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Content |
MERGA 2016 Contents
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Preface |
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List of Reviewers |
MERGA 39 Reviewers
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Keynote Address |
How Theory-Building Research on Instruction can Support Instructional Improvement: Toward a Modelling Perspective in Secondary Geometry
Patricio Herbst
Learning by Leading: Dynamic Mentoring to Support Culturally Responsive Mathematical Inquiry Communities |
Roberta Hunter, Jodie Hunter, Trevor Bills, & Zain Thompson
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Whither Statistics Education Research?
Jane Watson
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Practical Implication Award |
Let's Count: Improving Community Approaches to Early Years Mathematics Learning, Teaching and Dispositions through Noticing, Exploring and Talking about Mathematics
Bob Perry, Ann Gervasoni, Anne Hampshire, & Will O'Neill
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Symposium |
A highly capable Year 6 student's response to a challenging mathematical task
Sharyn Livy, Naomi Ingram, Marilyn Holmes, Chris Linsell, & Peter Sullivan
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Perceptions of Challenging Tasks and Achievement by New Zealand Students
Chris Linsell, Marilyn Holmes, Naomi Ingram, Sharyn Livy, & Peter Sullivan
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Teacher actions that encourage students to persist in solving challenging mathematical tasks
Naomi Ingram, Chris Linsell, Marilyn Holmes, Sharyn Livy, & Peter Sullivan
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The intent and processes of a professional learning initiative seeking to foster discussion around innovative approaches to teaching
Peter Sullivan, Marilyn Holmes, Naomi Ingram, Chris Linsell, Sharyn Livy, & Melody McCormick
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Research Paper |
Young Children's Drawings in Problem Solving
Kamariah Abu Bakar, Jennifer Way, & Janette Bobis
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Assessing Children's Progress in Taking Intellectual Risks in a Mathematical Inquiry Classroom with a Positive Learning Approach
Sue Allmond, Jude Hillman, Karen Huntly, Katie Makar, & Mia O'Brien
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Investigating the Impact of Context on Students' Performance
Felipe Almuna Salgado
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Developing a Theoretical Framework for Classifying Levels of Context Use for Mathematical Problems
Felipe Almuna Salgado
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Whither Ability Grouping: Changing the Object of Groupwork
Glends Anthony, Roberta Hunter, & Jodie Hunter
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Learning at the Boundaries: Collaboration between Mathematicians and Mathematics Educators Within and Across Institutions
Anne Bennison & Merrilyn Goos
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Discerning the Shared Beliefs of Teachers in a Secondary School Mathematics Department
Kim Beswick
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Opening Up the Profession: Inclusive Messages for Pre-Service Teachers from a Pedagogy Textbook
Amber Brass
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Preparing for the Numeracy Skills Test: Developing a Self- Perception for Success
Leni Brown & Lisa O'Keeffe
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Constructing Classroom Contexts that Engage Students in the Learning of Mathematics: a Teacher's Perspective
Raymond Brown & Trevor Redmond
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Teachers' Use of a Pedagogical Framework for Improvement in Mathematics Teaching: Case Studies from YuMi Deadly Maths
Merilyn (Lyn) Carter, Tom Cooper , & Robyn Anderson
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Large-Scale Professional Development Towards Emancipatory Mathematics: The Genesis of YuMi Deadly Maths
Tom Cooper, & Merilyn (Lyn) Carter
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The Priorities and Challenges of Primary Teachers' Knowledge in their Mathematics Planning.
Aylie Davidson
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A rich assessment task as a window into students' multiplicative reasoning
Ann Downton & Vince Wright
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The Relevance of Mathematics: Leaders and Teachers as Gatekeeper for Queensland Senior Calculus Mathematics
Michael Easey & Jim Gleeson
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Key Elements of a Good Mathematics Lesson as Seen by Japanese Junior High School Teachers
Marlon Ebaeguin & Max Stephens
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"Mathematics is just 1 + 1 = 2, what is there to argue about?": Developing a framework for Argument-Based Mathematical Inquiry
Jill Fielding-Wells
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Interpreting Association from Graphical Displays
Noleine Fitzallen
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Numeracy for Learners and Teachers: Evaluation of an MTeach coursework unit at Monash University
Helen Forgasz & Jennifer Hall
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Numeracy and Australian teachers
Helen Forgasz & Gilah Leder
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Early Childhood Teachers' integration of ICTs: Intrinsic and Extrinsic Barriers
Jillian Fox, Carmel Diezmann, & Janeen Lamb
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Designing Online Learning for Developing Pre-service Teachers' Capabilities in Mathematical Modelling and Applications
Vince Geiger, Liz Date-Huxtable, Rehez Ahlip, Marie
Herberstein, D. Heath Jones, E. Julian May, Leanne Rylands, Ian Wright,
and Joanne Mulligan
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Teachers as Designers of Effective Numeracy Tasks
Vince Geiger
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Hurdles in Acquiring the Number Word Sequence
Peter Gould
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Professional learning in mathematical reasoning: Reflections of a primary teacher
Sandra Herbert, Wanty Widjaja, Leicha A. Bragg, Esther Loong, & Colleen Vale
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Investigating Declining Enrolments in Secondary Mathematics
Gregory Hine
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Collaboration around observation of teaching: Powerful professional learning
Louise Hodgson
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Improving the efficiency of problem-solving practice for children with retrieval difficulties
Sarah Hopkins & Celeste de Villiers
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Assessing children's strategy choices to make better decisions about remediation
Sarah Hopkins
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A case study on the impact of teacher mathematical knowledge on pedagogical practices
Sally Hughes
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Sliding into Multiplicative Thinking: The Power of the "Marvellous Multiplier"
Chris Hurst & Derek Hurrell
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Assessing Children's Multiplicative Thinking
Chris Hurst & Derek Hurrell
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Commognitive Analysis of Undergraduate Mathematics Students' Responses in Proving Subgroup's Non-Emptiness
Marios Ioannou
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Investigating the Interconnections between Cognitive, Affective and Pedagogical Issues in the Learning of Group Theory
Marios Ioannou
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An Ecological Analysis of Mathematics Teachers' Noticing
Dan Jazby
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Middle Leadership: Critical Variables in Building and Implementing Digital Reforms in Primary Mathematics Education
Robyn Jorgensen (Zevenbergen), Janeen Lamb, & Kevin Larkin
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A Collaborative and Reflective Approach to Teaching for Metacognition
Berinderjeet Kaur & Lai-Fong Wong
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Changes in Teachers' Knowledge and Beliefs about Mathematics and Mathematics Teaching: A Case Study
Laurinda Lomas & Doug Clarke
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Sustainable improvements in student mathematics learning and disposition as a result of Prepare 2 Learn intervention
Bernadette Long
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Spatial Reasoning Influences Students' Performance on Mathematics Tasks
Tom Lowrie, Tracy Logan, & Ajay Ramful
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Early mathematical competencies and later outcomes: Insights from the longitudinal study of Australian children
Amy MacDonald & Colin Carmichael
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"I believe the most helpful thing was him skipping over the proof": Examining PCK in a senior secondary mathematics lesson
Nicole Maher, Helen Chick, & Tracey Muir
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Improving the Intellectual Quality of Pedagogy in Primary Classrooms through Mathematical Inquiry
Katie Makar
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Children noticing their own and others' mathematics in play
Amber Marcus, Bob Perry, Sue Dockett, & Amy MacDonald
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The Role of Reasoning in the Australian Curriculum: Mathematics
Catherine McCluskey, Joanne Mulligan, & Mike Mitchelmore
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Exploring the Cognitive Demand and Features of Problem Solving Tasks in Primary Mathematics Classrooms
Melody McCormick
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A Professional Experience Model for Primary Pre-service Teachers Specialising in Mathematics
Heather McMaster & Michael Cavanagh
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Young Indigenous Students en Route to Generalising Growing Patterns
Jodie Miller
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Developing Conceptual Understanding of Fractions with Year Five and Six Students
Judith Mills
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No more ˜What are we doing in maths today?" Affordances of the Flipped Classroom Approach
Tracey Muir
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Experiencing mathematics for connected understanding: using the RAMR framework for accelerating student' learning
David Nutchey, Edlyn Grant, & Lyn English
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A Preliminary Analysis of the Linguistic Complexity of Numeracy Skills Test Items for Pre Service Teachers
Lisa O'Keeffe
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The Power of Creativity: A Case-Study of a Mathematically Highly Capable Grade 5 Student
Linda Parish
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Competence with Fractions in Fifth or Sixth Grade as a Unique Predictor of Algebraic Thinking?
Catherine Pearn & Max Stephens
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It's Only Maths: The potential impact of a mentoring project to ameliorate mathematics anxiety in teacher education students
Timothy Perkins
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History-infused Lessons in Introductory Calculus at the Secondary level: Students' Learning and Perceptions
Wei Beng Poh & Jaguthsing Dindyal
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Supporting Teachers Developing Mathematical Tasks With Digital Technology
Iresha Ratnayake, Greg Oates & Mike Thomas
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Investigating Students' Mathematical Difficulties with Quadratic Equations
Bronwyn Reid O'Connor & Stephen Norton
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Learning from Lessons: Teachers' Insights and Intended Actions Arising from their Learning about Student Thinking
Anne Roche, Doug Clarke, David Clarke, & Man Ching Esther Chan
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Supporting Children with Special Needs in Learning Basic Computation Skills: The Case of Mia
Thomas Rottmann & Andrea Peter-Koop
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Insights from a financial literacy task designer: The curious case of problem context
Carly Sawatzki
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High school students' knowledge of a square as a basis for developing a geometric learning progression
Rebecca Seah, Marj Horne, & Adrian Berenger
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Understanding Time: A Research Based Framework
Margaret Thomas, Doug Clarke, Andrea McDonough, & Philip Clarkson
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Time: Assessing Understanding of Core Ideas
Margaret Thomas, Andrea McDonough, Philip Clarkson, & Doug Clarke
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Developing Teachers' Reasoning about Comparing Distributions: A Cross-Institutional Effort
Dung Tran, Hollylynne Lee, & Helen Doer
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Quality of Life: Domains for Understanding Maths Anxiety in First Year Pre-service Teachers through Identity Work
Sue Wilson
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Developing mathematical content knowledge for teaching: One preservice teacher and her planning.
Susanna Wilson
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Visualisation and Analytic Strategies for Anticipating the Folding of Nets
Vince Wright
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Developing early Place-value Understanding: A Framework for Tens Awareness
Jenny Young-Loveridge & Brenda Bicknell
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Distribution of high achieving students on NAPLAN across schools: Implications for policy and teacher training
Simone Zmood
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Staff Development: The Missing Ingredient in teaching Geometry to Year 3 Students
Kevin Larkin, Peter Grootenboer, and Peita Lack
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Short Communication (abstract only) |
A Five Question Approach to Teaching Mathematics
John Ley
According to Clements (2003), Dinham (2013) and Sullivan (1992, 2011, 2012) there
is an urgent need for change to the way in which mathematics is taught in Australian
Schools. The five question approach (FQA) to teaching mathematics, developed during my
thirty years of secondary teaching, occurs at the commencement of each mathematics
lesson. It is the subject of my doctoral research, currently at the early data analysis stage.
The research investigates if the FQA results in an increase in student academic
achievement, perceived and / or actual, and engagement.
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A Study of the Relationship between Conceptions of Mathematics and NAPLAN Numeracy Test Results
Sven Trenholm, Mohan Chinnappan, Bronwyn Hajek, Helen Ashman,& Amie Albrecht
Arguably, the NAPLAN Numeracy test is regarded as an effective instrument in
gauging students' ability to integrate multiple pieces of information during the course of
solving real-life problems (Lawson & Chinnappan, 2016). In this study, students were
administered the conceptions of mathematics questionnaire (Crawford, Gordon, Nicholas
& Prosser, 1998) alongside the grade 9 non-calculator NAPLAN numeracy test. We report
on the results of two correlational analysis (n=61 and n=68) for students taking two
different introductory level undergraduate mathematics courses. The results raise
questions about the claim that NAPLAN Numeracy tests are effective in assessing
knowledge connectedness in mathematical thinking.
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An Analysis of Senior Secondary Mathematics Written Examinations with Respect to Calculator Use
Hazel Tan
Prior research studies on senior secondary students' use of advanced calculators
(graphics and CAS calculators) have found that some students tended to either underutilise
calculators by preferring to solve even calculator-required questions by hand, while others
over-rely on calculators for computations and methods that can be replicated easily by
hand. Calculator use is also known to be influenced by assessment requirements. Thus this
study aims to investigate the questions in the senior secondary mathematics written
examination papers in Singapore and Victoria for the kinds of expected calculator use.
Preliminary findings will be presented and the implications discussed.
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An Application of the Five Processes of Mathematical Thinking to Numeracy Sample Items
Lisa O'Keeffe & Patrick Johnson
Numeracy skills testing is being introduced for pre-service teachers (PSTs) across
Australia in the coming years. ACER and the Australian Government (Dept. of Education
and Training, 2015) state that these skills tests are intended to demonstrate that PSTs are in
the top 30% for numeracy. Given that the South Australian Literacy and Numeracy
Strategy (Department for Education and Child Development, 2013, p.8) partially defines
numeracy as an 'ability to use mathematical information to solve problems' it is logical to
assume that categories of mathematical thinking should be evident in the numeracy test
items. As part of their initial analysis, the authors are exploring an application of the
National Council of Teachers of Mathematics' (NCTM) five processes of mathematical
thinking (Representation, Reasoning and Proof, Communication, Problem Solving, and
Connections) as a potential for mathematical characterisation of such numeracy items.
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An Exploratory Investigation on the Influence of Mathematical Modelling on Students' Real-world Problem Solving Skills
Siew Yee Lim, Hui Yi Ting, Deepa Patel, Linda Shear,& Eddie Tay
This study aims to investigate the influence of mathematical modelling on students' real-world problem solving skills. In mathematical modelling, students have to convert
real-world problem scenarios into mathematical problems. They then solve the
mathematical problems using known mathematical techniques before interpreting and
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translating the solutions for the scenarios. Using pre and post surveys, scoring of students' real-world problem solving skills, classroom observations as well as focus group
discussions, this study investigated how mathematical modelling influences Grade 9
students'perception of mathematics in practical situations, as well as how mathematical
modelling influences teachers' practices to provide students with the opportunities to form
links between theoretical and real-world situations.
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Beliefs about Mathematics and Teaching when Crossing Subject Boundaries to Teach Mathematics
Colleen Vale
Previous researchers have explored the relationships between a teachers beliefs about
the mathematics discipline and school subject, their beliefs about the teaching of
mathematics and their teaching practice. In Australia, there are many teachers who cross
subject boundaries to teach mathematics as an out-of-field teacher. Exploring out-of-field
teachers' beliefs about mathematics and the teaching of mathematics will enable us to
understand more about the way in which their in-field beliefs, school context and practices
influence their beliefs and practice when teaching mathematics. Some preliminary findings
from Out-of-Field Teaching: Sustaining Quality Practices Across Subjects project will be
presented.
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Breaking the Barrier Between Learning and Assessment
Kristen Di Cerbo & Denise Jacobsson
Use of digital environments has the potential to allow us to break down barriers
between learning and assessment by allowing us to gather data about students' proficiency
as they interact in the learning environment. This work describes a pilot of a learning
system including an online game, online digital activities, and in-person classroom
activities all aligned to a common learning progression describing how students learn the
concept of area. This work demonstrates how activities can be designed to align to the
progression and presents preliminary evidence of both learning and assessment from a
tryout with more than 300 students.
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Consumer and financial literacy education: Engaging primary teachers and their students in mathematics
Catherine Attard & Matt Thompson
This short communication will report some initial findings from a multiple case study
that investigated the use of consumer and financial literacy as a tool to improve student
engagement with mathematics in low socio-economic schools. Data from one of the
participating schools will be discussed and the impact of the study in relation to improving
student engagement, building community awareness of consumer and financial literacy and
improving teacher capacity will be shared.
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D.A.T.A.: Data, Analysis, Then Action - National Statistics Initiative
Peter Howley
Australian Teachers are saying "a rewarding experience", "a great competition", "21st
Century learning at its best, "a resounding success", "motivates and engages students".
Mentors are saying "I was inspired by their keenness", "provides students a unique
opportunity". What are they talking about? The successful annual National Schools
Statistics Poster Competition! This talk will: outline the national project-based learning
activity which facilitates boundary encounters (between secondary, tertiary, and industry
sectors and students having varied backgrounds and areas of interest) and develops key
communication, research and quantitative skills; and describe coming additions as part of a
national initiative to assist students with statistics.
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How Middle Years Students Create and Utilize Data Models to Estimate Population: A Case Study
Takashi Kawakami & Kosuke Mineno
Modelling ideas are now emphasised in the teaching and learning of statistics (e.g.,
Kawakami, 2015). This presentation reports on a case study examining how Year 9
students (14-15 year olds) created and utilized data models in estimating and predicting
Japanese population by 5-year age group. The analysis illustrated that the students
perceived the role of data and the necessity of shuttling between data and context in
developing data models to understand, estimate and decide on the trend of population.
Findings will inform educators on how to strengthen the link between statistical ideas and
modelling ideas in the teaching and learning of statistics.
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Increasing Parental Involvement
Monica Wong & Nicola Cull
Epstein and Sheldon (2006) posit that students' learning and development are enhanced
when: (a) families-parents/carers, (b) the school and (c) the local community work together
to guide and support them. Similarly, Goos (2004) found that to build successful,
sustainable long-term collaborative mathematics programs, parental and community
involvement is pivotal. When these principles were implemented in a mathematics
homework program which enabled parents to become involved and assist with their
children's learning both students and parents developed more positive feelings and
attitudes towards mathematics (Van Voorhis, 2011). This presentation explores the
introduction of a mathematics club in two primary schools in low SES areas of Sydney and
the activities undertaken to engage the school community.
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Reconceptualising Curriculum Design to Promote Students’ Conceptual Understanding of Mathematics: A Focus on Fractions
Maria Quigley
This report discusses the preliminary stages of a study into the impact of
reconceptualising curriculum design on the teaching of fractions in Kindergarten to Year 2.
A mixed methods approach is engaged using a questionnaire to explore current teacher
practices and a diagnostic assessment instrument to determine Year 3 students' current
understanding of fractions. Teachers will have training on using the new curriculum
documentation and will be interviewed and observed in the classroom implementing both
the old and new approaches.
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Secondary student's perceptions of what is important when they are learning Mathematics.
Bruce White
Students' perceptions of what teachers do and what students themselves do that helps
them learn gives an insight into what might be effective teaching and learning strategies in
a mathematics classroom. This paper looks at student perceptions of teaching in general
but also specifically in relation to the teaching and learning of mathematics. Data was
collected from students at two South Australian schools via an online survey on a range of
topics two of the topics examined the students perceptions of what teachers did to help
them learn and what they as students did that helped them learn. The initial analysis of the
results of the survey will be presented and will highlight areas that students think are most
important in learning mathematics.
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Student views on 21st Century Teaching and Learning of Mathematics
Bruce White
The term 21st Century Teaching & Learning highlights the 4Cs of collaboration,
critical thinking, creativity and communication and is often connected with the use of
technologies, in particular with the opportunities that being online offers. This presentation
reports on a study examining students perceptions of the mathematics teaching and
learning at a large suburban high school in South Australia that has made a significant
effort to develop 21st Century Teaching and Learning across the school which incorporated
a significant focus on the use of technologies. This presentation will report on students
impressions of the effectiveness of the pedagogies used in mathematics and more generally
on aspects of blended learning which was a focus for the changed pedagogy. The study
indicated that over 90% of the students indicated that the students for the new approaches
were effective or very effective for learning mathematics. Also, the student text responses
indicated that they were using it to access materials out of hours, with senior year's
students commenting how they found it very useful for revision when the mathematics
teachers uploaded the Interactive Whiteboard recordings.
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Teaching financial literacy for social justice in mathematic classrooms
Levon Blue & Peter Grootenboer
Financial literacy is often taught from a skills perspective focusing on budgeting. In
this presentation, we discuss teaching financial literacy for social justice in mathematics
classrooms. Conventional financial literacy curricula are taught from a deficit position
focusing on the individual and their ability to make "effective" financial decisions. We
explore the role of identity and socio-economic status (SES) in financial literacy education
and find that individuals are "blamed" for their SES, or "affirmed" for their high SES under
the conventional FLE curricula. A more compassionate approach to FLE for mathematics
classrooms is discussed in this presentation.
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The reSolve: Mathematics by Inquiry Protocol
Steve Thornton
reSolve: Mathematics by Inquiry is an Australian Government funded project to
develop and disseminate a suite of high quality, innovative mathematics resources for
students and teachers from F to Year 10 incorporating contemporary mathematics
pedagogy exemplifying an inquiry approach. The guiding principles behind the project are
elaborated in the reSolve: Mathematics by Inquiry Protocol, which addresses the elements
of mathematical purpose, challenge and access, and development of a supportive
knowledge-building culture. The poster will give examples of resources that exemplify the
Protocol and offer participants an opportunity to discuss critical questions related to
mathematics by inquiry.
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Using Metaphors, Models and Multi-modalities when Teaching Year 2
Students Part-Part-Whole Relationships: A Fine Grained Analysis
Paula Mildenhall & Barbara Sherriff
Recent research findings indicate that using multimodal learning experiences to teach
students about different models can be an effective teaching approach. Using a social
semiotic lens within a participationist framework, this paper reports on a professional
learning collaboration with a primary school teacher designed to explore the use of
different metaphors, models and modalities. This case study was conducted in a teacher's
Year 2 classroom over two terms, with the focus on one specific child's journey towards
understanding the part-part-whole relationship model. Video was the predominant research
tool. The initial findings have shown that the teacher was able to use specific gestures and
language to support the concrete model being used. This paper explores how the
metaphors, models and modalities were intertwined in the classroom discourse.
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Poster (abstract only) |
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Round Table (abstract only) |
Mathematical Inquiry Community
Katie Makar, Jill Fielding-Wells
In the Encyclopedia of Mathematics Education, the term "Inquiry-based Mathematics
Education" (IBME) is described as
a student-centered paradigm of teaching mathematics and science, in which students are invited to work
in ways similar to how mathematicians and scientists work. This means they have to observe phenomena,
ask questions, look for mathematical and scientific ways of how to answer these questions, interpret
and evaluate their solutions, and communicate and discuss their solutions effectively. (Dorier & Maass,
2014, p. 300)
The aim of this Round Table on IBME is to extend conversations within a community
interested in teaching, learning, assessment and research on mathematical inquiry. We invite
those interested in mathematical inquiry to participate and help to create a richer understanding
of work being done in this area. In 2015, a Round Table to initially gauge interest in
mathematical inquiry was held. Because of the large number of participants, there was little
opportunity for discussion. At this Round Table, the aim is to separate into smaller areas of
interest around particular themes. Possible strands around IMBE include: • Early Years • Primary • Secondary • Tertiary Mathematics • Initial Teacher Education • Professional Development • Assessment and Research Measures • Engaging with Stakeholders, Community and Policymakers • Classroom Norms and Argumentation • Theoretical and Methodological Perspectives • Social Justice and Inclusion • Affect • 21st Century Skills • Curriculum and Resources • Areas Needing More Research
A possible outcome could be a symposium, publication and/or online community. New and
previous participants equally welcome!
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Mathematics and Task Design
Christine Mae, Janette Bobis, & Jennifer Way
Teacher knowledge is a significant issue for mathematics education (Sullivan, 2008a).
Educational research has increasingly tried to identify characteristics of teacher knowledge for
effective mathematics teaching and their influence on student learning outcomes (Bobis,
Higgins, Cavanagh and Roche, 2012). With teacher performance standards now well iterated,
the questions of "what [teacher] knowledge matters more, and why" (Bobis et al, 2012, p.1),
remain central to improving mathematics education in Australia.
This round table will outline the rationale and theoretical underpinnings of a study into the
relationship between primary teachers' subject matter knowledge and pedagogical content
knowledge domains (Ball, Thames and Phelps, 2008). The Mathematics and Task Design
Project is a research study involving 65 primary teachers within a system of schools. The study
explores: (i) teachers' understandings of area and volume when solving problems; the level of
the tasks teachers design for their students; and, (iii) the nature of the feedback that teachers
provide when analysing student work samples, and (iv) the relationships between each of these
critical aspects of teacher knowledge. Data from the Task Design aspect of the study will be
used to provide the stimulus for a discussion of the challenge of identifying and designing
frameworks that can be applied to consistently analyse and describe the levels of opportunity
and challenge within mathematical tasks.
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Mathematics Education/Research in an Open and Big Data Era
Theodosia Prodromou
Data revolution enables citizens to have access to an enormous amount of complex data
sets. These emerging data sets include: 1) large-scale open databases, 2) the growing use of big
data, and 3) novel tools and ways of visualising data. The aim of this Round Table is to bring
together a community of researchers, who focus on the role of increasingly open data access
within mathematics education, the access to "big data", teaching and learning of
mathematics/Statistics, data visualisation in open data contexts, new statistical literacies in a
new open data and big data era, the increasing need of research tools that affords opportunities
to: 1) study classroom practices in sophisticated ways provided the access to "big data" and the
open-access nature of information, and 2) ways of visualising data. I invite those interested in "big data" and the increasingly open-access information to discuss their work or aspects of big
data" and the increasingly open-access data in Mathematics/Statistics Education that are in
need of research.
A few questions are listed below to provoke conversation. Bring your own!
1. What is the role of open-access information (open data) and big data in Australian
Mathematics classrooms?
2. What is the role of open-access information (open data) and big data in Mathematics
research?
3. How can open-access information (open data) and big data be used in Mathematics
(or Statistics) teaching and learning?
4. How do we need to change the way we think in terms of the nature of data and its
availability, the ways in which data is displayed and used, and the skills that are
required for its interpretation in order to take into account the full complexity of
data?
5. What views must be included in a framework for teaching mathematical/Statistical
literacy or data literacy in a new open data and big data era?
6. What the instructional and research dilemmas in data revolution era?
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Mathematics Support Teacher (MST): What has been the impact on the students?
Deborah Gibbs & Fiona Fox
The Mathematics Support Teacher (MST) intervention was designed for students who have
been identified as having severe learning difficulties in mathematics. The MSTs provide
intensive mathematics teaching support with the aim to accelerate the students progress. The
students were provided with four to five additional half hour lessons per week over a 15 to 20
week period. Initial involvement in the intervention has resulted in accelerated gains for the
majority of these students. This case study involved interviewing past students who had
maintained their learning gains after participating in the intervention in either 2011 or
2012. The students past teachers were also interviewed. Interviews were conducted using
three schools from different regions across New Zealand.
This round table forum presents impact stories of students, teachers and family after
involvement in a mathematics intervention. It will provide an opportunity for participants to
discuss the findings and consider the conditions and implications for students and their
mathematics learning.
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Provoking Contingent Moments: A New Model of Knowledge for Powerful Teaching at the Mathematical Horizon
Chris Hurst
Teacher knowledge continues to be a topic of debate in Australasia and in other parts of
the world. There have been many attempts by mathematics educators and researchers to define
knowledge needed by teachers to effectively teach mathematics, and a plethora of terms such
681
as mathematical content knowledge, pedagogical content knowledge, horizon content
knowledge and specialised content knowledge have been used to describe aspects of such
knowledge. Here, I put forward a new model for teacher knowledge that embraces aspects of
earlier models and which focuses on the notions of contingent knowledge and the
connectedness of "big ideas" of mathematics to enact what is described as "powerful teaching".
Its power lies in the teacher's ability to set up and provoke contingent moments to extend
children's mathematical horizons. The new model proposed here considers the various
cognitive and affective components and domains that teachers require to enact "powerful
teaching".
Contingency is described in Rowland's Knowledge Quartet as the ability to respond to
children's questions, misconceptions and actions and to be able to deviate from a teaching plan
as needed. It follows that a deeper level of knowledge might enable a teacher to respond better
and indeed to plan and anticipate contingent moments. Taking this further and considering
teacher knowledge as "dynamic", I suggest that instead of responding to contingent events,
powerful teaching is about provoking contingent events. In order to place genuine problem
solving at the heart of learning, the idea is to actually plan for contingent events, to provoke
them, and "set them up". The proposed model attempts to represent that process.
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Secondary teachers' participation in STEM professional development: Challenges and opportunities
Judy Anderson & Gaye Williams
Governments and school systems are investing resources into science, technology,
engineering and mathematics (STEM) education to address perceived shortages in these fields
in university enrolments as well as in the workforce. Many initiatives have been implemented
to capitalise on the increased focus on the STEM subjects in schools with universities
frequently leading the way by offering engaging and worthwhile programs for students and
teachers to promote the STEM subjects. However, many of these programs are "one off" or "once a year" events for small numbers of students in participating schools, potentially having
little ongoing impact on the larger cohort of students in each school. A different initiative
provides ongoing professional learning for teams of teachers of all STEM subjects from a small
number of schools and focuses not just on improving pedagogy in each of the subject areas but
encourages teachers to work in teams to design integrated approaches to curriculum. Our
experiences with this professional development program has raised many questions about
secondary teachers' engagement and participation in working together in multidisciplinary
teams to design integrated units of work. This roundtable will seek to explore the challenges in
bringing such teams together, the challenges in implementing integrated approaches in
secondary school contexts, and the opportunities afforded by integrating curriculum to enhance
connections for students.
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Teachers Collaborating to Accelerate Learning for Students Struggling in Mathematics
Jill Peterson, Anne Milburn, & Gaynor Terrill
Some mathematics learners need additional support to enable them to achieve at their
expected level in relation to the New Zealand curriculum and the mathematics standards.
Effective mathematics teachers can accelerate the learning of small groups of students in a
relatively short period of time when they provide targeted support within their daily classroom
programmes. This roundtable will begin by outlining the Accelerated Learning in Mathematics
intervention model where teachers are given an opportunity to design an intervention response
to accelerate the learning of students struggling in mathematics. We will discuss the early
findings of a research project that examined the conditions in twelve schools that enabled a
successful and sustainable intervention. Effective collaboration across a small group of
teachers was identified as a common feature that promoted changed teacher practice and
accelerated learning for targeted students. We will consider the different models of
collaboration that lead to a successful intervention for these schools. Results showed that the
collaborative nature developed in these schools led to an increased derivatisation of practice, a
shared responsibility for accelerated outcomes, a greater willingness to take risks, and teachers
became more reflective in their practice which led to deeper conversations around teaching and
learning.
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What is the Evidence for Best Practice in Mathematics Education?
Rosemary Callingham, Judy Anderson, Kim Beswick, Colin
Carmichael, Vince Geiger, Merrilyn Goos, Derek Hurrell, Christopher
Hurst, Tracey Muir, & Helen Watt
A recent national study aimed to provide an evidence base for best practice in mathematics
education in Australia. Schools were included in the study on the basis of growth in NAPLAN
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numeracy from 2011 to 2013, and 2012 to 2014, in Years 3 to 5 and Years 7 to 9. Using
Bronfenbrenner's (1989) Ecological Systems Theory as a structural framework, the study
aimed to identify goal orientations and costs associated with achieving these goals at system,
school, classroom, and individual level. Mastery goal orientations were defined as having a
focus on connections within mathematics, relevance, and cooperation, whereas performance
goal orientations were defined as having a focus on skill development, achievement, and
competition.
Findings suggest that successful schools, regardless of their social context, were consistent
in their focus on mathematics across the school, in classrooms and among individuals. Mastery
approaches were associated with reduced costs in terms of students'perceptions of effort,
social costs and mathematics difficulty. Teacher enthusiasm for mathematics teaching emerged
as a key factor.
Issues that arose from the study will provide starting point for discussion.
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