Full Proceedings |
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Keynote Addresses |
The "M" in STEM: National Perspectives
Alan Finkel |
We are Still Learning to Integrate Affect (and Mathematics) into our Research
Naomi Ingram
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Clements-Foyster Lecture |
In Search of Mathematical Structure: Looking Back, Beneath, and Beyond - 40 Years On
Joanne Mulligan |
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Invited Panel: MERGA1 to MERGA40 |
Progressing Along a "Road Less Traveled": The History of School Mathematics
M.A. (Ken) Clements |
Forty Years On: Mathematical Modelling in and for Education
Peter Galbraith |
Mathematics Performance and Future Occupation: Are They (Still) Related?
Gilah C. Leder |
"Does This Mean That Kindergarten Will Be a Remedial Year?"
Bob Perry
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Forty Years of Teaching Problem Solving
Kaye Stacey |
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Beth Southwell Practical Implication Award |
Framing, Assessing and Developing Children's Understanding of Time
Margaret Thomas, Doug Clarke, Andrea McDonough & Philip Clarkson
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Symposia |
Reframing Mathematical Futures: Using Learning Progressions to Support Mathematical Thinking in the Middle Years
Dianne Siemon, Lorraine Day, Max Stephens, Marj Horne, Rosemary Callingham, Jane Watson, & Rebecca Seah
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Research Engagement and Impact in Mathematics Education
Merrilyn Goos, Vince Geiger, Anne Bennison, Shelley Dole, & Helen Forgasz
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STEM Practices: A Reconceptualization of STEM in the Early Years
Ann Gervasoni, Tom Lowrie, Tracy Logan, Kevin Larkin, Claudette Bateup, & Caroline Kinny-Lewis
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Transitions in Mathematics Education
Gail FitzSimons
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STEM Professional Learning: Evaluating Secondary School Teachers' and Students' Experiences
Judy Anderson, Kathryn Holmes, Deborah Tully & Gaye Williams
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Research Papers |
The Prevalence of the Letter as Object Misconception in Junior Secondary Students
Zarina Akhtar & Vicki Steinle
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Developing Interactive ICT Tools for the Teaching and Learning of Vectors at A-Level
Khemduth Singh Angateeah, Savial Thapermall, & Ravi Jawahir
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Re-Examining a Framework for Teacher Identity as an Embedder-of-Numeracy
Anne Bennison
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Privileging a Contextual Approach to Teaching Mathematics: A Secondary Teacher's Perspective
Raymond Brown & Trevor Redmond
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Partial Credit in Multiple-Choice Items
Joan Burfitt
How Might the Use of Apps Influence Students' Learning Experiences? Exploring a Socio-Technological Assemblage |
Nigel Calder & Carol Murphy
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Entangled Modes: Social Interaction in Collaborative Problem Solving in Mathematics
Man Ching Esther Chan & David Clarke
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Investigating Teachers Perceptions of Enabling and Extending Prompts
Jill Cheeseman, Ann Downton, & Sharyn Livy
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The Impact of a Measurement-Focused Program on Young Childrens Number Learning
Jill Cheeseman & Yianna Pullen
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Snapshots of Productive Noticing: Orchestrating Learning Experiences Using Typical Problems
Ban Heng Choy & Jaguthsing Dindyal
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The Argument from Matriculation Used by Proprietors of Victorian Secondary Schools Around 1900
M. A. (Ken) Clements & Nerida F. Ellerton
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That First Step: Engaging with Mathematics and Developing Numeracy
Audrey Cooke
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"Maths Inside": A Project to Raise Interest in Mathematics
Mary Coupland, Marco Angelini, Anne Prescott, Sandy Schuck, Tapan Rai, & Carmen Lee
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Mastery Learning: Improving the Model
Mary Coupland, Danica Solina, & Gregory E. Cave
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The Interplay Between Pre-service Teachers' Intentions and Enacted Mathematical Content Knowledge in the Classroom
Leah Daniel
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Exploring Ways to Improve Teachers' Mathematical Knowledge for Teaching with Effective Team Planning Practices
Aylie Davidson
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Primary School Mathematics Leaders' Views of their Mathematics Leadership Role
Kerryn Driscoll
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Historical Perspectives on the Purposes of School Algebra
Nerida F. Ellerton, Sinan Kanbir, & M. A. (Ken) Clements
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Fourth-Graders' Meta-Questioning in Statistical Investigations
Lyn D. English, Jane M. Watson, & Noleine Fitzallen
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Essential Topics for Secondary Mathematics Success: What Mathematics Teachers Think
Melinda Evans
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Hypothesis of Developmental Dyscalculia and Down Syndrome: Implications for Mathematics Education
Rhonda Faragher
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Gender and VCE Mathematics Subject Enrolments 2001-2015 in Co-Educational and Single-Sex Schools
Helen Forgasz & Gilah Leder
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A Secondary Mathematics Teachers Perceptions of her Initial Attempts at Utilising Whiteboarding in her Classes
Tricia Forrester, Carolyn E. Sandison, & Sue Denny
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The Development of Addition and Subtractions Strategies for Children in Kindergarten to Grade 6: Insights and Implications
Ann Gervasoni, Kerry Giumelli, & Barbara McHugh
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Teaching Fractions for Understanding: Addressing Interrelated Concepts
Seyum Getenet & Rosemary Callingham
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Teachers' Understanding and Use of Mathematical Structure
Mark Gronow, Joanne Mulligan, & Michael Cavanagh
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Initial Teacher Education Students' Reasons for Using Digital Learning Objects When Teaching Mathematics
Ngārewa Hāwera, Sashi Sharma, & Noeline Wright
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Peer Observation as Professional Learning about Mathematical Reasoning
Sandra Herbert & Leicha A. Bragg
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Exploring Reasons Why Australian Senior Secondary Students Do Not Enrol in Higher-Level Mathematics Courses
Gregory Hine
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Does (Problem-Based) Practice Always Make Proficient?
Sarah Hopkins & James Russo
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Explicitly Connecting Mathematical Ideas: How Well Is It Done?
Chris Hurst & Ray Huntley
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Exploring Undergraduate Mathematics Students’ Difficulties with the Proof of Subgroup’s Closure under Operation
Marios Ioannou
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Is Mathematics Education Worthy? From Mathematics for Critical Citizenship to Productivity Growth
Dan Jazby
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Grade 10 Students' Mathematical Understanding and Retention in a Problem-Based Learning (PBL) Classroom
Premanan Juakwon & Duanghathai Katwibun
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Engaging Pre-Service Mathematics Teachers in Creating Spatially- Based Problems in a 3D Virtual Environment: A CAVE2TM Experience
Margaret Marshman, Geoff Woolcott, & Shelley Dole
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Structure in the Professional Vocabulary of Middle School Mathematics Teachers in Australia
Carmel Mesiti & David Clarke
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Using Coding to Promote Mathematical Thinking with Year 2 Students: Alignment with the Australian Curriculum
Jodie Miller & Kevin Larkin
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Online, Anytime, Anywhere: Enacting Flipped Learning in Three Different Secondary Mathematics Classes
Tracey Muir
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Learning from our Neighbours: The Value of Knowing Their Number History
Kay Owens
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Generalising Fraction Structures as a Means for Engaging in Algebraic Thinking
Catherine Pearn & Max Stephens
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First-Year University Students' Difficulties with Mathematical Symbols: The Lecturer/Tutor Perspective
Robyn Pierce & Meredith Begg
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11th Grade Students' Self-Regulated Learning in a Mathematics Problem-Based Learning (PBL) Classroom
Supatpong Promsawan & Duanghathai Katwibun
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Statistics Instructors' Beliefs and Misconceptions About p-values
Robyn Reaburn
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Revisiting Friedrich Froebel and his Gifts for Kindergarten: What are the Benefits for Primary Mathematics Education?
Simone Reinhold, Ann Downton, & Sharyn Livy
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Perceived Changes in Teachers' Knowledge and Practice: The Impact on Classroom Teachers from Leader Participation in Whole-School Reform of Mathematics Teaching and Learning
Anne Roche & Ann Gervasoni
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Examining the Impact of Lesson Structure when Teaching with Cognitively Demanding Tasks in the Early Primary Years
James Russo & Sarah Hopkins
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Pricing: Exploring the Intersection Between Values, Maths, Finance, and Entrepreneurship
Carly Sawatzki
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Using Activity Theory to Understand a Mathematics Leader's Motivations and Use of Mathematical Knowledge for Teaching
Matt Sexton & Janeen Lamb
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Exploring Critical Thinking in a Mathematics Problem-Based Learning Classroom
Rakkor Siriwat & Duanghathai Katwibun
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Maths Anxiety: The Nature and Consequences of Shame in Mathematics Classrooms
Sue Wilson
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Graphic-Rich Items within High-Stakes Tests: Indonesia National Exam (UN), PISA, and TIMSS
Destina Wahyu Winarti & Sitti Maesuri Patahuddin
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Pre-Service Teachers' and Tutors' Perceptions about the Value of Talk Moves
Vince Wright
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Knowledge, Beliefs, and Innovative Curriculum
Laurinda Lomas
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Indigenous Teacher Education: When Cultural Enquiry Meets Statistical Enquiry
Tony Trinick & Tamsin Meaney
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Short Communications (Abstract Only) |
A Developing Framework for Identifying Young Children's Engagement with the Spatial Features of Play Spaces
Catherine McCluskey & Joanne Mulligan
In this presentation, we report on our initial analysis of preschool children's
engagement with spatial features of play spaces. The analysis focusses on noticing an
awareness of mathematical pattern and structure (AMPS) evident in their play. The notion
of spatial structure in play contexts will distinguish features of dynamic action such as
children's movement through play spaces and the comparison, transformation, and
navigation of 3D objects. The pattern and structure of mathematical concepts identified in
this analysis will be compared with those evident in the Pattern and Structural Awareness
Program (PASMAP, Mulligan & Mitchelmore, 2016). Future areas for research will be
discussed.
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A Five Question Approach to the Teaching of Mathematics
John Ley
According to Clements (2003), Dinham (2012), and Sullivan (2013), there is an urgent
need to change the way that mathematics is taught in Australian schools. The Five
Question Approach (FQA) to teaching mathematics, developed during my 30 years of
secondary mathematics teaching, occurs at the commencement of every lesson. It is the
subject of my doctoral research, in which I am investigating if the FQA results in an
increase in students' academic achievement, perceived and/or actual, and engagement. I
will discuss the final data analysis and completion stage and some of the results and
implications in this session.
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Challenging Teacher Perceptions: Those Children will Struggle No Matter What You Do to Them
Glenda Anthony, Roberta Hunter & Jodie Hunter
Teachers' perceptions of students' capabilities are particularly important in efforts to
support instructional reforms. In this presentation, we explore the efforts of one teacher to
resolve conflicts and tensions as she engaged with new practices associated with ambitious
mathematics teaching. We look in particular at the influence of her diagnostic framing of
students' mathematical capabilities and her beliefs about knowledge acquisition on her
introduction of collaborative mixed-ability group work.
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Evaluating Learning Analytics of an Online System to Improve Teacher Education Students' Numeracy Skills Development
Thuan Thai, Amanda Yeung, Timothy Perkins, Kate Hartup, & Marguerite Maher
Since 2015, all teacher education students in Australia are required to pass the Literacy
and Numeracy Test for Initial Teacher Education (LANTITE) in order to meet
accreditation requirements. The purpose of the test is to ensure that graduate teachers meet
a satisfactory level of personal literacy and numeracy, roughly equivalent to the top 30% of
the adult population. To support and help students prepare for this test, we created an
online Literacy and Numeracy Practice System through the university's learning
management system, Blackboard. In this short communication, we will report our initial
findings from evaluating the learning analytics available with this system and discuss its
impact on students' numeracy skills development.
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Exploring Mathematics Pedagogy in Collaborative Teaching Environments
Bilinda Offen & Naomi Ingram
There is an increasing number of collaborative teaching environments in primary
schools. A collaborative teaching environment is a teaching situation in which two or more
teachers are responsible for the learning outcomes of a number of students commensurate
with the ratio of the number of teachers. What might traditionally have been two single
classrooms now have two teachers who are responsible for all students in a linked physical
environment. We share initial results of a study in which we explore the ways that
mathematics is taught in five collaborative environments, and compare these with best
practice (Anthony & Walshaw, 2007).
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Exploring Primary Teachers' Conceptions of Mathematical Fluency: Are We Speaking the Same Language?
Katherin Cartwright
Fluency in mathematics is defined in various forms, such as computational fluency,
procedural fluency, and mathematical fluency. However, terms like "procedural" and "computational" often leave teachers interpreting fluency as simply being able to follow a
set formula or to compute quickly. In this study, I explore practising primary teachers' conceptions of mathematical fluency, including how they define mathematical fluency,
what features they associate with the term, and what relationship, if any, understanding
plays within mathematical fluency. In this presentation, I will report some initial findings
from the questionnaire used in Phase 1 of the data collection for this research project.
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Factors Influencing Student Selection of Senior Secondary School Mathematics Subjects
Micheal Jennings, Merrilyn Goos & Peter Adams
Declining numbers of Advanced Mathematics (AM) students at secondary school are seen
as a major issue for the future of STEM in Australia and internationally (Noyes, Wake, &
Drake, 2011; Office of the Chief Scientist, 2014). Few large-scale research studies have
investigated why students choose particular mathematics subjects. The aim of this empirical
study was to identify the reasons why students choose or do not choose AM in the last two
years of secondary school. Quantitative data were collected via surveys from secondary
school mathematics students and teachers, and university mathematics lecturers. The
surveys contained 20 statements on reasons for choosing/not choosing AM, covering
intrinsic and extrinsic motivational factors.
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Fitness for Purpose of Tertiary Algebra Textbooks: An Arabic Case Study
Hassnaa Shaheed
I will outline my PhD research into fitness for purpose of tertiary algebra textbooks
used in Iraq in the education of pre-service teachers. I will consider (a) broad discourses
and the use of introductions, examples, and explanations in light of cross-cultural studies
such as the Japanese-U.S.A. comparison by Mayer et al., (b) pedagogies and assumptions
about knowledge that can be inferred from the presentation style, referencing Magolda's
theory linking forms to assessment to underlying theories of knowledge, (c) types of proof
used in light of the theories of Harel and Sowder, and Stacey and Vincent, and (d)
multilingual issues, given that some texts are translations and others are written in Arabic.
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High-Potential Mathematics Students and Their Mathematics-Related Activities Outside School
Simone Zmood
Two decades ago, Csikszentmihalyi, Rathunde, and Whalen (1997) investigated what
motivates young people to devote themselves to developing their potential. Studying
mathematics offers long-term extrinsic rewards, but school mathematics may not be
enjoyable or challenging. Hersh and John-Steiner (2011) suggested that supportive families
can make a substantial difference to mathematics talent development. During a recent
Australia-wide online survey of parents of school-aged children with high mathematical
potential, data were gathered on the outside-of-school mathematics activities engaged in by
the children. The data were examined by age and gender. The survey findings will be
discussed in this presentation.
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Impact of Culture in Parental Control and Mathematics Achievement of their Children
Daya Weerasinghe
The presentation is based on a study guided by a conceptual framework developed on
attributes of parental perceptions such as attitudes, beliefs, expectations, aspirations,
values, and standards; parental involvement; and academic achievement of children. The
participants were students (n = 128) and their parents (n = 85) from three secondary
schools in Melbourne, Australia. The data were gathered by means of questionnaires and
semi-structured interviews. The nature of research questions was both quantitative and
qualitative, requiring a mixed-methods approach. It was found that there were significant
differences in parental control between parents from European-Australian and Asian-
Australian backgrounds.
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Improving Mathematics Curriculum Support for Indigenous Language Speaking Students
Cris Edmonds-Wathen
A resource to support teaching the Australian Curriculum: Mathematics to students
who speak English as an additional language or dialect (Australian Curriculum,
Assessment and Reporting Authority, 2014), including Indigenous language speaking
(ILS) students, provides language and cultural considerations and suggested teaching
strategies linked to content descriptions. Critical analysis of this resource shows much
scope for improvement. There is inconsistency between the language expectations of the
resource and curriculum and the English language learning progressions of ILS students
(Northern Territory Department of Education and Training, 2009). Few suggestions are
specific for ILS students. I provide recommendations to improve the resource for teachers
of ILS students, drawing on substantial prior research.
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Influential Factors for Effective Problem Solving Practice in Primary Mathematics Teachers
Melody McCormick
Problem solving is described in Australian Curriculum as one of four proficiency
strands (understanding, fluency, problem solving, and reasoning), and an integral
component of mathematics teaching and learning. In this presentation, I discuss the
preliminary stages of a study in which I am exploring teacher knowledge and dispositions
of primary educators who effectively integrate problem solving to improve student
mathematics learning, as well as identify any constraints and opportunities including the
Australian Curriculum and professional learning experiences. Using a mixed methods
approach, in this study, I am examining past survey data from the Encouraging Persistence
Maintaining Challenge (EPMC) project to identify participants for subsequent case studies.
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Interbreeding Paradigms in Research on Mathematics Knowing and Learning
Thorsten Scheiner & Marcia Maria Fusaro Pinto
Often, structuralism and constructivism are framed as competing paradigms in
mathematics education from which one seems to have to choose. Here, we present
emerging theoretical insights that recognize, rather than deny, individuals in the creation of
the meaning of a mathematical concept, acknowledging the complex interaction between
individual and subject matter: An individual’s knowledge system is shaped by the meaning
of a mathematical concept, but the knowledge system also shapes the meaning of a
mathematical concept. These recent advances in research on mathematics knowing and
learning allow interbreeding of seemingly contradicting paradigms.
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Linguistic Obstacles to Second Language Learners' Access to Mathematical Talk for Individualised Sense-Making
Sally-Ann Robertson & Mellony Graven
Despite willingness, South African mathematics teachers teaching through a second
language (L2) often struggle to get their learners engaging in exploratory talk. Using
transcripts of talk in one South African teacher's Grade 4 mathematics lessons, plus
interview data, we will examine and share some effects that children's diminished access
to their strongest source of linguistic capital, mother tongue (L1), appears to have on their
epistemological access to mathematical sense-making. Our findings suggest that use of L2
exacerbates existing inequalities in mathematics achievement across South Africa’s socioeconomic
sectors (sectors which, due to the legacy of apartheid, generally coincide with "race).
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Looking Inside the Black Box of Mathematics Teacher Noticing
Ban Heng Choy & Jaguthsing Dindyal
Research in mathematics teacher noticing, an important component of teaching
expertise, has gained traction in recent years (Hunter, Hunter, Jorgensen, & Choy, 2016).
Despite the advances in our understanding of teacher noticing as a high leverage practice
(Sherin, Jacobs, & Philipp, 2011) and its application across a wide variety of contexts
(Amador, 2016; Choy, 2016; Seto & Loh, 2015; Simpson & Haltiwanger, 2016; Wager,
2014), the "complex interactions of cognitive and perceptual processes and activities in
dynamic situations (such as classrooms) have never been fully described in research on
teacher noticing" (Scheiner, 2016, p. 234). Many of these processes remain hidden in the "black box" of noticing (Scheiner, 2016). This begs the question: How do we look inside
the black box of teacher noticing? Scheiner (2016) suggests that researchers should draw
on the perceptual cycle model (Neisser, 1976) and blend insights from cognitive sciences
and human factors studies. In this short communication, we will present our initial idea of
using wearable eye trackers to investigate teacher noticing. More importantly, we will
invite feedback from the participants to explore how different video technologies could be
used with the FOCUS Framework (Choy, 2015), developed for characterising productive
noticing, to build a more comprehensive model of teacher noticing.
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Numeracy in Action in Family Shopping Experiences: A View from the Trolley
Amy MacDonald, Angela Fenton, & Christina Davidson
In this short communication, we will introduce a current pilot study in which we are
documenting the ways in which children and their families engage in everyday numeracy
as they participate in shopping experiences. The study is underpinned by the notion that
mathematical learning opportunities exist in the everyday activities of families, outside of
the home, childcare centre, or school. Six families, with children ranging from 18 months
to 10 years, were recorded whilst undertaking their shopping using a trolley mounted with
a custom-built Go-Pro© camera rig (nicknamed "trolley-cam"). In this presentation, we
will share selected "trolley-cam" data and vignettes of family numeracy engagement in
action.
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Numeracy of Undergraduate Business School Students
Chris Linsell, Brigid Casey, & Christine Smith-Han
There is growing concern of a mismatch between the numeracy of students upon entry
to university and the expectations of mathematical competence by university teachers
(Marr & Grove, 2010). Poor numeracy has been identified as an issue for undergraduate
students across a range of disciplines (Galligan & Hobohm, 2014; Hodgen, McAlinden, &
Tomei, 2014; Linsell & Anakin, 2012). In this study, we investigated student numeracy in
a compulsory 100-level business school statistics paper and found that 25% of students had
numeracy levels below that expected of a competent Year 9 student (13-year-old). There
was a highly significant relationship between low numeracy and failing quantitative
papers. Students with low numeracy were not necessarily low ability students but lacked
specific skills needed for quantitative work at university level.
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Practitioner Inquiry: Developing Capabilities in Mathematics Teachers
Jyoti Jhagroo
The 21st century has seen a definite shift from teacher training towards teacher
education in initial teacher education programmes. As a tertiary educator in a postgraduate
initial teacher education program, I have seen the dichotomous thinking in which some of
my education students embrace the idea of an inquiry-based mathematics approach with
multiple solutions, while others, for whom mathematics has always been about finding a
solution through learned steps of reasoning, face insurmountable challenges. While
mathematics educators continue to advocate for a constructivist approach to learning,
current practice has not overwhelmingly shifted from the symbol manipulation procedural
approach. Could this be attributed to the notion that how we teach mathematics may be an
internally learned habit from the way we were taught and that change is difficult because it
requires that habit to be broken? Through the lived experiences of first-year teachers as
inquiring practitioners, I explore the concept of practitioner inquiry and its implication for
mathematics practitioners, and I consider how practitioner inquiry could be a catalyst for
transforming mathematics education practices.
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South African Vocational Engineering Students' Conceptual
Understandings of Area, Surface Area, Volume, and Flow Rate Measurement:
A Case Study
Pamela Vale
Measurement is particularly important for vocational Engineering students, for whom
this is a key skill required in the workplace. It is also a skill that many students find
extremely challenging. In this research, I explored, through task-based interviews, 35
South African vocational Engineering students' measurement conceptualisations of area,
surface area, volume, and flow rate, in order to identify the specific learning needs of these
students. The amount, degree, and type of mediation required were used to map the
structure of the students' measurement conceptualisations. In this presentation, I reflect on
these students' conceptual understandings and the implications that these hold for
mathematics educators and researchers.
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Student Engagement in Mathematics
Alexandra Laird & Peter Grootenboer
Student engagement in mathematics and mathematics learning has been a concern for
educators for many years (Attard, 2011). There have been many studies and reports that
have suggested ways to improve student engagement in mathematics lessons, and these
seem to offer some useful approaches. In this presentation, we discuss some of the key
factors related to student engagement in primary mathematics learning as have been
identified in the literature reviewed. In particular, pedagogical approaches will be explored,
including the use of textbooks and investigations (Langer-Osuna, 2015), and classroom
factors including teacher rapport (Attard, 2011) and peer interactions (Way, Reese, Bobis,
Anderson, & Martin, 2016). Finally, we will discuss issues of student engagement visa-a -vis
other variables including gender, previous achievement, and socio-economic status. The
initial findings presented here will underpin some empirical work that is to be subsequently
undertaken.
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Student Errors in a Mathematical Literacy Examination and the Correlated English Language Features
Pamela Vale
Much research has established that when students have a poor command of the
language of learning, teaching, and assessment, they experience a complex and deep
learning disadvantage. This is the case for the majority of students in South African
vocational colleges. In this study, I analysed the errors made by English language learners
when writing a mathematical literacy examination in English, to determine whether the
linguistic complexity of items influenced their responses. A statistically significant
correlation was found between the linguistic complexity of items and certain errors, and it
was possible to isolate which features of the language contributed to these errors.
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Students' Espoused and Enacted Theories in an Inquiry Mathematics Classroom
Generosa Leach
Although inquiry classrooms as learning environments for mathematics have existed
for many years, only recently has literature emerged on what it means from the perspective
of students to learn mathematics in these contexts. Many researchers (e.g., Attard, 2011;
Fraivillig, Murphy, & Fuson, 1999; Grootenboer & Marshman, 2016; Hunter & Anthony,
2011; McDonough & Sullivan, 2014) argue the importance of listening to students' views
about their experiences in inquiry environments so that mathematics educators can better
meet students' learning needs. At the same time, there is a need for recognition that what
students say is important about learning mathematics may not connect to what they do
while learning mathematics. Previous research studies either focus on students' perspectives about classroom practices in mathematics lessons (e.g., Cobb, Gresalfi, &
Hodge, 2009; Hodge, 2008; Hunter, 2006) or their theory-in-use, through classroom
observations, as they engage in mathematical activity (e.g., McCrone, 2005; Perger, 2007;
Pratt, 2006). In contrast, in this presentation, I report on a group of students' (aged 9-10
years old) views and attitudes towards learning mathematics and their actions within the
classroom while an inquiry mathematics community was being developed.
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Students' Reflections on Portfolio Assessment in Mathematics
Hem Chand Dayal, Bronwen Cowie, & Salanieta Bakalevu
We discuss findings from a study that utilized students' portfolio entries to provide
initial insights into students' views about portfolio assessment. Two Fijian Year 9
mathematics teachers implemented portfolios as a means of assessing student learning in
measurement. While students in Jenny's class noted advantages in terms of learning new
content and skills, their difficulties with portfolio assessment were often bounded by the
various mathematical content. Students in Gavin's class provided insight into students' perspectives on value of portfolio assessment. Apart from discussing the various areas of
content, students in Gavin's class pointed out many other benefits of portfolio assessment.
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Task Modification to Facilitate Creativity by Korean Prospective Mathematics Teachers
Kyeong-Hwa Lee
Mathematical tasks play a critical role in the teaching and learning of mathematics.
Tasks with different natures can provide different opportunities to promote students’
mathematical thinking and understanding (Henningsen & Stein, 1997). Teachers can read
and evaluate curriculum material focusing on tasks in order to modify them based on
current reforms in mathematics education. Creativity is the essence of mathematics (Mann,
2006) and has been one of the main emphases of the Korean mathematics curriculum for
decades. Various attempts in the curriculum to enhance student creativity in mathematics
have been made.
Attempts to promote creativity education have been made by leading mathematics
teachers, and their approaches have been shared for several years in Korea (Lee, 2015).
Some of these approaches to promote creativity have included promoting communication
among students, practicing activity-based instruction, having students grasp fundamental
ideas and knowledge in advance and focus on discussions in class, and planning and
implementing storytelling lessons. Textbooks have also been redeveloped to include
opportunities for creativity cultivation.
When looking back over the past few years of creativity education in Korean
mathematics classrooms, one of the biggest concerns has been that we have not paid much
attention to the development of tasks that are appropriate for creativity development. The
majority of the tasks for cultivating creativity used in textbooks and classes have not been
suitable for cultivating creativity. This is because textbook authors and teachers have
attempted to design tasks without fully understanding what to consider in developing a task
suitable for creativity education.
In this paper, I aim to determine what points need to be considered in the design of
tasks for nurturing creativity. The definition of creativity varies, but I will discuss common
and meaningful pursuits for creativity in school mathematics by analyzing some empirical
data from the prospective teacher education course I ran in 2016. In order to maintain
consistency with the curriculum, task design was aimed at increasing opportunities for
creativity while retaining the learning objectives and content of existing textbooks. I will
report the patterns that Korean prospective mathematics teachers tend to follow when they
modify mathematical tasks in textbooks to facilitate creativity.
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Teachers Choosing Mathematics
Inge Koch & Janine McIntosh
The basis for teacher confidence, or the lack of it, in teaching mathematics varies
across the teaching cohort, with many reporting a range of degrees of comfort with their
own mathematical abilities. Through the CHOOSEMATHS Project, we have found some
interesting connections in the preliminary data and suggest some explanations for it.
CHOOSEMATHS is a national project aimed at getting more girls and young women into
mathematics through targeted teacher professional development, career awareness, and
mentoring and support across mathematics.
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The Road to Transformative Healing of Mathematics Anxiety: A Case Study in Progress
Timothy Perkins
Significant proportions of pre-service teachers in Australia are having their enthusiasm
to become capable and successful primary school teachers significantly dampened by their
inability to work confidently and capably with mathematical content. Wilson and Gurney
(2011) defined mathematics anxiety as "a learned emotional response characterised by a
feeling that mathematics cannot make sense, of helplessness, tension and lack of control
over one's learning" (p. 805). In an ongoing study into the mathematics anxiety
experienced by pre-service primary teachers at an Australian university, one significant
case study is explored in depth to highlight the mathematical journey of one participant in
the study who has had a transformational experience through mentoring.
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The Use of Contextual Patterning Tasks with Young Pasifika and Maori Students in New Zealand Mathematics Classrooms
Jodie Hunter & Jodie Miller
Mathematical achievement of culturally diverse students is a challenge in many countries. Teaching in ways responsive to the cultures of our students is vital towards enhancing equity of access to mathematics achievement and putting educational policy (e.g., Ministry of Education, 2011) into practice. Similar to other countries, New Zealand has a changing student population that is increasingly culturally diverse. This population includes a large number of Pāsifika and Maori students whose educational results are characterised by unenviable statistics in which a large percentage are under-achieving compared to their peers. Educators frequently attribute this under-achievement to the learners themselves and position Pāsifika and Maori cultures as being mathematically deficient (Hunter et al., 2016). However, both Pāsifika and Maori cultures have a rich background of mathematics, including a strong emphasis on patterns used within craft design (Finau & Stillman, 1995). In this presentation, we report on the preliminary findings of a study in which we are investigating how contextual Pāsifika and Maori patterning tasks can potentially support young children to develop their understanding of growing patterns.
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Unidoodle
Michael Jennings
Audience responses systems, commonly referred to as "clickers", are common in many
university classes. Typically the clicker allows a student to enter an answer to a multiplechoice
question. The teacher then displays the responses before (usually) either leading
students in a discussion of the merits of each answer choice or asking students to discuss
the question in pairs or small groups. The benefits of using clickers are well documented in
the research literature and include improved classroom interaction, motivation and
attendance, and improved student understanding. Unidoodle takes clickers one-step further
as it enables students to submit freehand drawing and sketch-style answers. Students can
write equations, draw graphs, or show their working. This allows teachers to receive much
richer feedback from their students.
In this short communication I will briefly present the Unidoodle system and the way in
which I have used it in two first-year mathematics classes. I will then pose some discussion
questions on the use of clickers.
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Use of Social Media in Preservice Mathematics Education Courses
Paul Brown
Facebook was used in preservice primary and secondary mathematics education units
to provide a forum for students. The innovation was readily received by most of the
students, but not all. Facebook was mainly used to share resources, but there was some
discussion suggestive of a community of enquiry. In this presentation, I explain how to set
up and run a closed Facebook group and explore the advantages and disadvantages of the
system. These include the immediacy, access, and continuity Facebook provides, and the
problems that inappropriate interactions generate. The research reported does not support
the idea that Facebook constitutes a distraction for tertiary students.
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Using Peer-Reflection to Develop Self-Regulated Learning Strategies in Year 10 Mathematics
Karen McMullen
Recent reforms to the Australian Curriculum and the Victorian Curriculum provide a
framework for developing students' awareness of metacognition and self-regulated
learning strategies. In this study, I use educational design research to develop and
implement a class-based intervention that aims to improve students' self-regulated learning
strategies. This educational intervention structures an approach to critical peer-reflection as
part of Year 10 mathematics lessons whereby students reflect, discuss, observe, and model
learning strategies. In this presentation, I will explore preliminary data that have informed
the development of the intervention.
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Round Tables (Abstract Only) |
Exploring Emotional Aspects of Pre-Service Mathematics Learning Environments
Joanna Higgins
Preparing primary teachers for mathematics teaching typically includes attention to
their existing beliefs and attitudes towards mathematics as a discipline. The potential of the
pre-service learning environment to enhance emotional engagement with mathematics
learning and teaching is a developing field of research. In the session, I will provide an
opportunity to discuss issues around initial teacher education learning environments in
terms of introducing structures to promote positive experiences in learning to teach
mathematics. I will examine emerging theories of emotions from a sociological perspective
that are useful for analyzing the emotional aspect of learning environments. In the round
table session, I will draw on survey data about emotional dispositions and beliefs in
mathematics as well as emotions associated with teaching mathematics. I will also draw on
case studies of individual students who were excited and enthusiastic about teaching
mathematics despite having had negative learning experiences themselves. The session
will provide an opportunity for participants to discuss (a) increased awareness of emotional
reactions to classroom events, (b) the connection between innovative teaching approaches
and mathematics teaching and learning, and (c) the potential of games to impact the
emotional aspects of learning environments.
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Mathematics Leadership in Primary Schools
McMaster, Bobis, & Way
In response to the recent Teacher Education Ministerial Advisory Group (TEMAG)
report (2014), teacher education providers are developing new units of study and pathways
of study within existing programs to cater for pre-service teachers (PSTs) who elect to
undertake a specialization in mathematics. Entry requirements for students electing such a
pathway are not specified; however, it is expected that when they graduate, they will have
demonstrated competence in mathematics and perhaps taken one or more additional units
in mathematics pedagogy.
Teacher education providers currently know little about the background experiences,
aspirations, and expectations of primary school PSTs who might elect and be accepted into
a primary mathematics specialization pathway. This gap in our knowledge is partly due to
prior research foci on primary PSTs who lack the mathematical content knowledge
required as a basis for teaching mathematics well (Callingham & Beswick, 2011).
Teacher education providers also know little about what potential employers are
expecting of PSTs who will graduate with a specialization in mathematics. This knowledge
is necessary for teacher education providers to be able to select appropriate candidates for a
mathematics specialization pathway and plan units of study for them.
In the round table, we will begin by presenting the aim of our research, some
preliminary data concerning the PSTs who have elected to undertake a new primary
mathematics specialisation at The University of Sydney, and the skills and characteristics
that some potential employers have identified as being essential or desirable for
mathematics leadership in primary
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Rethinking Mathematical Tasks
Ban Heng Choy & Jaguthsing Dindyal
Mathematics teachers invariably use a multitude of tasks in their day-to-day practice.
Indeed, "mathematical tasks provide tools for promoting learning of particular
mathematical concepts and are, therefore, a key part of the instructional process" (Simon &
Tzur, 2004, p. 93) Further, the National Council of Teachers of Mathematics (NCTM,
1991) postulated that tasks "convey messages about what mathematics is and what doing
mathematics entails" (p. 24). Over the years, several terms have been used to describe
mathematical tasks, such as worthwhile mathematical tasks (NCTM, 1991), challenging
tasks (Sullivan et al., 2014), high-level tasks (Henningsen & Stein, 1997), open-ended
tasks (Zaslavsky, 1995), and rich mathematical tasks (Grootenboer, 2009). While
acknowledging the benefits of using such tasks, research has also surfaced some
shortcomings. Stein, Grover, and Henningsen (1996) cautioned that "When employing the
construct of mathematical task, however, one needs to be constantly vigilant about the
possibility that the tasks with which students actually engage may or may not be the same
task that the teacher announced at the outset"(p. 462). In this round table presentation, we
will discuss the affordances that mathematical tasks such as those stated above offer to
teachers, as well as other alternatives that are available to teachers for enhancing students' learning of mathematics. We will provide some examples from one of our on-going
projects for further discussion.
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Scaling Up and Sustaining Successful Interventions in Mathematics Teaching
Merrilyn Goos, Robin Proffitt-White, & Anne Bennison
Education research journals regularly report on small-scale studies that have been
successful in changing mathematics teachers' classroom practices. However, it is rare to
find large-scale transfer of research knowledge into practice in mathematics education
(Begg, Davis, & Bramald, 2003). In this round table discussion, we will share some early
findings from research into an established, large-scale professional development project
initiated and sustained by a state education system at a regional level and involving a large
number of schools and teachers. In this project, we have developed a cluster model for
bringing primary and secondary school teachers and principals together to analyse student
performance data, create diagnostic tasks that reveal students' current mathematical
understanding, and promote teaching practices that address students' learning difficulties
in mathematics. The effectiveness of this approach is evidenced by reported improvements
in teacher confidence and knowledge and in student achievement and enjoyment of
mathematics, changes to mathematics teaching and assessment practices, and an everincreasing
number of schools volunteering to join the project and commit professional
development funding. In our research, we seek to identify critical factors that support these
mathematics teachers in instructional improvement on a large scale.
The round table will begin with an overview of the cluster model and then we will
present some insights from interviews that we have conducted with teachers and principals.
We invite MERGA members to join us and share their own experiences and ideas in
response to the following research questions that are guiding our study (based on Cobb &
Jackson, 2011):
1. What practices are effective in establishing a coherent instructional system
supporting mathematics teachers' development of ambitious teaching practices?
2. To what extent do teacher networks and mathematics coaching of teachers support
changes in mathematics teaching practice?
3. What features of school and district or regional leadership contribute to the
scalability and sustainability of a cluster-based professional development model?
We also invite colleagues to suggest new lines of inquiry that could contribute to a
theoretical rationale for sustained, scalable professional development.
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