecting the Points: Students Learning Decimal Place Value
Bruce Moody and Jenny Young-Loveridge

This presentation documents the learning journey of a group of six Year 5/6 students from a low decile school. These students worked with the first author over several sessions to build their understanding of fractions (i.e., tenths, hundredths), and the links between these fractions and the corresponding decimal places. Structured materials (plastic tubing cut to different lengths) based on a linear measurement model of the number line were used to help students appreciate the relationships between 1 whole, 1/10, and 1/100. Selected excerpts from the learning sessions are used to illustrate the insights that emerged during learning sessions. The findings are interpreted using the theoretical frameworks of Piaget and Vygotsky.

Errors Made by Student Teachers when Writing Test Items
Jaguthsing Dindyal

Learning to write good test items is an important aspect of the teacher preparation programmes in Singapore. This paper reports on the types of errors in writing test items in mathematics made by student teachers who were following the pre-service course for teaching at primary level. An analysis of the errors reveals that student teachers demonstrate some key shortcomings in: Use of language, mastery of content knowledge, use of diagrams as support, and use of appropriate context when writing the items.

Financial Modelling with Matlab
Peter Watson and Jiling Cao

Financial modelling is an accessible and practical way to expose students to the power of mathematical modelling and the Excel spreadsheet with its extensive collection of financial functions is often incorporated into courses on financial mathematics. At AUT University we have chosen to focus on the Excel spreadsheet for our introductory courses and this has served us well as students have developed modelling skills and Excel skills at the same time as being exposed to financial functions. In our more advanced course we have introduced students to the financial toolbox in Matlab. In this study we report on some experiences of this initial group of students as they grapple with the different mindset needed to relearn from a Matlab perspective functions they had mastered using Excel and explore the potential that Matlab offers to move beyond what Excel can offer. Our report will also identify some of the limitations we have uncovered as we have developed our course and allow us to demonstrate why financial modelling provides a fruitful source of worthwhile examples to help students to develop modelling skills.

Improving Language for Problem Solving
Benedicte Esterman

This study proposes to look at the nature of language required in a middle school mathematics classroom through a teaching experiment. The teaching intervention proposes to provide explicit teaching of the mathematical and non-mathematical language and orchestrate subsequent opportunities for students to engage in substantive communication through cooperative groupwork. The emphasis will be on conceptual understanding through language acquisition rather than solely through learning procedures. The study proposes to examine the impact of the teaching intervention on student motivation and engagement in mathematics.

Insights from Pre-service Secondary Mathematics Teachers on their Practicum Experience
Jaguthsing Dindyal

In this study, a sample of 73 pre-service secondary mathematics teachers, enrolled in the PGDE programme at the National Institute of Education in Singapore, completed a survey about their views on their practicum experience. Preliminary results show that most of the student teachers acknowledged that the practicum was a good learning experience but they differed in what they reported was the most important aspect of their learning about the teaching of mathematics and about what they perceived as their most and least memorable experiences while teaching mathematics during the practicum.

Motivation and Engagement in Mathematics: The Transition from Primary to Secondary School
Karen Skilling

This research will examine factors affecting engagement in Mathematics as students make the transition from primary and secondary schooling. This presentation will consider the background literature and include discussions on factors affecting motivation, engagement, and student learning in the middle years of schooling, such as teacher-student relationships, teacher content knowledge, and pedagogy. The research questions will be presented and an outline of the proposed methodology will be provided. Understanding the factors that affect students’ learning at this significant stage of education will better inform educators about the issues that may influence their subject choices beyond middle schooling.

Reflections on Exponential Functions
Sandra Herbert and Farhang Afshar

A pilot study, analysing twenty-one Year 10 students’ reflections on a unit on exponential functions taught using real-world problems, and supported by the use of CAS calculators. The real-world contexts explored during the unit provided a focus for follow-up interviews. Detailed analysis of the transcripts revealed four themes: Impact of technology; difficulty in expression; prediction; choice of scenario. Findings support results from related research reported in the literature and highlight the importance of the choice of real-world scenarios. Analysis revealed variation in students’ preference relating to scenarios. This variation provides a challenge in the preparation of appropriate material.

Scaffolding Students’ Understanding of Geometric Properties Using Dynamic Geometry Software
Sahar Bokosmaty

Significant technological tools have impacted on students’ learning of Mathematics. In this study, I wish to seek evidence that dynamic geometry enhances students’ understanding of certain geometric properties and can serve as a vehicle for discovering unknown properties. The aim of the study is to explore the impact of dynamic geometry on 40 Year 9 high school students’ understandings of geometric properties. A mixedmethodology will be utilized in order to confirm the findings from different data sources; such as interview, video and audio recordings, computer savings, students’ workbooks, and pre- and post-tests.

The Next Big Teaching Resource: Interactive White Boards But Where is the Research?
Philip C Clarkson

Schools are rapidly adopting Interactive White Boards (IWBs) [or alternatively termed Smart Boards]. The rapidity of uptake has not been in step with any well designed, comprehensive research effort that might inform patterns of adoption and implementation by teachers, nor any sufficient understanding about the impact IWBs might have on students and their learning in mathematics and other areas of the curriculum. This is not the first time that attractive resources have been rapidly taken up into the teaching of mathematics, based more on faith. Whether this matters is an interesting question to ask. In this short communication, I concentrate on insights from some of the relevant IWB research literature, noting gaps and deficiencies that need to be addressed. In particular it is noted that usually only self-report methods are used, there is a lack of studies that describe the impact of IWB use on cognition and that document actual changes in classroom interaction. As well studies often do not clearly focus on IWBs. These shortcomings make it difficult to assess the impact of IWB technology, if not impossible, in terms of any changes in the quality of student learning. Teachers certainly like them, but is this enough?

The Role of Mathematics Competitions
Brenda Bicknell

What role do competitions play in a mathematics programme? This question is examined from the multiple perspectives of fifteen students (11-13 year olds) identified as mathematically gifted and talented, and their teachers and parents. A variety of different types of mathematics competitions were subscribed to including local, national, and international competitions. There was varied access to the competitions and differing perspectives; students and parents shared similar views about the value of competitions but there was a difference of opinion among the teachers.

The Role of Pattern and Structure in Early Mathematics Learning: An Evaluation Study in the First Year of Formal Schooling
Joanne Mulligan, Lyn English and Mike Mitchelmore

An evaluation study aims to validate a new conceptual framework for mathematics learning based on the development of pattern and structure. It will evaluate the effectiveness of a school-entry mathematics program built on this framework using classroom observations and an interview-based student assessment. The Pattern and Structure Mathematics Awareness Program (PASMAP) focuses on unit of repeat, multiplicative reasoning, spatial structuring, and congruence and similarity. The program will be evaluated in Kindergarten classes from four large primary schools in Brisbane and Sydney.

Poster (abstract only)
Round Table (abstract only)
MERGA: Including the X and Y in Mathematics Education Research
Peter Grootenboer and Naomi Ingram

MERGA has enjoyed a strong and rich history since its inception over 30 years ago. In that time it has been instrumental in supporting and developing a prominent group of mathematics education researchers who have made a significant contribution to the field. The purpose of this Round-Table Discussion is to consider how MERGA and its members might continue to promote, support and encourage mathematics educators from generation X and generation Y (and beyond), so they can stand on the shoulders of those who have gone before, and continue to build the stellar reputation of mathematics education research in Australasia. This discussion is open to both experienced and novice researchers, and hopefully it will lead to some strategies and ideas for succession planning that will ensure the health of MERGA and mathematics education research into the future.

Moving Beyond the Script: Addressing Numeracy Needs of Low Achieving Students through Quality Professional Development
Moira Blair and Anuja Singh

The New Zealand Numeracy Development Project (NDP) was introduced to combat the disparity between high and low achieving students. It originated as a pilot project in 1999 as an extension and modification of the Australian ‘Count Me In Too’ project, and was implemented by the Ministry of Education in 2001. Whilst some improvements have been noted, there is evidence of continuing disparity between Maori and Pakeha student achievement, and underachievement of these students remains a concern. A vital component of NDP was that teachers were provided opportunities for professional development. A Ministry of Education Quality Teacher Research and Development (QTRD) program was introduced in 2007, supporting teachers in action research to raise student achievement. This presentation analyses the experiences of a group of teachers who undertook the QTRD course to develop more effective teaching practices to enhance the learning of low achieving Maori and Pasifika students. We provide complementary perspectives on our participation in the project, and the dual benefits of increased student achievement and ongoing professional learning for the teachers. We argue that quality, theory-based professional development and reflective practice are necessary to enhance the teaching and learning of disadvantaged students. In the Round Table we hope to stimulate discussion with Australian, New Zealand, and other international colleagues about: • The nature of successful professional development partnerships between teachers and university researchers; • Characteristics of effective numeracy education programs for disadvantaged students; • Challenges in working with teachers and students in low socio-economic or disadvantaged areas.

Student Achievement in Mathematics: Learning through Home School Partnership
Honor Ronowicz and Gaynor Terrill

The Home School Partnership Numeracy facilitators will start the round table discussion by presenting the findings from three small studies: i) Two case studies investigating if schools change the way they communicate student achievement to parents as a result of participating in the Home School Partnership project. ii) A small research project involving all of the schools across the Waikato region that have been involved in Home School Partnership projects in the last three years. The international evidence cited in Alton-Lee (2003) positively supports the enhancement of student learning through home and school partnerships. In New Zealand, two Best Evidence Syntheses research also highlight the importance of establishing effective relationships between home and school (Alton-Lee, 2003; Biddulph, Biddulph, & Biddulph, 2003). The Home School Partnership project reflects the acknowledgement of parents as first teachers and the desire to continue to encourage parents to confidently interact and communicate with their children about mathematics. Effective relationships within the school community encourage parents to take an active role in the shared responsibility of their children’s education. Aspects that might be considered in this discussion include: Background information about home and school partnerships; successful learning communities involving facilitators, lead teacher and lead parents; and communication of student achievement to parents. Alton-Lee, A. (2003). Quality teaching for diverse students in schooling: Best evidence synthesis. Wellington: Ministry of Education. Biddulph, F., Biddulph, J. & Biddulph, C. (2003). The complexity of community and family influences on children’s achievement in New Zealand: Best evidence synthesis. Wellington: Ministry of Education.

There is scant research on the role of graphics in students’ mathematical performance. This paper distinguishes between the contextual and informational roles of graphics and provides an overview of the types of information graphics. It also presents
Catherine Attard

The purpose of this roundtable is to describe a research proposal and seek feedback and advice on the proposed study. The research project aims to investigate current concerns of a downturn in motivation and engagement levels as students move through the middle years of schooling (Years 5 to 8 in New South Wales). Current research has shown at this time of transition from primary schooling to secondary many of these students begin to perceive mathematics to be a special domain in which smart students succeed and others merely get by or fail. Although students feel mathematics is important, many are not pursuing mathematics in the later years of school. This choice is seriously influenced by attitudes towards and performance in mathematics and significantly shaped by school mathematical experiences. While there is a wealth of research investigating issues surrounding the motivation and engagement of students in mathematics during the middle years, there is a gap in the research in terms of longitudinal studies. Through this longitudinal study there will be opportunity investigate if and how levels of motivation and engagement change within students as they progress through the transition from primary to secondary schooling. Within the study factors affecting any changes in motivation and engagement will be investigated and factors that play a role in increasing or sustaining levels motivation and engagement in mathematics will be identified.