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Content |
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Preface |
A Tribute to the Research Work of Dr. Glendon Lean
Alan J. Bishop
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Preface
Judy Mousley
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List of Reviewers |
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Keynote Address |
Opportunities to Learn Mathematics
Anne Watson
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The TIMSS 1999 Video Study and its Relevance to Australian Mathematics Education Research, Innovation, Networking, and Opportunities
Hilary Hollingsworth
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Working Together to Enhance Australian Aboriginal Students' Mathematics Learning
Susan Matthews, Peter Howard, Bob Perry
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Practical Implication Award |
Using Case Stories as a Tool for Listening More and Telling Less in Mathematics Teacher Education
Tracey Smith
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Symposium |
Identifying and Overcoming Barriers to Mathematics Learning
PETER SULLIVAN & JUDITH MOUSLEY & ROBYN ZEVENBERGEN & Robyn Turner Harrison & PAM HAMMOND & Carmel Diezmann
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Perceptions of Barriers to Numeracy
Judith A. Mousley
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Teachers' Perceptions of How Open-Ended Mathematics Tasks Assist in Overcoming Barriers to Learning
Robyn Turner-Harrison
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The Potential of Open-Ended Mathematics Tasks for Overcoming Barriers to Learning
Peter Sullivan
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Research Paper |
Students' Knowledge of Rates: A Case for a Foundation Year Program in South Africa
Kabelo Chuene
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Investigating the Concerns of Preservice Secondary Mathematics Teachers Through Critical Incident Reflective Journals
Joanne E. Goodell
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Developing Prospective Primary Teachers' Personal Content Knowledge of Mathematics
Roger Harvey
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Trigonometric Graph and the Real World: The Technical Students' Experience
Madihah Khalid
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Ethnomathematical Ideas in the Curriculum
Shehenaz Adam
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Searching for Mathematical Ideas in Stone Walls
Wilfredo Alangui
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Implementing Beliefs, Knowledge and Practices: A Beginning Teacher's StOlY
Shame Aldridge & Janette Bobis
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Teachers' Choice of Tasks: A Window Into Beliefs About the Role of Problem Solving in Learning Mathematics
Judy Anderson
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Pizza for Dinner: "How Much?" or "How Many?"
Glenda Anthony & Margaret Walshaw
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Bicultural Perspectives in a Pre-service Mathematics Education Course
Robin Averill & Pӓnia Te Maro
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A Window Into Mathematics Communities of Practice in Australia and New Zealand
Jack Bana & Margaret Walshaw
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Secondary Mathematics Teachers' Beliefs About Assessment and Factors That Influence These Beliefs
Anastasios Barkatsas & John Malone
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Investigations Into the Introduction of Logarithm Tables in Victoria
Chris Barling
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Patterns of Participation in Small-Group Collaborative Work
Mary Barnes
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Ability Grouping and the Construction of Different Types of Learner in Mathematics Classrooms
Hannah Bartholomew
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The Mathematics Enhancement Project: Using the Concepts of Cultural Conflict, Critical Mathematics Education, and Didactic Contract
Bill Barton
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Curriculum: Developing a Systems Theory Perspective
Andy Begg
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Accounting for the Contextual Nature of Teachers' Beliefs in Considering Their Relationship to Practice
Kim Beswick
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Children's Perspectives on Mathematics and Game Playing
Leicha Bragg
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Defining Moments in Determining a Complete Graph in a Graphing Calculator Teaching and Learning Environment
Jill Brown
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Subject Knowledge in Pre-service Teacher Education
Tim Burgess & Brenda Bicknell
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A Comparison Among Three Different Approaches to Mathematics Assessment
Rosemary Callingham
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The Positioning of Mathematics in an Environmental Thematic Curriculum
Coral Campbell
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Transnumeration and the Art of Data Representation
Helen Chick
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Maps That Come Alive: Numeracy Engagement Across Multimodal Texts
Susan Clancy & Tom Lowrie
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Similarity and Difference in International Comparative Research in Mathematics Education
David Clarke
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Addressing the Challenge of Legitimate International Comparisons: Lesson Structure in Australia and the USA
David Clarke & Carmel Mesiti
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More Perspectives on the Impact of Globalisation on Mathematics Education in Higher Education in Australasia
Philip Clarkson & Bill Atweh
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Windows Into Mathematics Teaching Through Data Maps
Carmel M Diezmann
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Teaching in a Different Direction
Helen Doerr & K. Jamie King
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Designing Research on Teachers' Knowledge Development
Helen Doerr & Richard Lesh
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Hops, Steps and Jumps: Mathematical Progress in the Early Years
Brian Doig & Molly de Lemos
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Questioning Numeracy Programs for At-Risk Students In The Middle Years Of Schooling
Shelley Dole
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Secondary Students' Perceptions of Instructional Approaches: Implications for Mathematics Learning
Sabita M. D'Souza & Leigh N. Wood
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Designing Assessment Using the MATH Taxonomy
Sabita M. D'Souza & Leigh N. Wood
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Development of a Web-Based Learning Tool to Enhance Formal Deductive Thinking in Geometry
Madduma Bandara Ekanayake & Christine Brown &
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The Victorian Curriculum and Assessment Authority (VCAA) Mathematical Methods (CAS) Pilot Study Examinations, 2002
Michael Evans & Pam Norton & David Leigh-Lancaster
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On Student Observation and Student Assessment
Ruhama Even & Tali Wallach
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Mathematics as Conversation: A Model for a Mathematics Retrieval Programme Conducted With Small Groups
Judith Falle
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Copying on a Graphics Calculator and Implications for Mathematical Understanding
Patricia A. Forster
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Re-visioning Curriculum: Towards Communicative Competence
Patricia A. Forster
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Using Mathematics Teaching Portfolios to Empower Pre-Service Primary Teachers
Sandra Frid & Len Sparrow
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Gender and Approaches to Studying Tertiary Mathematics
Mary-Ruth Freislich & Alan Bowen-James
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From Description to Analysis in Technology Aided Teaching and Learning: A Contribution From Zone Theory
Peter Galbraith & Merrilyn Goos
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A Teacher-Researcher Perspective on CAS in Senior Secondary Mathematics
Sue Garner & David Leigh-Lancaster
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What Students Say: Analysis of Structured Survey Data in Relation to Technology and Mathematics Learning
Vince Geiger
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Difficulties Children Face When Learning to Count
Ann Gervasoni
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Student Perspectives on Equation: Constructing the Mathematical Object
David Godfrey & Michael Thomas
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Learning to Teach Mathematics With Technology: A Study of Beliefs-In-Context
Merrilyn Goos
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Facilitating Affective Change With Preservice Primary Teachers
Peter Grootenboer
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Mental Computation: Refining the Cognitive Frameworks
Ann M. Heirdsfield
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Designing a Discussion: Teacher as Designer
Margret A. Hjalmarson
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Mathematics in Indigenous Contexts: A Case Study
Peter Howard & Bob Perry & Kevin Lowe & Suzanne Ziems & Anthony McKnight
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Constructing and Using a Personal Numeracy Teaching Model in a Classroom Setting
Peter Hughes & Lynne Petersen
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Percentages: A Foundation for Supporting Students' Understanding of Decimals
Roberta Hunter & Glenda Anthony
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The Development of Multiplicative Thinking in Young Children
Lorraine Jacob & Sue Willis
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Julia's Journey: Teacher Research in the Primary Mathematics Classroom
Stephen Keast
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Achievement Self-Rating and the Gender Stereotyping of Mathematics
Gilah C. Leder & Helen J. Forgasz
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Australian Secondary School Teachers' Use of the Internet for Mathematics
Esther Loong
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Teaching Mathematics Using the Internet
Esther Loong & Bruce White
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Posing Problems in ICT-Based Contexts
Tom Lowrie
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Monitoring Standards in Education: Mathematics 2002 Assessment
Andrew Stephanou, Barry McCrae, Rhonda Farkota, John Lindsey, Elena Stoyanova
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Tensions and Possibilities: Indigenous Parents Doing Mathematics Curriculum Development
Tamsin Meaney & Uenuku Fairhall
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Count Me In Too and the Basic Skills Test in New South Wales
Michael Mitchelmore & Paul White
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Shaping Practice: Worksheets as Social Artefacts
Judith A. Mousley
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First Graders' Use of Structure in Visual Memory and Unitising Area Tasks
Joanne Mulligan & Anne Prescott
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Re-visioning Curriculum: Shifting the Metaphor From Science to Jazz
Jim Neyland
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Individualization of Knowledge Representation in Teacher Education in Mathematics
Engelbert Niehaus
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Organising and Representing Grouped Data
Steven Nisbet
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A Whole School Approach to the Provision of Mathematics for Low-Achieving Girls in a Secondary School
Bob Perry & Jane Fulcher
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Interactive Animation Provides a Vehicle for Exploring Students' Understandings of Derivatives
Robyn Pierce & Lyn Atkinson
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Is it Better to Burn Out or to Rust?
Peter Rawlins
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Links Between Beliefs of Pre-Service Teachers About Literacy and Numeracy Learning
Anne Scott
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High School Students' Interpretation of Tables and Graphs: Some Findings From Fiji
Sashi Sharma
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Identifying Effective Scaffolding Practices Through Structured Peer Observation and Review
Dianne Siemon & Jo Virgona
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Gambling Behaviour and Understanding of Probability Concepts Among University Students
Donald Smith
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Exploring the Right, Probing Questions to Uncover Decimal Misconceptions
Vicki Steinle & Kaye Stacey
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Monitoring Standards in Education: Mathematics 2002 Assessments
Andrew Stephanou, Barry McCrae, Rhonda Farkota, John Lindsey & Elena Stoyanova |
Probing Whole Number Dominance With Fractions
Max Stephens & Catherine Pearn
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Metacognitive Intervention in a Cognitive-apprenticeship-computer-based Environment
Teong Su Kwang
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A Model of Early Number Development
Kaye Treacy & Sue Willis
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Gender and Attitudes to Computer Use in Junior Secondary Mathematics
Colleen Vale
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Year 8 Students' Reasoning in a Cabri Environment
Jill Vincent
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Sociomathematical Worlds: Investigating Children's Developing Relationships With Mathematics
Fiona Walls
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Number Combinations and Arithmetic Structure: Implications for Early Algebra
Elizabeth Warren
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Inference From a Pictograph: Statistical Literacy in Action
Jane M. Watson & Ben Kelly
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Predicting Dice Outcomes: The Dilemma of Expectation Versus Variation
Jane M. Watson & Ben Kelly
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The Development of Children's Reasoning Strategies in Probability Tasks
Jenni Way
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Lesson Study: A Model of Professional Development for Teachers of Mathematics in Years 7 to 12
Allan L. White & Beth Southwell
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Associations Between Student Pursuit of Novel Mathematical Ideas and Resilience
Gaye Williams
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Assessing Generalisation of Advanced Multiplicative Strategies
Vince Wright
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Changes in Teachers' Perceptions of Technology in Mathematics
Shirley M. Yates
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The Perspectives of Two Children who Participated in the Advanced Numeracy Project
Jenny Young-Loveridge & Merilyn Taylor
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Mathematical Errors in Fractions: A Case of Bruneian Primary 5 Pupils
Jamilah Yusof & John Malone
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Numeracy in New Times: Implications for Youth, Work and Employment
Robyn Zevenbergen & Kelly Zevenbergen
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Reforming Mathematics Education: A Case Study Within the Context of New Times
Robyn Zevenbergen
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Teachers' Conceptions of School Algebra and its Teaching: Preliminary Findings from a Study in Colombia
Cecilia Agudelo-Valderrama, & Alan Bishop
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Short Communication (abstract only) |
A Student's Strategies in Deriving Quartic Modelling Functions Using Rates of Changes
Karoline Afamasaga-Fuata't
This paper reports findings from a research study which examined students' strategies for deriving modelling
functions from numerical patterns with rates of changes in contrast to the equation-graph matching approach
prevalent in schools. Students involved were final year mathematics undergraduate students some of whom
were practicing teachers of mathematics or were intending to teach. Students had already examined the cases
of linear, quadratic, cubic and some exponential functions and were requested to extend their projects to
quartics, other exponential functions and a trigonometric or logarithmic function. This paper presents and
discusses the data from the quartic project of one of the 8 students involved in the study.
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Classroom and Learning Factors Preferred by Year 9 Students in the Teaching and Learning of Mathematics
Barbara Tadich
This report describes a recent case study research which provides evidence that student learning, and student
achievement can be accomplished by teachers working with a greater knowledge of student development.
The key elements investigated in the study include both classroom and learning features. In particular an
understanding of Kohlberg's (1963, 1973) stages of moral development is addressed. Giddens' (1984)
concepts of the reflective cycle and its ability to lead to empowered action and to the uncovering of the range
of choices (for the students and teacher) to act, or not to act, to make a difference to events is included. The
data collected via personal observations, students' perceptions and voice, emphasized that an understanding
of Kohlberg's and Giddens' work can add new dimensions to the middle years of schooling debate regarding
adolescent teaching and learning. An understanding of young adolescents, especially in Year 9, requires
greater knowledge of developmental and learning theories with a holistic approach to teaching and learning.
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Developing a Framework of Growth Points in Secondary Students' Understanding of Function
Erlina Ronda, Doug Clarke, Marj Horne
It is widely accepted that teachers' knowledge of students' thinking in acquiring concepts and procedures in a
specific mathematical domain can be a powerful tool in informing instruction. The framework of growth
points in the understanding of function developed in the present study may provide such a contribution. This
paper is a progress report of the development of the framework of growth points. The basis of the framework
was an initial survey of the literature, which was progressively revised, using data from students in Years 8 to
10 in Victoria and The Philippines.
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How is the Motivation of the Two Year 13 Pacific Islands Mathematics Learners Shaped by their Culture? A Case Study
Viliami Finau Latu
The aim of this project is to link research to the improvement of mathematics teaching practice by
investigating ways in which mathematics educators and teachers can foster Pacific Islands learners' motivation to learn mathematics. An important area to investigate is the ways in which Pacific Islands
learners' motivation is shaped by their culture. A small study involving two students was conducted with the
specific aim of exploring cultural influences that contributed to their motivation to learn mathematics. The
factors that appeared to have the most influence on motivation were; the aspiration of students to do well so
that they can help their families financially, the need to do mathematics to obtain a job, and the disparities
between home and school.
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Persisting Teen/ty Confusions as an Indicator of a Specific Learning
Difficulty in Mathematics: Implications for Assessment and Instruction
Maureen Finnane
A specific difficulty in memorizing basic arithmetic facts has been well established as a persisting problem
for students with learning difficulties in mathematics. Theories for underlying causes range from low
working memory capacity to a failure to encode numbers semantically. Understanding the quantity meaning
of the teen numbers is a particular difficulty for some students. This paper will present an intervention
designed for a Year 2 Queensland student with persisting teen/ty confusions and a self-acknowledged
difficulty in memorising the large doubles facts. Making the tens/ones structure of the teen numbers more
transparent to the student provided a foundation for him to learn his large doubles to the point of fluency.
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Professional Learning in the Teaching of Area
Diane McPhail
Seventeen Year 1 and Year 2 teachers participated in a professional development program focusing on the
teaching of area. The teachers were offered three different levels of consultancy support. A comparison of
results from the students and teachers indicates that the success of the teacher professional development, as
measured by student learning and teachers' change in practice, was determined by teachers' ability to work in
school-based teams, and an initial desire to improve their teaching of mathematics. The success of the
program as a teacher professional development activity was not dependent on the level of consultancy
support provided for teachers.
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Questions in Primary Mathematics Classrooms
Colleen Vale
In this paper data gathered from teachers who participated in a professional development program designed
to improve the quality of questioning in mathematics classrooms are presented. Teachers from five primary
schools participated in the program. It was designed by the teachers and funded as a Quality Teacher Project.
At the beginning and end of the school year, data were gathered by questionnaire about teachers' practice
and, in particular, the types of questions that they used in their mathematics teaching. The types of questions
that these primary teachers used when teaching mathematics are discussed.
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The Predictive Factors of Classroom Learning Environments on High School Students' Mathematics Anxiety
Bret A. Taylor
The purpose of this research was to examine the possible associations between the perceived classroom
environment of high school students in Southern California and the level of mathematics anxiety that they
possess. Data were gathered using a revised version of Plake and Parker's (1982) Revised Mathematics
Anxiety Ratings Scale and the What is Happening In This Classroom learning environment survey created by
Fraser, McRobbie, and Fisher (1996). This research involved both quantitative and qualitative data obtained
via the research instruments and interviews with those having extremely high or low math anxiety.
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Poster (abstract only) |
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Round Table (abstract only) |
Collective Mathematical Understanding as Improvisation
Lyndon Martin & Jo Towers
This research is concerned with the nature of the growth of mathematical understanding, and
more specifically with how a group of learners can develop a collective understanding for a
mathematical concept. We seek to characterise collective mathematical understanding as a
creative and emergent improvisational process, through drawing on theoretical perspectives
from the fields of jazz (Becker, 2000; Berliner, 1994; 1997), theatre (Sawyer 1997; 2000) and
conversation (Sawyer, 2001). In considering video data, taken from an initial pilot study, we
extend improvisational theory to begin to consider collective mathematical understanding as a
process with a similar nature and characteristics.
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Numeracy Equipment and Year 3 Children: Bright, Shiny Stuff, or Supporting the Development of Part-whole Thinking?
Linda Bonne
New Zealand teachers' use of equipment has increased as a result of their participation in the
Numeracy Development Projects. However, the equipment choices of the four teachers
interviewed in this study were not strongly consistent with the equipment use recommended in
the NDP materials. In the teachers' reasons for equipment choices, the surface features of
equipment seemed equally important as the conceptual development it can support. In contrast,
the reasons given for equipment choices by the 34 Year 3 children who were interviewed were
almost exclusively concerned with how the equipment might help them to solve the given
problem. The children's success rates at solving the problem declined as the equipment became
more structured; this paralleled the teachers' equipment choices.
The ultimate goal for teacher educators must be for all teachers to have a richly connected
conceptual map of numeracy, in order for teachers to be able to effectively use equipment in
ways that help children to construct their own meaningful connections as they learn about
number. Rather than talking about equipment as "bright, shiny stuff", teachers must have a clear
focus on the role that equipment can play in the development of children's part-whole thinking.
In this round table presentation the findings from this study, which was conducted during 2002
as part of a Masters thesis, will be discussed.
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Professional Development for Mathematics Education Researchers
Helen J. Forgasz
As mathematics educators, we frequently speak of the professional development needs of
mathematics teachers. Many of us run professional development sessions or courses. Others of
us conduct research and in our scholarly writings reflect on the implications of our findings on
teacher professional development. Less often do we think about our own professional
development needs.
In my capacity as MERGA Vice-President (Research), I have often thought about how
MERGA might assist in promoting the range of skills that mathematics education researchers
might need to serve as the providers and nurturers of the next generation of researchers in our
discipline, and to function as more effective and fruitful researchers whose findings are widely
disseminated, highly acclaimed, and broadly implemented for the betterment of mathematics
teaching and learning at all levels.
I am proposing this round table session as the means to commence a discussion on what the
professional needs of mathematics education researchers might be and what MERGA might do
with respect to them. Some of the ideas floating around in my head include: various types of
reviewing (conference papers, scholarly articles, book chapters, ARC grants), supervising
higher degree students, examining theses, preparing grant applications (large/small/other),
developing tenders, writing for different audiences, approaching publishers, learning about
new/different research approaches/techniques, using computer software effectively for
conducting research and/or analysing data, mentoring others, developing teaching/research
portfolios, and promoting interviewing skills (as interviewer and/or interviewee). I'm sure there
are other needs. Come and share your concerns and ideas
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Student Beliefs & Their Impact on Participation in Mathematics in the Middle School
Robyn Turner-Harrison
This round table discussion will focus on a proposed study of middle school children's beliefs
about their participation in mathematics classrooms.
In the study the motivation of students when undertaking mathematics tasks, and the influence
of motivation on strategies for coping with frustration when experiencing difficulties, will be
investigated. It is suspected that some students may not have established perceptions of the
benefits of being competent in mathematics, nor be aware that there is potential for them to be
empowered by competency.
One determinant of participation in education is student perceptions of goals, and the influence
that perceptions play on motivation. Students who feel in control of their lives are more likely
to have opportunities for success both within schools and without (Lapadat, 1998). Dweck
(2000) investigated perceptions of intelligence and contended that students may hold beliefs
that inhibit their participation at school; that students can be taught that both intelligence is
incremental and a mastery orientation can be taught through explicit instruction.
Students of one grade six class will complete an assessment in which each task is incrementally
harder to complete. Once each task is completed, they will be asked to evaluate their work. If
correct they will continue to the next task. If not, they will be asked how they feel, and what
teaching they require in order to continue. Various background data will be gathered to seek to
identify contributing factors, and a survey adapted from Dweck's instrument will seek data on
their beliefs concerning mathematical intelligence.
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