Conference Proceedings 2004


Mathematics Education for the Third Millennium, Towards 2010
Editors: Ian Putt, Rhonda Faragher and Mal McLean
Table of Contents
MERGA 2004 Conference Proceedings
Ian J. Putt
List of Reviewers
Keynote Address
Australian Mathematics Learning in an International Context
Barry McGaw
Mathematics Education for the Third Millennium: Visions of a future for handheld classroom technology
Stephen Arnold
MERGA: A Community of Practice
Glenda Anthony
Practical Implication Award
ICT-Numeracy Practices in a School Serving a Disadvantaged Community
Peter D. Renshaw
Researching Numeracy Teaching and Learning with ICT: Facing the Problems of Innovation
Steve Lerman
Scaffolding and Problem Posing: Supporting Student Engagement
Chris Judd
Using ICTs to Support Numeracy Learning: The way of the future? Whose future?
Robyn Zevenbergen
Research Paper
A Novice Teacher's Conception of the Crucial Determinants of his Teaching of Beginning Algebra
Cecilia Agudelo-Valderrama
The Influence of Perceived Constraints on Teachers' Problem-Solving Beliefs and Practices
Judy Anderson, Peter Sullivan and Paul White
Towards a Model of Social Justice in Mathematics Education and its Application to Critique of International Collaborations
Bill Atweh
Understandings of the Implications of the Treaty of Waitangi in Mathematics Programs
Robin Averill, Dayle Anderson, Herewini Easton and Anne Hynds
The Relationship between the Estimation and Computation Abilities of Year 7 Students
Jack Bana and Phuntsho Dolma
Equity and Empowerment in Mathematics: Some Tensions From the Secondary Classroom
Hannah Bartholomew
The Mathematical Discourse of Advanced Undergraduate Mathematics
Bill Barton, Robert Chan, Chris King and Phillipa Neville-Barton
The Mathematics of Indigenous Card Games: Implications for Mathematics Teaching and Learning
Annette R Baturo, Stephen Norton and Tom J Cooper
Talking and Writing About the Problem Solving Process
Kim Beswick and Tracey Muir
Time, Resources, Information Overload and Classroom Management: Issues surrounding Professional Development
Janette Bobis
Teacher Approaches to Graphing a Difficult Cubic Function
Jill Brown
Can the Notion of Affordances be of Use in the Design of a Technology Enriched Mathematics Curriculum?
Jill Brown, Gloria Stillman and Sandra Herbert
Developing Geometrical Reasoning
Margaret Brown, Keith Jones, Ron Taylor and Ann Hirst
Integrating Everyday and Scientific Ways of Knowing Mathematics Through Forms of Participation in Classroom Talk
Raymond Brown and Peter Renshaw
Shaping Understanding: How Does Investigating in a Spreadsheet Environment Affect the Conversations of Initial Training Students Doing Mathematics?
Nigel Calder
Primary Students' Understanding of Proof
Rosemary Callingham, Judith Falle and Garry Clark
Perception of Mental Computation Practice: Reports From Middle School Teachers and Students
Annaliese Caney
Tools for Transnumeration: Early Stages in the Art of Data Representation
Helen Chick
Numeracy Enacted: Preschool Families Conceptions of Their Children's Engagements with Numeracy
Barbara Clarke and Jill Robbins
Algebraic Thinking in Geometry at High School Level: Students' Use of Variables and Unknowns
Jaguthsing Dindyal
Teachers' Characteristics: One Lesson ─ Two Learning Environments
Carmel Diezmann
Two Pathways to Multiplicative Thinking
Fiona Ell, Kay Irwin and Stuart McNaughton
Mathematical Modelling in the Primary School
Lyn D. English
Learning Through Interacting with Students' Ways of Thinking
Lyn D. English and Helen M. Doerr
Supporting Reflection as Pre-Service Primary Teachers Develop a Mathematics Teaching Portfolio
Sandra Frid and Len Sparrow
The Challenge of Meeting the Instructional Needs of Grade 1 and Grade 2 Children Who Are at Risk in Mathematics
Ann Gervasoni
Numeracy for Nurses: The Case for Traditional Versus Non-traditional Methods for Teaching Drug Calculation
Roslyn Gillies
What Do They See When They Look? Student Perspectives on Equations
David Godfrey and Michael O. J. Thomas
Emergence of a Pre-Service Community of Practice
Merrilyn Goos and Anne Bennison
Building Partnerships with Families and Communities to Support Children's Numeracy Learning
Merrilyn Goos and Lesley Jolly
Addressing the Needs of Mathematically Anxious Preservice Primary Teachers
Ngarewa Hawera
An Investigation into the Modelling of Word Problems
Ruth Hubbard
Operating with Decimal Fractions as a Part-Whole Concept
Kathryn C Irwin and Murray S. Britt
Professional Development of Mathematics Teachers in Low Socio-Economic Secondary Schools in New Zealand
Barbara Kensington-Miller
Preservice Teacher Education in Mathematics: Thinking Innovatively About Innovation.
Mary Klein
How Binary Thinking in School Mathematics Masks and Maintains its Coercive and Conservative Effects: A Poststructuralist Analysis
Mary Klein and Linda Saunders
There is More to Learning Mathematics than Mathematics: Attributional Beliefs and Motivation of Maori and Pacific Island Students
Viliami Finau Latu
Authentic Artefacts: Influencing Practice and Supporting Problem Solving in the Mathematics Classroom
Tom Lowrie
When is Three Quarters not Three Quarters? Listening for Conceptual Understanding in Children's Explanations in a Fraction Interview
Annie Mitchell and Doug Clarke
Alternative Learning Trajectories
Judith Mousley, Peter Sullivan and Robyn Zevenbergen
The Numeracy Research in NSW Primary Schools Project 2001-2003
Joanne Mulligan and Susan Busatto
Effortless Mastery and the Jazz Metaphor
Jim Neyland
Social Justice and the Jazz Metaphor
Jim Neyland
Primary Teachers' Beliefs and Practices with Respect to Compulsory Numeracy Testing
Steven Nisbet and Peter Grimbeek
Using Lego Construction to Develop Ratio Understanding
Stephen Norton
School Mathematical Achievement as a Predictor of Success in a First Year University Mathematics Foundations Unit
Robert Peard
Why You Have to Probe to Discover What Year 8 Students Really Think About Fractions
Catherine Pearn and Max Stephens
Addressing Changing Assessment Agendas: Experiences of Secondary Mathematics Teachers in Rural NSW
John Pegg and Debra Panizzon
Learning Approaches in University Calculus: The Effects of an Innovative Assessment Program
Marina Penglase
Fermi Problems in Primary Mathematics Classrooms: Pupils' Interactive Modelling Processes
Andrea Peter-Koop
CAS: Student Engagement Requires Unambiguous Advantages
Robyn Pierce, Sandra Herbert and Jason Giri
Numbers and Maps: The Dynamic Interaction of Internal Meanings and External Resources in Use
Dave Pratt and Amanda Simpson
Investigating Parental Attitudes and Beliefs in Mathematics Education
Ruth Pritchard
When Does Successful Comparison of Decimals Reflect Conceptual Understanding?
Anne Roche and Doug Clarke
Structured Peer Interactions to Enhance Learning in Mathematics
Kathryn Rowe and Brenda Bicknell
Shifting the Lens of Inquiry into the Socialisation of Mathematics Teachers: Nature of Value Differences
Wee Tiong Seah
Classics Counts Over Calculus: A Case Study
Fiona Shannon
Learning in a Community of Inquirers: Developing an Inquiry Stance
Tracey J. Smith
MERJ: Reviewing the Reviews
Beth Southwell
A Longitudinal Study of Students' Understanding of Decimal Notation: An Overview and Refined Results
Vicki Steinle and Kaye Stacey
The 'Mathematically Able Child' in Primary Mathematics Education: A Discursive Approach
Fiona Walls
Becoming Knowledgeable in Practice: The Constitution of Secondary Teaching Identity
Margaret Walshaw
Mathematical Patterning in Early Childhood Settings
Jillian Waters
A Two-Year Study of Students' Appreciation of Variation in the Chance and Data Curriculum
Jane M. Watson and Ben A. Kelly
Beliefs about Chance in the Middle Years: Longitudinal Change
Jane M. Watson, Annaliese Caney and Ben A. Kelly
Background Knowledge and Connectedness: The Case of Mathematics
Paul White and Michael Mitchelmore
Explaining Thai and Japanese Student Errors in Solving Equation Problems: The Role of the Textbook
Duangmanee Ya-amphan and Alan Bishop
Numeracy Practices in Contemporary Work: Changing Approaches
Robyn Zevenbergen and Kelly Zevenbergen
Short Communication (abstract only)
Expansion of Binomials and Factorisation of Quadratic Expressions: Exploring a Vedic Method
Mala Saraswathy Nataraj and Michael O. J. Thomas

Many students have traditionally found the processes of algebraic manipulation, especially factorisation, difficult to learn. This study investigated the value of introducing students, after standard methods, to a Vedic method of multiplication of numbers that is very visual in its application. We wondered whether applying the method to quadratic expressions would assist student understanding, not only of the processes but also the concepts of expansion and factorisation. We found that there was some evidence this was the case, with some students preferring to use the new method. Thus results suggest it may be a useful adjunct to traditional approaches.

Integration or Incorporation? An Examination of the Use of Technology in Tertiary Mathematics Courses
Greg Oates

Many proponents of the use of technology in mathematics education argue that to be effective, such usage should be fully integrated, but exactly what is meant by integrated technology is seldom defined. A number of tertiary mathematics teachers were surveyed to investigate the degree to which technology is used in their courses, and the information received was used to identify several aspects critical to an examination of integrated technology. The paper then proposes a model for helping to describe and compare the degree of integration of technology in different courses.

Monitoring Early Mathematical Development in Transition from Pre-school to Formal Schooling: An Intervention Study
Marina Papic

This project assesses the underlying mathematical knowledge of 53 children from two Sydney pre-schools, one year prior to formal schooling, and monitors their on-going mathematical development. The ability to generate and abstract simple mathematical patterns is explored through a range of problem-solving tasks. Data comprise structured videotaped individual interviews, children?s representations, observational and anecdotal records. A case study of one pre-school analyses an early mathematics intervention program highlighting mathematical patterns, structures and relationships. The study analyses teacher and community perceptions; the effectiveness of this intervention on children?s mathematics learning, the professional development of pre-school staff and their programs.

Practicum and Affective Development in Mathematics
Peter Grootenboer

An integral part of all initial teacher education programs is the school-based practicum where preservice teachers get an opportunity to develop their teaching skills and knowledge in a classroom. Many have suggested that these experiences are very powerful in shaping prospective teachers views of teaching as they are perceived as being 'real' as opposed to the 'artificial' environment of the tertiary courses. This can mean that the practicum experiences can legitimate or negate the learning that occurs within tertiary courses. In particular, preservice teachers can make significant positive changes in their affective responses to mathematics, but the longevity and stability of these changes can be severely challenged through their school-based practicum experiences.

Student's Willingness to Attend to Mathematics: A Year 9 Mathematics Classroom Case Study
Barbara Tadich

Teaching young adolescents today requires not only an understanding of content and pedagogical knowledge, but an understanding of students' developmental stages and an approach which prioritises the students' preferred learning environment. From a case study of a Year 9 mathematics classroom, this report will identify and explain how certain characteristics and qualities of a student-directed program and a range of classroom conditions influenced student attitudes to the learning of mathematics. The focus will be student perceptions of the learning of mathematics along with an examination of students' preferred learning conditions and the influence of the classroom environment on mathematical learning.

Teaching and Learning Mathematics: Have We Lost the Spirit?
Beth Southwell

The benefits of a holistic approach to education has been acknowledged by educators and, in view of the historical background of mathematics as a discipline, it may enhance performance in mathematics if more emphasis is placed on the wonder and mystery formally associated with the subject than is currently the case. In a tentative trial in this regard, two secondary pre-service students were asked to respond to a series of questions and images related to the spirit of mathematics and their own views of spirituality. From two different backgrounds, these responses identified concepts of order and relationships as key factors in their views of mathematics and its spirit.

Poster (abstract only)
Round Table (abstract only)
Analysing Students' Thinking: Strategies Employed In Early Equation Solving
George Toth and Loretta Weedon

Researchers have emphasized the importance of developing relational thinking in regard to early equation solving. An assessment instrument was designed to assist and facilitate the process of improving the development of students? strategies. The purpose of the instrument was to assist teachers to analyse and classify students' reasoning by examining students' responses to a variety of tasks involving number sentences. The assessment instrument focuses on concepts of equality, identifying strategies employed, as well as the ability of students to generalise number behaviour. This assessment instrument was trialled with 51 Year 5/6 and 26 Year 8 students. The paper focuses on a limited number of test items within the assessment instrument. In particular, it analyses the different types of strategies utilised and the proportions of students who employed those strategies. We seek advice and direction from participants regarding further possible development of the assessment instrument as well as the identification of tests items that would provide useful information to improve the practice of teachers.

Numeracy Intervention in Junior Secondary Mathematics
Colleen Vale

The diversity of mathematics achievement in junior secondary mathematics and the problems of engaging students have been well documented. Many researchers including regular presenters at MERGA conferences have explored the misconceptions and mathematical thinking strategies of students who are at risk of not achieving the numeracy benchmark standards. Howard and colleagues have reported the successful outcomes of a structured intervention program conducted in the middle years with students in schools in New South Wales. However teachers in junior secondary mathematics classrooms struggle to adopt reform practices and implement intervention strategies or programs that adequately address the needs of at risk students. During this round table discussion, the findings from a numeracy intervention project in which teachers from one school participated in action research will be presented. The teachers gained new insights and understanding of their students' mathematical thinking and made small steps in changing classroom practices and learning activities that enabled improvements for some students in their classes. Division thinking and the relationship of division concepts to fractions emerged as one issue for further research that participants of the round table discussion may want to pursue in particular. Through this round table I would like to invite other researchers to discuss their experiences of working with secondary school teachers on intervention with a view to collaborating in the development of a large-scale numeracy intervention project for students in junior secondary mathematics.