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Mathematics: Essential Research, Essential Practice
Editors: Jane Watson and Kim Beswick
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Content |
Table of Contents
MERGA 2007 Conference Proceedings
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Preface |
Preface
Kim Beswick and Jane Watson
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List of Reviewers |
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Keynote Address |
Introducing Students to Data Representation and Statistics
Richard Lehrer
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Studies in the Zone of Proximal Awareness
John Mason, Helen Drury and Liz Bills
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Teaching and Learning by Example
Helen L. Chick
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The Beginnings of MERGA
Ken Clements
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Practical Implication Award |
Empowered to Teach: A Practice-based Model of Teacher Education
Janette Bobis
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Symposium |
Children's Number Knowledge in the Early Years of Schooling
Ann Gervasoni
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Early Childhood Mathematics Education Research: What is Needed Now?
Bob Perry and Sue Dockett
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International Perspectives on Early Years Mathematics
Jillian Fox
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Listening to Student Opinions about Group Assessment
Judith Mousley and Coral Campbell
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Listening to Students' Voices in Mathematics Education
Brian Doig, Susie Groves, Coral Campbell, Judith Mousley and Gaye Williams
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Research Enriched by the Student Voice
Gaye Williams
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Students' Pedagogical Knowledge: A Source of Pedagogical Content Knowledge
Brian Doig and Susie Groves
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Trimangles and Kittens: Mathematics Within Socio-dramatic Play in a New Zealand Early Childhood Setting
Shiree Lee
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Research Paper |
Communicating Students' Understanding of Undergraduate Mathematics using Concept Map
Karoline Afamasaga-Fuata'i
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Primary Student Teachers' Diagnosed Mathematical Competence in Semester One of their Studies
Karoline Afamasaga-Fuata'i, Paul Meyer & Naomi Falo
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An Online Survey to Assess Student Anxiety and Attitude Response to Six Different Mathematical Problems
Vincent Anderson
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Mathematical Investigations: A Primary Teacher Educator?s Narrative Journey of Professional Awareness
Judy Bailey
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Describing Mathematics Departments: The Strengths and Limitations of Complexity Theory and Activity Theory
Kim Beswick, Anne Watson & Els De Geest
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Three Student Tasks in a Study of Distribution in a 'Best Practice' Statistics Classroom
Anthony Bill & Jane Watson
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Teacher Researchers Questioning their Practice
Linda Bonne & Ruth Pritchard
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Imagined Classrooms: Prospective Primary Teachers Visualise their Ideal Mathematics Classroom
Kathy Brady
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Early Notions of Functions in a Technology-Rich Teaching and Learning Environment (TRTLE)
Jill Brown
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Collective Argumentation and Modelling Mathematics Practices Outside the Classroom
Raymond Brown and Trevor Redmond
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Visual Perturbances in Digital Pedagogical Media
Nigel Calder
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Professional Experience in Learning to Teach Secondary Mathematics: Incorporating Pre-service Teachers into a Community of Practice
Michael Cavanagh and Anne Prescott
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Young Children's Accounts of their Mathematical Thinking
Jill Cheeseman and Barbara Clarke
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Mathematical Reform: What Does the Journey Entail for Teachers'
Linda Cheeseman
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Year Six Fraction Understanding: A Part of the Whole Story
Doug M. Clarke, Anne Roche and Annie Mitchell
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Teaching as Listening: Another Aspect of Teachers' Content Knowledge in the Numeracy Classroom
Ngaire Davies and Karen Walker
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Essential Differences between High and Low Performers' Thinking about Graphically-Oriented Numeracy Items
Carmel M. Diezmann, Tom J. Lowrie and Nahum Kozak
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High School Students' Use of Patterns and Generalizations
Jaguthsing Dindyal
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The Teacher, The Tasks: Their Role in Students? Mathematical Literacy
Katherine Doyle
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Informal Knowledge and Prior Learning: Student Strategies for Identifying and Locating Numbers on Scales
Michael Drake
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Documenting the Knowledge of Low-Attaining Third- and Fourth-Graders: Robyn's and Bel's Sequential Structure and Multidigit Addition and Subtraction
David Ellemor-Collins, Robert Wright and Gerard Lewis
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Interdisciplinary Modelling in the Primary Mathematics Curriculum
Lyn English
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Students' Tendency to Conjoin Terms: An Inhibition to their Development of Algebra
Judith Falle
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Towards 'Breaking the Cycle of Tradition' in Primary Mathematics
Sandra Frid and Len Sparrow
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Exploring the Number Knowledge of Children to Inform the Development of a Professional Learning Plan for Teachers in the Ballarat Diocese as a Means of Building Community Capacity
Ann Gervasoni, Teresa Hadden and Kathie Turkenburg
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Technology-Enriched Teaching of Secondary Mathematics: Factors Influencing Innovative Practice
Merrilyn Goos and Anne Bennison
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Supporting an Investigative Approach to Teaching Secondary School Mathematics: A Professional Development Model
Merrilyn Goos, Shelley Dole and Katie Makar
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Identity and Mathematics: Towards a Theory of Agency in Coming to Learn Mathematics
Peter Grootenboer and Robyn Zevenbergen
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Categorisation of Mental Computation Strategies to Support Teaching and to Encourage Classroom Dialogue
Judy Hartnett
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Student Experiences of VCE Further Mathematics
Sue Helme and Stephen Lamb
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Video Evidence: What Gestures Tell us About Students? Understanding of Rate of Change
Sandra Herbert and Robyn Pierce
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The Role of Dynamic Interactive Technological Tools in Preschoolers' Mathematical Patterning
Kate Highfield and Joanne Mulligan
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Students Representing Mathematical Knowledge through Digital Filmmaking
Geoff Hilton
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What Does it Mean for an Instructional Task to be Effective?
Lynn Hodge, Jana Visnovska, Qing Zhao and Paul Cobb
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A School-Community Model for Enhancing Aboriginal Students' Mathematical Learning
Peter Howard and Bob Perry
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Benchmarking Preservice Teachers' Perceptions of their Mentoring for Developing Mathematics Teaching Practices
Peter Hudson
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Relational or Calculational Thinking: Students Solving Open Number Equivalence Problems
Jodie Hunter
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Scaffolding Small Group Interactions
Roberta Hunter
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Numeracy in Action: Students Connecting Mathematical Knowledge to a Range of Contexts
Chris Hurst
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A Story of a Student Fulfilling a Role in the Mathematics Classroom
Naomi Ingram
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Secondary-Tertiary Transition: What Mathematics Skills Can and Should We Expect This Decade?
Nicolas Jourdan, Patricia Cretchley and Tim Passmore
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The Power of Writing for all Pre-service Mathematics Teachers
Keith McNaught
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'Connection Levers': Developing Teachers' Expertise with Mathematical Inquiry
Katie Makar
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Acquiring the Mathematics Register in te reo Mӓori
Tamsin Meaney, Uenuku Fairhall and Tony Trinick
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Teaching Ratio and Rates for Abstraction
Mike Mitchelmore, Paul White and Heather McMaster
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Setting a Good Example: Teachers' Choice of Examples and their Contribution to Effective Teaching of Numeracy
Tracey Muir
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Developing the Concept of Place Value
Mala Saraswathy Nataraj and Michael O. J. Thomas
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Interdisciplinary Learning: Development of Mathematical Confidence, Value, and the Interconnectedness of Mathematics Scales
Dawn Kit Ee Ng and Gloria Stillman
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Mathematical Methods and Mathematical Methods Computer Algebra System (CAS) 2006 - Concurrent Implementation with a Common Technology Free Examination
Pam Norton, David Leigh-Lancaster, Peter Jones and Michael Evans
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A Concrete Approach to Teaching Symbolic Algebra
Stephen Norton and Jane Irvin
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Developing Positive Attitudes Towards Algebra
Stephen Norton and Jane Irvin
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Changing Our Perspective on Measurement: A Cultural Case Study
Kay Owens and Wilfred Kaleva
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Enhancing Student Achievement in Mathematics: Identifying the Needs of Rural and Regional Teachers in Australia
Debra Panizzon and John Pegg
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The Growth of Early Mathematical Patterning: An Intervention Study
Marina Papic and Joanne Mulligan
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Whole Number Knowledge and Number Lines Help to Develop Fraction Concepts
Catherine Pearn and Max Stephens
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Identifying and Analysing Processes in NSW Public Schooling Producing Outstanding Educational Outcomes in Mathematics
John Pegg, Debra Panizzon and Trevor Lynch
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Teachers Research their Practice: Developing Methodologies that Reflect Teachers' Perspectives
Ruth Pritchard and Linda Bonne
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Teacher Professional Learning in Mathematics: An Example of a Change Process
Pauline Rogers
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Seeking Evidence of Thinking and Mathematical Understandings in Students' Writing
Anne Scott
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Utilising the Rasch Model to Gain Insight into Students? Understandings of Class Inclusion Concepts in Geometry
Penelope Serow
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Exploring Teachers' Numeracy Pedagogies and Subsequent Student Learning across Five Dimensions of Numeracy
Jane Skalicky
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The Complexities for New Graduates Planning Mathematics Based on Student Need
Carole Steketee and Keith McNaught
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Students'Emerging Algebraic Thinking in the Middle School Years
Max Stephens
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A Framework for Success in Implementing Mathematical Modelling in the Secondary Classroom
Gloria Stillman, Peter Galbraith, Jill Brown and Ian Edwards
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Eliciting Positive Student Motivation for Learning Mathematics
Peter Sullivan and Andrea McDonough
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Learning from Children about their Learning with and without ICT using Video-Stimulated Reflective Dialogue
Howard Tanner and Sonia Jones
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Dependency and Objectification in a Year 7 Mathematics Classroom: Insights from Sociolinguistics
Steve Thornton
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Pedagogical Practices with Digital Technologies: Pre-service and Practicing Teachers
Colleen Vale
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Procedural Complexity and Mathematical Solving Processes in Year 8 Mathematics Textbook Questions
Jill Vincent and Kaye Stacey
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Designing Effective Professional Development: How do we Understand Teachers' Current Instructional Practices?
Jana Visnovsk
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'Doing Maths': Children Talk About Their Classroom Experiences
Fiona Walls
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The Role of Pedagogy in Classroom Discourse
Margaret Walshaw and Glenda Anthony
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Australian Indigenous Students: The Role of Oral Language and Representations in the Negotiation of Mathematical Understanding
Elizabeth Warren, Janelle Young and Eva deVries
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Student Change Associated with Teachers' Professional Learning
Jane Watson, Kim Beswick, Natalie Brown and Rosemary Callingham
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Choosing to Teach in the 'STEM' Disciplines: Characteristics and Motivations of Science, ICT, and Mathematics Teachers
Helen M. G. Watt, Paul W. Richardson and James Pietsch
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Percentages as Part Whole Relationships
Paul White, Sue Wilson, Rhonda Faragher and Mike Mitchelmore
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My Struggle with Maths May Not Have Been a Lonely One: Bibliotherapy in a Teacher Education Number Theory Unit
Sue Wilson
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Students' Conceptual Understanding of Equivalent Fractions
Monica Wong and David Evans
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Statistics Teachers as Scientific Lawyers
Joanne Woodward and Maxine Pfannkuch
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Developing Pedagogical Tools for Intervention: Approach, Methodology, and an Experimental Framework
Robert Wright, David Ellemor-Collins and Gerard Lewis
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Pedagogy and Interactive Whiteboards: Using an Activity Theory Approach to Understand Tensions in Practice
Robyn Zevenbergen and Steve Lerman
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Short Communication (abstract only) |
'I Have a Fear of Maths and it Does Worry Me a Bit as a Future Teacher': The Cycle of Maths Anxiety
Gillian Frankcom
The maths anxiety of 29 pre-service primary
teachers, which was measured using a questionnaire, was exhibited in
writing a response to two different stimulus statements. These students
used the word fear on many occasions and other metaphors to describe
their anxiety about the sort of teacher they might become and whether
they might break the cycle of maths anxious teachers producing maths
anxious children. Their words are used to illustrate this desire to
break the cycle.
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Activity Theory as a Framework to Analyse the Positive Influence of Formative Assessment on Student Learning
Trish O'Toole
In this short communication, I provide an example
of a student's work to illustrate the power of assessment for learning.
This approach has been adopted to support both teachers and students to
come to aspects of mathematical learning. Drawing on the literature on
assessment and how it is integral to learning rather than as the end
product to show what learning has occurred, I provide examples of one
case to illustrate the power of assessment for learning. By drawing on
aspects of second generation activity, I provide examples of aspects of
the learning milieu to frame the analysis of the student's work. Through
the use of activity theory, a coherent approach to understanding the
complex milieu of classroom learning environment can be developed.
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An Insight into Norwegian Students' Thoughts about Mathematics
Kirsti Kislenko
Students' beliefs about mathematics were the
focus of a pilot study based on fieldwork carried out in Norway in early
2005. A web-based Likert-scale questionnaire about beliefs in
mathematics was administered to students in 6 schools from one urban
area. Two hundred and seventy-six students from grades 7 (12-13 years), 9
(14-15 years), and 11 (16-17 years) completed the questionnaire.
Despite lacking interest in mathematics, students acknowledged the
usefulness, importance, and need to work hard in mathematics.
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Autobiographical Research and Mathematics Curriculum
Andy Begg
Research methods such as narrative inquiry and
autobiographical research are increasingly accepted in education. In
this paper I discuss why and how I used autobiography in my research,
the value of this to my work in mathematics education, and my emerging
view of school mathematics, curriculum, and the related development
processes.
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Building Early Childhood Educators' Knowledge, Skills and Confidence
in the Facilitation and Assessment of Young Children's Mathematical
Learning
Bob Perry, Elspeth Harley and Sue Dockett
This paper is a report of a sustained
professional development project in South Australia in which a small
group of preschool teachers worked with the authors to develop their own
skills in facilitating young children?s mathematical learning through
investigative approaches and their own assessment of this learning
through the use of learning stories. After providing some background
information about the project, this paper considers the impact of the
project on the early childhood educators themselves and their growth in
knowledge, skills, and confidence in early childhood mathematics.
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CAS in the Middle Secondary Years: Strengths, Weaknesses, Opportunities and Threats
Robyn Pierce
Computer Algebra Systems (CAS) are used in middle
secondary classrooms as a tool to support learning and sometimes in
preparation for senior secondary mathematics. This paper presents an
analysis of strengths, weaknesses, opportunities, and threats identified
in the literature and perceived by twelve secondary teachers working
with year 9 and 10 students. CAS is valued for calculation and
manipulation capabilities, the option of alternative representations,
the opportunity for systematic exploration, and for prompting rich
discussion. However the technical overhead, initial workload for the
teacher, and unresolved questions about the contribution of machine and
by-hand work to learning must also be considered.
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Defining Teacher Knowledge Needed in the Teaching of Statistics at Primary School Level
Tim Burgess
A study of teacher knowledge, necessary for and
used in the teaching of statistics investigations, was conducted in four
New Zealand primary classrooms in 2006. This presentation reports on
the framework that was developed to describe the components of teacher
knowledge with regard to statistics. The framework integrates six
dimensions of statistical thinking with four types of teacher knowledge:
knowledge of content, both common and specialised; and pedagogical
content knowledge, related to both students and teaching. Video and
stimulated-recall interview data were analysed in relation to the
framework to develop descriptions of knowledge used in the real-time
tasks of teaching.
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Exploring Data Representation and Statistical Reasoning through Integrated Investigations in a Grade 2 Classroom
Karen Ahearn
Grade 2 students, experienced in the use of
technological tools in learning, were engaged in measurement and data
investigations related to an integrated unit 'How I have changed?'. Data
analysis skills were developed as students were encouraged by the
mathematics specialist teacher to pose and interpret questions,
experiment with data handling methods, draw inferences, and make
connections with prior representations. This pilot study focused on the
impact of students' use of Excel software on their understanding of the
relationship between the data and different graphical representations.
The study also identified both student misconceptions and advanced
development of proportional reasoning.
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Improving Procedures for Effective Teaching
Murray Black, Farida Kachapova and Ilias Kachapov
The paper gives a brief overview of the relations
between procedural and conceptual knowledge and emphasizes the
importance of developing effective mathematical techniques. The paper
describes and analyses some teaching strategies used by the authors in a
classroom in order to improve students? learning of some mathematical
techniques and their understanding of the relevant concepts. We show how
the substitution method can be applied to some classes of mathematical
problems where traditionally other methods are used. The problems are
completing the square, solving quadratic equations, evaluating the
limits of indeterminate form 0/0 and integrating rational functions with
a quadratic in the denominator. We also analyse how the method of
probability trees is used in problems about conditional probability and
the ways to improve this teaching strategy.
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Mathematical Modelling in CAS Clothing
Vince Geiger, Rhonda Faragher and Trevor Redmond
This paper considers the potential of Computer
Algebra Systems (CAS) to enhance the processes associated with
mathematical modelling and application tasks. In doing so, the role of
technology in the cyclical development of mathematical models will be
theorised. Finally, a theoretical framework will be outlined for a
classroom-based investigation into the implementation of CAS
technologies into classroom contexts where mathematical modelling and
applications are a focus.
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Mathematically Gifted Students Managing School Transfer
Brenda Bicknell
This paper reports on the school transfer of 15
mathematically gifted Year 6 and Year 8 students. The data are extracted
from a longitudinal qualitative study that examines student and parent
perspectives, and programme provision for mathematically gifted and
talented students before and after a change of schools. Two groups of
primary school students made the transfer to intermediate school (Years 7
and 8) or to a Years 7-13 high school. Another group of students from
intermediate school made the transfer to high school. The students' and
their teachers' and parents' perceptions of the transfer are described.
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Measuring the Effectiveness and Efficiency of Language-In-Use for
Algebra Learning: A Multi-Level Nested Modelling and DEA Approach
Robert de la Serna
This study investigates the effectiveness and
efficiency of mathematics instruction in two languages (English vs.
Cebuano/English Code-Switching) on the performances of Filipino algebra
students in 11 classes of a Philippine private high school. Conducted in
2005-2006, a quasi-experiment addressed the question: Between the two
languages of instruction, which promotes better algebra learning among
Filipino bilingual students' The analyses are limited to evaluating the
performances of high-ability students (comprising 3 classes) by using
Multi-level Nested Modelling to compare the impact of languages-in-use
on student achievement, and Data Envelopment Analysis (DEA) "a novel
economic modelling approach" to measure the relative efficiencies of
student learning outcomes.
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Misconceptions in Locating Negative Decimals on the Number Line
Wanty Widjaja, Kaye Stacey and Vicki Steinle
This paper explores misconceptions revealed when
pre-service teachers locate negative decimals on a number line. Written
responses from 96 pre-service teachers to tests and group worksheets and
video-recorded observation of their classroom discussions and
interviews provide extensive data. Three misconceptions are identified.
Two relate to incorrect analogies between the positive and negative
parts of the number line. The other is a 'repair' to overcome an
inconsistency, made more likely by intuition that negative
decimals are very small. Implications for teaching are drawn.
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Myths and Positioning: Insights from Hermeneutics
Steve Thornton
School mathematics values abstract reasoning over
practical knowledge, propagating the myth of reference. School
mathematics also makes claims that mathematics is essential for
effective functioning in society, thus propagating the myth of
participation. This paper uses hermeneutics to examine a worksheet used
in a year 7 mathematics classroom to illustrate the myths of reference
and participation. The continuation of these myths, together with
discourse that is localising and limiting, devalues students? informal
knowledge and positions them as subservient to mathematics rather than
as subjects having mathematical agency.
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Pre-service Primary Teachers Developing Positive Attitudes Towards Teaching Mathematics
Julie Clark
There is ongoing concern about the negative
attitude large numbers of pre-service primary teachers have towards
mathematics. The participants in this study were students in year-long
primary mathematics curriculum studies courses that focussed on beliefs
and attitudes, alongside content and pedagogy. Throughout the year,
pre-service teachers personally experienced supportive and effective
mathematics communities. As a result, many pre-service teachers
developed a deeper conceptual understanding of mathematics.
The majority of the pre-service teachers expressed increased confidence
in their ability to teach mathematics and a willingness to continue
gaining skills and knowledge in
mathematics pedagogy.
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Proportional Reasoning: A Global or Localised Development?
Vince Wright
The study of 29 year 8 students investigated
whether the development of proportional reasoning was localised or
generalised. It found support for localised early development and a
generalised later development. Multiplicative thinking with whole
numbers was found to be a necessary, but not sufficient, condition for
proportional reasoning.
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Reform and Assessment Practice: The Need for an Investigation
Julie Anderson
Public education in Victoria is currently
undertaking a major reform process involving a number of initiatives
including reporting and assessment. This paper will describe the
identification of a gap between assumptions made by Department of
Education and Training about teachers' assessment practice and about
what teachers actually do when they assess student progress. A
description and findings of a pilot study is included justifying the
need for a wider investigation.
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Revisions and Extensions of a Pirie-Kieren-Based Teaching Model
Peter Hughes
A teaching model based on Pirie-Kieren Theory was
devised for the teaching of strategic thinking for the New Zealand
Numeracy Project. This was used in the design of teacher material that
was progressively available to most New Zealand primary teachers in the
period 2001 to 2006. The ways in which teachers mis-implemented the
model in their classrooms led to some significant alterations. In
particular, the meaning of imaging is better defined and support for
real-time formative assessment of students to inform the teaching is
revised and extended.
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Te Poutama Tau (TPT): An Indigenous Response to the Numeracy Development Project 2002-2006
Wini Emery and Leeana Herewini
Maori medium education in New Zealand has been in
existence for more than 20 years. Te Poutama Tau (TPT), similar to the
mainstream Numeracy Project, is responsive to the Ministry of
Education?s strategy for improving levels of literacy and numeracy in
New Zealand schools. The major difference between the Numeracy Project
and TPT is that TPT is situated within the context of Mӓori development,
including the maintenance and revitalisation of the Mӓori language.
Since 2002, there have been four evaluation reports tracking the
progress in Te Poutama Tau. The reports have been used to show trends in
student achievement, and the teaching of mathematics via Te Reo Mӓori.
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Teaching Geometry with CAS in the Junior Secondary Classroom: A Case Study
Warren Palmer
Computer Algebraic System (CAS) calculators are
currently being trialled in a number of junior secondary New Zealand
mathematics classrooms. In this case study, two geometry lessons are
described where the teacher has successfully incorporated the technology
into his teaching so that a problem that might otherwise have proved to
be a stumbling block is surmounted, and insights into the nature of
mathematical proof are explored. The observed lessons reflect a problem
solving approach advocated by the teacher himself and they appear to be
engaging yet challenging for the students. The lessons illustrate, in a
positive manner, what can be accomplished once a teacher has attained a
solid grasp of the relatively new technology.
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The Cognitive and Pedagogical Affordances of Digital Learning Tools on Early Mathematical Development
Kristy Goodwin, Joanne Mulligan and John Hedberg
Significant technological change has impacted on
the representational modalities employed in mathematics learning. Yet,
studies evaluating their impact and efficacy are not entirely
unequivocal. This study investigates the unique contribution of
interactive, digital technologies in the learning of early mathematical
concepts in the first years of schooling. The study describes the
pedagogical and technological affordances upon differences in observed
learning outcomes. The impact of digital, pedagogical interventions on
children?s internalised representations of concepts is explored. Case
studies of the development of children's mathematical representations
are presented through the use of digital agents, such as learning
objects, interactive whiteboards, and wireless mobile learning devices.
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The Impact of an Intervention on the Development of Mathematical Pattern and Structure in the First Year of Schooling
Joanne Mulligan, Mike Mitchelmore, Coral Kemp, Jennie Marston and Kate Highfield
Using a design approach, this study monitors the
influence of patterning tasks on the mathematics learning of 10
Kindergarten children. The children were engaged in a Pattern and
Structure Mathematics Awareness Program over 15 weekly teaching
episodes. Children were pre- and post-tested using an interview
assessment of pattern and structure (PASA) and a standardised
mathematics test. Nine of the 10 children showed impressive growth in
their ability to represent and symbolise simple and complex patterns,
arrays, grids, partitions, borders, and growing patterns. They also
showed substantial improvement in mathematical skills such as counting
in multiples, sequencing, similarity and congruence, and co-linear
structure.
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The Impact of Didactical Contract on Students? Perceptions of their Intentional Learning Acts
Troels Lange and Tamsin Meaney
This paper considers how the didactical contract
between students and their teacher is influenced by students' foregrounds and backgrounds and the impact that this has on their
learning of mathematics. It uses examples of two students in two primary
classrooms, one in Denmark and the other in New Zealand. It is possible
to see in both situations that students develop non-conventional
mathematical learning. We speculate on how students' perceptions of the
didactical contract are affected by considerations such as those to do
with social interactions and the impact of these perceptions and
consideration on possibilities for learning.
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Using Cabri Geometry to Explore the Geometric Properties of Parallelograms in Year 7 Mathematics Classrooms
Sahar Bokosmaty
A teaching experiment was conducted to explore
the impact of Cabri Geometry on 6 Year 7 students' understanding of
parallelograms. Students worked in pairs, and were guided through
activities designed to introduce the software and to encourage discovery
and exploration of specific geometric properties. Students were also
required to use this knowledge to solve geometric problems. Over several
lessons, data were collected via taperecorded observations of student
interactions and discussions, work samples, and test results. The
dynamic investigation promoted deeper understanding of the underlying
geometric properties of parallelograms and students' abilities to solve
geometric problems.
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Using Counter-Examples and Paradoxes in Teaching Probability: Students? Attitudes
Murray Black, Farida Kachapova, Sergiy Klymchuk and Ilias Kachapov
The paper presents and analyses students' attitudes towards using counter-examples and paradoxes as a pedagogical
strategy in teaching/learning of a first-year university course in
probability theory and applications. Our intentions of using this
strategy were: to achieve deeper conceptual understanding; to reduce or
eliminate common misconceptions; to advance one's statistical thinking,
which is neither algorithmic nor procedural; to enhance generic critical
thinking skills , analysing, justifying, verifying, checking, proving;
to increase motivation and interest in the subject; and make learning
more active and creative. The majority of the students reported that the
strategy was effective and made learning more challenging, interesting,
and creative.
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Using Electronic Handwriting and Tablet PCs to Enhance Distance
Students' Understanding of First Year Mathematics at University
Linda Galligan, Birgit Loch, Janet Taylor and Christine McDonald
Communicating mathematics to distance students is
often difficult. This presentation reports on preliminary research in
three areas. (1) The trial of an electronic handwriting tool in MSN
Messenger in a large mathematics service course in Semester 1 2006 for
online synchronous group work and individual consultations. (2) The use
of a tablet PC and a computer software program 'Camtasia' to record live
lectures involving electronic handwriting for transmittion to distance
students. (3) The use of pre-recorded online 'Breeze' presentations to
highlight particular 'tricky questions'. The presentation will
demonstrate the use of these technologies, discuss some of their
advantages and disadvantages, and report on initial results of the
research.
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Wanted: One Great Maths Teacher!
Pamela Perger
The New Zealand Teachers Council identifies
factors important for teacher registration. These factors must also be
considered the foundation criteria for effective teachers of
mathematics. What is it that makes an effective mathematics teacher?
This article presents a picture of the ideal mathematics teacher as
described by a group of Year 7 and 8 Pasifika students (11-12 year
olds). The criteria identified by these students fell into two
categories. One category addressing factors that were associated with
personal qualities of the teacher and the second category that related
to the learning environment the students saw as most supportive to their
mathematical learning.
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Year 12 Students' Participation in Higher Mathematics Courses
Mohan Chinnappan, Stephen Dinham, Tony Herrington and Dale Scott
Australia?s future prosperity and our ability to
compete in the global arena demand that our education systems develop
human capital that is highly skilled and knowledgeable.
Participation in mathematics, in particular higher mathematics, is an
important prerequisite for young Australians if we are to develop the
range of skills that underpin this capital. This is a report on a study
in progress focusing on the concern that participation in Mathematics at
Year 12 and at universities in Australia is declining. In the context
of this larger issue, we identify a number of questions we will be
investigating with students, teachers, universities, and other
stakeholders.
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Poster (abstract only) |
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Round Table (abstract only) |
An Investigation of Mathematics Strategies in Traditional School Contexts and Real-World Contexts
Julie Clark and Kathy Brady
The purpose of this roundtable is to describe a
proposed research project and to seek advice, ideas, and suggestions
from participants. The project will address two main questions. Firstly,
how do mathematical strategies used in traditional school contexts
compare with strategies used in real-world contexts? Research continues
to highlight the lack of connections that students make between
mathematics used in school and in everyday life. The National Council
for Teachers of Mathematics emphasise the importance of students being
able to use mathematics in varying situations (2000). In this study
students will be presented with basic mathematics tasks in different
contexts. For example, they will be asked how much change they would get
from $5 for something that cost 65 cents. Next, they will be asked to
answer a similar question presented traditionally: 500 ? 65. The second
research question associated with this project is: What perceptions do
teachers have of students? mathematical strategies? Fennema and Franke
(1992) indicate
that it is important for teachers to understand students? mathematical
thinking and to have good knowledge of various instructional approaches.
Teachers will be interviewed concerning their perceptions of students?
mathematics learning. During the interviews they will watch DVD excerpts
of students solving problems and be asked to make comments on the
strategies used.
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Mӓori Student's Perspective on Their Mathematical Journey Through Mӓori Medium
Leeana Herewini
The focus of this round table is to invite
colleagues to inform, contribute to, and explore some of the key themes
that arose in this study. These being the transition from
primary school to secondary school, the role of students? perspectives
in mathematics research, and mathematics education in an indigenous
language. This study set out to explore the perspectives of 10 year 8
students on their mathematics learning and in particular the transition
from Kura Kaupapa Mӓori (Mӓori medium primary schools) to secondary
school (Mӓorii medium education in the Waikato region has extended from
Kōhanga Reo to wharekura). The Kura Kaupapa Mӓori in this region are at
least 10 years old. The 10 students interviewed in this study were
identified as successful learners of mathematics in their year 8
programme, with outcomes at Stage 7 or above on the number framework.
The students? teachers had participated in professional development in
Te Poutama Tau/Numeracy project. Kaupapa Mӓori methodology and
interviews were key approaches undertaken in this study. Interviews took
place with students and a questionnaire was given to the students' year
9 teachers. The interview process was a powerful vehicle in accessing
student voice. Results indicated there were differences between the
students' perceptions of their year 8 and year 9 mathematics programmes.
The students viewed mathematics positively and had formed opinions
regarding mental strategies and where and how to use them. Some students
were able to discern what constituted effective teaching and had formed
ideas on the value of the mathematics taught they had learned. An
interesting area to emerge in the research was the self report by the
girls in the study on their ability.
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Profiles of Thinking Skills and Levels of Motivation in a Problem-Solving Task
Sarah Buckley, Mary Ainley and Pip Pattison
In the following project, we investigated
students' use of mathematical thinking skills in an interactive,
computer problem-solving task. Within the program Between The Lines
(BTL) (Ainley & Hidi, 2002), a range of statistical information was
presented. Students were required to integrate these different types of
mathematical information in line with constructive assessment. This
approach promotes problem solutions that move beyond the simple
reproduction of answers and formulae and are representative of higher
order thinking (Clarke, 1996). Note-taking is a process known to
facilitate learning and the development of ideas (Kiewra, 1989), thus
the program also asked students to take notes as they worked through the
information. These notes were then used to create a problem solution.
Students? motivational reactions (i.e., their interest levels) were also
monitored throughout the task.
Two-hundred and eighty-six Year 8 students (151 males and 135 females)
participated in the project. The SOLO taxonomy (Biggs & Collis,
1982) was used to code students' notes whereas their solutions and notes
were marked for understanding of the material presented. Associations
between students' level of thinking and understanding were investigated
in relation to levels of on-task interest and other indicators of
motivational engagement.
In this roundtable presentation, examples of students' problem solutions
and notes will be presented. Profiles of students' thinking, for
example, higher order versus low order thinking, and their relationship
with on-task motivation will be examined. Discussion will focus on
interpretation and implications of the data.
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Progress in Mathematics : Learning through Home School Partnership
Denise Smith and Gaynor Terrill
The Home School Partnership Numeracy facilitators
will start the round table discussion by presenting the findings from
three small studies:
i) New Zealand Council for Education Research (NZCER) National
Exploratory Home School Partnership Research
ii) A case study on increasing parents' confidence in order to support
their children's learning in numeracy
iii) A case study on the clarity of communication between home and
school in relation to student achievement in numeracy. The international
evidence cited in Alton-Lee (2003) positively supports the enhancement
of student learning through home and school partnerships. In New
Zealand, two Best Evidence Syntheses research studies also highlight the
importance of establishing effective relationships between home and
school (Alton-Lee, 2003; Biddulph, Biddulph, & Biddulph, 2003). The
Home School Partnership project reflects the acknowledgement of parents
as first teachers and the desire to continue to encourage parents to
confidently interact and communicate with their children about
mathematics. Effective relationships within the school community
encourage parents to take an active role in the shared responsibility of
their children?s education. Immigrants, refugees and parents who
sometimes speak English as a second language are the focus of the
community partnerships, especially Pasifika families. Pasifika students
are identified through National Numeracy data as achieving well below
National benchmarks.
Aspects that might be considered in this discussion include: the
establishment and sustainability of home and school partnerships;
successful learning communities involving
facilitators, lead teacher, and lead parents; mathematics as a 'frightening focus' for parents and community sessions in parents' first
language.
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Some Methodological Considerations in the Estonian Study about Students? Beliefs in Mathematics: Is Triangulation Necessary?
Kirsti Kislenko
A study about students' beliefs and attitudes
towards mathematics was carried out in Estonia in early 2006. The study
aimed, firstly, to investigate students' views towards
mathematics and the underlying rationale, and secondly, to gain an
understanding of the regular mathematics classroom activities in
Estonia. The study used methodological triangulation, that is to use
different methods on the same object of the study (Cohen, Manion, &
Morrison, 2000). Firstly, a web-based Likert-scale questionnaire with 98
statements about beliefs in mathematics was administered to seven
schools in an urban area in Estonia. Five hundred and eighty students
from grades 7 (14 yrs.), 9 (16 yrs.), and 11 (18 yrs.) completed the
questionnaire. Secondly, 26 semi-structured interviews were conducted
with students and teachers for illuminating their thoughts about
mathematics, and the learning and teaching of mathematics. Thirdly,
during a three month period I participated in 11 teachers? lessons
observing 55 mathematics lessons. Field notes gathered reflected a
general picture of the classroom activities, teachers' activities,
methods, behaviour, relationship with students, and so on; and also
personal impressions from different situations that I found interesting.
Participants of the round table will be asked to consider the following
questions: What are the appropriate tools for these kinds of
investigations? What are the strengths and weaknesses of the methods
used in my study? What are the possible strengths and weaknesses in
combining quantitative and qualitative data collection methods?
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