Conference Proceedings 2009


Verso page
Crossing divides: Proceedings of the 32nd annual conference of the Mathematics Education Research Group of Australasia
Preface, including review process
Roberta Hunter, Brenda Bicknell, Tim Burgess
List of Reviewers
Keynote Address
Being Mathematical, Holding Mathematics: Further Steps in Mathematical Knowledge for Teaching
Bill Barton
Developing Pedagogies in Teacher Education to Support Novice Teachers’ Ability to Enact Ambitious Instruction
Elham Kazemi, Megan Franke, Magdalene Lampert
Practical Implication Award
Symposium 1.1: Developing Mathematical Concepts in Australian Pre-school Settings: The Background
Judith Mousley, Bob Perry
Symposium 1.2: Developing Mathematical Concepts in Australian Pre-school Settings: Children’s Mathematical Thinking
Marina Papic, Joanne Mulligan, Janette Bobis
Symposium 1.3: Mathematical Thinking of Young Children Through the Eyes of Preschool Practitioners
Robert Hunting, Catherine Pearn
Symposium 1.4: Mathematical Thinking of Preschool Children in Rural and Regional Australia: Implications for the Future
Bob Perry
Symposium 1: Cover page: Developing Mathematical Concepts in Australian Pre-school Settings
Symposium 2.0: Crossing Philosophical Divides to Better Understand the Complexity of the Learning Process in Mathematics
Symposium 2.1: Uniting Psychological, Sociocultural and Poststructural Axes of Analysis to Better Understand Learning in Mathematics
Mary Klein
Symposium 2.2: Bridging Understandings, Interest and Identity Gaps in a First Year Numeracy Subject
Kerry Smith
Symposium 2.3: Crossing the Divide between Teacher Professionalism and National Testing in Middle School Mathematics?
Silvia Dimarco
Symposium 2.4: Crossing Philosophical Divides: Adding Poststructuralist Insight into Building, Maintaining and Changing Teaching for Better Learning
Mary Klein
Symposium 3.0: A New Approach to Mathematical Problem Solving in the School Curriculum
Symposium 3.1: Reconceptualising Problem Solving in the School Curriculum
Jaguthsing Dindyal, Toh Tin Lam, Quek Khiok Seng, Leong Yew Hoong, Tay Eng Guan
Symposium 3.2: Assessment in a Problem Solving Curriculum
Toh Tin Lam, Quek Khiok Seng, Leong Yew Hoong, Dindyal Jaguthsing, Tay Eng Guan
Symposium 4.0: Reforming Mathematical Pedagogy in Remote Indigenous Context
Symposium 4.1: Rich Mathematical Tasks in the Maths in the Kimberley (MITK)
Peter Grootenboer
Symposium 4.2: Cooperative Learning Environments
Robyn Jorgensen (Zevenbergen)
Symposium 4.3: The Use of Home Language in the Mathematics Classroom
Richard Niesche
Symposium 4.4: Describing Teacher Actions After Student Learning from Rich Experiences
Peter Sullivan
Symposium 5.0: Task Types and Mathematics Learning
Symposium 5.1: The Task Types and Mathematics Learning Research Project
Helen O'Shea, Irit Peled
Symposium 5.2: Using Tasks Involving Models, Tools and Representations: Insights from a Middle Years Mathematics Project
Barbara Clarke
Symposium 5.3: Opportunities and Challenges for Teachers and Students Provided by Tasks Built Around “Real” Contexts
Doug Clarke, Anne Roche
Symposium 5.4: Constraints and Opportunities When Using Content-specific Open-ended tasks
Peter Sullivan
Symposium3.3: Teacher Preparation for a Problem Solving Curriculum
Leong Yew Hoong, Toh Tin Lam, Quek Khiok Seng, Jaguthsing Dindyal, Tay Eng Guan
Research Paper
Issues in bridging between senior secondary and first year university mathematics
Michael Jennings
Students’ Perceptions of the Impacts of Parents, Teachers and Teaching upon their Anxiety about the Learning of Fractions
Michelle Jennison, Kim Beswick
Insights into the Beliefs and Practices of Teachers in a Remote Indigenous Context
Robyn Jorgensen (Zevenbergen), Peter Grootenboer, Richard Niesche
Innovative Problem Solving and Students' Mathematics Attitudes
Karoline Afamasaga-Fuata'i
“My Favourite Subject is Maths. For Some Reason No-one Really Agrees With Me”: What Year 6 Students Say About Mathematics
Catherine Attard
Re-focussing Research Agendas
Andy Begg
Guessing Answers to Pass a 5-item True False Test: Solving a Binomial Problem Three Different Ways
Anthony Bill, Jane Watson, Peter Gayton
Concept Maps: Implications for the Teaching of Function for Secondary School Students
Jill P Brown
Students’ Recollections of Participating in Collective Argumentation When Doing Mathematics
Raymond Brown, Brooke Reeves
Changing Teachers’ Classroom Practice through Developmental Assessment: Constraints, Concerns and Unintended Impacts
Rosemary Callingham, John Pegg, Teresa Wright
The Development and Validation of the Students’ Self-efficacy for Statistical Literacy Scale
Colin Carmichael, Ian Hay
Gender Differences in Middle School Students’ Interests in a Statistical Literacy Context
Colin Carmichael, Ian Hay
Group Metacognition During Mathematical Problem Solving
Christina Chalmers
Challenging Mathematical Conversations
Jill Cheeseman
Teaching the Distributive Law: Is Fruit Salad Still on the Menu?
Helen Chick
Mathematics Education, Language, and Culture: Ponderings From a Different Geographic Context
Marta Civil
Institutional Gaps in Mathematics Education Research Procedures Between a Developed and Developing Country
Ernest Kofi Davis, Wee Tiong Seah, Alan J. Bishop
Developing Year 5 Students’ Understanding of Density: Implications for Mathematics Teaching
Shelley Dole, Doug Clarke, Tony Wright, Geoff Hilton
It Seems to Matters Not Whether it is Partitive or Quotitive Division When Solving One Step Division Problems
Ann Downton
Developing Conceptual Place Value: Instructional Design for Intensive Intervention
David Ellemor-Collins, Robert (Bob) Wright
I, You and It: Pronouns and Students’ Understanding of Introductory Algebra
Judith Falle
Teachers' Use of Mathematics Tasks: The Impact on the Mathematics Learning and Affective Responses of Low-attaining Upper Primary Students
Sarah Ferguson
Textbook Dilemmas
Tricia Forrester
The Master, Servant, Partner, Extension-of-self Framework in Individual, Small Group and Whole Class Contexts
Vince Geiger
Investigating the Professional Learning and Development of Mathematics Teacher Educators: A Theoretical Discussion and Research Agenda
Merrilyn Goos
Revealing Conceptions of Rate of Change
Sandra Herbert, Robyn Pierce
Competencies, Skills and Assessment
Tomas Hojgaard
Success for Underachievers: How Do They Get It?
Marilyn Holmes, Sandi Tait-McCutcheon
Teachers’ Perspectives on the Transition from Secondary to Tertiary Mathematics Education
Ye Yoon Hong, Suzanne Kerr, Sergiy Klymchuk, Johanna McHardy, Priscilla Murphy, Sue Spencer, Mike Thomas, Peter Watson
Developing a Productive Discourse Community in the Mathematics Classroom
Jodie Hunter
Exploring Whether Multiple Intelligences Facilitate ‘Valuing and Working With Difference’ within Mathematics Classrooms
Fiona Jackson, Raymond Brown
Identifying Effective Leadership Practices for Implementing a New Mathematics Curriculum in Taipei
Brandon Kao, Peter Hudson
Being Numerate for Teaching: The Indivisibility of Learning Landscape, Participation and Practice
Mary Klein, Kerry Smith
Leading Change in Mathematics: The Queensland Mathematics Syllabus
Janeen Lamb, Gayle Spry
Publishing in Mathematics Education: A Matter of Gender?
Gilah C. Leder, Helen J. Forgasz
Enhancement of Fractions from Playing a Game
Ya Ling Lee
A Hierarchy of Strategies for Solving Linear Equations
Chris Linsell
Using Web-Based Mathematical Interactive Exercises and Exploratory Investigations: The Possibilities and Pitfalls
Esther Yook-Kin Loong
Young Children’s Explorations of Average in an Inquiry Classroom
Katie Makar, Debra McPhee
Achieving in Mathematics Contested Spaces and Voices
Colleen McMurchy-Pilkington, Hannah Bartholomew
The Option of Selecting Higher-level Mathematics Courses: Transitional Tensions
Greg McPhan, John Pegg
There are More Than Part-Whole Strategies at Work in Understanding Non-Equal-Parts Fraction-Area-Models
Annie Mitchell, Marj Horne
Evolving Mathematics Classroom Assessment Cultures
Rohani Mohamad
Numeracy Test Item Readability During Transition from Pre-School to School
Judith A. Mousley
At Home With Numeracy: Empowering Parents to be Active Participants in their Child’s Numeracy Development
Tracey Muir
Teacher Perception and Motivational Style
Hannah Newman, Jenni Way
Applying Mathematical Knowledge in a Design-Based Interdisciplinary Project
Kit Ee Dawn Ng, Gloria Stillman
A Professional Learning Tool to Help Stimulate Mathematics Teachers to Reflect on their Pedagogical Practice
Richard O'Donovan
Relative Values of Curriculum Topics in Undergraduate Mathematics in an Integrated Technology Environment
Greg Oates
Analogical Reasoning Errors in Mathematics at Junior College Level
Wai-Kit Alwyn Pang, Jaguthsing Dindyal
Highlighting the Similarities and Differences of the Mathematical Knowledge and Strategies of Year 4 Students
Catherine Pearn
Reconceptualising Agency in a Senior Mathematics Classroom
Trevor Redmond, Joanne Sheehy
Scaffolding for Learning Equation Solving
Daphne Robson, Walt Abell, Therese Boustead
Making Sense of Partitive and Quotitive Division: A Snapshot of Teachers’ Pedagogical Content Knowledge
Anne Roche, Doug Clarke
Lesson Study: An Effective School-Based Teacher Professional Learning Model for Teachers of Mathematics
Peter Sanders
The Development of Fraction Ideas Among Students with Disabilities
Rebecca Seah
Investigating Students’ Numerical Misconceptions in Algebra
Vicki Steinle, Eugene Gvozdenko, Beth Price, Kaye Stacey, Robyn Pierce
Probing Some Key Junctures in Relational Thinking: A Study of Year 6 and Year 7 Students from Australia and China
Max Stephens, Wang Xu
Softly, Softly: Curriculum Change in Applications and Modelling in the Senior Secondary Curriculum in Queensland
Gloria Stillman, Peter Galbraith
Investigating Feelings towards Mathematics among Chinese Kindergarten Children
Huayu Sun
Development of an Instrument for Ways of Using Graphics Calculators: Preliminary Findings
Hazel Tan
Multimodal Use of Semiotic Resources in the Construction of Antiderivative
Michael O. J. Thomas, Caroline Yoon, Tommy Dreyfus
Learning About Building Mathematics Instruction from Students’ Reasoning: A Professional Development Study
Jana Visnovska, Paul Cobb
Exploring the Identity of a Pre-Service Teacher: Communal Processes During the Practicum
Margaret Walshaw
Probing Teachers’ Pedagogical Content Knowledge in Statistics: “How will Tom get to school tomorrow?”
Jane Watson, Rosemary Callingham, Erica Nathan
Reflection in Self-Assessed Online Discussion
Jenni Way
Counting On 2008: Diagnostic and Remedial Mathematics Program for Middle Years Students
Allan White
Growth of Pre-service Teachers’ Knowledge and Teaching Ideas About Decimals and Fractions: The Case of Vivi
Wanty Widjaja, Kaye Stacey
Engaged to Learn Pedagogy: Theoretically Identified Optimism Building Situations
Gaye Williams
“Better You Than Me”: Mathematics Anxiety and Bibliotherapy in Primary Teacher Professional Learning
Sue Wilson
What Did My Students Do When They Did Their Homework Last Weekend?
Regina M.F. Wong, Michael J. Lawson
Modelling the Height of the Antiderivative
Caroline Yoon, Tommy Dreyfus, Michael O. J. Thomas
The "Back to Basics" Dilemma for Middle School Mathematics Teachers
Shirley Yates
Concepts, Connections and Commitment: Locating Mathematics in a Typical School Day
Fiona McDiarmid, Ruth Pritchard
Teaching Multi-digit Multiplication using Array-based Materials
Jenny Young-Loveridge, Judith Mills
Linear Algebra Snapshots through APOS and Embodied, Symbolic and Formal Worlds of Mathematical Thinking
Sepideh Stewart, Mike Thomas
Short Communication (abstract only)
A Narrative Study on the Use of Computer Software and Hands-on Activities in Developing Young Children’s Mathematical Minds
Po Wah Chan, Tse Lok Tin

(Poster) The study is a collaborative effort between a teacher educator and three preschool practitioners. It adopted a narrative approach and yielded a ‘practical’ experience bearing direct relevant as well as significance value to preschool teacher educator and practitioners in the teaching and learning of math for young children. Examples of how children learn mathematical concepts through the use of computer software and hands-on activities will be showed in the poster.

Applying a Systems Approach to Understanding Children’s Performance in System Assessments
Patricia Morley

Large-scale assessments such as NAPLAN (Australia) provide a wealth of data about the mathematical understanding and achievement of students. However, measurement is only the first step in the implementation of systems aimed at achieving improvement. This paper presents a framework for analysis of NAPLAN data from the perspective informed by the systems approach. Rather than ask how well the children perform, the exploratory analysis presented here focuses on identifying the obstacles to children’s success.

Brain-burn, Swirling Numbers, an Evil Textbook: Accessing Students’ Beliefs About Maths Through Their Drawings
Catherine Solomon, Alison Gilmore, John Hannah, Mick Grimley

Approximately 200 students from two focus schools were asked to draw ‘what maths or doing maths means to you’. This task was used to augment information from a larger study of students’ beliefs about mathematics, collected from questionnaires containing likert-type questions and open-ended questions requiring written responses; 848 year 5 and 6 students, aged between 9 and 11, from 17 New Zealand primary schools completed the questionnaire. The concern was that not all students of this age are able to express their beliefs through a method reliant on their literacy skills. The results showed marked differences between the tasks.

Development and Validation of Mathematical Thinking Assessment Framework
Tee Yong Hwa, Chap Sam Lim

The study aims to develop and validate Mathematical Thinking Assessment (MaTA) framework. It involved a total of 7 classes of 16 years old students and their mathematics teachers from Malaysia. The MaTA is implemented in the school context to assess students’ mathematical thinking: the performance assessment is administered to elicit students’ thinking processes during problem-solving; the Metacognition Rating Scale is used to specify students’ awareness while working on problems; the Mathematical Dispositions Rating Scale is used to indicate students’ disposition towards learning of mathematics whereas the Mathematical Thinking Scoring Rubric is used to score and grade students’ mathematical thinking according to the domains defined in this study.

Diagnostic Assessment of Mathematics in Schools
Majeda Awawdeh

(Poster) The poster illustrates two programs in numeracy assessment: the International Competitions and Assessments for Schools (ICAS) and the Early Literacy and Numeracy Assessment (ELNA). ICAS is a 40-item assessment of mathematics skills and content for Year 3-12 students which allows horizontal and vertical equating of student performance. ELNA is an online diagnostic computer-adaptive assessment program that assesses literacy and numeracy skills and knowledge for Pre-school-Year 2 students. Strands tested in numeracy are number, space and measurement, and patterns. ELNA enables individualised assessment and eliminates the ‘ceiling effect’. ICAS and ELNA provide an interesting research area in mathematics education.

Enactments of Instructional Leadership of Mathematics in Primary Schools
Joanna Higgins, Linda Bonne

School-based instructional leadership of professional development initiatives is important to embedding high quality instructional practices, so that students’ mathematics achievement is enhanced. By looking beyond designated leadership positions it may be possible to explicate alternative enactments of leadership in primary schools as they are played out in the school setting, with a specific focus on setting up school structures that support mathematics teaching. This paper uses a backward mapping strategy to explore ways of conceptualising instructional leadership in primary mathematics, as well as identifying school support structures that enable teachers to advance towards a vision of high quality mathematics instruction.

Fine Tuning the Teaching Methods Used for Second Year University Mathematics Based on Student Perceptions about Mathematics
Leng Leng Lim, David Thiel, Jeung-Hwan Doh, Debra Bernhardt

Each year a new cohort of 240 students undertakes the challenge of second year mathematics. The student feedback from one year is often a reversal of that received about the course run in previous years. The 2009 class was surveyed on their attitudes to mathematics at both the beginning and the end of the course. This paper reports changes in teaching methods implemented in response to the first survey, changes in student perceptions about mathematics and on the student feedback compared to previous years. From this data, some conclusions are made about how students’ best learn.

First Year Pre-service Teachers’ Patterns of Responses to a Mathematical Skills and Knowledge Test
Sharyn Livy

The aim of this study was to gain a better understanding of the misconceptions and ways in which pre-service teachers responded to a mathematical skills and knowledge test during their first year of the Bachelor of Education. Two hundred and ninety seven pre-service teachers’ results were collected. This paper will explore the answer of one question identified as difficult for nearly 90% of the cohort.

From Foot to Shoe Project
Lai Ha Freda Yuen

(Poster) This poster discusses a project about feet, undertaken by the class of children ranging in 4 to 5 years in a kindergarten of Hong Kong. Throughout this project, the children studied parts of leg, measured and compared their feet, found out the relation between the size of their feet and shoes, and experimented with making their own shoes. The article documents the children’s work through photographs, and provides the teachers’ reflections.

Historical Evolution and Student Perspectives on Large Numbers
Mala Nataraj

The importance of a consideration of large numbers in primary and early secondary school should not be underestimated. A study of history of India (and of the Maya) reveals that contemplation of large numbers provided the impetus for a construction of place value number system. While today’s students do not have to create a number system they do need to understand its structure in order to develop number sense and operations and to progress to algebra. This can perhaps be done more quickly by contemplating on large numbers. This study examined and categorised Year 9 students’ responses to a questionnaire on large numbers. The results suggest that many students show competence in naming and using large numbers and some are in the process of thinking beyond their curriculum level.

Inquiring into Preservice Secondary School Teachers’ Generalisation Strategies in a Quadratic Generalising Task
Boon Liang Chua, Celia Hoyles

This paper reports how a group of prospective secondary school teachers in Singapore solved a quadratic generalising task. The findings show that the teachers were capable of deriving multiple equivalent expressions for the task. Three approaches were used to work out the rule: numerical, figural and pragmatic, with the last two being more predominant. It was also found that the same expression could be obtained from different visual representations, and conversely, the same visual representation could also produce different expressions.

Instrumental Genesis as a Theoretical Framework to Examine Probability Simulations
Anthony Bill

Within a larger study of a Year 9 class investigating sample size students examined explicitly the legitimacy of the data generated by a Fathom die simulation. Instrumental genesis - the process where students adopt a tool as their own - is an established analytical framework used with computer algebra systems (CAS), and this framework has potential application in electronic probability simulations. In addition to a examination of students adopting the simulation's procedures and features, any reservations students have regarding the legitimacy of the data generated may act as a potential impediment to learning. More recently instrumental genesis has been extended to acknowledge the role of the teacher and the classroom environment through a process defined as instrumental orchestration.

Lead Teacher Role: Keeping the Momentum
Anne Milburn, Viv Thompson, Deb Gibbs

In New Zealand by the end of 2009 most primary schools will have participated in Phase 1 professional development of the Numeracy Development Project (NDP). The project is now in its 9th year after the pilot ‘Count Me In Too’. Having self-managing schools in numeracy is the focus of Phase 2 of the project. Therefore the direction of support in the future will be towards maintaining quality teaching in classrooms. As schools are working on sustainability of good numeracy teaching and learning, the role of Lead Teacher is becoming more critical. They have as part of their role the continuous improvement of teacher practice. They also have a greater responsibility in improving, monitoring and reporting progress of students. Maintaining the momentum can be a difficult task and requires support from principals and facilitators in order to carry out Lead Teacher multi-layered responsibilities. Further to Deb Gibbs and Marilyn Holmes roundtable presentation at MERGA in 2006, facilitators have continued to explore issues around the role of Lead Teachers. Three years later, have changes for the better taken place or has the status quo remained? This small study focuses on how well the Lead teachers make use of the time allowed and looks at answers to the following questions: 1.Has the perceived value of the Lead Teacher role increased over time? 2.Has the support given to Lead Teachers to carry out their role effectively changed? Discussion around this study will highlight implications for lead teachers, principals and facilitators in numeracy.

Lesson Starter Activities in New Zealand Secondary Mathematics Lessons
Liping Ding, Margaret Walshaw

The beginning of any lesson is an important event and may take on many forms and functions. In this presentation we reveal how three mathematics teachers began their year 9 lessons. Using data from the New Zealand component of the Learner’s Perspective Study (LPS) we examine the lesson event characterised as the ‘starter’. Within all three classrooms, the starter activities typically involved students in solving teacher-provided problems. However, closer analysis of video and interview data from each classroom sequences of ten lessons reveals differences in the intent, the nature, and the enactment of student/teacher activity. We explore how particular learning opportunities and modes of participation, both in the moment and later in the lesson, are interwoven with the starter activity.

Middle School Students’ Responses to Two-tier Tasks
Shajahan Haja, David Clarke

The structure of two tier testing is such that the first tier consists of a multiple-choice question and the second tier requires justifications for choices of answers made in the first tier. This study aims to evaluate two-tier tasks in ‘proportion’ in terms of students’ capacity to write and select justifications and to examine the effect of different two-tier formats on student performance. Twenty students each from Y7 and Y8 participated in the study in Melbourne in March 2008. The students took eight similar tests with each test having eight two-tier tasks. Eight students were interviewed individually after the testing. Analysis of students’ responses revealed that i) Y7 and Y8 students were able to select and write justifications to two-tier tasks, ii) Y7 and Y8 students’ success in writing or selecting justifications varied on ‘marked answer’ and ‘select answer’ formats, and iii) Y7 and Y8 students’ justifications gave some information about their misconceptions in proportional reasoning. Implications for teachers looking for alternative assessment tasks tracing students’ reasoning behind their correct and incorrect answers are discussed.

Models of Professional Learning in Mathematics, Science and Technology Education: Experienced Critical Friends Rate the Impact of Models on Teacher and Student Learning
Pamela Hammond, Doug Clarke, Ken Smith

A range of models of teacher professional learning have been utilised within Australian schools, with varying success. The views of 125 university-based ‘Critical Friends’ in the Australian Schools Innovation in Science, Technology and Mathematics (ASISTM) project were sought on the relative effectiveness of 15 models of professional development in relation to their capacity to impact on teacher professional learning and student learning respectively. The findings are shared, along with recommendations to those considering these models for future professional development programs.

Oh Yea, But It’s Not a Real Dice
Anthony Bill

(Poster) Year 9 students compared explicitly the fairness of three dice: a standard factory-made die, a die students fabricated using Sculpey (TM) modelling clay, and a virtual die in a Fathom (TM) simulation. During class discussion students developed a fairness measure - a single statistic quantifying the fairness of the die - calculated as the difference between the observed and the expected frequency in 30 rolls of the die. The students pooled the fairness measures and constructed poster-size dot plots, and the dot plots were then used in whole-class discussion to compare the fairness of the three dice.

One-on-one Numeracy Intervention: A Pilot Study
Steve Thornton, Gina Galluzzo, Mary Quinane

This short presentation provides some preliminary results of a one-on-one numeracy intervention program developed as part of the Commonwealth Government Literacy and Numeracy Pilot Projects in low SES schools. The intervention was modelled on a reading recover program (Clay, 1993), using a lesson structure based on research into how the brain learns mathematics (Sousa, 2007). Students identified as having low numeracy levels in years 1, 4 and 8 at several Catholic schools in the West and South of the Archdiocese of Canberra and Goulburn were withdrawn for thirteen weeks and given on-on-one intervention by a specially trained teacher.

Primary Students' Mindset, Mathematics Self-efficacy, and Mathematics Achievement: Investigating the Relationships
Linda Bonne

A student's mathematics achievement can be promoted or obstructed by their beliefs about intelligence in general (mindset), and about their own mathematical capability in particular (mathematics self-efficacy). Ways of investigating the effects of a mindset intervention and a mathematics self-efficacy intervention, and how these effects might be associated with changes in students' mathematics achievement, will be discussed. An exploratory study with Year 4-5 students and their teachers, drawing on design research methodology and including quantitative and qualitative methods, will be described. A case will be argued for extending our understanding of New Zealand students' self-beliefs in relation to mathematics.

Streaming for Mathematics in Victorian Secondary Schools
Helen Forgasz, Hazel Tan

Streaming (or ability grouping) for mathematics is a hotly debated and contentious issue. In this paper, data are presented from 44 Victorian secondary teachers who responded to an online survey. The aims of the study were to explore the extent to which streaming is implemented in Victorian post-primary schools, and to examine teachers views on the policies adopted in their schools. The findings indicated that streaming is widespread, even at grade 7, and that most teachers supported the policies in place. In supporting their views, various limitations to the streaming practices were also identified.

Students’ Performance on Two Task Structures: Two Case Studies
Shajahan Haja, David Clarke

This paper reports the effect of task structure on two Y7 students’ performance in a pre-post testing situation. The tests consisted equal number of ‘tasks with confidence level’ and ‘tasks with safety-net’ structures. Two cases were analysed: i) one girl’s performance in eight weeks gap, and ii) one boy’s performance in two weeks gap. The boy’s performance was consistent and showed little effect from task structure. The girl’s performance seemed significantly affected showing progress in safety-net tasks which could be attributed to teacher’s feedback. Task structures uncovered different patterns of girl’s reasoning between the tests which was confirmed in interview.

Teachers’ Perceptions Towards School-based Assessment: The Malaysian Context
Tee Yong Hwa, Chap Sam Lim

The over emphasis of examination results has created phenomenon where teachers teach-to-test and students learn by rote such as memorizing all the facts without really know how to apply the knowledge and skills in the real life context. In order to reduce the focus on examination results, the Blueprint of Education Development suggested that students’ assessment should be measure through school-based grading system which is holistic in nature. In Malaysia context, there is yet available a well-established school-based mathematics assessment framework to be used by the school teachers. Hence, this study aims to develop and validate a framework for Mathematical Thinking Assessment (MaTA). However, prior to this, we see the importance of seeking teachers’ perceptions about school- based assessment. Hence, this paper discusses the interview analysis of 18 mathematics teachers from six secondary schools on the issues and possible challenges faced for the implementation of school-based assessment for mathematics. The results show that the lack of exposure, availability of assessment guidelines, preference to current traditional assessment, time constraint, students’ mathematical ability and English language proficiency; are the main concerns of the participating teachers in this study.

Teaching Algebra Using a Multifaceted Variable Approach: What Do Year 7 Students Understand about Variables?
Salma Tahir, Mike Mitchelmore, Michael Cavanagh

Student difficulties in learning algebra can arise from the diverse meanings assigned to variables. We propose teaching different aspects of variables (unknown, generalised number and function) in parallel with each other using real contexts and call this a multifaceted variable approach. We are investigating whether learning about variables using a multifaceted variable approach before moving on to symbol manipulations can reduce student misconceptions regarding variables and improve their algebra learning outcomes. This paper reports results from student interviews administered after the algebra teaching intervention. Results indicate that students of the experimental classes showed fewer misconceptions regarding variables than comparison classes and they were able to recognise that variables can have multiple values.

Thai Students’ Perceptions of Cooperative Learning in the Mathematics Classroom
Tippawan Nuntrakune

Thai education is moving toward student-centred learning. However, Thai students have had little experience with cooperative learning strategies. This qualitative study reports on Thai students’ perceptions about their engagement in cooperative learning in mathematics classrooms. The study found that Grade 4 students utilised four different but complementary processes (peer tutoring, peer relationships, peer assessment and group role) to facilitate their cooperative group work learning. These findings indicated that the alternative teacher preparation workshops need to provide additional workshops to improve the implementation of peer relationships, peer assessment and group role.

The Development of SAPP: Self-Analysis Professional Portfolio
Anne Scott, Philip Clarkson, Andrea McDonough

This paper proposes a new technique for data collection in classroom studies. The approach adopted is to regard teachers as a co-researcher and give them the decisions of what and when to collect data by using hand held video cameras in the classroom. Coupled with the data collection is an emphasis on the teachers following through a process that enables them to self critique their data and consider whether they have changed their practice. Pitfalls and successes in our first attempts at using this technique are documented.

The Effect of Real-life Context in Learning Complex Concepts in Mathematics: A Cognitive Load Perspective
Majeda Awawdeh

A controlled randomized experiment was conducted to examine the hypothesis that by using real-life cover stories from learners' real-life to explain fractions, the new concepts could be more readily assimilated into existing knowledge held in long-term memory compared to the more traditional geometric contexts. Grade 5 students (n=32) from a Sydney public school participated in this study. A 2x2 ANOVA with repeated measures was used to analyse the results. The result supported the hypothesis.

The Impact of the Secondary Numeracy Project on Mathematics Teaching in Senior Secondary Schools
Roger Harvey

This paper explores the impact of the project on the teaching of mathematics in senior secondary classrooms. The Secondary Numeracy Project provides professional development for secondary mathematics teachers. Schools opting into the project participate in school based in-service development of their mathematics teaching team. The specific focus of the Secondary Numeracy Project is on enhancing the teaching of mathematics to students in their first two years of secondary school. The impact on pedagogy in the senior secondary school mathematic resulting from the project, as reported by mathematics teachers who participated in the project, will be discussed.

The MAaCAS Project - Mathematical Applications and Computer Algebra Systems
Vincent Geiger

(Poster) This poster outlines a study that aimed to investigate the potential of Computer Algebra Systems (CAS) to enhance the processes associated with mathematical modelling and application tasks. Data for the study was drawn from a one year study of five different secondary school classrooms. Analysis of the data revealed that there were significant differences in the uptake of CAS technology and of the use of applications of mathematics between schools. Implementation of technology rich approaches to mathematical modelling varied from classroms where students engaged in complex rich tasks to those where use of applications of mathematics was limited. This poster also highlights the affordances and constraints experienced by teachers in implementing new approaches to learning/teaching mathematical modelling through the use of technology.

The Times (Tables): They Are a Changing
Brenda Sherley, Sandi Tait-McCutcheon

The teaching and learning of basic facts is a topic of perennial interest and significance to teachers, teacher educators, and the mathematics education community. This study builds on to a prior study of basic facts teaching and learning in New Zealand by examining in detail the practice of one teacher as she reflects on her teaching and learning programme. From this study the authors seek to advance knowledge and lead to the provision of advice for teachers and researchers.

Towards Mathematically Significant Classrooms: A Video Study
Steve Thornton, Kathryn Moyle

This presentation provides some preliminary results of the use of videos as a vehicle for reflection and planning with pre-service secondary teachers. A lesson was developed to illustrate the elements of a framework that we term ‘mathematically significant classrooms’, consisting of tasks (Watson & Mason, 2007), norms (Yackel & Cobb, 1996) and conversations (Chapman, 1993). Students’ responses to the framework, including their use of it in planning lessons during professional experience, will be discussed. The framework provides a robust framework through which teachers can reflect on the intellectual quality of a mathematics classroom (Gore, Griffiths & Ladwig, 2004).

Using Collective Argumentation to Teach Mathematics
Margaret Marshman

This study explores how Collective Argumentation has given the students in a middle-school mathematics classroom a framework which allows them participate in mathematical discussions to develop the skills and desire to think, reason and work mathematically, where personal understandings can be expressed, re-considered, shared and co-authored. This has led to students sharing the authority and promoted student engagement

Using the Model Method to Solve Simple Word Problems
Suat Khoh Lim-Teo, Bee Kwang Poh

In Singapore primary schools, an approach of representing relationships between quantities using blocks, called the model method, is used to solve word problems. While very useful for difficult problems at upper primary grades, this method is taught at primary two for solving simple one- or two-step problems. A research study was designed to find out whether beginning primary three pupils would prefer to use the method or other methods for simple word problems. The pupils’ ability to handle the component parts of the method and the difficulties encountered were also investigated. This presentation will describe the findings of this study.

Whose Mathematics?
Judy Bailey

With the release of the New Zealand Curriculum document (2007) we, as two pre-service teacher educators, formalised our ongoing conversations about the nature of mathematics. A literature review is being undertaken as part of these conversations. This reveals a wide variety of explicitly made and implicit conceptions of mathematics. Of particular interest is Barton's description of NUC (near-universal conventional) mathematics and the suggestion that 'mathematics could have taken many forms, the forms and preferences of NUC-mathematics were not inevitable; they are the result of a particular historical trajectory that includes many social influences, including language' (2008, p. 24). Implications for mathematics in the NZC, and our work as pre-service teacher educators are being considered.

‘It Just Feels Different!’ Engaging Students in Mathematics Using Virtual Grand Prix Racing
Angela Jones, Ruth Pritchard

This project involved a teacher examining her use of an interactive mathematics program with a class of 13-14 year old boys to promote engagement in mathematics. Students identified a variety of mathematical concepts implicit in the learning experience, and described ways in which it presented opportunities to encounter, apply or develop these ideas. It provides an example of how the affordances of such software can be accessed by teachers developing new approaches to teaching through in-depth professional development. The teacher’s heightened awareness allowed her to capitalise on the novel context to promote increased opportunities for learning and participation in mathematics.

Poster (abstract only)
Round Table (abstract only)
Captivate - Video Screen Capture Technology for Data Collection
Anthony Bill

"Captivate", a product from the Adobe(TM) suite, is a video screen capture software that records students’ actions on a computer as a video recording. The software operates in parallel and behind the primary software - a typical example is Microsoft(TM) Excel. Students are aware that Captivate is running, but they soon ignore its presence and this allows a natural recording of students’ use. The software includes a audio recorder; if students work in pairs and are encouraged to discuss their work the audio recording adds immensely to the richness of the data collected. The video recordings are easily exported to widely-used file formats such as AVI and MPEG, and this allows the video-clip to be used independently of Captivate. The files may then be analysed, using for example, N-Vivo, and edited, reproduced, transmitted, and displayed as needed. Practising teachers may find application of the software as an instructional tool. Teachers could create short instructional video for students that they can replay on-demand in computer laboratories. This has the potential to improve teaching practice by liberating the teacher from some repetitive classroom tasks. The round-table seeks to discuss other researchers’ use of screen capture technology as a data source. The presenter will demonstrate recordings made during class and small group interviews.

Developing Communication and Participation Patterns in Mathematics with Diverse Learners
Roberta Hunter, Glenda Anthony, Zain Thompson, Heather Howe

Current shifts in teaching and learning practices in mathematics classrooms challenge teachers to develop mathematical communities which offer all participants opportunities to engage in mathematical inquiry, explanations, justification and generalisations. The complexities and challenges to achieve this are many, particularly with the diverse learners in our classrooms. We want to explain a framework we have developed to explore ways teachers can constitute classroom norms which support such dialogue. Teachers participating in the research study will describe how they have adapted and used the framework in their numeracy classrooms and also how they have used it as a reflective tool to plan next possible growth areas. In this session we seek feedback on where adjustments need to be made to meet the explicit needs of Maori and Pasifika students in particular. Whilst knowledge of how to develop productive communication and participation patterns with diverse learners in New Zealand is the focus of our study we hope that experiences from Australia and other countries will add to the discussion.

Successful Ways of Enhancing Achievement of Maori Students in Mainstream Settings
Honor Ronowicz, Tracey Muir

The University of Waikato Numeracy advisers will start the round table discussion by presenting the findings from a case note and a small research project involving teachers with significant numbers of Maori students in their classrooms and Maori students from schools that are working in depth in numeracy across the Waikato region. The international evidence cited in Wendy Nielsen, Cynthia Nichol, and Jenipher Owuor (2008) positively supports the enhancement culturally responsive pedagogy has on student’s connection with the learning process. In New Zealand, Best Evidence Synthesis research highlights the importance of relationship building with Maori students to increase engagement and raise achievement (Alton -Lee 2003). Aspects that might be considered in this discussion include the underpinning principles of Te Ao Maori, classroom strategies that seem to improve achievement for Maori students, Ka Hikitia, the Ministry of Education, Maori Education Strategy, and the work of Dr Russell Bishop et al.

Teaching the Mathematics of Gambling to Reinforce Responsible Attitudes Towards Gambling
Robert Peard

The general acceptance afforded the national image of Australians as gamblers have given gambling a legitimacy rare in other countries. Concerns with the social effects of this have led many State governments to implement programs to counteract negative social effects. The Queensland Treasury has allocated funds for the development of teaching resources for this purpose including the development of the Unit presented here. In 2006 the author constructed a Unit of work for Queensland Senior Secondary (Years 11 and 12) Mathematics classes entitled ‘The Mathematics of Responsible Gambling’ as a consultancy to the Queensland State Government. Towards the end of 2007 the ‘Secondary Mathematics Teaching Resources Kit’ was distributed to all secondary government schools. This paper describes the activities of the Unit, their relationship to the Queensland Syllabus objectives, the research upon which the Unit is based, and the current research into the effectiveness of its implementation which began in November 2008 and will continue in Semester 1 of 2009.

The Effect of Reform-Oriented and Other Mathematics Curricula on Students’ College Mathematics Placement Test Scores
Jon D. Davis, Jeffrey C. Shih

This study examined the college mathematics placement exam results of 1,277 students learning from nine secondary mathematics curricula and two Advanced Placement (AP) mathematics programs in 25 different high schools in the United States. The results suggest that students learning from several traditional mathematics programs and AP Calculus significantly outperformed students learning from the reform-oriented mathematics program, Core-Plus Mathematics Project, on algebra manipulation and calculus readiness questions. Prior mathematics achievement, course completion, and gender also significantly influenced mathematics placement scores.