MERGA

2004 Conference Proceedings

2004 Conference Proceedings

2004 Full Conference Proceedings

TABLE OF CONTENTS

KEYNOTE ADDRESSES

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

SYMPOSIA

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 PAPERS

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 COMMUNICATIONS

Expansion of Binomials and Factorisation of Quadratic Expressions: Exploring a Vedic Method – Mala Saraswathy Nataraj and Michael O. J. Thomas

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

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

Practicum and Affective Development in Mathematics – Peter Grootenboer

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

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

ROUND TABLES

Analysing Students’ Thinking: Strategies Employed In Early Equation Solving – George Toth and Loretta Weedon

Numeracy Intervention in Junior Secondary Mathematics – Colleen Vale

Short Communications & Round Tables

The following documents are essential to read and complete when considering submitting a short communication or round table to the MERGA conference (available in the Submission section of this website).

  • MERGA Paper Template – to be used to write the abstracts which are then submitted to the MERGA conference website
  • MERGA Publication Agreement – to be submitted on the MERGA conference website at the time of the abstract submission

Submissions not exceeding one page are required for short communications and round tables. The submissions must be prepared using the conference template, and can include essential references. They will be reviewed by the Editorial Team and, if accepted, will be published in the conference proceedings as one-page abstracts (not as papers). Presenters are invited to prepare a paper for distribution at the conference, but these papers will not be included in the proceedings.

Short communications are suitable for reports on research in mathematics education that do not fully meet the requirements for published papers. These might include works in preliminary stages, reports of pilot projects, initial reviews of literature, ideas or suggestions for future study, and briefer discussions of particular issues. Short communications allow new researchers to obtain feedback on projects in a constructive and supportive environment, and foster the building of links between researchers with similar interests.

Short communications are presented by author(s) only, allocated half of the time for research reports (in past, this was 20 minutes). At least 5 minutes is to be allocated for audience questions and open discussion.

Round tables are suitable for presenters seeking involved interaction with the audience in relation to their research or topic of interest in mathematics education, and for those sharing their insights and advice with the early career colleagues. These might include discussion of an emerging topic, co-analysis of provided student work, solving a mathematical task, or discussing the demands and benefits of reviewing for high quality journals. Round tables allow finding peers with similar research interests, exploration of new research avenues, and building the capacity of MERGA community.

Round tables are led by author(s) only, allocated the same time as research reports (in past, this was 40 minutes). The abstracts should make clear the interactive element of the proposed activity, with no more than 15 min of the session time in a presentation mode.

Beth Southwell Practical Implications Award

The Beth Southwell Practical Implications Award (BSPIA) recognises high-quality mathematics education that produces insights for the teaching profession and/or student learning.

The award consists of $500 and a plaque to be presented at the Conference.

Nomination process 

There are two ways a paper can be nominated for the BSPIA:

  • Self-nomination: When you submit your conference paper, check the box that asks if you would like to apply for the BSPIA.
  • Nomination via peer-review: Anyone who submits a Conference paper for peer-review will be considered for nomination by the reviewers. 

Single and co-authored papers are eligible for consideration.

When you write your paper, please ensure that you observe all general paper submission requirements including the maximum page length.

Judging process

Submissions must be deemed eligible for publication in the Conference proceedings by the initial reviewing panel. Submissions accepted for presentation only will be excluded from consideration.

The judging panel will consist of two MERGA members and two AAMT nominees and will be chaired by the VP Development.

The judging criteria are:

  • Identification of a persistent and significant research problem
  • Synthesis of recent research literature and relevant policy initiatives
  • Robust methodology producing valid, reliable findings
  • Insightful discussion of practical implications for the teaching profession and/or student learning
  • Clear, succinct style of academic writing

Winners are notified four weeks prior to the Conference and are invited to present a keynote at the annual conference.

The Beth Southwell Practical Implications Award page on this website provides further information, including the history of the award and recent winners.  

Research Papers

The following documents are essential to read and complete when considering submitting a research paper to the MERGA conference (available in the Submission section of this website).

  • MERGA Paper Template – to be used to write the papers which are then submitted to the MERGA conference website
  • MERGA Publication Agreement – to be submitted on the MERGA conference website at the time of the paper submission

Research papers can take two major forms: 

1. Reports of empirical investigations 

When empirical investigations are reported (such as in an experimental intervention, confirmatory study, or action research, etc.), the paper should also include

  • a statement of rationale for methodologies used in collecting and analysing data;
  • a critical discussion of data findings in the light of the research literature; and
  • in the literature review, prior work in the area should be acknowledged and an explanation of how the work reported in the paper builds on that earlier work should be included.

2. Reports that are not based on empirical research including:

  • a theoretical discussion;
  • a position paper;
  • a report of scholarly enquiry in progress;
  • a literature review, a meta-study;
  • an account of a new initiative;
  • a reflective critique of practice; or
  • any mixture of these or other recognised scholarly forms.

When the work is a theoretical discussion, a position paper, a report of scholarly inquiry in progress, a review of literature, a theoretical study, a meta-study, an account of a new initiative, a reflective critique of practice or any mixture of these or other recognised scholarly forms, the material presented must be discussed critically, and alternative points of view relating to themes presented should be appropriately argued.
It is expected that presenting authors will have 40 minutes to present their work at the conference. At least 10 minutes must be allowed to field questions and comments from the audience.

Structure of research papers – All papers for publication in the conference proceedings should contain the following:

  • a statement of the problem/issue and a discussion of its significance;
  • a critical analysis of the research literature as it relates to the topic of the paper; and
  • conclusions and implications for mathematics education derived from the study.

All papers must respect MERGA’s ethical guidelines relating to research work. Papers should not be more than the set length. In addition, papers must be: readable; free of grammatical, spelling and typographical errors; and adhere strictly to style requirements advertised by the conference proceedings Editorial Team.

Originality – Only research papers that are substantially different from work that has been published previously will be considered for publication in the conference proceedings and/or presentation at the conference.

Reviewing of research papers – Research papers will be blind reviewed by a panel of peers approved by the conference committee. The main purpose of the refereeing process is to contribute to the growth and development of quality practice in mathematics education research. Thus reviewers are asked to assist authors by providing helpful feedback and to comment on the suitability of papers for presentation at the conference. Accordingly, it will not be assumed that published papers presented at the conference will be as polished as articles in scholarly journals. Referees will be asked to assess papers being reviewed against the accepted norms for scholarly works presented at MERGA conferences, as set out above.

Each conference proceedings’ Editorial Team will exercise discretion over the reviewing process. Reviewers’ comments will be returned to the authors. Authors whose papers are not accepted for publication may be invited by the editorial panel to present their paper at the conference as a Short Communication, with a 1-page abstract (which they will be invited to provide) being published in the proceedings. Papers may be rejected outright, with no opportunity for presentation at the conference in an alternative form.

Research Symposia

The following documents are essential to read and complete when considering submitting a research symposium to the MERGA conference (available in the Submission section of this website).

  • MERGA Paper Template (to be used to write the papers which are then submitted to the MERGA conference website)
  • MERGA Publication Agreement (to be submitted on the MERGA conference website at the time of the paper submission)

Presentation of groups of published papers related by theme in the form of a research symposium is encouraged. The symposium forum will be particularly suitable for presentations relating to a single large project or presentations that explore topical themes from different and/or related perspectives. Special Interest Groups [SIGs] are encouraged to consider the symposium option as a means for sharing and discussing current research.

A symposium should consist of no more than four presentations of about 15 minutes duration each. The written papers should be half the length of research papers as described for research papers. Both research report types – empirical or non-empirical – are acceptable as published symposium papers.

A brief overview of the symposium (limit one page), including a symposium title, an introduction to the theme/project, and a short introduction to each of the 3-4 contributions, must be submitted with the set of short papers. Please list the symposium convenors as the authors on the first page, and name the paper authors in the text description.

The symposium proposer will also nominate a person to chair the symposium, and a discussant can also be named if desired. This information should accompany the collection of papers submitted for review.

The set of symposium papers (and the overview) will be blind reviewed by a review panel. The main purpose of the reviews is the same as for published papers, and the same criteria are used. The reviewers will be asked to consider the cohesiveness of the set of symposium papers. They will indicate whether the symposium as a whole, and each paper within it, should be “accepted”, “rejected” or if it “requires revision”. If it is deemed that one, some or all of the papers are in need of revision, the reviewers will outline which papers need to be revised and provide suggestions for the required changes. When the revisions are made, the symposium papers will be re-submitted and the set of papers will be sent to the same review panel for further consideration. As with research papers, the final decision about which symposium papers will be published is at the discretion of the Editorial Team.

The date for submission of the collection of symposium papers is the same as for Early Bird papers. This date has been set for the benefit of the group of authors of symposia papers. Should the symposium papers require revision, the authors will have the time to make the corrections and resubmit the set of symposium papers to be re-reviewed by the original reviewers.

Presentation of symposia: Symposia are presented by author(s) only, usually within a 90 min block. At least 10 minutes must be allocated for audience questions and open discussion.

Early Career Research Award

In order to encourage new researchers in mathematics education, MERGA sponsors an award to an author in the early part of her/his career. The award, for excellence in writing and presenting a piece of mathematics education research, consists of a plaque and a prize of $500 and is presented at the annual conference. 

Applying for the award

Entry for the Early Career Research Award is by submission of a written paper for presentation at the conference through the Early Bird process. Conditions of eligibility, information about the judging process, and the criteria judges will observe are indicated below. If you are applying for the Early Career Research Award, please ensure that when you upload your paper on the conference website, you also send an email to the Conference Secretariat indicating that you are an entrant for the Early Career Research Award. Note that at some MERGA conferences there is also a form to complete or a box to tick on the registration form, so check the conference website carefully. Please note that co-authored papers ARE NOT eligible for entry into the Early Career Research Award, nor are Round Table or Symposium papers.

Rules and eligibility for the Early Career Award

The Early Career Research Award page on this website provides further information about this award, including a list of recent winners.

Early Bird Review Process

The Early Bird review process is a form of mentoring, principally for new researchers. However, anyone is eligible to make use of it. Research papers submitted through the Early Bird process must be received by the Early Bird due date (i.e., the closing date in January). They must meet the requirements as set out for MERGA Research Papers. Early Bird papers should be uploaded following a link on the conference website. Authors will be asked to create a login into Oxford Abstracts (our conference management system) and submit the blinded file (anonymised) in the correct template for review.

Early Bird papers undergo a double-blind MERGA reviewing process. There are three possible outcomes of the review, and actions the authors need to follow.

  1. When the paper is accepted (for presentation at the conference and publication in the proceedings), the authors will be asked to provide their full unblinded manuscript and publication agreement.
  2. When small revisions are required, the revised papers will need to be resubmitted by the main submission deadline in March. The changes are considered by the editors, and the papers are not usually sent out for review again. The editors decide whether the paper is accepted for publication as well as presentation at the conference.
  3. When more major revisions are required, the reviewers will provide the author/s with feedback on how to how to strengthen the paper. The paper will need to be resubmitted by the main submission deadline in March, and it will be sent out for a new double-blind review.

Authors are notified of the outcome as soon as possible (usually within a few weeks, and in time for resubmission). Letters are sent to authors to indicate (a) accepted for publication, (b) small revisions required, (c) or major rewriting required.