Conference Proceedings 2014


Curriculum in Focus: Research Guided Practice
Judy Anderson, Michael Cavanagh, Anne Prescott (Eds.)
List of Reviewers
List of Reviewers
Keynote Address
Custodians of Quality: Mathematics Education in Australasia Where from? Where at? Where to? 
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
A Framework for Teachers' Knowledge of Mathematical Reasoning
Sandra Herbert
A Primary Teacher's Developing Understanding of Mathematical Reasoning
Esther Yook-Kin Loong
Design-based 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 Edmonds-Wathen, 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: Pre-service Teachers as Half-empty or Becoming Fluent?
Megan Anakin & Chris Linsell
Foundation Content Knowledge: Pre-service Teachers' Attainment and Affect
Naomi Ingram & Chris Linsell
Foundation Content Knowledge: Providing support for pre-service teachers
Chris Linsell & Naomi Ingram
Personal Number Sense and New Zealand Pre-Service Teachers
Karen Major & Pamela Perger
Pre-service 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 Edmonds-Wathen, & Priscilla Sakopa
Students' Mathematical Reasoning and Teachers' Developing Understanding of Mathematical Reasoning
Colleen Vale, Leicha Bragg, Sandra Herbert, Esther Loong, & Wanty Widjaja
Technology-Enhancement for Papua New Guinean Professional Learning
Vagi Bino & Cris Edmonds-Wathen
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 Pre-service 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 Self-belief 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 Edmonds-Wathen, Priscilla Sakopa, Kay Owens, & Vagi Bino
Development of Fourth-grade 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 Under-Resourced 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 Edwards-Groves
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 Decision-Making Methods to Teachers' In-Class 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 Face-to-Face 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
Pre-Service 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 Pre-service Teachers' Understanding of Probability
Nicole Maher & Tracey Muir
PPELEM: A "Creative" Interviewing Procedure for Gaining Insights into Teacher and Student Mathematics-related 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 Mojica-Casey, John Dekkers, & Rose-Marie 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' Meta-Representational Competence through Integrated Mathematics and Science Investigations
Joanne Mulligan & Lyn English
The Complexity of One-Step 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 One-to-one 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 Pre-service 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 Andrew-Ihrke
Supporting the Development of Number Fact Knowledge in Five- and Six-year-olds
Jenny Young-Loveridge & Brenda Bicknell
Fostering the Promise of High Achieving Mathematics Students through Curriculum Differentiation
Simone Zmood
Comparing the Score Distribution of a Trial Computer-Based Examination Cohort with that of the Standard Paper-Based Examination Cohort
Nathan Zoanetti, Magdalena Les, & David Leigh-Lancaster
Arithmetical Strategies of a Student with Down syndrome
Rumi Rumiati
Developing Pre-Service 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 Hernandez-Martinez

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 large-scale 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 school-based 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 real-world 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 co-existence 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, 527-539. Williams, A. (2012). A teacher's perspective of dyscalculia: Who counts? An interdisciplinary overview. Australian Journal of Learning Difficulties, 2012(Oct), 1-16. 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 prior-to-school 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 Pre-service 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 pre-service teachers, mathematicians and educators in targeted interactions designed to ground pre-service teacher education in contexts relevant to daily life. The feedback module, designed for self-evaluation, involves pre-service 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 pre-service 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 (student-content, student-instructor and student-student) 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 de-emphasis on student-student interactions and an emphasis on computer-based student-content 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 5-7) students' engagement in mathematics. Motivation and engagement levels in mathematics were assessed prior to and at the completion of a year-long 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 (

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 two-year Ako Aotearoa-funded project that aims to identify, observe, and report on the full spectrum of desired learning outcomes for undergraduate mathematics, that is, not only content-based 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 Pre-Service Primary Mathematics Teachers: Working at the Coal-face without having to Look over your Shoulder
Timothy Perkins

Increasing numbers of students enrolled in primary pre-service 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 well-planned 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 pressure-cooker 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 model-and-practice 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 longer-term 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.

Self-efficacy and Attitude toward Mathematics: A Multigroup Invariance Analysis and Gender Difference
Elizar & I Gusti Ngurah Darmawan

The study examined multigroup invariance of Mathematics Self-efficacy 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 t-test 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, 65-87. 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 cross-cultural 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.

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 real-life situations. A pilot study was conducted aimed to identify the level of mathematical modelling skills of 183 pre-university 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 school-based 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, re-interpret 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 higher-order, open-ended 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 curriculum-wide 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.361-362). 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, 29-39. (in Japanese)

Using iPads for Assessment in the Mathematics Classroom
Naomi Ingram & Sandra Williamson-Leadley

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 (Williamson-Leadley & Ingram, 2014) that found this feature enabled three primary teachers to gather detailed evidence of how their students solved mathematical problems. References Williamson-Leadley, S., & Ingram, N. (2014). Show and tell: Using iPads for assesment in mathematics. Computers in New Zealand Schools: Learning, Teaching, Technology, 25(1-3), 117-137.

Using Metaphors to Investigate Pre-service 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 pre-service 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 pre-service 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. Twenty-seven 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

Cross-grouping (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 ability-grouping practices on student progress in mathematics. British Educational Research Journal, 30 (2), 279-239.

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. In-depth research into the existing beliefs and assessment literacy of mathematics teachers has implications for the review of curriculum-pedagogy-assessment 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 multi-factored, human-designed system and complexity theory appears to be useful in explaining phenomena within this system (Davis, Sumara & Luce-Kapler, 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 multi-mediator 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., & Luce-Kapler, 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), 25-43. 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:/

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, 948–967.

Round Table (abstract only)
Co-constructing 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 co-constructing mathematical inquiry communities. This year the project has widened to include involving twenty-eight 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 co-construct 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 groups—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 'Three-point 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 7-8 mathematics classrooms. The potential benefits of mindfulness – the cultivation of non-judgmental awareness and attention to the present moment – 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 two-year state-wide 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, Judy-Anne Osborn, Caz Sandison, James Dalitz, Kathryn Holmes, & Elena Prieto-Rodriguez

In Australia, pre-service 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 content-specific 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 pre-service 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 preparation– recruitment into teaching careers, participation in the pre-service 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, socio-economic 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 re-think 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.