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