Conference Proceedings 2003

A Tribute to the Research Work of Dr. Glendon Lean
Alan J. Bishop
Judy Mousley
List of Reviewers
Keynote Address
Opportunities to Learn Mathematics
Anne Watson
The TIMSS 1999 Video Study and its Relevance to Australian Mathematics Education Research, Innovation, Networking, and Opportunities
Hilary Hollingsworth
Working Together to Enhance Australian Aboriginal Students' Mathematics Learning
Susan Matthews, Peter Howard, Bob Perry
Practical Implication Award
Using Case Stories as a Tool for Listening More and Telling Less in Mathematics Teacher Education
Tracey Smith
Identifying and Overcoming Barriers to Mathematics Learning
Perceptions of Barriers to Numeracy
Judith A. Mousley
Teachers' Perceptions of How Open-Ended Mathematics Tasks Assist in Overcoming Barriers to Learning
Robyn Turner-Harrison
The Potential of Open-Ended Mathematics Tasks for Overcoming Barriers to Learning
Peter Sullivan
Research Paper
Students' Knowledge of Rates: A Case for a Foundation Year Program in South Africa
Kabelo Chuene
Investigating the Concerns of Preservice Secondary Mathematics Teachers Through Critical Incident Reflective Journals
Joanne E. Goodell
Developing Prospective Primary Teachers' Personal Content Knowledge of Mathematics
Roger Harvey
Trigonometric Graph and the Real World: The Technical Students' Experience
Madihah Khalid
Ethnomathematical Ideas in the Curriculum
Shehenaz Adam
Searching for Mathematical Ideas in Stone Walls
Wilfredo Alangui
Implementing Beliefs, Knowledge and Practices: A Beginning Teacher's StOlY
Shame Aldridge & Janette Bobis
Teachers' Choice of Tasks: A Window Into Beliefs About the Role of Problem Solving in Learning Mathematics
Judy Anderson
Pizza for Dinner: "How Much?" or "How Many?"
Glenda Anthony & Margaret Walshaw
Bicultural Perspectives in a Pre-service Mathematics Education Course
Robin Averill & Pӓnia Te Maro
A Window Into Mathematics Communities of Practice in Australia and New Zealand
Jack Bana & Margaret Walshaw
Secondary Mathematics Teachers' Beliefs About Assessment and Factors That Influence These Beliefs
Anastasios Barkatsas & John Malone
Investigations Into the Introduction of Logarithm Tables in Victoria
Chris Barling
Patterns of Participation in Small-Group Collaborative Work
Mary Barnes
Ability Grouping and the Construction of Different Types of Learner in Mathematics Classrooms
Hannah Bartholomew
The Mathematics Enhancement Project: Using the Concepts of Cultural Conflict, Critical Mathematics Education, and Didactic Contract
Bill Barton
Curriculum: Developing a Systems Theory Perspective
Andy Begg
Accounting for the Contextual Nature of Teachers' Beliefs in Considering Their Relationship to Practice
Kim Beswick
Children's Perspectives on Mathematics and Game Playing
Leicha Bragg
Defining Moments in Determining a Complete Graph in a Graphing Calculator Teaching and Learning Environment
Jill Brown
Subject Knowledge in Pre-service Teacher Education
Tim Burgess & Brenda Bicknell
A Comparison Among Three Different Approaches to Mathematics Assessment
Rosemary Callingham
The Positioning of Mathematics in an Environmental Thematic Curriculum
Coral Campbell
Transnumeration and the Art of Data Representation
Helen Chick
Maps That Come Alive: Numeracy Engagement Across Multimodal Texts
Susan Clancy & Tom Lowrie
Similarity and Difference in International Comparative Research in Mathematics Education
David Clarke
Addressing the Challenge of Legitimate International Comparisons: Lesson Structure in Australia and the USA
David Clarke & Carmel Mesiti
More Perspectives on the Impact of Globalisation on Mathematics Education in Higher Education in Australasia
Philip Clarkson & Bill Atweh
Windows Into Mathematics Teaching Through Data Maps
Carmel M Diezmann
Teaching in a Different Direction
Helen Doerr & K. Jamie King
Designing Research on Teachers' Knowledge Development
Helen Doerr & Richard Lesh
Hops, Steps and Jumps: Mathematical Progress in the Early Years
Brian Doig & Molly de Lemos
Questioning Numeracy Programs for At-Risk Students In The Middle Years Of Schooling
Shelley Dole
Secondary Students' Perceptions of Instructional Approaches: Implications for Mathematics Learning
Sabita M. D'Souza & Leigh N. Wood
Designing Assessment Using the MATH Taxonomy
Sabita M. D'Souza & Leigh N. Wood
Development of a Web-Based Learning Tool to Enhance Formal Deductive Thinking in Geometry
Madduma Bandara Ekanayake & Christine Brown &
The Victorian Curriculum and Assessment Authority (VCAA) Mathematical Methods (CAS) Pilot Study Examinations, 2002
Michael Evans & Pam Norton & David Leigh-Lancaster
On Student Observation and Student Assessment
Ruhama Even & Tali Wallach
Mathematics as Conversation: A Model for a Mathematics Retrieval Programme Conducted With Small Groups
Judith Falle
Copying on a Graphics Calculator and Implications for Mathematical Understanding
Patricia A. Forster
Re-visioning Curriculum: Towards Communicative Competence
Patricia A. Forster
Using Mathematics Teaching Portfolios to Empower Pre-Service Primary Teachers
Sandra Frid & Len Sparrow
Gender and Approaches to Studying Tertiary Mathematics
Mary-Ruth Freislich & Alan Bowen-James
From Description to Analysis in Technology Aided Teaching and Learning: A Contribution From Zone Theory
Peter Galbraith & Merrilyn Goos
A Teacher-Researcher Perspective on CAS in Senior Secondary Mathematics
Sue Garner & David Leigh-Lancaster
What Students Say: Analysis of Structured Survey Data in Relation to Technology and Mathematics Learning
Vince Geiger
Difficulties Children Face When Learning to Count
Ann Gervasoni
Student Perspectives on Equation: Constructing the Mathematical Object
David Godfrey & Michael Thomas
Learning to Teach Mathematics With Technology: A Study of Beliefs-In-Context
Merrilyn Goos
Facilitating Affective Change With Preservice Primary Teachers
Peter Grootenboer
Mental Computation: Refining the Cognitive Frameworks
Ann M. Heirdsfield
Designing a Discussion: Teacher as Designer
Margret A. Hjalmarson
Mathematics in Indigenous Contexts: A Case Study
Peter Howard & Bob Perry & Kevin Lowe & Suzanne Ziems & Anthony McKnight
Constructing and Using a Personal Numeracy Teaching Model in a Classroom Setting
Peter Hughes & Lynne Petersen
Percentages: A Foundation for Supporting Students' Understanding of Decimals
Roberta Hunter & Glenda Anthony
The Development of Multiplicative Thinking in Young Children
Lorraine Jacob & Sue Willis
Julia's Journey: Teacher Research in the Primary Mathematics Classroom
Stephen Keast
Achievement Self-Rating and the Gender Stereotyping of Mathematics
Gilah C. Leder & Helen J. Forgasz
Australian Secondary School Teachers' Use of the Internet for Mathematics
Esther Loong
Teaching Mathematics Using the Internet
Esther Loong & Bruce White
Posing Problems in ICT-Based Contexts
Tom Lowrie
Monitoring Standards in Education: Mathematics 2002 Assessment
Andrew Stephanou, Barry McCrae, Rhonda Farkota, John Lindsey, Elena Stoyanova
Tensions and Possibilities: Indigenous Parents Doing Mathematics Curriculum Development
Tamsin Meaney & Uenuku Fairhall
Count Me In Too and the Basic Skills Test in New South Wales
Michael Mitchelmore & Paul White
Shaping Practice: Worksheets as Social Artefacts
Judith A. Mousley
First Graders' Use of Structure in Visual Memory and Unitising Area Tasks
Joanne Mulligan & Anne Prescott
Re-visioning Curriculum: Shifting the Metaphor From Science to Jazz
Jim Neyland
Individualization of Knowledge Representation in Teacher Education in Mathematics
Engelbert Niehaus
Organising and Representing Grouped Data
Steven Nisbet
A Whole School Approach to the Provision of Mathematics for Low-Achieving Girls in a Secondary School
Bob Perry & Jane Fulcher
Interactive Animation Provides a Vehicle for Exploring Students' Understandings of Derivatives
Robyn Pierce & Lyn Atkinson
Is it Better to Burn Out or to Rust?
Peter Rawlins
Links Between Beliefs of Pre-Service Teachers About Literacy and Numeracy Learning
Anne Scott
High School Students' Interpretation of Tables and Graphs: Some Findings From Fiji
Sashi Sharma
Identifying Effective Scaffolding Practices Through Structured Peer Observation and Review
Dianne Siemon & Jo Virgona
Gambling Behaviour and Understanding of Probability Concepts Among University Students
Donald Smith

Exploring the Right, Probing Questions to Uncover Decimal Misconceptions
Vicki Steinle & Kaye Stacey

Monitoring Standards in Education: Mathematics 2002 Assessments
Andrew Stephanou, Barry McCrae, Rhonda Farkota, John Lindsey & Elena Stoyanova
Probing Whole Number Dominance With Fractions
Max Stephens & Catherine Pearn
Metacognitive Intervention in a Cognitive-apprenticeship-computer-based Environment
Teong Su Kwang
A Model of Early Number Development
Kaye Treacy & Sue Willis
Gender and Attitudes to Computer Use in Junior Secondary Mathematics
Colleen Vale
Year 8 Students' Reasoning in a Cabri Environment
Jill Vincent
Sociomathematical Worlds: Investigating Children's Developing Relationships With Mathematics
Fiona Walls
Number Combinations and Arithmetic Structure: Implications for Early Algebra
Elizabeth Warren
Inference From a Pictograph: Statistical Literacy in Action
Jane M. Watson & Ben Kelly
Predicting Dice Outcomes: The Dilemma of Expectation Versus Variation
Jane M. Watson & Ben Kelly
The Development of Children's Reasoning Strategies in Probability Tasks
Jenni Way
Lesson Study: A Model of Professional Development for Teachers of Mathematics in Years 7 to 12
Allan L. White & Beth Southwell
Associations Between Student Pursuit of Novel Mathematical Ideas and Resilience
Gaye Williams
Assessing Generalisation of Advanced Multiplicative Strategies
Vince Wright
Changes in Teachers' Perceptions of Technology in Mathematics
Shirley M. Yates
The Perspectives of Two Children who Participated in the Advanced Numeracy Project
Jenny Young-Loveridge & Merilyn Taylor
Mathematical Errors in Fractions: A Case of Bruneian Primary 5 Pupils
Jamilah Yusof & John Malone
Numeracy in New Times: Implications for Youth, Work and Employment
Robyn Zevenbergen & Kelly Zevenbergen
Reforming Mathematics Education: A Case Study Within the Context of New Times
Robyn Zevenbergen
Teachers' Conceptions of School Algebra and its Teaching: Preliminary Findings from a Study in Colombia
Cecilia Agudelo-Valderrama, & Alan Bishop
Short Communication (abstract only)
A Student's Strategies in Deriving Quartic Modelling Functions Using Rates of Changes
Karoline Afamasaga-Fuata't

This paper reports findings from a research study which examined students' strategies for deriving modelling functions from numerical patterns with rates of changes in contrast to the equation-graph matching approach prevalent in schools. Students involved were final year mathematics undergraduate students some of whom were practicing teachers of mathematics or were intending to teach. Students had already examined the cases of linear, quadratic, cubic and some exponential functions and were requested to extend their projects to quartics, other exponential functions and a trigonometric or logarithmic function. This paper presents and discusses the data from the quartic project of one of the 8 students involved in the study.

Classroom and Learning Factors Preferred by Year 9 Students in the Teaching and Learning of Mathematics
Barbara Tadich

This report describes a recent case study research which provides evidence that student learning, and student achievement can be accomplished by teachers working with a greater knowledge of student development. The key elements investigated in the study include both classroom and learning features. In particular an understanding of Kohlberg's (1963, 1973) stages of moral development is addressed. Giddens' (1984) concepts of the reflective cycle and its ability to lead to empowered action and to the uncovering of the range of choices (for the students and teacher) to act, or not to act, to make a difference to events is included. The data collected via personal observations, students' perceptions and voice, emphasized that an understanding of Kohlberg's and Giddens' work can add new dimensions to the middle years of schooling debate regarding adolescent teaching and learning. An understanding of young adolescents, especially in Year 9, requires greater knowledge of developmental and learning theories with a holistic approach to teaching and learning.

Developing a Framework of Growth Points in Secondary Students' Understanding of Function
Erlina Ronda, Doug Clarke, Marj Horne

It is widely accepted that teachers' knowledge of students' thinking in acquiring concepts and procedures in a specific mathematical domain can be a powerful tool in informing instruction. The framework of growth points in the understanding of function developed in the present study may provide such a contribution. This paper is a progress report of the development of the framework of growth points. The basis of the framework was an initial survey of the literature, which was progressively revised, using data from students in Years 8 to 10 in Victoria and The Philippines.

How is the Motivation of the Two Year 13 Pacific Islands Mathematics Learners Shaped by their Culture? A Case Study
Viliami Finau Latu

The aim of this project is to link research to the improvement of mathematics teaching practice by investigating ways in which mathematics educators and teachers can foster Pacific Islands learners' motivation to learn mathematics. An important area to investigate is the ways in which Pacific Islands learners' motivation is shaped by their culture. A small study involving two students was conducted with the specific aim of exploring cultural influences that contributed to their motivation to learn mathematics. The factors that appeared to have the most influence on motivation were; the aspiration of students to do well so that they can help their families financially, the need to do mathematics to obtain a job, and the disparities between home and school.

Persisting Teen/ty Confusions as an Indicator of a Specific Learning Difficulty in Mathematics: Implications for Assessment and Instruction
Maureen Finnane

A specific difficulty in memorizing basic arithmetic facts has been well established as a persisting problem for students with learning difficulties in mathematics. Theories for underlying causes range from low working memory capacity to a failure to encode numbers semantically. Understanding the quantity meaning of the teen numbers is a particular difficulty for some students. This paper will present an intervention designed for a Year 2 Queensland student with persisting teen/ty confusions and a self-acknowledged difficulty in memorising the large doubles facts. Making the tens/ones structure of the teen numbers more transparent to the student provided a foundation for him to learn his large doubles to the point of fluency.

Professional Learning in the Teaching of Area
Diane McPhail

Seventeen Year 1 and Year 2 teachers participated in a professional development program focusing on the teaching of area. The teachers were offered three different levels of consultancy support. A comparison of results from the students and teachers indicates that the success of the teacher professional development, as measured by student learning and teachers' change in practice, was determined by teachers' ability to work in school-based teams, and an initial desire to improve their teaching of mathematics. The success of the program as a teacher professional development activity was not dependent on the level of consultancy support provided for teachers.

Questions in Primary Mathematics Classrooms
Colleen Vale

In this paper data gathered from teachers who participated in a professional development program designed to improve the quality of questioning in mathematics classrooms are presented. Teachers from five primary schools participated in the program. It was designed by the teachers and funded as a Quality Teacher Project. At the beginning and end of the school year, data were gathered by questionnaire about teachers' practice and, in particular, the types of questions that they used in their mathematics teaching. The types of questions that these primary teachers used when teaching mathematics are discussed.

The Predictive Factors of Classroom Learning Environments on High School Students' Mathematics Anxiety
Bret A. Taylor

The purpose of this research was to examine the possible associations between the perceived classroom environment of high school students in Southern California and the level of mathematics anxiety that they possess. Data were gathered using a revised version of Plake and Parker's (1982) Revised Mathematics Anxiety Ratings Scale and the What is Happening In This Classroom learning environment survey created by Fraser, McRobbie, and Fisher (1996). This research involved both quantitative and qualitative data obtained via the research instruments and interviews with those having extremely high or low math anxiety.

Poster (abstract only)
Round Table (abstract only)
Collective Mathematical Understanding as Improvisation
Lyndon Martin & Jo Towers

This research is concerned with the nature of the growth of mathematical understanding, and more specifically with how a group of learners can develop a collective understanding for a mathematical concept. We seek to characterise collective mathematical understanding as a creative and emergent improvisational process, through drawing on theoretical perspectives from the fields of jazz (Becker, 2000; Berliner, 1994; 1997), theatre (Sawyer 1997; 2000) and conversation (Sawyer, 2001). In considering video data, taken from an initial pilot study, we extend improvisational theory to begin to consider collective mathematical understanding as a process with a similar nature and characteristics.

Numeracy Equipment and Year 3 Children: Bright, Shiny Stuff, or Supporting the Development of Part-whole Thinking?
Linda Bonne

New Zealand teachers' use of equipment has increased as a result of their participation in the Numeracy Development Projects. However, the equipment choices of the four teachers interviewed in this study were not strongly consistent with the equipment use recommended in the NDP materials. In the teachers' reasons for equipment choices, the surface features of equipment seemed equally important as the conceptual development it can support. In contrast, the reasons given for equipment choices by the 34 Year 3 children who were interviewed were almost exclusively concerned with how the equipment might help them to solve the given problem. The children's success rates at solving the problem declined as the equipment became more structured; this paralleled the teachers' equipment choices. The ultimate goal for teacher educators must be for all teachers to have a richly connected conceptual map of numeracy, in order for teachers to be able to effectively use equipment in ways that help children to construct their own meaningful connections as they learn about number. Rather than talking about equipment as "bright, shiny stuff", teachers must have a clear focus on the role that equipment can play in the development of children's part-whole thinking. In this round table presentation the findings from this study, which was conducted during 2002 as part of a Masters thesis, will be discussed.

Professional Development for Mathematics Education Researchers
Helen J. Forgasz

As mathematics educators, we frequently speak of the professional development needs of mathematics teachers. Many of us run professional development sessions or courses. Others of us conduct research and in our scholarly writings reflect on the implications of our findings on teacher professional development. Less often do we think about our own professional development needs. In my capacity as MERGA Vice-President (Research), I have often thought about how MERGA might assist in promoting the range of skills that mathematics education researchers might need to serve as the providers and nurturers of the next generation of researchers in our discipline, and to function as more effective and fruitful researchers whose findings are widely disseminated, highly acclaimed, and broadly implemented for the betterment of mathematics teaching and learning at all levels. I am proposing this round table session as the means to commence a discussion on what the professional needs of mathematics education researchers might be and what MERGA might do with respect to them. Some of the ideas floating around in my head include: various types of reviewing (conference papers, scholarly articles, book chapters, ARC grants), supervising higher degree students, examining theses, preparing grant applications (large/small/other), developing tenders, writing for different audiences, approaching publishers, learning about new/different research approaches/techniques, using computer software effectively for conducting research and/or analysing data, mentoring others, developing teaching/research portfolios, and promoting interviewing skills (as interviewer and/or interviewee). I'm sure there are other needs. Come and share your concerns and ideas

Student Beliefs & Their Impact on Participation in Mathematics in the Middle School
Robyn Turner-Harrison

This round table discussion will focus on a proposed study of middle school children's beliefs about their participation in mathematics classrooms. In the study the motivation of students when undertaking mathematics tasks, and the influence of motivation on strategies for coping with frustration when experiencing difficulties, will be investigated. It is suspected that some students may not have established perceptions of the benefits of being competent in mathematics, nor be aware that there is potential for them to be empowered by competency. One determinant of participation in education is student perceptions of goals, and the influence that perceptions play on motivation. Students who feel in control of their lives are more likely to have opportunities for success both within schools and without (Lapadat, 1998). Dweck (2000) investigated perceptions of intelligence and contended that students may hold beliefs that inhibit their participation at school; that students can be taught that both intelligence is incremental and a mastery orientation can be taught through explicit instruction. Students of one grade six class will complete an assessment in which each task is incrementally harder to complete. Once each task is completed, they will be asked to evaluate their work. If correct they will continue to the next task. If not, they will be asked how they feel, and what teaching they require in order to continue. Various background data will be gathered to seek to identify contributing factors, and a survey adapted from Dweck's instrument will seek data on their beliefs concerning mathematical intelligence.