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Navigating currents and charting directions
Editors: Merrilyn Goos, Ray Brown and Katie Makar
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Content |
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Preface |
Preface
Merrilyn Goos
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List of Reviewers |
Judges and Reviewers for MERGA 31
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Keynote Address |
Praxis and Practice Architectures in Mathematics Education
Stephen Kemmis
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Stars, Compass, and GPS: Navigating Currents and Charting Directions for Mathematics Education Research on Gender Issues
Helen Forgasz
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Practical Implication Award |
Facilitating Communities of Mathematical Inquiry
Roberta Hunter
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Symposium |
A Longitudinal Study of Student Performance on Items Rich in Graphics
Tom Lowrie
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Graphics and the National Numeracy Tests
Carmel Diezmann
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Standardised Assessment in Mathematics: The Tale of Two Items
Tracy Logan and Jane Greenlees
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The Construction of Knowledge: Theoretical Approaches
Tommy Dreyfus, Michael O. J. Thomas, Jill P. Brown and Gaye Williams
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The Role of Information Graphics in Mathematical Proficiency
Carmel Diezmann and Tom Lowrie
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Research Paper |
Assessing Primary Preservice Teachers’ Mathematical Competence
Karoline Afamasaga-Fuata’i, Paul Meyer and Naomi Falo
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The 2007 Common Technology Free Examination for Victorian Certificate of Education (VCE) Mathematical Methods and Mathematical Methods Computer Algebra System (CAS)
David Leigh-Lancaster, Pam Norton, Peter Jones, Magdalena Les, Michael Evans and Margaret Wu
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Teachers’ Motivation to Attend Voluntary Professional Development in K-10 Mathematics
Judy Anderson
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Using National Numeracy Testing to Benefit Indigenous Students: Case Studies of Teachers Taking Back Control of Outcomes
Annette R. Baturo, Tom J. Cooper, Matthew T. Michaelson and Jessica Stevenson
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Recollections of Mathematics Education: Approaching Graduation and 5 Years Later
Kim Beswick and Shelley Dole
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Using Paper-Folding in the Primary Years to Promote Student Engagement in Mathematical Learning
Kathy Brady
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The Case of Mathematical Proof in Lower Secondary School: Knowledge and Competencies of Pre-service Teachers
Jill Brown, Gloria Stillman, Björn Schwarz and Gabriele Kaiser
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Employing Mathematical Modelling to Respond to Indigenous Students’ Needs for Contextualised Mathematics Experiences
Kelli Brown
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Reconceptualising Agency Through Teachers Talking About a Sociocultural Approach to Teaching Mathematics in the Classroom
Raymond Brown and Trevor Redmond
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Middle School Students’ Interest in Statistical Literacy
Colin Carmichael and Ian Hay
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One Secondary Teacher’s Use of Problem-Solving Teaching Approaches
Michael Cavanagh
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Does Student Success Motivate Teachers to Sustain Reform-Oriented Pedagogy?
Linda Cheeseman
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Year Five Students Solving Mental and Written Problems: What Are They Thinking?
Julie Clark
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Mathematics for Engineering Education: What Students Say
Mary Coupland, Anne Gardner and Georgina Carmody
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Advancing Research Into Affective Factors in Mathematics Learning: Clarifying Key Factors, Terminology and Measurement
Patricia C. Cretchley
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Explorations of Early Childhood – New Entrant Transition in Mathematics
Ngaire M. Davies and Karen Walker
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Eliciting Growth in Teachers’ Proportional Reasoning: Measuring the Impact of a Professional Development Program
Shelley Dole, Doug Clarke, Tony Wright, Geoff Hilton and Anne Roche
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Links Between Children’s Understanding of Multiplication and Solution Strategies For Division
Ann Downton
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Intervention Instruction in Structuring Numbers 1 to 20: The Case of Nate
David Ellemor-Collins and Robert (Bob) Wright
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Interdisciplinary Problem Solving: A Focus on Engineering Experiences
Lyn D. English
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Addressing Verbal Memory Weaknesses to Assist Students with Mathematical Learning Difficulties
Maureen Finnane
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Validation of an Assessment Instrument Developed for Eliciting Student Prior Learning in Graphing and Data Analysis
Noleine Fitzallen
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Using Valsiner
Linda Galligan
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CAS Enabled Devices as Provocative Agents in the Process of Mathematical Modelling
Vince Geiger, Rhonda Faragher, Trevor Redmond and Jim Lowe
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Researcher-Teacher Relationships in Mathematics Education
Merrilyn Goos
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Towards a Sociocultural Framework for Understanding the Work of Mathematics Teacher-Educator-Researchers
Merrilyn Goos
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Identity as a Lens to Understand Learning Mathematics: Developing a Model
Peter Grootenboer and Robyn Zevenbergen
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Capturing Students’ Thinking about Strategies used to Solve Mental Computations by Giving Students Access to a Pedagogical Framework
Judy Hartnett
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A Review of Recent Research in Early Mathematics Learning and Technology
Kate Highfield and Kristy Goodwin
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The Development of Students’ Use of Justification Strategies
Jodie Hunter and Glenda Anthony
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Using Task-Based Interviews to Assess Mathematical Thinking of Primary School Students
Chris Hurst
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Who a Student Sits Near to in Maths: Tension between Social and Mathematical Identities
Naomi Ingram
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Social Constructivism in the Classroom: From A Community of Learners to A Community of Teachers
Jane Irvin
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Primary Teachers’ Beliefs About the Use of Mathematics Textbooks
Romina Jamieson-Proctor and Carmen Byrne
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Abstraction in Context, Combining Constructions, Justification and Enlightenment
Ivy Kidron and Tommy Dreyfus
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How Humanism Can Foster Mediocrity in Early Years Mathematics Education: A Poststructuralist Comparison
Mary Klein
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Preservice Teachers and Numeracy Education: Can Poststructuralism Contribute?
Mary Klein
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High Achievers in Mathematics: What Can We Learn From and About Them?
Gilah Leder
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Focusing Year 8 Students on Self-Regulating their Learning of Mathematics
Andrea McDonough and Peter Sullivan
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Feedback About Professional Growth for Teachers of Mathematics: A Developmental Perspective
Greg McPhan, John Pegg and Stefan Horarik
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Fraction Number Line Tasks and the Additivity Concept of Length Measurement
Annie Mitchell and Marj Horne
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“Zero is Not a Number”: Teachable Moments and their Role in Effective Teaching of Numeracy
Tracey Muir
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Students’ Attitude Towards Using Materials to Learn Algebra: A Year 7 Case Study
Stephen Norton and Will Windsor
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Teaching Mathematics and Technology through Design Practice
Stephen Norton and Tom J Cooper
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Engaging Mathematics Teachers in Professional Learning by Reflecting on their Pedagogical Practice
Richard O’Donovan
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Primary Teachers’ Perceptions of Their Knowledge and Understanding of Measurement
Michelle O’Keefe and Janette Bobis
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Use of the Internet for Teacher Professional Development and for Teaching Mathematics: Supports and Inhibitors
Sitti Maesuri Patahuddin
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A Situated Perspective on Learning to Teach Secondary Mathematics
Anne Prescott and Michael Cavanagh
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The Hospital Problem Revisited. Tertiary Student’s Perceptions of a Problem Involving the Binomial Distribution
Robyn Reaburn
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The Identification of Partially Correct Constructs
Gila Ron, Rina Hershkowitz and Tommy Dreyfus
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Making Connections: Promoting Connectedness in Early Mathematics Education
Abigail Sawyer
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Engagement versus Deep Mathematical Understanding: An Early Career Teacher’s Use of ICT in a Lesson
Anne Scott, Ann Downton, Donna Gronn and Adam Staples
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Investigating a Phase Approach to Using Technology as a Teaching Tool
Penelope Serow
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The Introduction of Interactive Whiteboard Technology in the Primary Mathematics Classroom: Three Case Studies
Penelope Serow and Rosemary Callingham
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School Readiness: What Do Teachers Expect of Children in Mathematics on School Entry?
Brenda Sherley and Megan Clark
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Gaining Insight into Alice’s Pedagogy with Respect to Five Dimensions of Numeracy
Jane Skalicky
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Modes of Reasoning in Explanations in Year 8 Textbooks
Kaye Stacey and Jill Vincent
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What Does Three-quarters Look Like? Students’ Representations of Three-quarters
Vicki Steinle and Beth Price
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Some Key Junctures in Relational Thinking
Max Stephens
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Chinese Young Children’s Strategies on Basic Addition Facts
Huayu Sun
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Self-Efficacy in Mathematics: Affective, Cognitive, and Conative Domains of Functioning
S. L. Tait–McCutcheon
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Neuropsychological Evidence for the Role of Graphical and Algebraic Representations in Understanding Function
Michael O. J. Thomas, Anna J. Wilson, Michael C. Corballis and Vanessa K. Lim
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Speaking with Different Voices: Knowledge Legitimation Codes of Mathematicians and Mathematics Educators
Steve Thornton
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Recognising Different Starting Points in Aboriginal Students’ Learning of Number
Kaye Treacy and Sandra Frid
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Deepening the Mathematical Knowledge of Secondary Mathematics Teachers who Lack Tertiary Mathematics Qualifications
Colleen Vale and Alasdair McAndrew
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Indigenous Students’ Early Engagement with Numeracy: The Case of Widgy and Caddy
Elizabeth Warren, Janelle Young and Eva De Vries
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Building Informal Inference in Grade 7
Jane Watson and Julie Donne
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Proportional Reasoning: Student Knowledge and Teachers’ Pedagogical Content Knowledge
Jane Watson, Rosemary Callingham and Julie Donne
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Counting On 2007: A Program for Middle Years Students who have Experienced Difficulty with Mathematics
Allan White
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How Group Composition Can Influence Opportunities for Spontaneous Learning
Gaye Williams
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Success and Consistency in the Use of Heuristics to Solve Mathematics Problems
Khoon Yoong Wong
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Fractions as a Measure
Monica Wong and David Evans
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Mixing Colours: An ICT Tool Based on a Semiotic Framework for Mathematical Meaning-Making about Ratio and Fractions
Andy Yeh and Rod Nason
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Secondary School Students Investigating Mathematics
Joseph Yeo
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Teaching Area and Perimeter: Mathematics-Pedagogical-Content Knowledge-in-Action
Kai Kow Joseph Yeo
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Problem Solving Activities in a Constructivist Framework: Exploring how Students Approach Difficult Problems
Oleksiy Yevdokimov and Tim Passmore
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Creating Equitable Practice in Diverse Classrooms: Developing a Tool to Evaluate Pedagogy
Robyn Zevenbergen, Richard Niesche, Peter Grootenboer and Jo Boaler
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Short Communication (abstract only) |
Achieving Computational Fluency in Multi-Digit Multiplication and Division
Kristen Tripet
Current teaching practice has been greatly
enriched through valuable research into students’ acquisition of deep
understanding and skills in early multiplication and division. Research
in multi-digit multiplication and division is still relatively
undeveloped. This proposed study will explore how students achieve
computational fluency in multiplication and division. This paper
outlines the background literature and research into multiplication and
division. It then proposes questions to be explored and the intended
methodology to determine effective pedagogical approaches that encase
both mental and written computational methods.
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Coaching and Mentoring Numeracy Lead Teachers to Improve Student Learning: The Journey of Two Year Seven and Eight Teachers
Judith Mills
The Numeracy Development Project has been
systematically introduced into New Zealand schools since its conception
in 2001. For many teachers, successful implementation of this
mathematics education reform required a transformation of long held
beliefs and practices. This shift involved moving from a view of
mathematics learning as individualistic and passive, towards one in
which students come to do and understand mathematics through
participating in collaborative activity. This change in pedagogy and the
required content knowledge has brought a range of challenges for many
teachers.
The purpose of this short presentation is to share the journey of two
lead teachers (coaches) working with a mentor to enhance their
understanding of number in the mathematics classroom. The mentor was a
school adviser and the coaches came from schools that had previously
been involved in the Numeracy Development Project. The process took
place over six months and was aimed at improving both pedagogy and
content knowledge of the in-school coaches and other teachers within
their schools. A particular emphasis was placed on improving student
learning in multiplicative and proportional thinking.
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Connecting the Points: Students Learning Decimal Place Value
Bruce Moody and Jenny Young-Loveridge
This presentation documents the learning journey
of a group of six Year 5/6 students from a low decile school. These
students worked with the first author over several sessions to build
their understanding of fractions (i.e., tenths, hundredths), and the
links between these fractions and the corresponding decimal places.
Structured materials (plastic tubing cut to different lengths) based on a
linear measurement model of the number line were used to help students
appreciate the relationships between 1 whole, 1/10, and 1/100. Selected
excerpts from the learning sessions are used to illustrate the insights
that emerged during learning sessions. The findings are interpreted
using the theoretical frameworks of Piaget and Vygotsky.
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Errors Made by Student Teachers when Writing Test Items
Jaguthsing Dindyal
Learning to write good test items is an important
aspect of the teacher preparation programmes in Singapore. This paper
reports on the types of errors in writing test items in mathematics made
by student teachers who were following the pre-service course for
teaching at primary level. An analysis of the errors reveals that
student teachers demonstrate some key shortcomings in: Use of language,
mastery of content knowledge, use of diagrams as support, and use of
appropriate context when writing the items.
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Financial Modelling with Matlab
Peter Watson and Jiling Cao
Financial modelling is an accessible and
practical way to expose students to the power of mathematical modelling
and the Excel spreadsheet with its extensive collection of financial
functions is often incorporated into courses on financial mathematics.
At AUT University we have chosen to focus on the Excel spreadsheet for
our introductory courses and this has served us well as students have
developed modelling skills and Excel skills at the same time as being
exposed to financial functions. In our more advanced course we have
introduced students to the financial toolbox in Matlab. In this study we
report on some experiences of this initial group of students as they
grapple with the different mindset needed to relearn from a Matlab
perspective functions they had mastered using Excel and explore the
potential that Matlab offers to move beyond what Excel can offer. Our
report will also identify some of the limitations we have uncovered as
we have developed our course and allow us to demonstrate why financial
modelling provides a fruitful source of worthwhile examples to help
students to develop modelling skills.
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Improving Language for Problem Solving
Benedicte Esterman
This study proposes to look at the nature of
language required in a middle school mathematics classroom through a
teaching experiment. The teaching intervention proposes to provide
explicit teaching of the mathematical and non-mathematical language and
orchestrate subsequent opportunities for students to engage in
substantive communication through cooperative groupwork. The emphasis
will be on conceptual understanding through language acquisition rather
than solely through learning procedures. The study proposes to examine
the impact of the teaching intervention on student motivation and
engagement in mathematics.
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Insights from Pre-service Secondary Mathematics Teachers on their Practicum Experience
Jaguthsing Dindyal
In this study, a sample of 73 pre-service
secondary mathematics teachers, enrolled in the PGDE programme at the
National Institute of Education in Singapore, completed a survey about
their views on their practicum experience. Preliminary results show that
most of the student teachers acknowledged that the practicum was a good
learning experience but they differed in what they reported was the
most important aspect of their learning about the teaching of
mathematics and about what they perceived as their most and least
memorable experiences while teaching mathematics during the practicum.
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Motivation and Engagement in Mathematics: The Transition from Primary to Secondary School
Karen Skilling
This research will examine factors affecting
engagement in Mathematics as students make the transition from primary
and secondary schooling. This presentation will consider the background
literature and include discussions on factors affecting motivation,
engagement, and student learning in the middle years of schooling, such
as teacher-student relationships, teacher content knowledge, and
pedagogy. The research questions will be presented and an outline of the
proposed methodology will be provided. Understanding the factors that
affect students’ learning at this significant stage of education will
better inform educators about the issues that may influence their
subject choices beyond middle schooling.
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Reflections on Exponential Functions
Sandra Herbert and Farhang Afshar
A pilot study, analysing twenty-one Year 10
students’ reflections on a unit on exponential functions taught using
real-world problems, and supported by the use of CAS calculators. The
real-world contexts explored during the unit provided a focus for
follow-up interviews. Detailed analysis of the transcripts revealed four
themes: Impact of technology; difficulty in expression; prediction;
choice of scenario. Findings support results from related research
reported in the literature and highlight the importance of the choice of
real-world scenarios. Analysis revealed variation in students’
preference relating to scenarios. This variation provides a challenge in
the preparation of appropriate material.
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Scaffolding Students’ Understanding of Geometric Properties Using Dynamic Geometry Software
Sahar Bokosmaty
Significant technological tools have impacted on
students’ learning of Mathematics. In this study, I wish to seek
evidence that dynamic geometry enhances students’ understanding of
certain geometric properties and can serve as a vehicle for discovering
unknown properties. The aim of the study is to explore the impact of
dynamic geometry on 40 Year 9 high school students’ understandings of
geometric properties. A mixedmethodology will be utilized in order to
confirm the findings from different data sources; such as interview,
video and audio recordings, computer savings, students’ workbooks, and
pre- and post-tests.
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The Next Big Teaching Resource: Interactive White Boards But Where is the Research?
Philip C Clarkson
Schools are rapidly adopting Interactive White
Boards (IWBs) [or alternatively termed Smart Boards]. The rapidity of
uptake has not been in step with any well designed, comprehensive
research effort that might inform patterns of adoption and
implementation by teachers, nor any sufficient understanding about the
impact IWBs might have on students and their learning in mathematics and
other areas of the curriculum. This is not the first time that
attractive resources have been rapidly taken up into the teaching of
mathematics, based more on faith. Whether this matters is an interesting
question to ask. In this short communication, I concentrate on insights
from some of the relevant IWB research literature, noting gaps and
deficiencies that need to be addressed. In particular it is noted that
usually only self-report methods are used, there is a lack of studies
that describe the impact of IWB use on cognition and that document
actual changes in classroom interaction. As well studies often do not
clearly focus on IWBs. These shortcomings make it difficult to assess
the impact of IWB technology, if not impossible, in terms of any changes
in the quality of student learning. Teachers certainly like them, but
is this enough?
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The Role of Mathematics Competitions
Brenda Bicknell
What role do competitions play in a mathematics
programme? This question is examined from the multiple perspectives of
fifteen students (11-13 year olds) identified as mathematically gifted
and talented, and their teachers and parents. A variety of different
types of mathematics competitions were subscribed to including local,
national, and international competitions. There was varied access to the
competitions and differing perspectives; students and parents shared
similar views about the value of competitions but there was a difference
of opinion among the teachers.
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The Role of Pattern and Structure in Early Mathematics Learning: An Evaluation Study in the First Year of Formal Schooling
Joanne Mulligan, Lyn English and Mike Mitchelmore
An evaluation study aims to validate a new
conceptual framework for mathematics learning based on the development
of pattern and structure. It will evaluate the effectiveness of a
school-entry mathematics program built on this framework using classroom
observations and an interview-based student assessment. The Pattern and
Structure Mathematics Awareness Program (PASMAP) focuses on unit of
repeat, multiplicative reasoning, spatial structuring, and congruence
and similarity. The program will be evaluated in Kindergarten classes
from four large primary schools in Brisbane and Sydney.
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Poster (abstract only) |
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Round Table (abstract only) |
MERGA: Including the X and Y in Mathematics Education Research
Peter Grootenboer and Naomi Ingram
MERGA has enjoyed a strong and rich history since
its inception over 30 years ago. In that time it has been instrumental
in supporting and developing a prominent group of mathematics education
researchers who have made a significant contribution to the field. The
purpose of this Round-Table Discussion is to consider how MERGA and its
members might continue to promote, support and encourage mathematics
educators from generation X and generation Y (and beyond), so they can
stand on the shoulders of those who have gone before, and continue to
build the stellar reputation of mathematics education research in
Australasia. This discussion is open to both experienced and novice
researchers, and hopefully it will lead to some strategies and ideas for
succession planning that will ensure the health of MERGA and
mathematics education research into the future.
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Moving Beyond the Script: Addressing Numeracy Needs of Low Achieving Students through Quality Professional Development
Moira Blair and Anuja Singh
The New Zealand Numeracy Development Project
(NDP) was introduced to combat the disparity between high and low
achieving students. It originated as a pilot project in 1999 as an
extension and modification of the Australian ‘Count Me In Too’ project,
and was implemented by the Ministry of Education in 2001. Whilst some
improvements have been noted, there is evidence of continuing disparity
between Maori and Pakeha student achievement, and underachievement of
these students remains a concern. A vital component of NDP was that
teachers were provided opportunities for professional development. A
Ministry of Education Quality Teacher Research and Development (QTRD)
program was introduced in 2007, supporting teachers in action research
to raise student achievement. This presentation analyses the experiences
of a group of teachers who undertook the QTRD course to develop more
effective teaching practices to enhance the learning of low achieving
Maori and Pasifika students. We provide complementary perspectives on
our participation in the project, and the dual benefits of increased
student achievement and ongoing professional learning for the teachers.
We argue that quality, theory-based professional development and
reflective practice are necessary to enhance the teaching and learning
of disadvantaged students.
In the Round Table we hope to stimulate discussion with Australian, New
Zealand, and other international colleagues about:
• The nature of successful professional development partnerships between
teachers and university researchers;
• Characteristics of effective numeracy education programs for
disadvantaged students;
• Challenges in working with teachers and students in low socio-economic
or disadvantaged areas.
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Student Achievement in Mathematics: Learning through Home School Partnership
Honor Ronowicz and Gaynor Terrill
The Home School Partnership Numeracy facilitators
will start the round table discussion by presenting the findings from
three small studies:
i) Two case studies investigating if schools change the way they
communicate student achievement to parents as a result of participating
in the Home School Partnership project.
ii) A small research project involving all of the schools across the
Waikato region that have been involved in Home School Partnership
projects in the last three years.
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 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.
Aspects that might be considered in this discussion include: Background
information about home and school partnerships; successful learning
communities involving facilitators, lead teacher and lead parents; and
communication of student achievement to parents.
Alton-Lee, A. (2003). Quality teaching for diverse students in
schooling: Best evidence synthesis. Wellington: Ministry of Education.
Biddulph, F., Biddulph, J. & Biddulph, C. (2003). The complexity of
community and family influences on children’s achievement in New
Zealand: Best evidence synthesis. Wellington: Ministry of Education.
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There is scant research on the role of graphics in students’
mathematical performance. This paper distinguishes between the
contextual and informational roles of graphics and provides an overview
of the types of information graphics. It also presents
Catherine Attard
The purpose of this roundtable is to describe a
research proposal and seek feedback and advice on the proposed study.
The research project aims to investigate current concerns of a downturn
in motivation and engagement levels as students move through the middle
years of schooling (Years 5 to 8 in New South Wales). Current research
has shown at this time of transition from primary schooling to secondary
many of these students begin to perceive mathematics to be a special
domain in which smart students succeed and others merely get by or fail.
Although students feel mathematics is important, many are not pursuing
mathematics in the later years of school. This choice is seriously
influenced by attitudes towards and performance in mathematics and
significantly shaped by school mathematical experiences. While there is a
wealth of research investigating issues surrounding the motivation and
engagement of students in mathematics during the middle years, there is a
gap in the research in terms of longitudinal studies. Through this
longitudinal study there will be opportunity investigate if and how
levels of motivation and engagement change within students as they
progress through the transition from primary to secondary schooling.
Within the study factors affecting any changes in motivation and
engagement will be investigated and factors that play a role in
increasing or sustaining levels motivation and engagement in mathematics
will be identified.
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