Title 
Curriculum in Focus: Research Guided Practice
Judy Anderson, Michael Cavanagh, Anne Prescott (Eds.)


Content 

Preface 

List of Reviewers 
List of Reviewers


Keynote Address 
Peter Galbraith 
Evolution of Singapore's School Mathematics Curriculum
Berinderjeet Kaur

Mathematics Education Development Research in Teaching Learning in Practice
Barbara Jaworski


Practical Implication Award 

Symposium 
A Framework for Teachers' Knowledge of Mathematical Reasoning
Sandra Herbert

A Primary Teacher's Developing Understanding of Mathematical Reasoning
Esther YookKin Loong

Designbased Research for Professional Learning for Cultural Mathematics
Geori Kravia & Kay Owens

Developing Noticing of Reasoning through Demonstration Lessons
Leicha A. Bragg & Colleen Vale

Elementary Teachers in Papua New Guinea's Professional Learning for Cultural Mathematics
Kay Owens, Vagi Bino, Geori Kravia, Cris EdmondsWathen, Priscilla Sakopa, Kila Tau, & Martha Kull

Evaluating the Professional Learning for Cultural Mathematics in Papua New Guinea's Elementary Schools
Vagi Bino, Priscilla Sakopa, Kila Tau, & Martha Kull

Foundation Content Knowledge: Preservice Teachers as Halfempty or Becoming Fluent?
Megan Anakin & Chris Linsell

Foundation Content Knowledge: Preservice Teachers' Attainment and Affect
Naomi Ingram & Chris Linsell

Foundation Content Knowledge: Providing support for preservice teachers
Chris Linsell & Naomi Ingram

Personal Number Sense and New Zealand PreService Teachers
Karen Major & Pamela Perger

Preservice Teachers Mathematics Content Knowledge
Chris Linsell, Megan Anakin, Naomi Ingram, Karen Major, & Pamela Perger

Professional Learning for Cultural Mathematics in Papua New Guinea's Elementary Schools
Kay Owens, Geori Kravia, Cris EdmondsWathen, & Priscilla Sakopa

Students' Mathematical Reasoning and Teachers' Developing Understanding of Mathematical Reasoning
Colleen Vale, Leicha Bragg, Sandra Herbert, Esther Loong, & Wanty Widjaja

TechnologyEnhancement for Papua New Guinean Professional Learning
Vagi Bino & Cris EdmondsWathen

Year 3/4 Children's Forms of Justification
Wanty Widjaja


Research Paper 
Item Context Factors Affecting Student's Performance on Mathematics Items
Felipe Almuna Salgado & Kaye Stacey

From Arithmetic to Algebra: Sequences and Patterns as an Introductory Lesson in Seventh Grade Mathematics
Diana Grace Aniban, Von Christopher Chua, Jellen Garcia, & Levi Esteban Elipane

Early Career Teachers, Mathematics and Technology: Device Conflict and Emerging Mathematical Knowledge
Catherine Attard & Joanne Orlando

Linking GeoGebra to Explorations of Linear Relationships
Belinda Aventi, Penelope Serow, & Steve Tobias

Undergraduate Mathematics Students’ Pronumeral Misconceptions
Caroline Bardini, Jill Vincent, Robyn Pierce, & Deborah King

Teacher Identity and Numeracy: Evaluating a Conceptual Framework for Identity as a Teacher of Numeracy
Anne Bennison

Towards a Fresh Understanding of the Relationship Between Teacher Beliefs about Mathematics and their Classroom Practices
Kathy Brady

Affordances: Ten Years On
Jill P. Brown & Gloria Stillman

Gender, Parental Beliefs and Children's Mathematics Performance: Insights from the Longitudinal Study of Australian Children
Colin Carmichael

Primary Students' Perceptions of their Mathematics Learning
Jill Cheeseman & Angela Mornane

Exploring Group Dynamics of Primary 6 Students Engaged in Mathematical Modelling Activities
Chan Chun Ming Eric

Noticing Critical Incidents in a Mathematics Classroom
Ban Heng Choy

Preliminary Investigations of Preservice Teacher Numeracy
Audrey Cooke

The Value of Emoticons in Investigating Student Emotions Related to Mathematics Task Negotiation
Fabio D'Agostin

Undergraduate Mathematics Study Groups: What Mathematical Talk Actually Takes Place?
James Dalitz

Asking Questions and Performing Mathematics Identity
Lisa Darragh

The Mathematical Selfbelief of Year 7 Students
Nicole Dimarakis, Janette Bobis, Jenni Way, & Judy Anderson

How Students Explain and Teachers Respond
Ove Gunnar Drageset

Why Lesson Study Works in Japan: A Cultural Perspective
Marlon Ebaeguin & Max Stephens

Indigenous Languages and Mathematics in Elementary Schools
Cris EdmondsWathen, Priscilla Sakopa, Kay Owens, & Vagi Bino

Development of Fourthgrade Students' Understanding of Experimental and Theoretical Probability
Lyn English & Jane Watson

A Working Understanding of Numeracy in the Secondary Setting
Elizabeth Ferme

An Investigation of Students' Errors in Logarithms
Raman Ganesan & Jaguthsing Dindyal

Devising Principles of Design for Numeracy Tasks
Vince Geiger, Merrilyn Goos, Helen Forgasz, & Anne Bennison

Race in the Outback: Investigating Technology Designed to Support Number Development in a Preschool Serving an UnderResourced Community
Kristy Goodwin & Peter Gould

The Association between Students' Number Knowledge and Social Disadvantage at School Entry
Peter Gould

Different Versions of the Same Lesson Plan: Implications on the Lesson Design
Jane Greenlees, Sitti Maesuri Patahuddin, & Tom Lowrie

Mathematics Teaching as Praxis
Peter Grootenboer & Christine EdwardsGroves

Developing a 'Conjecturing Atmosphere' in the Classroom through Task Design and Enactment
Jodie Hunter

Big Challenges and Big Opportunities: The Power of 'Big Ideas' to Change Curriculum and the Culture of Teacher Planning
Chris Hurst

Do Teachers Make Decisions Like Firefighters? Applying Naturalistic DecisionMaking Methods to Teachers' InClass Decision Making In Mathematics
Dan Jazby

Social Theories of Learning: A Need for a New Paradigm in Mathematics Education
Robyn Jorgensen

Using Coaching to Improve the Teaching of Problem Solving to Year 8 Students in Mathematics
Christine Anestis Kargas & Max Stephens

Comparison of a Targeted Intervention Program Delivered FacetoFace and by Personal Videoconferencing for Primary and Middle School Students with Mathematical Learning Difficulties
Eugenie Kestel

Probabilistic Reasoning and Prediction with Young Children
Virginia Kinnear & Julie Clark

Will this Net Work?: Development of a Diagnostic Interview
Rose Knight & Vince Wright

The Effect of Professional Learning on Early Algebra Teachers' Content Knowledge in Nigeria
Omolola Ladele, Christine Ormond, & Mark Hackling

Leading a New Pedagogical Approach to Australian Curriculum Mathematics: Using the Dual Mathematical Modelling Cycle Framework
Janeen Lamb, Takashi Kawakami, Akihiko Saeki, & Akio Matsuzaki

PreService Teachers' Use of Library Databases: Some Insights
Janeen Lamb, Sarah Howard, & Michael Easey

Using Video Diaries to Record Student Attitudes and Emotions towards Mathematics in Year Three and Year Six Students
Kevin Larkin & Robyn Jorgensen

Teachers Repositioning Culturally Diverse Students as Doers and Thinkers of Mathematics
Generosa Leach, Roberta Hunter, & Jodie Hunter

Learning from Assessment: NAPLAN and Indigenous Students
Gilah Leder & Helen Forgasz

Who is Really Interested in Mathematics? An Investigation of Lower Secondary Students' Mathematical Role Models
Kester Lee & Judy Anderson

Learning Stories: Making Mathematics Learning Visible
Rachel Lim, Glenda Anthony, & Claire McLachlan

Opportunities to Promote Mathematical Content Knowledge for Primary Teaching
Sharyn Livy & Sandra Herbert

The Impact of an Intervention Program on Student Approaches to Learning: A Case Study
Bernadette Long

Do Students Solve Graphic Tasks with Spatial Demands Differently in Digital Form?
Tom Lowrie, Ajay Ramful,Tracy Logan, & Siew Yin Ho

"I don't really understand probability at all": Final Year Preservice Teachers' Understanding of Probability
Nicole Maher & Tracey Muir

PPELEM: A "Creative" Interviewing Procedure for Gaining Insights into Teacher and Student Mathematicsrelated Beliefs
Andrea McDonough & Sarah Ferguson

Does Inquiry Based Learning Affect Students' Beliefs and Attitudes Towards Mathematics?
Darren McGregor

Young Australian Indigenous Students' Growing Pattern Generalisations: The Role of Gesture when Generalising
Jodie Miller

Research Guided Practice: Student Online Experiences during Mathematics class in the Middle School
Maria MojicaCasey, John Dekkers, & RoseMarie Thrupp

A Reflective Approach to NAPLAN: Exploring the Implications of Students' Responses to an "Adding Fractions" Item
Patricia Morley

Flipping the Classroom: A Case Study of a Mathematics Methods Class
Tracey Muir & Helen Chick

Developing Young Students' MetaRepresentational Competence through Integrated Mathematics and Science Investigations
Joanne Mulligan & Lyn English

The Complexity of OneStep Equations
Bing Ngu

Defining Mathematical Giftedness
Linda Parish

Online Students' Perceptions of Interactive Tools to Support Postgraduate Learning of Mathematics
Elena Prieto & Kathryn Holmes

Quantitative Relationships Involving Additive Differences: Numerical Resilience
Ajay Ramful & Siew Yin Ho

Mental Calculation Strategies of a Student Attending a Special School for the Intellectually Disabled
Rumi Rumiati & Robert J. Wright

Connecting Social and Mathematical Thinking: The Use of "Real Life" Contexts
Carly Sawatzki

What Australian Primary School Students Value in Mathematics Learning: A WIFI Preliminary Study
Wee Tiong Seah & Tasos Barkatsas

Newcomers' Experiences of MERGA 36
Yvette Semler & Michael Cavanagh

School Mathematics Leaders' Perceptions of Successes and Challenges of their Leadership Role within a Mathematics Improvement Project
Matt Sexton & Ann Downton

Teacher Practices: How they Promote or Hinder Student Engagement in Mathematics
Karen Skilling

Using Percentages to Describe and Calculate Change
Beth Price, Kaye Stacey, Vicki Steinle, & Eugene Gvozdenko

Students' Willingness to Engage with Mathematical Challenges: Implications for Classroom Pedagogies
Peter Sullivan, Doug Clarke, Jill Cheeseman, Angela Mornane, Anne Roche, Carly Sawatzki, & Nadia Walker

The Role of Challenging Mathematical Tasks in Creating Opportunities for Student Reasoning
Peter Sullivan & Aylie Davidson

The Technological Enframing of Mathematics Education
Steve Thornton

Beliefs of Teachers Who Teach Intensive Onetoone Intervention about Links to Classroom Teaching
Thi L.Tran & Robert J. Wright

Improving the Effectiveness of the Whole Class Discussion in the Summary Phase of Mathematics Lessons
Nadia Walker

Developing Students' Functional Thinking in Algebra through Different Visualisations of a Growing Pattern's Structure
Karina J Wilkie & Doug Clarke

"Change my Thinking Patterns towards Maths": A Bibliotherapy Workshop for Preservice Teachers' Mathematics Anxiety
Sue Wilson & Monica Raven

The Effect of Language, Gender and Age in NAPLAN Numeracy Data
Tim Wilson & Tasos Barkatsas

Symmetrical Measuring: An Approach to Teaching Elementary School Mathematics Informed by Yup'ik Elders
Monica Wong, Jerry Lipka, & Dora AndrewIhrke

Supporting the Development of Number Fact Knowledge in Five and Sixyearolds
Jenny YoungLoveridge & Brenda Bicknell

Fostering the Promise of High Achieving Mathematics Students through Curriculum Differentiation
Simone Zmood

Comparing the Score Distribution of a Trial ComputerBased Examination Cohort with that of the Standard PaperBased Examination Cohort
Nathan Zoanetti, Magdalena Les, & David LeighLancaster

Arithmetical Strategies of a Student with Down syndrome
Rumi Rumiati

Developing PreService Teacher Capacity to Make Appropriate Choices of Tasks and Resources through Diagnostic Assessment of Children's Work
Chris Hurst


Short Communication (abstract only) 
Collegial Peer Observation as a Means of Influencing Change in University Mathematics Teaching
Merrilyn Goos & Paul HernandezMartinez
This paper presents insights into the
transformation of teaching practices in an undergraduate engineering
mathematics course. Adopting a developmental design research approach,
the second author introduced mathematical modelling and group work into
his teaching of the course, while the first author offered peer
observation and feedback to support pedagogical change. The paper uses a
sociocultural framework to examine how the peer observation process
supported the mathematics lecturer in implementing the teaching
innovation. A previously developed adaptation of Valsiner's zone
theory is used to analyse the productive tensions experienced by the
lecturer and the observer's role in promoting change.

Conceptual Development in Mathematics: Longitudinal Connections from Network Analysis of Multiple Choice Assessments
Geoff Woolcott, Daniel Chamberlain, & Rassoul Sadeghi
Network analysis may be used to enrich
understanding of conceptual relationships in mathematics and their
development over time and is used to examine spatiotemporal connectivity
of learned concepts, or outcomes, and concepts inherent in multiple
choice items. The network representations derived from this analysis
show the connections between concepts for individuals completing
multiple choice assessment tasks in years 3 to 6 in a largescale
testing program. The longitudinal relationships described in this
analysis of measurement items offer a way for teachers to address poorly
learned concepts that may have compounded over time, particularly for
the design of revision and intervention.

Cultural Identities and Mathematics Learning
Angel Mok
Leung (2002) suggests the high TIMSS performance
of Singapore, Hong Kong, and Taiwan, which have high proportions of
Chinese students, may be influenced by cultural and family values.
However, comparative studies of Chinese students' mathematics
performance often focus on what Chinese families do to support
children's learning, with few studies examining why. Using an
ethnographic case study, this research focuses on six Chinese families
living in Sydney to explore how their cultural identities influence
their children's mathematical learning. Initial findings suggest
parents perceive mathematics as an important, yet not difficult subject,
and believe their children can be trained to improve.

Designing Professional Development: Beyond General Principles
Seyum Getenet, Rosemary Callingham, & Kim Beswick
This study describes the importance of context
analysis in designing professional development guidelines to support
Ethiopian mathematics teacher educators to integrate technology in their
teaching. The study was conducted at departments of mathematics in two
Colleges of Teacher Education using a combination of qualitative and
quantitative data. Sixteen mathematics teacher educators completed a
questionnaire as part of a larger study. The data were analysed using
descriptive statistics and theme grouping of the qualitative data. The
study showed that analysis of the learning context and teacher
educators' context are found to be important to suggest relevant
professional development guidelines.

Developing Critical Reflection for Primary School Mathematics Teachers through Laboratory Class Cycle
Lu Pien Cheng
This presentation examines how a Critical
Commentator (CC, the author) facilitated reflection amongst seven
Singapore primary mathematics teachers during a schoolbased
professional development programme. Laboratory class cycle involving
planning, observing and critiquing mathematics lessons was used as a
framework for the programme. With the aid of a questioning framework,
the CC was able to help these teachers improve the quality of their
reflections, moving from Level 1 technical reflection, to the Level 3
critical reflection. The difficulties in recalling exact details of the
observed lesson which prompted the teachers to embrace video technology
for their reflection were also examined.

Development of a Set of Mathematical Modelling Rubrics
Siew Yee Lim & Hui Yi Ting
There has been increasing interest in the use of
mathematical modelling to better prepare students for the 21st century.
However, established rubrics that assess students' ability to apply
their mathematical skills in mathematical modelling tasks are scarce.
This study proposes to develop a set of mathematical rubrics based on
four standard mathematical modelling steps of formulating, solving,
interpreting and reflecting. Validity and reliability of the rubrics
will be assessed with 200 high school students from Singapore. The
rubrics will then be used to investigate the effects of using a
mathematical modelling teaching package on students' ability to solve
realworld problems.

Dyscalculia, from a Teacher's Perspective
Ann Williams
This presentation is based on a literature review
(Williams, 2012).The puzzle of why "able children are unable to learn
arithmetic" (Butterworth & Laurillard, 2010, p. 536), has different
names. It affects the ability to count hence the ability to do
arithmetic but not the ability to do higher levels of mathematics. The
incidence of dyscalculia is about 5%. However, there is a high degree of
coexistence between all learning disabilities. For example, over 50%
of students with dyslexia are likely to have dyscalculia. Another issue
for dyscalculics is time. They often have working memory problems so
need extra processing.
References
Butterworth, B., & Laurillard, D. (2010). Low numeracy and
dyscalculia: Identification and intervention. ZDM Mathematics Education,
42, 527539.
Williams, A. (2012). A teacher's perspective of dyscalculia: Who counts?
An interdisciplinary overview. Australian Journal of Learning
Difficulties, 2012(Oct), 116. doi: 10.1080/19404158.2012.727840

Early Childhood Educators as Teachers of Mathematics
Susan McDonald & Louise Thomas
The past decade has seen an increase in the
attention given to education in priortoschool settings, and as a
result, two areas of interest have emerged: (1) the intent and nature of
this phase of education, and (2) the identity of the educator in these
settings. This paper presents data from a project seeking to identify
how teachers in this phase identify themselves as teachers of numeracy,
and how they articulate their role in the implementation of early
childhood mathematics curricula.

Enhancing Mathematics and Science Teacher Education in Regional
Australia: Modules for Primary Mathematics Preservice teachers
Geoff Woolcott, Adam Harris, Jackie Reid, & Robert Whannell
This presentation describes a project designed to
enhance mathematics and science teacher education in regional
Australia. Iterative processes are used to develop and trial enhancement
and feedback modules, involving preservice teachers, mathematicians
and educators in targeted interactions designed to ground preservice
teacher education in contexts relevant to daily life. The feedback
module, designed for selfevaluation, involves preservice teachers
analysing critical affective states recorded while teaching. The aim is
to improve performance through an investigation of the contribution of
competence, developed via the enhancement and feedback modules, to
preservice teacher confidence.

Evidence of Evolutionary Changes in the Nature of Interactions in Fully Asynchronous Online Mathematics Courses
Sven Trenholm
The role and status of interactions
(studentcontent, studentinstructor and studentstudent) are considered
foundational to current online learning theory (Anderson & Elloumi,
2008). This research investigates these interactions in fully
asynchronous online mathematics courses taught in the US public higher
education context. It reports on problems with human interactions in
general and evidence for a deemphasis on studentstudent interactions
and an emphasis on computerbased studentcontent interactions.
Findings are discussed in relation to current theory and prior research
with concerns raised concerning the quality of associated learning.
References
Anderson, T., & Elloumi, F. (2008). The theory and practice of
online learning. Alberta, Canada: AU Press.

Exploring Mathematics Engagement in the Middle Years of School
Janette Bobis, Jenni Way, & Maryam Khosronejad
This presentation reports on an intervention
study aimed at improving middle year (Years 57) students' engagement
in mathematics. Motivation and engagement levels in mathematics were
assessed prior to and at the completion of a yearlong intervention for
two different cohorts of students in 2012 (N=339) and 2013 (N=319) using
the Motivation and Engagement Scale (Martin, 2008). While 2012 data
found downward shifts in student engagement were generally abated and
even reversed for some aspects, 2013 results revealed a greater mix of 'ups' and 'downs' in student engagement levels. Reasons for the
variation in findings of the two cohorts are explored.
References
Martin, A.J. (2008). The Motivation and Engagement Scale. Sydney:
Lifelong Achievement Group (www.lifelongachievement.com).

Investigating the Representations of Students' Problem Solving Strategies
Nor Azura Hj Abdullah, Masitah Shahrill, & Maureen Siew Fang Chong
We investigated the strategies used by Year 7
students in answering a problem solving question. The strategies mostly
used by students were Estimation and Check (46%) and Drawing Pictures
(19%). A total of 125 students, from the 650 responses collected overall
responded using a 'Drawing Pictures' strategy while another 299
students opted for 'Estimation and Check' strategy. Here we attempt
to categorise further these specific strategies to help us analyse the
level of students' problem solving proficiencies. It has been found in
previous studies that student's solution strategies are indicators to
show students' level of proficiency in problem solving skills.

Learning in Undergraduate Mathematics: The Trial of a Delivery Innovation
Bill Barton
LUMOS is a twoyear Ako Aotearoafunded project
that aims to identify, observe, and report on the full spectrum of
desired learning outcomes for undergraduate mathematics, that is, not
only contentbased outcomes. The project includes the development of
three innovative delivery methods for undergraduate mathematics. As we
enter the second year, we can report on the first and second trial of an
innovation that places the responsibility for learning onto students,
but also offers them authentic mathematical experiences.

Like Topsy, "it just growed"? Or did it? The Ongoing Development of a Strategy Teaching Model
Gregor Lomas
The development of a strategy teaching model
associated with the New Zealand Numeracy Development Projects is
presented and examined against a Design Research framework. The
development while informed by literature, multiple forms of feedback
from practitioners, and a clear intent to make it workable for teachers,
was a responsive and organic process. It can appear not to have been
the result of research or been formally researched overall. However,
this examination of the development of the Numeracy Development Projects
Strategy Teaching Model suggests otherwise indicating that it is the
result of a research process albeit an informal one.

Mathematics and English Teachers' Views and Expectations of iPads: A Pilot Study
Janelle Hill
As a new technology, the uptake of iPads in
Australian schools is increasing. As part of a current case study,
numeracy and literacy teachers from an Independent school in Victoria,
Australia in which iPads had been introduced were interviewed and their
views on teaching with iPads were explored. A number of concerns arose
related to the use of this technology, including teachers expressing the
opinion that their teaching had not changed, not seeing benefits for
students and concerns about assessment. A discussion of these concerns
and possible educational implications is presented.

Mentoring to Alleviate Anxiety in PreService Primary Mathematics
Teachers: Working at the Coalface without having to Look over your
Shoulder
Timothy Perkins
Increasing numbers of students enrolled in
primary preservice teacher (PST) Education degrees in Australia enter
university with insufficient mathematical content knowledge and low
confidence levels about their ability to teach and do the mathematics
required for their intended role as classroom teachers. Mentoring of
PST's by highly capable and experienced classroom teachers within the
framework of a structured and wellplanned mentoring programme, has the
potential for developing the confidence, and thus alleviating the
mathematics anxiety exhibited by PST's. This study examines a novel
approach to mentoring outside the pressurecooker of the professional
experience block.

Middle Years Students Using Mathematics to Communicate a Local Issue
Margaret Marshman
Middle Years students often do not see the value
and usefulness of mathematics while the Australian Curriculum:
Mathematics aims for students to be "confident and creative users and
communicators of mathematics (ACARA, 2012). This paper discusses how a
group of middle year students have used mathematics to communicate a
local issue. The data were analysed in terms of the "working
mathematically" moments, in particular problem negotiation,
formulation, and solving. The paper will show how these students have
made a difference in their local community by using mathematics to
communicate the young people's view.

Modelled Lessons Raise More Questions than Answers
Louise Hodgson
The focus of this presentation is to report on an
exploration of what teachers observed when watching modelled lessons.
Focusing on two modelled lessons in one school, data are presented that
indicate that observation of teaching practice raises many questions
related to the meaning of explicit teaching, the structure of lessons,
catering for diversity and the implementation of the Australian
Mathematics Curriculum. It seems that a modelled lesson and subsequent
inquiry into the teaching practice being modelled can provide an
opportunity to challenge teacher beliefs as well as demonstrate what is
possible.

Multiple Multiplication Methods
Jyoti Jhagroo
I advocate for a shift from the traditional role
of the teacher in developing computational proficiency through a single
method modelandpractice teaching approach to a pedagogy that promotes
learning through diversity. By examining mathematics through different
lenses, alternative ways of thinking may be nurtured in the learning
environment. Drawing on the lived experiences of immigrant secondary
students I present some perspectives that diverse learners have of
learning mathematics in their classrooms. In an attempt to understand
different ways of solving mathematics problems, I present alternative
multiplication strategies from India, Japan and Scotland.

Responses to "the Scary Question": How Teaching Challenges Impact the Use of Knowledge and its Development
Kim Beswick & Helen Chick
This paper reports on teachers' experiences of
being out of their comfort zone in their mathematics teaching. We
describe examples of experiences that the teachers considered "scary", their reported responses to those situations, and the
longerterm effects of such experiences. Implications for the
acquisition of knowledge for teaching mathematics are discussed, and
questions raised about the possible impacts of confidence and experience
on the interaction between discomforting experiences and teacher
learning.

Scaffolding Formative Assessment Approach  Visualize Learning
Annika Grotherus
This is a presentation of an evaluation and
assessing method in mathematics using the concepts of scaffolding,
formative assessment and writing to learn intertwined. The scaffolding
formative assessment approach is a product of over ten years of
development of teaching and assessing mathematics in both compulsory
school and secondary education. The aim was to make learning visible and
make students reflect on their own learning, what strategies they might
use and what needs to develop further. Furthermore, a way of using
tests in mathematics as an additional learning opportunity was
considered by using summative tests in a scaffolding and formative
manner.

Selfefficacy and Attitude toward Mathematics: A Multigroup Invariance Analysis and Gender Difference
Elizar & I Gusti Ngurah Darmawan
The study examined multigroup invariance of
Mathematics Selfefficacy and Attitude Scales (MSAS) and examined gender
differences of MSAS across gender. The analysis of invariance was
conducted to examine whether the items in the MSAS were operating
equivalently between Year 9 female and male students in the state of
Aceh, Indonesia. The analysis discovered the evidence of multigroup
equivalence of the MSAS across gender (p value is not statistically
significant or ?CFI = 0.01). An independent ttest found that
attitude toward mathematics was significantly different between female
and male students. Females had a more positive attitude toward
mathematics.

SPOT Diagrams of a Partially Correct Construct
Caroline Yoon
SPOT (Structures Perceived Over Time) diagrams
(Yoon, 2012) are analytical tools for visualising changes in the
mathematical structures students create, attend to, and manipulate over
time. SPOT diagrams use animated networks to portray relationships
between mathematical objects and their attributes, as well as changes in
these structures. In this presentation, I show how SPOT diagrams can be
used to analyse the role of a participants Partially Correct
Construct (PaCC) (Ron, Dreyfus and Hershkowitz, 2010) as she developed a
method for determining relationships between a function, its
derivative, and its antiderivative
References
Ron, G, Dreyfus, T. & Hershkowitz, R. (2010). Partially correct
constructs illuminate students' inconsistent answers. Educational
Studies in Mathematics, 75, 6587.
Yoon, C. (2012, July). Mapping Mathematical Leaps of Insight. Regular
Lecture presented at the 12th International Congress on Mathematical
Education, Seoul, Korea.

Teachers' Beliefs and Practice in Teaching Early Algebra
Christina Lee, Omolola Ladele, & Christine Ormond
To teach mathematics in the 21st century, and
more specifically to teach early algebra, the teacher should bring to
the classroom a particular cluster of skills, understandings and
knowledge. Early algebra is crucial for students' success in higher
mathematics. While a written curriculum is needed for teaching, a
teacher's beliefs and knowledge are also important determiners of the
algebra content taught in the classroom. In this crosscultural study,
we examine the similarities and differences found in two recent and
concurrent mixed methods research projects in both Australia and
Nigeria. The two research studies showed teachers' beliefs had a
meaningful influence on the teachers' practice.

The Contribution of a Poetics of Mathematics Classroom Interaction to Curriculum Design
John Kusznirczuk
This paper presents an argument in support of the
proposition that a poetics of mathematics classroom interaction is
necessary to the effective design of mathematics curricula. Drawing on
an account of the "interaction order" (after Goffman, 1983), which
is one aspect of a theoretical investigation of the tools needed to
systematically describe mathematics classroom interaction (Kusznirczuk,
2012). I argue that an educator's "critical literacy" with respect
to the rhetorical structure and function of the interaction that
realises a "mathematics period" amounts to a "poetics of
mathematics classroom interaction and that the effectiveness of
mathematics curriculum design depends on such poetics.
References
Goffman, E. (1983). The interaction order: American Sociological
Association, 1982 Presidential Address. American Sociological Review(1),
1. doi: 10.2307/2095141
Kusznirczuk, J. (2012). In search of the zone of proximal development:
Introducing a map used to navigate a confusion of categories and things.
Paper presented at the Contemporary Approaches to Research in
Mathematics, Science, Health and Environmental Science Symposium,
Melbourne. http://www.deakin.edu.au/artsed/efi/conferences/car2012/

The Development in Integrating Mathematical Modelling into the Curriculum: Results of a Pilot Study
Maureen Siew Fang Chong & Masitah Shahrill
A mathematical modelling framework called MODEL
(Meanings, Organise, Develop, Execute and Link) was designed to assess
students' application of abstract mathematical knowledge into
reallife situations. A pilot study was conducted aimed to identify the
level of mathematical modelling skills of 183 preuniversity students in
Brunei Darussalam. Test items were employed and students' responses
were evaluated using the MODEL framework. The results revealed that the
maximum level attained by the students was at the Execute (E) level
only. They managed to obtain mathematical solutions and contextualised
their solutions but all had failed to justify for validation at the Link
(L) level.

The Flipped Classroom Model: A Literature Review
Duncan Symons & Cath Pearn
The Flipped Classroom Model is an approach to
blended learning that is currently being trialled in many settings from
mathematics teacher education to the primary mathematics classroom. This
literature review offers a general introduction to the model, a
discussion of key components of the model including analysis of the
opinions of both critics and proponents of the model, and lastly a
series of recommendations/ areas for further research.

The Meaning Making of Meaning Makers "Experienced Mathematics
Teachers" Interpretations of their Own Professional Practice
Malin Lindwall Ehrnlund
This study is an exploration of the ways in which
experienced mathematics teachers recognize and learn about issues that
shape their own professional practice. In a schoolbased professional
development program teachers collaboratively analyzed their teaching
practice in order to recognize and interpret concerns and teaching
needs, as well as link them with corresponding decision making and
teaching actions. Findings indicate that by systematically "unpacking" teaching and students learning and making
rationalizations about their practice explicit, the teachers came to
articulate, reinterpret and challenge what they need to know about
teaching in order to orchestrate meaningful classroom practice.

The Performance Characteristics of Early Education Children in
Mainstream Classrooms with Respect to Critical Mathematical Thinking
Chrissy Monteleone, Roger Vallance, & Paul White
Critical mathematical thinking is the ability to
reason and make judgments to solve mathematics problems. In order to
identify young children's critical mathematical thinking processes,
mainstream classroom teachers may ask higherorder, openended stimulus
questions to elicit the thinking of these children. This research
focuses on teachers' understanding of critical mathematical thinking
and their current processes of identification. The study will use
purposively constructed mathematical stimulus questions with children,
which focus on a range of mathematical conceptual understandings. The
focus children are in their first year of formal school (Kindergarten)
in a NSW setting.

Towards an Investigation of the Pedagogical Content Knowledge of University Mathematics Teachers
Greg Oates, John Hannah, David Holgate, & Kevin McLeod
Recent studies suggest that, similar to secondary
school teaching, appropriate mathematical and pedagogical content
knowledge (MCK; PCK) and pedagogical technology knowledge (PTK) may also
be necessary in order to make informed decisions about curricular
values in undergraduate mathematics. There are a growing number of
studies that examine these teacher competencies at the secondary school
level, but there are few such studies in undergraduate mathematics. This
paper discusses the design of a study that looks to examine university
lecturers' PCK and PTK, as a basis for a curriculumwide examination
of relative content value in first year undergraduate mathematics
courses.

TPACK as an Analytical Tool to Understand Mathematics Teaching with Technology
Sitti Maesuri Patahuddin & Barney Dalgarno
This paper addresses the question "what
specialised knowledge is needed by teachers to teach mathematics
effectively using digital learning resources? It outlines how a
specific theoretical framework (the Technological Pedagogical Content
Knowledge or TPACK framework) may help us understand the complexity of
teaching mathematics using tehnology. The framework is used to analyse a
100 minute video of teaching "comparing fractions using an
exploratory type of website". The findings suggest that the effective
integration of technology in mathematics teaching is determined by a
teacher's TPACK and strong TPACK may not be possible without adequate
PCK, TPK, and TCK.

Understanding Media in Mathematics Education: Media and Extensions of the Students
Hiro Ozasa, Takeshi Okawa, & Akio Matsuzaki
The aim of this presentation is to analyze the
extensions of the students in a mathematics lesson. The method is the
following. Firstly we review the media theory (McLuhan, 1994; Tokitsu,
2012) to extract a viewpoint for mathematics lessons. Secondly we plan
and implement a mathematics lesson (Okawa, Ozasa, & Matsuzaki,
2013). Finally we discuss what the students can do or cannot do bodily,
and mathematically, by focusing on the viewpoint.
References
McLuhan, M. (1994). Understanding media: The extensions of man. London,
UK: The MIT Press.
Okawa, T., Ozasa, H. & Matsuzaki, A. (2013) The integration between
mathematics and physical education for connecting two representations:
Through the ICT having motion capture function and the dance create
activity. Proceedings of the 46th Annual Meeting of JSSE (pp.361362).
Tsu, Japan: Mie University. (in Japanese)
Tokitsu, K. (2012). A consideration about the construction of
educational practice by media: Focusing on communication media and
material, Departmental Bulletin Paper of Hiroshima Bunka Gakuen
University, 2, 2939. (in Japanese)

Using iPads for Assessment in the Mathematics Classroom
Naomi Ingram & Sandra WilliamsonLeadley
This short communication reports on the use of an
iPad application for mathematical assessment in New Zealand primary and
secondary schools. This iPad application enables the user to make
notes, while recording sound in real time. Students' voices are
recorded as they work and explain how they solved a mathematical problem  at the same time as recording anything they write down. This study
builds on a pilot study (WilliamsonLeadley & Ingram, 2014) that
found this feature enabled three primary teachers to gather detailed
evidence of how their students solved mathematical problems.
References
WilliamsonLeadley, S., & Ingram, N. (2014). Show and tell: Using
iPads for assesment in mathematics. Computers in New Zealand Schools:
Learning, Teaching, Technology, 25(13), 117137.

Using Metaphors to Investigate Preservice Primary Teachers' Attitudes to Mathematics
Kathy Brady & Tiffany Winn
The use of metaphor as a reflective writing tool
to explore attitudes towards mathematics has been embraced by
researchers in recent years. In this study, first year preservice
primary teachers incorporated inventive concepts and contexts in a
personal mathematical metaphor to create strong and meaningful images
articulating how they felt about mathematics. The findings reveal the
complexity of their attitudes and that despite a perception that these
preservice teachers generally had negative attitudes to mathematics
there existed a preparedness to approach mathematics in a reasonably
positive manner.

Using Picture Books to Implement the Mathematics Curriculum: The Missed Opportunities
Jennie Marston
Picture books have been shown to provide
opportunities for developing mathematical concepts in young children.
Twentyseven professionals (academics, teachers and preservice teachers)
completed 118 evaluations of 36 mathematical picture books for
opportunities of mathematical concept development using a seven category
likert scale. This presentation highlights the range of scores in
identifying mathematical content, connections to the curriculum and
application to problem solving. It appears that without a good
understanding of mathematics and ways to implement problem solving
within the classroom, opportunities to use picture books for rich
mathematical learning experiences are lost.

What does Ability Mean in Mathematics Learning?
Rose Golds
Crossgrouping (or streaming) in mathematics
requires students to be grouped by ability. Schools differ as to whether
there is a fixed or flexible view of ability (Wiliam & Bartholomew,
2004). The notion of a 'fixed ability' jeopardises the education of
many when these decisions are frequently made very early in a child's
educational life (Boaler, 1997). Ability is a very ambiguous concept
and factors related to class, gender, ethnicity and behaviour can be
seen to have an influence on decisions made. This paper will look at the
potential difficulties involved in deciding exactly what ability means
in the mathematics classroom.
References
Boaler, J. (1997). Experiencing school mathematics: Teaching styles, sex
and setting. London: Open University Press.
Wiliam, D., & Bartholomew, H. (2004). It's not which school but
which set you're in that matters: The influence of abilitygrouping
practices on student progress in mathematics. British Educational
Research Journal, 30 (2), 279239.

Why Knowledge of Fractions is Important for Algebraic Readiness in the Middle Years of Schooling
Catherine Pearn
In this presentation the importance of developing
both fractional number understanding and algebraic reasoning will be
articulated. I argue that arithmetical thinking about fractions
necessarily involves multiplicative thinking as opposed to additive
thinking. However in moving from arithmetical thinking to algebraic
thinking involving fractions, a necessary intermediate stage for middle
years' students is effective representational and relational thinking
of fractions. The aim is to identify the key stages and develop a
Screening Test of algebraic readiness.


Poster (abstract only) 
Assessment Literacy among Primary School Mathematics Teachers
Hazel Tan, Ng Kit Ee Dawn, & Cheng Lu Pien
Assessment has been perceived as a key to
educational reforms. Teachers often mediate their curriculum
interpretations and pedagogy based on their understanding of current
assessment formats. Indepth research into the existing beliefs and
assessment literacy of mathematics teachers has implications for the
review of curriculumpedagogyassessment alignment and teacher education
programmes. This exploratory study aims to develop a preliminary
framework of teacher competency on assessment literacy specifically for
primary mathematics teachers. It intends to examine teachers' beliefs,
identify possible levels of assessment literacy, and document effective
strategies displayed by teachers in their mediation attempts between
curriculum, pedagogy, and assessment.

Mathematics Learning and Exceptionality through a Complexity Lens
Rumi Rumiati & Geoff Woolcott
Mathematics learning can be seen as a
multifactored, humandesigned system and complexity theory appears to
be useful in explaining phenomena within this system (Davis, Sumara
& LuceKapler, 2008). The poster proposes a model for understanding
and interpreting complex interactions in the mathematics learning of
exceptional students. The model uses approaches based in studies of
metapatterns and complex systems (Volk & Bloom, 2007) and the
multimediator approaches used in White and Levin (2013) to represent
the emergence of a complex mathematics learning system. The model allows
inclusion of social, cultural and environmental factors which may
affect mathematics learning for exceptional students.
References
Davis, B., Sumara, D., & LuceKapler, R. (2008). Engaging
minds:Changing teaching in complex times (2nd ed.). New York &
London: Routledge.
Volk,T., & Bloom, J. (2007). The use of metapatterns for research
into complex systems of teaching, learning and schooling. Complicity: An
international Journal of Complexity and Education, 49 (1), 2543.
White, D.G., & Levin, J.A. (2013). Navigating the turbulent waters
of school reform guided by complexity theory. Paper presented at the
meetings of the American Educational Researcher Association, San
Fransisco, CA. paper accessed from
http:/tinyurl.com/WhiteLevinAERA2013.

The Ebb and Flow of Themes in 37 years of Mathematics Education Research by MERGA
Harry Kanasa
A Leximancer analysis will be conducted on the
corpus of research conducted by the members of MERGA since its inception
to discover the research interests of this group of Australian
mathematics education researchers from 1977 to 2013. Papers over this
time period will be organised into equal piles before analysis. This
analysis will not only provide a large scale view of the research
interests of mathematics education researchers in Australia but also
possibly point to directions for future research.

Using the Interconnected Model of Professional Growth as a Dynamic Tool for School Improvement
Malin Lindwall Ehrnlund
This poster reports on a study of a group of
mathematics teachers' learning experiences in an explicit professional
development (PD) program. In order to recognize and interpret the
complex processes underlying teacher learning, the Interconnected Model
of Professional Growth (ICMPG) of Clarke and Hollingsworth (2002) was
used as a tool for communication between the participating teachers and
the researcher. Findings indicate that the teachers identify learning
outcomes and their own learning trajectories, however they also
emphasize various elements apparently connected to concrete challenges
they each experience in their professional work.
References
Clarke, D., & Hollingsworth, H. (2002). Elaborating a model of
teacher professional growth. Teaching and Teacher Education, 18,
948â€“967.


Round Table (abstract only) 
Coconstructing Mathematical Inquiry Communities through Professional Development with Teachers
Roberta Hunter, Jodie Hunter, Zain Thompson, & Trevor Bills
New Zealand along with many other countries has
an ongoing concern with a 'tail' of low achievers. Many of these low
achievers attend schools in low socioeconomic areas and are comprised
of a disproportionately large group of students of Pasifika
ethnicities. One project which has been successful in significantly
increasing achievement outcomes for this group of students is the
Pasifika Success Project. This project extended aspects of the New
Zealand Numeracy Project, built on and used subsequent research
evidence, and included providing explicit attention to aspects of
culture, language and identities of the Pasifika learners. Over the
past three years the Pasifika Success Project has consistently resulted
in greater than expected improvement in Numeracy results and stanines
when normed tests are used. However, the project has only been in a
small number of schools and involved one researcher who led professional
development days and worked closely with teachers in classrooms
coconstructing mathematical inquiry communities. This year the project
has widened to include involving twentyeight schools over a two year
period and two full time facilitators. Through this round table we
invite other researchers to discuss their experiences with working with
teachers to coconstruct mathematical inquiry communities in low
socioeconomic communities. We seek other researchers' input in
possible development of further work in investigating ways to support
minority students (for example, Pasifika students) in learning
proficient mathematical practices within inquiry communities.

Enhancing Productive Mathematical Noticing During Lesson Planning with Lesson Play
Halilah Bte Salim Alkhatib, Chen Ailing, Winnie Koh Mei Ling, Kang Hway Choon, & Choy Ban Heng
Good lesson planning is an important part of
effective teaching, but it can be very challenging to plan lessons that
focus on working with students' reasoning In this project, we aimed
to sharpen teachers'focus on facilitating students' mathematical
reasoning by making teachers' mathematical noticing more productive.
The key question guiding the inquiry was: How teachers could notice
students'reasoning more productively? The project took place across
two groupsâ€”a lower and an upper secondary group; involving 11 teachers
at a Secondary School in Singapore. Guided by Choy's (2013) framework
of productive noticing, we incorporated lesson play into our existing
lesson study protocol to plan teachers' responses to students' reasoning. More specifically, we applied the 'Threepoint Framework' to help us focus on key ideas, students' cognitive difficulties, and
how we might support students in their learning of Set Language and
Notation (lower secondary) and Solving Trigonometric Equations (upper
secondary). Initial findings suggest that teachers began noticing
salient mathematical features of students' thinking during the study.
The study has heightened our sensitivity towards students' thinking
and provided opportunities to hone our questioning techniques. In this
round table discussion, we hope to seek suggestions to enhance our
noticing for future iterations.

Exploring Mindfulness within Mathematics Learning Environments
Joanna Higgins & Raewyn Eden
The emotional climate of classrooms is important
to the teaching and learning of mathematics. To date there have been few
studies connecting emotions to learning environments. Starting from the
premise that teaching is emotional work, we are interested in exploring
physical, cognitive and psychological effects associated with a
mindfulness intervention in Year 78 mathematics classrooms. The
potential benefits of mindfulness â€“ the cultivation of nonjudgmental
awareness and attention to the present moment â€“ are an emerging field
of inquiry for psychology and education researchers. For instance,
findings from a growing body of studies suggest that a focus on
breathing for a short time each day can mediate the impact of negative
emotions in classroom events. The roundtable will begin by discussing
emerging theoretical frameworks for understanding emotions with a focus
on mindfulness practices in classrooms, and associated methodologies for
studying mindfulness. The session will provide an opportunity to
discuss: teachers' and students' increased awareness of their
emotional reactions to classroom events; the connection between a
breathing intervention and mathematics teaching and learning; and the
potential of a mindfulness intervention to improve the emotional climate
of learning environments.

Factors Influencing Student Decision on Senior Secondary School Subjects
Michael Jennings & Peter Adams
There are substantial and ongoing concerns in the
Australian and international secondary and tertiary education sectors
about students' transition from secondary to tertiary mathematics.
Declining enrolments in university mathematics and increasing failure
rates in first year are often attributed to falling participation in
advanced mathematics in secondary school and less stringent university
entry requirements, which have adversely affected students' mathematical
preparedness for university study. In this round table I will present
data collected on three topics: reasons for choosing/not choosing
advanced mathematics in secondary school; attitudes towards learning
mathematics at school; and attitudes towards learning mathematics at
university. These data were collected from four separate groups of
people: secondary school mathematics students; secondary school
mathematics teachers; university mathematics academics; and university
mathematics education academics. The results suggest that there are
distinct differences in students' thoughts depending on which
mathematics they study in the last two years of secondary school. There
are also differences between what students say are the reasons for their
subject choice and what mathematics academics think are the reasons.
The data also shed light on subject choice myths. This presentation is
part of a twoyear statewide longitudinal project that is investigating
the transition from secondary to tertiary mathematics.

Inspiring Mathematics and Science in Australian Teacher Education
Merrilyn Goos, Judy Anderson, Kim Beswick, JudyAnne Osborn,
Caz Sandison, James Dalitz, Kathryn Holmes, & Elena PrietoRodriguez
In Australia, preservice teacher education
programs are structured so that future teachers of secondary school
mathematics and science learn the content they will teach by taking
courses in the university's schools of mathematics and science, while
they learn how to teach this content by taking contentspecific pedagogy
courses in the school of education. Such program structures provide few
opportunities to interweave content and pedagogy in ways that help
develop professional knowledge for teaching. This round table session
will invite feedback on the early stages of a national project that is
developing interdisciplinary approaches to mathematics and science
preservice teacher education. The project aims to foster collaborations
between academics from different communities of practice  mathematics, science, education  in order to design and implement new
teacher education approaches. It is hoped that these approaches will
institutionalise new ways of integrating the content and pedagogical
expertise of STEM academics and mathematics and science educators to
enrich three key stages in teacher preparationâ€“ recruitment into
teaching careers, participation in the preservice program, and
continuing professional learning following graduation. The goal of this
Round Table session is to engage participants as critics, interpreters,
and potential adopters of the products and processes of our project.
Topics for discussion could include: the structures and cultures of STEM
teacher education programs in different institutional, socioeconomic
and geographical contexts; examples of innovative teacher education
approaches being implemented in other universities; barriers to and
enablers of interdisciplinary collaboration.

Mathematics Support Teacher (MST): How Do We Help Students Maintain Mathematical Gains?
Fiona McDiarmid
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 aiming 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 study is aimed at
tracking the progress of students who participated in the intervention
in either 2011 or 2012. Longitudinal data were received from eight
schools from different regions across New Zealand. Preliminary analysis
of the results indicates that approximately half of the students
maintained their progress and are on track to achieving at the expected
level in relation to the mathematics standards. The remaining students
have maintained their learning gains but have not continued to
accelerate their mathematics progress. Approximately five percent of the
students have made limited or no measurable progress. This round table
forum presents longitudinal data after involvement in a mathematics
intervention. It will provide an opportunity for participants to review
the data, discuss findings and identify solutions for those students not
sustaining progress after the MST intervention.

Numeracy ... Scientificity: Identifying, Linking and Using the 'Big Ideas' of Mathematics and Science for More Effective Teaching
Chris Hurst
Recent curriculum documents such as the Common
Core State Standards for Mathematics and the Australian Curriculum:
Mathematics F to 10 continue the practice of presenting content in a
linear and compartmentalized manner and appear not to accentuate the
links and connections that are present in the 'big ideas'of
mathematics. Both documents seem to pay lip service to the 'big
process ideas' or proficiencies which should be the vehicles for
developing and making explicit links between and within the 'big
content ideas'. To some extent, the same criticism could be levelled
at the recently developed Australian Curriculum: Science F to 10
although that document at least embeds key process ideas as one of the
three strands called Science Inquiry Skills. However, it is suggested
that it may be beneficial to rethink the nature of key content and to
organise it for teaching based on the 'big ideas' of mathematics and
science, emphasizing the links and connections within and between them.
In attempting to deal with the 'crowded curriculum', teachers would
do well to consider similarities between 'big mathematical ideas' and 'big scientific ideas' and to make connections explicit for
children. For many teachers, this would represent a change in the way in
which they view content knowledge. Teachers should be encouraged to
actively seek links and connections within and between concepts and
bodies of knowledge and explicitly show children how those links exist
and can be used. This round table will consider these and related issues
such as the nature of 'big ideas', models for numeracy and what an
equivalent model for its scientific equivalent might look like.
