Conference Proceedings 2005


Building Connections: Research, Theory and Practice - MERGA28
Editors: Philip Clarkson, Ann Downton, Donna Gronn, Marj Horne,Andrea McDonough, Robyn Pierce, Anne Roche
Table of Contents
MERGA 2005 Conference Proceedings
Colleen Vale and Philip Clarkson
List of Reviewers
Judges and Reviewers for MERGA28
Keynote Address
Essential Complementarities: Arguing for an Integrative Approach to Research in Mathematics Classrooms
David Clarke
The Impact of Mathematics Education Reform in New Zealand: Taking Children?s Views into Account
Jenny Young-Loveridge
Practical Implication Award
Variation and Expectation as Foundations for the Chance and Data Curriculum
Jane M. Watson
A Mathematics Teacher Educator's Perspective of Building Connections between Research, Theory, and Practice
Colleen McMurchy-Pilkington
Building connections: Research, Theory and Practice - A view from a Practitioner
Vicki Nally
Building connections: Research, Theory and Practice - A View from the Profession
Will Morony
Building Connections: Research, Theory, and Practice
Di Siemon
From the Hill to the Swamp: Combining Research and Practice
Peter Gould
Research Paper
Conceptions and Tensions in Globalisation and Their Effects on Mathematics Educators
Bill Atweh and Phillip Clarkson
Using Jamie's Experiences: An Investigation into Using Teachers' Stories in Pre-service Mathematics Teacher Education
Robin Averill and Roger Harvey
Students' Views on Using CAS in Senior Mathematics
Lynda Ball and Kaye Stacey
Rates of Change and an Iterative Conception of Quadratics
Karoline Afamasaga-Fuata'i
The Role of Attention in Classroom Practice: Developing a Methodology
Janet Ainley and Michael Luntley
Use of a Cultural Metaphor in Pre-service Mathematics Teacher Education
Dayle Anderson, Robin Averill, Herewini Easton and Derek Smith
Implementing Problem Solving in Mathematics Classrooms: What Support do Teachers Want?
Judy Anderson
I Didn't Know What I Didn't Know: A Case Study of Growth in Teacher Knowledge within the Intermediate Numeracy Project
Julie Anderson
A New Scale for Monitoring Students' Attitudes to Learning Mathematics with Technology (MTAS)
Anastasios Barkatsas
It Depends on the Students: Influencing Teachers' Beliefs about the Ends and Means of Numeracy Teaching
Kim Beswick
Experienced and Novice Teachers' Choice of Examples
Chris Bills and Liz Bills
Teachers' Preferences and Practices Regarding Values in Teaching Mathematics and Science
Alan Bishop, Barbara Clarke, Debbie Corrigan and Dick Gunstone
The Mathematics Talk of a Secondary School Teacher of Mathematics and Physics
Michelle L. W. Bower
Algebraic Thinking in the Numeracy Project: Year One of a Three-Year Study
Murray S. Britt and Kathryn C. Irwin
Affordances of a Technology-Rich Teaching and Learning Environment
Jill P Brown
'I Type What I Think and Try It': Children's Initial Approaches to Investigation Through Spreadsheets
Nigel Calder
Primary Students' Mental Computation: Strategies and Achievement
Rosemary Callingham
Developing Effective Teachers of Mathematics: Factors Contributing to Development in Mathematics Education for Primary School Teachers
Jean Carroll
Enhancing Mathematical Understanding Through Self-assessment and Self-Regulation of Learning: The Value of Meta-Awareness
Rosemaree Caswell and Steven Nisbet
The Value of Play to Enhance Mathematical Learning in the Middle Years of Schooling
Rosemaree Caswell
Early Numeracy Coordinators in Victorian Primary Schools: Components of the Role, Highlights and Challenges
Jill Cheeseman and Doug Clarke
Teaching Elementary Probability: Not Leaving it to Chance
Helen Chick and Monica Baker
Children's Mappings of Part-Whole Construct of Fractions
Mohan Chinnappan
Prospective Teacher's Representations of Multiplication
Mohan Chinnappan
The Evaluation of the Success in Numeracy Education Program
Doug Clarke, Gerard Lewis, Max Stephens and Ann Downton
Conceptual Understanding of Spatial Measurement
Margaret Curry and Lynne Outhred
Learning to Notice: One Aspect of Teachers' Content Knowledge in the Numeracy Classroom
Ngaire Davies and Karen Walker
How Unusual is the Gender Specificity of Mathematical Test Item Types Reported for Dutch Primary School Students'
Lorraine Davis, David Clarke and Marja van den Heuvel-Panhuizen
Assessing Primary Students' Knowledge of Networks, Hierarchies and Matrices using Scenario-Based Tasks
Carmel Diezmann
Pedagogy by my Standards: A Teacher's Views on Two Process Standards
Jaguthsing Dindyal
Primary and Secondary Mathematics Practice: How Different is it?
Brian Doig, Susie Groves, Russell Tytler and Annette Gough
A Mathematics Education Ghost Story: Herbartianism and School Mathematics
Nerida F. Ellerton and M. A. (Ken) Clements
Seventh-Graders' Mathematical Modelling on Completion of a Three-Year Program
Lyn D. English and Jillian L. Fox
Mathematical Methods Computer Algebra System (CAS) 2004 Pilot Examinations and Links to a Broader Research Agenda
Michael Evans, Pam Norton and David Leigh-Lancaster
From Arithmetic to Algebra: Novice Students' Strategies for Solving Equations
Judith Falle
Towards a Language-based Model of Students' Early Algebraic Understandings: Some Preliminary Findings
Judith Falle
Integrating ICT into Professional Practice:A Case Study of Four Mathematics Teachers
Noleine Fitzallen
Mathematics Teachers: A Study of Life Inside School and Beyond
Helen J. Forgasz and Gilah C. Leder
Master, Servant, Partner and Extension of Self: A Finer grained View of this Taxonomy
Vince Geiger
The Growth of Schematic Thinking about Derivative
Alan Gil delos Santos and Michael O. J. Thomas
The Role of Online Discussion in Building a Community of Practice for Beginning Teachers of Secondary Mathematics
Merrilyn Goos and Anne Bennison
Year 6 Students' Methods of Comparing the Size of Fractions
Peter Gould
Reflections on Teaching Mathematics in an Exam-Driven School: An Autoethnography
Fiona Hagan
How do we Provide Tasks for Children to Explore the Definitions of Quadrilaterals?
Alice Hansen and Dave Pratt
Mental Computation: The Benefits of Informed Teacher Instruction
Ann Heirdsfield and Janeen Lamb
Discourse as a Catalyst for Facilitating Practitioner Research
Beth Herbel-Eisenmann
Potential of Technology and a Familiar Context to Enhance Students' Concept of Rate of Change
Sandra Herbert and Robyn Pierce
The Effects of Number Knowledge at School Entry on Subsequent Number Development: A Five-year Longitudinal Study
Marj Horne
Reforming Communication in the Classroom: One Teacher's Journey of Change
Roberta Hunter
Mentoring Mathematics Teachers in Low Socio-Economic Secondary Schools in New Zealand
Barbara Kensington-Miller
The Contested Notion of Sustainability: Possibility or Pipe Dream for Numeracy Reforms in New Zealand
Nicky Knight
Students' Use of Context Knowledge in Interpreting Data
Cynthia Langrall, Edward Mooney and Nicole Williams
Language Factors that affect Mathematics Teaching and Learning of Pasifika Students
Viliami F. Latu
How Primary Pre-service Teachers Perceive Mathematics Teacher Educators' Practice: A Case Study
Gregor Lomas
Establishing a Numeracy Culture in a Distance Education Learning Environment: A Case Study
Tom Lowrie
Formalising the Role of Indigenous Counting Systems in Teaching the Formal English Arithmetic Strategies Through Local Vernaculars: An Example From Papua New Guinea
Rex A. Matang
Does Mathematics Education in Australia Devalue Indigenous Culture? Indigenous Perspectives and non-Indigenous Reflections
Chris Matthews, Leesa Watego, Tom J. Cooper and Annette R. Baturo
Professional Development as a Catalyst for Changes in Beliefs and Practice: Perspectives from the Early Numeracy Research Project
Andrea McDonough and Barbara Clarke
Growth of Teacher Knowledge within an On-line Collaborative Learning Environment
Mathew McDougall and Rod Nason
The Use of Algebra in Senior High School Students' Justifications
Tamsin Meaney
Measuring Fractions
Annie Mitchell
What Does Mathematics Understanding Look Like?
Judith Mousley
Where Did I Go Wrong? Students' Success at Various Stages of the Problem-Solving Process
Tracey Muir and Kim Beswick
Understanding Students' Reasoning While Comparing Expressions
Shweta Naik, Rakhi Banerjee and K Subramaniam
Regional Differences in the Professional Development Needs and Preferences of Teachers of Primary Mathematics
Steven Nisbet
Mathematics and the Construction of Feminine Gender Identity
Stephen Norton
Do Teachers Change Their Practices While Participating in a Lesson Study?
Jo Clay Olson
Teachers' Development of Substantive Communication about Mathematics
Kay Owens
Preschoolers' Mathematical Patterning
Marina Papic and Joanne Mulligan
The Effect of Money as a Context on the Mental Computation Performance of Students in Years 3, 5, 7 and 9
Anne Paterson and Jack Bana
Mathematical Beliefs and Achievement of Pre-service Primary Teachers
Bob Perry, Jenni Way, Beth Southwell, Allan White and John Pattison
Student Misconceptions about Projectile Motion
Anne Prescott and Michael Mitchelmore
Subject Matter Knowledge: Mathematical Errors and Misconceptions of Beginning Pre-Service Teachers
Julie Ryan and Barry McCrae
Education for Early Mathematical Literacy: More Than Maths Know-How
Abigail Sawyer
Preservice Teachers' Intentions to Provide Good Examples and Help Children Replicate Them
Anne Scott
Understanding the Role of Assumptions in Mathematical Modeling: Analysis of Lessons with Emphasis on 'the awareness of assumptions'
Tatsuhiko Seino
Exploring Pre-service Teachers' Reasoning about Variability: Implications for Research
Sashi Sharma
Building a Methodology for the Comparison and Evaluation of Middle-Years Mathematics Textbooks
Mal Shield
Assessing Multiple Objectives with a Single Task in Statistics
Jane Skalicky
Relative Risk Analysis of Educational Data
Kaye Stacey and Vicki Steinle
Concerns Relating to the CAS Use at University Level
Sepideh Stewart
The Integration of Mathematics and Music in the Primary School Classroom
Kathryn Still and Janette Bobis
Interactive Whole Class Teaching and Interactive White Boards
Howard Tanner, Sonia Jones, Steve Kennewell and Gary Beauchamp
Children's Views of their Teacher's Role in Helping them Learn Mathematics
Merilyn Taylor, Ngarewa Hawera and Jenny Young-Loveridge
Students' Attempts to Solve Two Elementary Quadratic Equations: A Study in Three Nations
Pongchawee Vaiyavutjamai, Nerida F. Ellerton and M. A. (Ken) Clements
Glimpses of Generative Practice: Constructing Pre-service Teachers' Learning in Partnership
Colleen Vale and Anne Davies
Challenging Task-driven Pedagogies of Mathematics
Fiona Walls
Patterns Supporting the Development of Early Algebraic Thinking
Elizabeth A. Warren
An Indigenous Perspective on Mathematics Contextualisation in a Pre-school: From Safety to Empowerment
Leesa Watego
Statistical Literacy over a Decade
Jane M. Watson, Ben A. Kelly and John F. Izard
Teaching Percentage as a Multiplicative Relationship
Paul White and Michael Mitchelmore
'I am really not alone in this anxiety': Bibliotherapy and Pre-service Primary Teachers' Self-image as Mathematicians
Sue Wilson and Steve Thornton
Language Appropriate for the New Zealand Numeracy Project
Joanne Woodward and Kathryn C. Irwin
Results of a Teaching Experiment to Foster the Conceptual Understanding of Multiplication Based on Children's Literature
Amanda Worlley and Romina Jamieson-Proctor
Prioritising the Voice of Researched: Using Photographs to Elicit Mathematical Thinking of Participants
Robyn Zevenbergen
The Victorian Curriculum and Assessment Authority (VCAA) Mathematical Methods Computer Algebra System (CAS) Pilot Study Examinations 2003
Michael Evans, Pam Norton and David Leigh-Lancaster
"Open your textbooks to page blah, blah, blah": "So I just blocked off!"
Bronwyn Ewing
Student Expectations of Studying Mathematics at University
Keith Hirst, Susan Meacock and Elfrida Ralha
High School Students' Understanding of Samples and Sampling Variability: Implications for Teaching and Research
Sashi Sharma
Short Communication (abstract only)
"My Mom Thinks I Should be an Engineer': Parental influences and Girls on Track for Math-Related Careers
Maria Droujkova, Sarah B. Berenson, Irena Rindos and Sue Tombes

Despite increasing girl retention in advanced high school mathematics programs, female college entrants disproportionately avoid math-related IT majors (National Academy of Engineering, 2002; National Research Council, 2001). Girls on Track (Berenson, 2004; Berenson, Vouk, & Robinson, 2002; Howe & Berenson, 2003), a longitudinal multi-institutional intervention program, works to increase middle-grade girls' interest in math-related careers. Project data shows that parental influence is a key factor in the girls' success in school mathematics and in their career choice. We identify four major roles of parents: Providing learning infrastructure such as books, software and tutoring, Being a role model and providing access to other community role models, Managing time and tasks, Emotional support and encouragement

An Investigation of the Selection Process of Mathematically Gifted Students
Kyunghwa Lee, Kyungmee Park and Jaehoon Yim

In Korea, the gifted education appears to gain much popularity lately that it has become a 'hot issue' in the education circle. Unusual enthusiasm of Korean parents for education led them to take their children to a reputable centre for gifted education programs, which enormously increases the demand for gifted education. Gifted education programs were primarily operated by gifted education centres run by universities. Now many elementary and secondary schools have started launching gifted educational programs because government's policies encourage gifted education. At this juncture where gifted education has been rampantly expanding without thorough planning, it is necessary to review the gifted education form a reflective perspective. Gifted education is mainly implemented following three: selection, education and evaluation for reselection. In this paper, the issues of selection and evaluation for reselection will be touched upon from a critical point of view. The aim of this paper is to investigate mainly problems for the selection and reselection of mathematically gifted students. Inappropriate and appropriate problems and examples of student answers will be presented.

Graphs, Transformations, Rates of Change and Quadratic Context Variations
Karoline Afamasaga-Fuata'i

This paper presents a case study of a student who developed quadratic schemes by solving a contextual problem during a teaching experiment. Mary reflectively abstracted patterns from graphical transformations, critical points, rates of change and equations representing variations of a base context whilst interacting and negotiating meanings with the researcher. A multi-representational software assisted Mary in verifying/justifying her conjectures. Findings include Mary's schemes to characterize quadratic covariations. The student-researcher interactions fostered the development and consolidation of Mary's quadratics conceptions.

Mathematical Problem-Solving Frameworks of Different Mathematics-Anxiety Levels Students
Yeo Kai Kow Joseph

This paper explores the problem-solving frameworks of 621 Secondary 2 students (13 to 14 years old). These students were asked to complete in writing the statement 'When I am given a mathematics problem to solve, this is what I do...'. The data were coded under the four phases of problem solving which were arrived at from a preliminary analysis of the data. The four phases: Understand / Represent the Problem (U), Find a Way to Solve the Problem (F), Solve the Problem (S), and Check the Solution (C) were noted. Secondary 2 students were found to rely on individual problem-solving frameworks to guide them when solving problems. The frameworks of different mathematics-anxiety students were similar, brief and specific in nature.

Message from Student Teacher Constructed Posters
Shajahan Haja

This paper reports the upshot of a poster contest 'Mathematics-Language of the Universe' conducted for prospective teachers on 10.11.2002 in 'Tuticorin, India'. 20 student teachers (12 females& 8 males) from 7 colleges of education in 'India' participated in the poster contest. I designed the poster contest to meet the objective of out bringing the concept orientation of student teachers (STs) towards mathematics and to provide an opportunity to organise their thinking about mathematics in a creative way. The contest delineates the specific objectives of exposing the significance of mathematics, utility value of mathematics in daily life and social values of mathematics by way of eliciting the prospective math teacher's ideas. Philosophy in Mathematics, aesthetic beauty of Mathematics, Mathematics and art of living, Mathematics and religious tolerance are some of the themes selected by the STs. Role of Mathematics in the development of human science, Mathematical symbols and shapes used in daily life, Mathematics and aeronautics are some other concepts used by the contestants. 4 STs depicted how Mathematics promotes other subjects by choosing different personification of Mathematics such as the rising sun, tree root, the sun with planets and peacock with feathers. One contestant tried linking mathematics with the structure of chemical molecules. This contest served as a window to analyse the beliefs of future teachers about Mathematics as a subject.

Persistent Mathematics Misperceivers: Two Case Studies
Martin Lamb, John Malone, Daniel Boase-Jelinek, and Scott Lewis

In a study of 744 Western Australian Year 8 and 9 students, three different types of misperception were identified when students performed linear transformations. To examine their particular perceptual problems, nine persistent misperceivers (those who misperceived in the same way on three tests) were given one-on-one remedial instruction. Case studies of two different types of persistent misperceiver are presented here, one involving angles, the other involving reflections, to demonstrate to maths teachers what may be happening in their classrooms unbeknown to them.

The Language of Zero: An Understanding of Place Value
Tracey Snape

The acquisition of the 'language of zero' is important in the developmental progression of place value understanding. This short communication paper reveals the 'language of zero that children and teachers use in Christchurch primary school classrooms and considers educational implications of research findings from a larger study. Key international literature regarding place value development and acquisition of number are referenced. The paper is intended to invite feedback to inform subsequent studies regarding the acquisition of place value language.

Young Children Reasoning with Tables: Toward a Model
Maria Droujkova

While there is more research on kids ages eight and up, less is known about young children reasoning with tables. A series of design experiments (Droujkova, In preparation, In press) led to a table reasoning model (TRM) describing children, ages three to eight, working with qualitative and numeric tables. TRM includes four components of reasoning: *Sameness/variation: what and how entities are varied or kept the same. *Action/object: ways children conceptualise entities as objects and actions. * Local/global: reasoning about neighbour cell patterns vs. thinking of rows and columns. *Coordinates/function: focus on the position of entries, or on functions forming entries. Competent work with tables requires fluent use of all components in multiple contexts. Moving toward such competency, young children exhibit a variety of reasoning patterns, often surprisingly different from adult approaches (Brizuela & Lara-Roth, 2002). For example, a beginner typically fills every cell with the same picture with no variation. Children view the 2*3 cell in the multiplication table as a product (action) of two numbers (objects), or as a doubling (action) of the number three (object). During missing cell value tasks, children search clues in row and column interactions, exhibiting global reasoning, or look at local neighbour cell patterns. In ?jigsaw? tasks of putting cut-up tables back together, children can focus on coordinates of each cell within table structures, and/or on the function used to create the cell entry. TRM helps to analyse ways children reason about tables. It is a robust tool for designing learning activities developing table reasoning.

Poster (abstract only)
Round Table (abstract only)
Challenges for Mathematics Education in Pacific Island Nations in the 21st Century
Andy Begg

The purpose of the roundtable is to discuss with interested people the challenges for mathematics education faced by Pacific Island Nations. The form of the roundtable will be oral presentations and discussion rather than papers to reflect the oral style traditionally used in Pacific Island countries. The session will start with people working in these countries speaking about the problems in their particular localities with a focus on cultural, political, geographic, and economic influences on mathematics education. This will be followed by a more general discussion about the possible ways that some of these challenges might be addressed. Particular issues that are expected to be discussed include: ? the ways that members of MERGA might possibly help the Island nations; ? the possible role of research; ? the types of research that might be appropriate, and ? the involvement of non-indigenous researchers. Although research will be a major focus of discussion, other development activities are also likely to be discussed.

Do High School Students Need Mathematics to Prepare for the Academic Numeracy Demands of University?
Janet A Taylor and Linda Galligan

High school students across Australia traditionally take at least one mathematics subject in their senior years of study. These subjects are seen as necessary for success at university and an important part of a students' well rounded education. Similarly statements are often released relating the importance of mathematics in the changing technologically based world. Yet more and more universities have removed the mathematics entry requirements from their courses and few universities list numeracy as an attribute of one of their graduates. Currently in Queensland, the majority of students planning to study at university still choose to study mathematics in their senior years, although there have been significant decreases in the number of students studying calculus inclusive mathematics courses. But will students still opt to study mathematics at all if universities do not include it as a prerequisite? This round table discussion will present preliminary results of research into the current status of mathematics entry requirements in Australian universities and the academic numeracy demands of courses for which senior mathematics is not an entry requirement. We aim to investigate, through discussion, how to determine what mathematics is required for university study, to answer the question 'What are the numeracy demands of university study?'

Keeping it Going: Exploring Ways to Sustain Professional Development in Numeracy
Fiona McDiarmid and Ruth Pritchard

Numeracy has been a major focus of recent professional development initiatives for primary school teachers in many countries. Research has shown that a variety of factors contribute to a school?s ability to sustain gains after completion of professional development programmes. An exploratory action research study undertaken with five inner-city primary schools focused on identifying and providing a variety of tools to sustain effective numeracy practices. Teacher surveys, professional discussions with staff, and classroom observations informed the intervention. Numeracy facilitators/researchers worked with principals and Lead Teachers in mathematics to develop increased knowledge and understanding of issues surrounding numeracy teaching and learning. A central theme was the use of reflective practices which promoted the use of critical peers, observation, and videoing of mathematics lessons. Major issues found to be inhibiting sustainability included: leadership and staff changes within schools, a lack of school wide numeracy policies, and teachers? lack of in-depth knowledge of numeracy content and pedagogy. Interim findings suggest that teachers require further support and opportunities to experiment with, and reflect on, new ideas encountered within the professional development. Offering external support, creating a forum to address the issues, and promoting professional learning communities within the schools, enabled the schools to refocus on effective numeracy practices. Some reluctance by teachers to deprivatise or critically reflect on their practice was apparent. Round table participants are invited to contribute to a discussion of factors which may contribute to the sustainability of effective numeracy practices, to inform further research.

Preparing for Assessments of our Research Productivity
Peter Sullivan

We have already entered an era of greater scrutiny of the nature and impact of our research from practitioners and we are about to receive active evaluations of our research productivity from the government and other funding agencies. First, we need to understand DEST policy developments and implications. Next, we need to understand the processes used by funding agencies in awarding grants, especially the ARC. Then we need to consider the types of projects that will have an impact on the field of education, and especially mathematics education. This roundtable will allow participants to share understandings of policy directions, especially the anticipated research assessments and the implications for our activities, it will review processes for applying for competitive grants, and it will allow discussion of implications for future mathematics education research. There will also be discussion of the MERGA research policy and consideration of whether variations or additions are needed to anticipate the forthcoming evaluative environments.

Use of Projects in the Teaching of Statistics
Murray Black

The aim of this round table discussion is to examine the merits of a project-based teaching approach for teaching statistics. My proposed research involves the lecturer using a project-based teaching approach that covers all of the prescribed content concepts in a statistics paper. This project would be introduced initially, and then every concept would be taught with respect to its relevance in the project analysis. The taught content would include the method of sampling, data analysis and the drawing of conclusions. Data measuring the level of reasoning in statistics along with student confidences in using statistics would be measured for students taught a similar content in two different ways. It will be hypothesised that students will display significantly greater ability to reason statistically with more confidence than those that have been taught using a traditional topic order approach with a multitude of examples. Yesilay (2000) suggested that students tend to learn more by doing a project than in any regular coursework. Murtonen & Lehtinen (2003) identified linking theory with practice as one of five difficulties experienced by education and sociology students in quantitative methods courses. It is hoped that the use of a project will enable the student to learn more effectively as it will provide a link from theory to a real world problem. Discussions will revolve around the use of a project-based teaching approach in either the assessment or delivery of a paper in statistics. Specific questions addressed will be: How have you used projects in the teaching of statistics? How effective did you find the use of these projects?