CONTENTS

VOLUME 1

KEYNOTE LECTURES…………………………………………………………………	
Preamble to the ‘Annual Clements / Foyster Lecture’
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 (PIA) LECTURE33
Variation and Expectation as Foundations for the Chance and Data Curriculum
Jane M. Watson 

INVITED SYMPOSIUM43
Building Connections: Research, Theory, and Practice
Di Siemon 
A Mathematics Teacher Educator’s Perspective of Building Connections between Research, Theory, and Practice
 Colleen McMurchy-Pilkington 
From the Hill to the Swamp:  Combining Research and Practice
Peter Gould 
Building connections:  Research, Theory and Practice — A View from the Profession
Will Morony 
Building connections:  Research, Theory and Practice — A view from a Practitioner
Vicki Nally 

RESEARCH PAPERS
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 
Conceptions and Tensions in Globalisation and Their Effects on Mathematics       Educators 
Bill Atweh and Philip 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 
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 

VOLUME 2

RESEARCH PAPERS  (continued) ………………………………………………….	417

Mental Computation: The Benefits of Informed Teacher Instruction …………………	419
	Ann Heirdsfield and Janeen Lamb 
Discourse as a Catalyst for Facilitating Practitioner Research………………………..	427
	Beth Herbel-Eisenmann 
Potential of Technology and a Familiar Context  to Enhance Students' Concept of 
Rate of Change………………………………………………………………………	435
	Sandra Herbert and Robyn Pierce 

The Effects of Number Knowledge at School Entry on Subsequent Number 
Development: A Five-year Longitudinal Study………………………………………..	443
	Marj Horne 
Reforming Communication in the Classroom: One Teacher's Journey of Change……	451
	Roberta Hunter  
Mentoring Mathematics Teachers in Low Socio-Economic Secondary Schools in New 
Zealand ………………………………………………………………………………..	459
	Barbara Kensington-Miller 
The Contested Notion of Sustainability: Possibility or Pipe Dream for Numeracy 
Reforms in New Zealand………………………………………………………………	467
	Nicky Knight 
Students' Use of Context Knowledge in Interpreting Data……………………………..	475
	Cynthia Langrall, Edward Mooney and Nicole Williams 
Language Factors that affect Mathematics Teaching and Learning of Pasifika 
Students……………………………………………………………………………….	483
	Viliami F Latu 
How Primary Pre-service Teachers Perceive Mathematics Teacher Educators' 
Practice:    A Case Study……………………………………………………………..	491
	Gregor Lomas 
Establishing a Numeracy Culture in a Distance Education Learning Environment:             
A Case Study…………………………………………………………………………..	498
	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………………………………………………………………………..	505
	Rex A. Matang 
Does Mathematics Education in Australia Devalue Indigenous Culture? Indigenous 
Perspectives and non-Indigenous Reflections…………………………………………	513
	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……………………………	521
	Andrea McDonough and Barbara Clarke 
Growth of Teacher Knowledge within an On-line Collaborative Learning 
Environment……………………………………………………………………………	529
	Mathew McDougall and Rod Nason 
The Use of Algebra in Senior High School Students' Justifications………………….	537
	Tamsin Meaney 
Measuring Fractions………………………………………………………………….	545
	Annie Mitchell  
What Does Mathematics Understanding Look Like?…………………………………	553
	Judith Mousley 
Where Did I Go Wrong? Students' Success at Various Stages of the Problem-Solving 
Process………………………………………………………………………………..	561
	Tracey Muir and Kim Beswick 
Understanding Students' Reasoning While Comparing Expressions…………………	569
	Shweta Naik, Rakhi Banerjee and K. Subramaniam 
Regional Differences in the Professional Development Needs and Preferences of 
Teachers of Primary Mathematics…………………………………………………	577
	Steven Nisbet 
Mathematics and the Construction of Feminine Gender Identity……………………..	585
	Stephen Norton  
Do Teachers Change Their Practices While Participating in a Lesson Study?……….	593
	Jo Clay Olson 
Teachers' Development of Substantive Communication about Mathematics………..	601
	Kay Owens 
Preschoolers' Mathematical  Patterning……………………………………………..	609
	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……………………………………………………	617
	Anne Paterson and Jack Bana 
Mathematical Beliefs and Achievement of Pre-service Primary Teachers……………	625
	Bob Perry, Jenni Way, Beth Southwell, Allan White and John Pattison 
Student Misconceptions about Projectile Motion…………………………………….	633
	Anne Prescott and Michael Mitchelmore 
Subject Matter Knowledge: Mathematical Errors and Misconceptions of Beginning 
Pre-Service Teachers………………………………………………………………..	641
	Julie Ryan and Barry McCrae 
Education for Early Mathematical Literacy: More Than Maths Know-How………..	649
	Abigail Sawyer 
Preservice Teachers' Intentions to Provide Good Examples and Help Children 
Replicate Them……………………………………………………………………….	656
	Anne Scott 
Understanding the Role of Assumptions in Mathematical Modeling: Analysis of 
Lessons with Emphasis on  'the awareness of assumptions'…………………………..	664
	Tatsuhiko Seino 
Exploring Pre-service Teachers' Reasoning about Variability: Implications for        
Research………………………………………………………………………………	672
	Sashi Sharma  
Building a Methodology for the Comparison and Evaluation  of Middle-Years 
Mathematics Textbooks………………………………………………………………	680
	Mal Shield 
Assessing Multiple Objectives with a Single Task in Statistics……………………..	688
	Jane Skalicky 
Relative Risk Analysis of Educational Data  …………………………………………  696
	Kaye Stacey and Vicki Steinle 
Concerns Relating to the CAS Use at University Level……………………………….	704
	Sepideh Stewart 
The Integration of Mathematics and Music in the  Primary School Classroom……….	712
	Kathryn Still and Janette Bobis 
Interactive Whole Class Teaching and Interactive White Boards…………………….	720
	Howard Tanner, Sonia Jones, Steve Kennewell and Gary Beauchamp 
Children's Views of their Teacher's Role in Helping them Learn Mathematics………	728
	Merilyn Taylor, Ngarewa Hawera and Jenny Young-Loveridge  
Students' Attempts to Solve Two Elementary Quadratic Equations: A Study in Three 
Nations………………………………………………………………………………	735
	Pongchawee Vaiyavutjamai, Nerida F. Ellerton and M. A. (Ken) Clements 
Glimpses of Generative Practice: Constructing Pre-service Teachers' Learning in 
Partnership…………………………………………………………………………….	743
	Colleen Vale and Anne Davies 
Challenging Task-driven Pedagogies of Mathematics ………………………………..	751  
	Fiona Walls 
Patterns Supporting the Development of Early Algebraic Thinking………………	759
	Elizabeth A. Warren 
An Indigenous Perspective on Mathematics Contextualisation  in a Pre-school: From 
Safety to Empowerment……………………………………………………………….	767
	Leesa Watego 
Statistical Literacy over a Decade……………………………………………………..	775
	Jane M. Watson, Ben A. Kelly and John F. Izard 
Teaching Percentage as a Multiplicative Relationship……………………………….	783
	Paul White and Michael Mitchelmore 
'I am really not alone in this anxiety': Bibliotherapy and Pre-service Primary 
Teachers' Self-image as Mathematicians……………………………………………	791
	Sue Wilson and Steve Thornton 
Language Appropriate for the New Zealand Numeracy Project……………………..	799
	Joanne Woodward and Kathryn C. Irwin 
Results of a Teaching Experiment to Foster the Conceptual Understanding of 
Multiplication Based on Children's Literature……………………………………..	807
	Amanda Worlley and Romina Jamieson-Proctor 
Prioritising the Voice of Researched: Using Photographs to Elicit Mathematical 
Thinking of Participants…………………………………………………………….	815
	Robyn Zevenbergen 

SHORT COMMUNICATIONS……………………………………………………	823

Graphs, Transformations, Rates of Change and Quadratic Context Variations……….	825
	Karoline Afamasaga-Fuata'i 
Young Children Reasoning with Tables: Toward a Model…………………………..	825
	Maria Droujkova 
"My Mom Thinks I Should be an Engineer": Parental Influences and Girls on Track 
for Math-Related Careers…………………………………………………………….	826
	Maria Droujkova, Sarah B. Berenson, Irena Rindos and Sue Tombes 
Message from Student Teacher Constructed Posters………………………………..	826
	Shajahan Haja 
Persistent Mathematics Misperceivers: Two Case Studies…………………………….	827
	Martin Lamb, John Malone, Daniel Boase-Jelinek and Scott Lewis 
An Investigation of the Selection Process of Mathematically Gifted Students………..	827
	Kyunghwa Lee, Kyungmee Park and Jaehoon Yim 
The Language of Zero: An Understanding of Place Value……………………………	828
	Tracey Snape 
Mathematical Problem-Solving Frameworks of Different Mathematics-Anxiety 
Levels Students………………………………………………………………………..	828
	Yeo Kai Kow Joseph 

ROUND TABLE DISCUSSIONS…………………………………………………..	830

Challenges for Mathematics Education in Pacific Island Nations in the 21st Century	832
	Andy Begg 
Use of Projects in the Teaching of Statistics…………………………………………..	832
	Murray Black 
Keeping it Going: Exploring Ways to Sustain Professional Development in Numeracy	833
	Fiona McDiarmid and Ruth Pritchard 
Preparing for Assessments of our Research Productivity………………………………	834
	Peter Sullivan 
Do High School Students Need Mathematics to Prepare for the Academic Numeracy 
Demands of University?……………………………………………………………..	834
	Janet A Taylor and Linda Galligan