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Title
 
Content
MERGA 2016 Contents
 
Preface
 
List of Reviewers
MERGA 39 Reviewers
 
Keynote Address
How Theory-Building Research on Instruction can Support Instructional Improvement: Toward a Modelling Perspective in Secondary Geometry 183 downloads
Patricio Herbst
Learning by Leading: Dynamic Mentoring to Support Culturally Responsive Mathematical Inquiry Communities 186 downloads
Roberta Hunter, Jodie Hunter, Trevor Bills, & Zain Thompson
Whither Statistics Education Research? 184 downloads
Jane Watson
 
Practical Implication Award
Let’s Count: Improving Community Approaches to Early Years Mathematics Learning, Teaching and Dispositions through Noticing, Exploring and Talking about Mathematics 191 downloads
Bob Perry, Ann Gervasoni, Anne Hampshire, & Will O'Neill
 
Symposium
A highly capable Year 6 student’s response to a challenging mathematical task 186 downloads
Sharyn Livy, Naomi Ingram, Marilyn Holmes, Chris Linsell, & Peter Sullivan
Perceptions of Challenging Tasks and Achievement by New Zealand Students 189 downloads
Chris Linsell, Marilyn Holmes, Naomi Ingram, Sharyn Livy, & Peter Sullivan
Teacher actions that encourage students to persist in solving challenging mathematical tasks 185 downloads
Naomi Ingram, Chris Linsell, Marilyn Holmes, Sharyn Livy, & Peter Sullivan
The intent and processes of a professional learning initiative seeking to foster discussion around innovative approaches to teaching 184 downloads
Peter Sullivan, Marilyn Holmes, Naomi Ingram, Chris Linsell, Sharyn Livy, & Melody McCormick
 
Research Paper
Young Children’s Drawings in Problem Solving 185 downloads
Kamariah Abu Bakar, Jennifer Way, & Janette Bobis
Assessing Children’s Progress in Taking Intellectual Risks in a Mathematical Inquiry Classroom with a Positive Learning Approach 185 downloads
Sue Allmond, Jude Hillman, Karen Huntly, Katie Makar, & Mia O'Brien
Investigating the Impact of Context on Students’ Performance 183 downloads
Felipe Almuna Salgado
Developing a Theoretical Framework for Classifying Levels of Context Use for Mathematical Problems 188 downloads
Felipe Almuna Salgado
Whither Ability Grouping: Changing the Object of Groupwork 185 downloads
Glends Anthony, Roberta Hunter, & Jodie Hunter
Learning at the Boundaries: Collaboration between Mathematicians and Mathematics Educators Within and Across Institutions 185 downloads
Anne Bennison & Merrilyn Goos
Discerning the Shared Beliefs of Teachers in a Secondary School Mathematics Department 184 downloads
Kim Beswick
Opening Up the Profession: Inclusive Messages for Pre-Service Teachers from a Pedagogy Textbook 185 downloads
Amber Brass
Preparing for the Numeracy Skills Test: Developing a Self- Perception for Success 181 downloads
Leni Brown & Lisa O'Keeffe
Constructing Classroom Contexts that Engage Students in the Learning of Mathematics: a Teacher’s Perspective 183 downloads
Raymond Brown & Trevor Redmond
Teachers’ Use of a Pedagogical Framework for Improvement in Mathematics Teaching: Case Studies from YuMi Deadly Maths 179 downloads
Merilyn (Lyn) Carter, Tom Cooper , & Robyn Anderson
Large-Scale Professional Development Towards Emancipatory Mathematics: The Genesis of YuMi Deadly Maths 185 downloads
Tom Cooper, & Merilyn (Lyn) Carter
The Priorities and Challenges of Primary Teachers’ Knowledge in their Mathematics Planning. 187 downloads
Aylie Davidson
A rich assessment task as a window into students’ multiplicative reasoning 185 downloads
Ann Downton & Vince Wright
The Relevance of Mathematics: Leaders and Teachers as Gatekeeper for Queensland Senior Calculus Mathematics 187 downloads
Michael Easey & Jim Gleeson
Key Elements of a Good Mathematics Lesson as Seen by Japanese Junior High School Teachers 181 downloads
Marlon Ebaeguin & Max Stephens
“Mathematics is just 1 + 1 = 2, what is there to argue about?”: Developing a framework for Argument-Based Mathematical Inquiry 185 downloads
Jill Fielding-Wells
Interpreting Association from Graphical Displays 187 downloads
Noleine Fitzallen
Numeracy for Learners and Teachers: Evaluation of an MTeach coursework unit at Monash University 187 downloads
Helen Forgasz & Jennifer Hall
Numeracy and Australian teachers 194 downloads
Helen Forgasz & Gilah Leder
Early Childhood Teachers’ integration of ICTs: Intrinsic and Extrinsic Barriers 180 downloads
Jillian FOx, Carmel Diezmann, & Janeen Lamb
Designing Online Learning for Developing Pre-service Teachers’ Capabilities in Mathematical Modelling and Applications 185 downloads
Vince Geiger, Liz Date-Huxtable, Rehez Ahlip, Marie Herberstein, D. Heath Jones, E. Julian May, Leanne Rylands, Ian Wright, and Joanne Mulligan
Teachers as Designers of Effective Numeracy Tasks 195 downloads
Vince Geiger
Hurdles in Acquiring the Number Word Sequence 187 downloads
Peter Gould
Professional learning in mathematical reasoning: Reflections of a primary teacher 189 downloads
Sandra Herbert, Wanty Widjaja, Leicha A. Bragg, Esther Loong, & Colleen Vale
Investigating Declining Enrolments in Secondary Mathematics 187 downloads
Gregory Hine
Collaboration around observation of teaching: Powerful professional learning 185 downloads
Louise Hodgson
Improving the efficiency of problem-solving practice for children with retrieval difficulties 186 downloads
Sarah Hopkins & Celeste de Villiers
Assessing children’s strategy choices to make better decisions about remediation 184 downloads
Sarah Hopkins
A case study on the impact of teacher mathematical knowledge on pedagogical practices 183 downloads
Sally Hughes
Sliding into Multiplicative Thinking: The Power of the ‘Marvellous Multiplier’ 180 downloads
Chris Hurst & Derek Hurrell
Assessing Children’s Multiplicative Thinking 182 downloads
Chris Hurst & Derek Hurrell
Commognitive Analysis of Undergraduate Mathematics Students’ Responses in Proving Subgroup’s Non-Emptiness 180 downloads
Marios Ioannou
Investigating the Interconnections between Cognitive, Affective and Pedagogical Issues in the Learning of Group Theory 178 downloads
Marios Ioannou
An Ecological Analysis of Mathematics Teachers’ Noticing 182 downloads
Dan Jazby
Middle Leadership: Critical Variables in Building and Implementing Digital Reforms in Primary Mathematics Education 181 downloads
Robyn Jorgensen (Zevenbergen), Janeen Lamb, & Kevin Larkin
A Collaborative and Reflective Approach to Teaching for Metacognition 183 downloads
Berinderjeet Kaur & Lai-Fong Wong
Changes in Teachers’ Knowledge and Beliefs about Mathematics and Mathematics Teaching: A Case Study 180 downloads
Laurinda Lomas & Doug Clarke
Sustainable improvements in student mathematics learning and disposition as a result of Prepare 2 Learn intervention 180 downloads
Bernadette Long
Spatial Reasoning Influences Students’ Performance on Mathematics Tasks 179 downloads
Tom Lowrie, Tracy Logan, & Ajay Ramful
Early mathematical competencies and later outcomes: Insights from the longitudinal study of Australian children 179 downloads
Amy MacDonald & Colin Carmichael
“I believe the most helpful thing was him skipping over the proof”: Examining PCK in a senior secondary mathematics lesson 178 downloads
Nicole Maher, Helen Chick, & Tracey Muir
Improving the Intellectual Quality of Pedagogy in Primary Classrooms through Mathematical Inquiry 177 downloads
Katie Makar
Children noticing their own and others’ mathematics in play 176 downloads
Amber Marcus, Bob Perry, Sue Dockett, & Amy MacDonald
The Role of Reasoning in the Australian Curriculum: Mathematics 176 downloads
Catherine McCluskey, Joanne Mulligan, & Mike Mitchelmore
Exploring the Cognitive Demand and Features of Problem Solving Tasks in Primary Mathematics Classrooms 177 downloads
Melody McCormick
A Professional Experience Model for Primary Pre-service Teachers Specialising in Mathematics 177 downloads
Heather McMaster & Michael Cavanagh
Young Indigenous Students en Route to Generalising Growing Patterns 177 downloads
Jodie Miller
Developing Conceptual Understanding of Fractions with Year Five and Six Students 177 downloads
Judith Mills
No more ‘What are we doing in maths today?’ Affordances of the Flipped Classroom Approach 178 downloads
Tracey Muir
Experiencing mathematics for connected understanding: using the RAMR framework for accelerating students’ learning 176 downloads
David Nutchey, Edlyn Grant, & Lyn English
A Preliminary Analysis of the Linguistic Complexity of Numeracy Skills Test Items for Pre Service Teachers 176 downloads
Lisa O’Keeffe
The Power of Creativity: A Case-Study of a Mathematically Highly Capable Grade 5 Student 177 downloads
Linda Parish
Competence with Fractions in Fifth or Sixth Grade as a Unique Predictor of Algebraic Thinking? 178 downloads
Catherine Pearn & Max Stephens
It’s Only Maths: The potential impact of a mentoring project to ameliorate mathematics anxiety in teacher education students 178 downloads
Timothy Perkins
History-infused Lessons in Introductory Calculus at the Secondary level: Students’ Learning and Perceptions 177 downloads
Wei Beng Poh & Jaguthsing Dindyal
Supporting Teachers Developing Mathematical Tasks With Digital Technology 178 downloads
Iresha Ratnayake, Greg Oates & Mike Thomas
Investigating Students’ Mathematical Difficulties with Quadratic Equations 179 downloads
Bronwyn Reid O’Connor & Stephen Norton
Learning from Lessons: Teachers’ Insights and Intended Actions Arising from their Learning about Student Thinking 176 downloads
Anne Roche, Doug Clarke, David Clarke, & Man Ching Esther Chan
Supporting Children with Special Needs in Learning Basic Computation Skills: The Case of Mia 178 downloads
Thomas Rottmann & Andrea Peter-Koop
Insights from a financial literacy task designer: The curious case of problem context 177 downloads
Carly Sawatzki
High school students’ knowledge of a square as a basis for developing a geometric learning progression 178 downloads
Rebecca Seah, Marj Horne, & Adrian Berenger
Understanding Time: A Research Based Framework 179 downloads
Margaret Thomas, Doug Clarke, Andrea McDonough, & Philip Clarkson
Time: Assessing Understanding of Core Ideas 177 downloads
Margaret Thomas, Andrea McDonough, Philip Clarkson, & Doug Clarke
Developing Teachers’ Reasoning about Comparing Distributions: A Cross-Institutional Effort 177 downloads
Dung Tran, Hollylynne Lee, & Helen Doer
Quality of Life: Domains for Understanding Maths Anxiety in First Year Pre-service Teachers through Identity Work 177 downloads
Sue Wilson
Developing mathematical content knowledge for teaching: One preservice teacher and her planning. 175 downloads
Susanna Wilson
Visualisation and Analytic Strategies for Anticipating the Folding of Nets 176 downloads
Vince Wright
Developing early Place-value Understanding: A Framework for Tens Awareness 177 downloads
Jenny Young-Loveridge & Brenda Bicknell
Distribution of high achieving students on NAPLAN across schools: Implications for policy and teacher training 177 downloads
Simone Zmood
Staff Development: The Missing Ingredient in teaching Geometry to Year 3 Students 179 downloads
Kevin Larkin, Peter Grootenboer, and Peita Lack
 
Short Communication (abstract only)
A Five Question Approach to Teaching Mathematics
John Ley

According to Clements (2003), Dinham (2013) and Sullivan (1992, 2011, 2012) there is an urgent need for change to the way in which mathematics is taught in Australian Schools. The five question approach (FQA) to teaching mathematics, developed during my thirty years of secondary teaching, occurs at the commencement of each mathematics lesson. It is the subject of my doctoral research, currently at the early data analysis stage. The research investigates if the FQA results in an increase in student academic achievement, perceived and / or actual, and engagement.

A Study of the Relationship between Conceptions of Mathematics and NAPLAN Numeracy Test Results
Sven Trenholm, Mohan Chinnappan, Bronwyn Hajek, Helen Ashman,& Amie Albrecht

Arguably, the NAPLAN Numeracy test is regarded as an effective instrument in gauging students’ ability to integrate multiple pieces of information during the course of solving real-life problems (Lawson & Chinnappan, 2016). In this study, students were administered the conceptions of mathematics questionnaire (Crawford, Gordon, Nicholas & Prosser, 1998) alongside the grade 9 non-calculator NAPLAN numeracy test. We report on the results of two correlational analysis (n=61 and n=68) for students taking two different introductory level undergraduate mathematics courses. The results raise questions about the claim that NAPLAN Numeracy tests are effective in assessing knowledge connectedness in mathematical thinking.

An Analysis of Senior Secondary Mathematics Written Examinations with Respect to Calculator Use
Hazel Tan

Prior research studies on senior secondary students’ use of advanced calculators (graphics and CAS calculators) have found that some students tended to either underutilise calculators by preferring to solve even calculator-required questions by hand, while others over-rely on calculators for computations and methods that can be replicated easily by hand. Calculator use is also known to be influenced by assessment requirements. Thus this study aims to investigate the questions in the senior secondary mathematics written examination papers in Singapore and Victoria for the kinds of expected calculator use. Preliminary findings will be presented and the implications discussed.

An Application of the Five Processes of Mathematical Thinking to Numeracy Sample Items
Lisa O’Keeffe & Patrick Johnson

Numeracy skills testing is being introduced for pre-service teachers (PSTs) across Australia in the coming years. ACER and the Australian Government (Dept. of Education and Training, 2015) state that these skills tests are intended to demonstrate that PSTs are in the top 30% for numeracy. Given that the South Australian Literacy and Numeracy Strategy (Department for Education and Child Development, 2013, p.8) partially defines numeracy as an “ability to use mathematical information to solve problems” it is logical to assume that categories of mathematical thinking should be evident in the numeracy test items. As part of their initial analysis, the authors are exploring an application of the National Council of Teachers of Mathematics’ (NCTM) five processes of mathematical thinking (Representation, Reasoning and Proof, Communication, Problem Solving, and Connections) as a potential for mathematical characterisation of such numeracy items.

An Exploratory Investigation on the Influence of Mathematical Modelling on Students' Real-world Problem Solving Skills
Siew Yee Lim, Hui Yi Ting, Deepa Patel, Linda Shear,& Eddie Tay

This study aims to investigate the influence of mathematical modelling on students’ real-world problem solving skills. In mathematical modelling, students have to convert real-world problem scenarios into mathematical problems. They then solve the mathematical problems using known mathematical techniques before interpreting and 689 translating the solutions for the scenarios. Using pre and post surveys, scoring of students’ real-world problem solving skills, classroom observations as well as focus group discussions, this study investigated how mathematical modelling influences Grade 9 students’ perception of mathematics in practical situations, as well as how mathematical modelling influences teachers’ practices to provide students with the opportunities to form links between theoretical and real-world situations.

Beliefs about Mathematics and Teaching when Crossing Subject Boundaries to Teach Mathematics
Colleen Vale

Previous researchers have explored the relationships between a teacher’s beliefs about the mathematics discipline and school subject, their beliefs about the teaching of mathematics and their teaching practice. In Australia, there are many teachers who cross subject boundaries to teach mathematics as an out-of-field teacher. Exploring out-of-field teachers’ beliefs about mathematics and the teaching of mathematics will enable us to understand more about the way in which their in-field beliefs, school context and practices influence their beliefs and practice when teaching mathematics. Some preliminary findings from Out-of-Field Teaching: Sustaining Quality Practices Across Subjects project will be presented.

Breaking the Barrier Between Learning and Assessment
Kristen Di Cerbo & Denise Jacobsson

Use of digital environments has the potential to allow us to break down barriers between learning and assessment by allowing us to gather data about students' proficiency as they interact in the learning environment. This work describes a pilot of a learning system including an online game, online digital activities, and in-person classroom activities all aligned to a common learning progression describing how students learn the concept of area. This work demonstrates how activities can be designed to align to the progression and presents preliminary evidence of both learning and assessment from a tryout with more than 300 students.

Consumer and financial literacy education: Engaging primary teachers and their students in mathematics
Catherine Attard & Matt Thompson

This short communication will report some initial findings from a multiple case study that investigated the use of consumer and financial literacy as a tool to improve student engagement with mathematics in low socio-economic schools. Data from one of the participating schools will be discussed and the impact of the study in relation to improving student engagement, building community awareness of consumer and financial literacy and improving teacher capacity will be shared.

D.A.T.A.: Data, Analysis, Then Action - National Statistics Initiative
Peter Howley

Australian Teachers are saying “a rewarding experience”, “a great competition”, “21st Century learning at its best”, “a resounding success…motivates and engages students”. Mentors are saying “I was inspired by their keenness”, “provides students a unique opportunity”. What are they talking about? The successful annual National Schools Statistics Poster Competition! This talk will: outline the national project-based learning activity which facilitates boundary encounters (between secondary, tertiary, and industry sectors and students having varied backgrounds and areas of interest) and develops key communication, research and quantitative skills; and describe coming additions as part of a national initiative to assist students with statistics.

How Middle Years Students Create and Utilize Data Models to Estimate Population: A Case Study
Takashi Kawakami & Kosuke Mineno

Modelling ideas are now emphasised in the teaching and learning of statistics (e.g., Kawakami, 2015). This presentation reports on a case study examining how Year 9 students (14-15 year olds) created and utilized data models in estimating and predicting Japanese population by 5-year age group. The analysis illustrated that the students perceived the role of data and the necessity of shuttling between data and context in developing data models to understand, estimate and decide on the trend of population. Findings will inform educators on how to strengthen the link between statistical ideas and modelling ideas in the teaching and learning of statistics.

Increasing Parental Involvement
Monica Wong & Nicola Cull

Epstein and Sheldon (2006) posit that students’ learning and development are enhanced when: (a) families-parents/carers, (b) the school and (c) the local community work together to guide and support them. Similarly, Goos (2004) found that to build successful, sustainable long-term collaborative mathematics programs, parental and community involvement is pivotal. When these principles were implemented in a mathematics homework program which enabled parents to become involved and assist with their children’s learning both students and parents developed more positive feelings and attitudes towards mathematics (Van Voorhis, 2011). This presentation explores the introduction of a mathematics club in two primary schools in low SES areas of Sydney and the activities undertaken to engage the school community.

Reconceptualising Curriculum Design to Promote Students’ Conceptual Understanding of Mathematics: A Focus on Fractions
Maria Quigley

This report discusses the preliminary stages of a study into the impact of reconceptualising curriculum design on the teaching of fractions in Kindergarten to Year 2. A mixed methods approach is engaged using a questionnaire to explore current teacher practices and a diagnostic assessment instrument to determine Year 3 students’ current understanding of fractions. Teachers will have training on using the new curriculum documentation and will be interviewed and observed in the classroom implementing both the old and new approaches.

Secondary student’s perceptions of what is important when they are learning Mathematics.
Bruce White

Students' perceptions of what teachers do and what students themselves do that helps them learn gives an insight into what might be effective teaching and learning strategies in a mathematics classroom. This paper looks at student perceptions of teaching in general but also specifically in relation to the teaching and learning of mathematics. Data was collected from students at two South Australian schools via an online survey on a range of topics two of the topics examined the students perceptions of what teachers did to help them learn and what they as students did that helped them learn. The initial analysis of the results of the survey will be presented and will highlight areas that students think are most important in learning mathematics.

Student views on 21st Century Teaching and Learning of Mathematics
Bruce White

The term 21st Century Teaching & Learning highlights the 4Cs of collaboration, critical thinking, creativity and communication and is often connected with the use of technologies, in particular with the opportunities that being online offers. This presentation reports on a study examining students perceptions of the mathematics teaching and learning at a large suburban high school in South Australia that has made a significant effort to develop 21st Century Teaching and Learning across the school which incorporated a significant focus on the use of technologies. This presentation will report on students impressions of the effectiveness of the pedagogies used in mathematics and more generally on aspects of blended learning which was a focus for the changed pedagogy. The study indicated that over 90% of the students indicated that the students for the new approaches were effective or very effective for learning mathematics. Also, the student text responses indicated that they were using it to access materials out of hours, with senior year’s students commenting how they found it very useful for revision when the mathematics teachers uploaded the Interactive Whiteboard recordings.

Teaching financial literacy for social justice in mathematic classrooms
Levon Blue & Peter Grootenboer

Financial literacy is often taught from a skills perspective focusing on budgeting. In this presentation, we discuss teaching financial literacy for social justice in mathematics classrooms. Conventional financial literacy curricula are taught from a deficit position focusing on the individual and their ability to make ‘effective’ financial decisions. We explore the role of identity and socio-economic status (SES) in financial literacy education and find that individuals are ‘blamed’ for their SES, or ‘affirmed’ for their high SES under the conventional FLE curricula. A more compassionate approach to FLE for mathematics classrooms is discussed in this presentation.

The reSolve: Mathematics by Inquiry Protocol
Steve Thornton

reSolve: Mathematics by Inquiry is an Australian Government funded project to develop and disseminate a suite of high quality, innovative mathematics resources for students and teachers from F to Year 10 incorporating contemporary mathematics pedagogy exemplifying an inquiry approach. The guiding principles behind the project are elaborated in the reSolve: Mathematics by Inquiry Protocol, which addresses the elements of mathematical purpose, challenge and access, and development of a supportive knowledge-building culture. The poster will give examples of resources that exemplify the Protocol and offer participants an opportunity to discuss critical questions related to mathematics by inquiry.

Using Metaphors, Models and Multi-modalities when Teaching Year 2 Students Part-Part-Whole Relationships: A Fine Grained Analysis
Paula Mildenhall & Barbara Sherriff

Recent research findings indicate that using multimodal learning experiences to teach students about different models can be an effective teaching approach. Using a social semiotic lens within a participationist framework, this paper reports on a professional learning collaboration with a primary school teacher designed to explore the use of different metaphors, models and modalities. This case study was conducted in a teacher’s Year 2 classroom over two terms, with the focus on one specific child’s journey towards understanding the part-part-whole relationship model. Video was the predominant research tool. The initial findings have shown that the teacher was able to use specific gestures and language to support the concrete model being used. This paper explores how the metaphors, models and modalities were intertwined in the classroom discourse.

 
Poster (abstract only)
 
Round Table (abstract only)
Mathematical Inquiry Community
Katie Makar, Jill Fielding-Wells

In the Encyclopedia of Mathematics Education, the term “Inquiry-based Mathematics Education” (IBME) is described as a student-centered paradigm of teaching mathematics and science, in which students are invited to work in ways similar to how mathematicians and scientists work. This means they have to observe phenomena, ask questions, look for mathematical and scientific ways of how to answer these questions … interpret and evaluate their solutions, and communicate and discuss their solutions effectively. (Dorier & Maass, 2014, p. 300) The aim of this Round Table on IBME is to extend conversations within a community interested in teaching, learning, assessment and research on mathematical inquiry. We invite those interested in mathematical inquiry to participate and help to create a richer understanding of work being done in this area. In 2015, a Round Table to initially gauge interest in mathematical inquiry was held. Because of the large number of participants, there was little opportunity for discussion. At this Round Table, the aim is to separate into smaller areas of interest around particular themes. Possible strands around IMBE include: • Early Years • Primary • Secondary • Tertiary Mathematics • Initial Teacher Education • Professional Development • Assessment and Research Measures • Engaging with Stakeholders, Community and Policymakers • Classroom Norms and Argumentation • Theoretical and Methodological Perspectives • Social Justice and Inclusion • Affect • 21st Century Skills • Curriculum and Resources • Areas Needing More Research A possible outcome could be a symposium, publication and/or online community. New and previous participants equally welcome!

Mathematics and Task Design
Christine Mae, Janette Bobis, & Jennifer Way

Teacher knowledge is a significant issue for mathematics education (Sullivan, 2008a). Educational research has increasingly tried to identify characteristics of teacher knowledge for effective mathematics teaching and their influence on student learning outcomes (Bobis, Higgins, Cavanagh and Roche, 2012). With teacher performance standards now well iterated, the questions of “what [teacher] knowledge matters more, and why” (Bobis et al, 2012, p.1), remain central to improving mathematics education in Australia. This round table will outline the rationale and theoretical underpinnings of a study into the relationship between primary teachers’ subject matter knowledge and pedagogical content knowledge domains (Ball, Thames and Phelps, 2008). The Mathematics and Task Design Project is a research study involving 65 primary teachers within a system of schools. The study explores: (i) teachers’ understandings of area and volume when solving problems; the level of the tasks teachers design for their students; and, (iii) the nature of the feedback that teachers provide when analysing student work samples, and (iv) the relationships between each of these critical aspects of teacher knowledge. Data from the Task Design aspect of the study will be used to provide the stimulus for a discussion of the challenge of identifying and designing frameworks that can be applied to consistently analyse and describe the levels of opportunity and challenge within mathematical tasks.

Mathematics Education/Research in an Open and Big Data Era
Theodosia Prodromou

Data revolution enables citizens to have access to an enormous amount of complex data sets. These emerging data sets include: 1) large-scale open databases, 2) the growing use of big data, and 3) novel tools and ways of visualising data. The aim of this Round Table is to bring together a community of researchers, who focus on the role of increasingly open data access within mathematics education, the access to “big data”, teaching and learning of mathematics/Statistics, data visualisation in open data contexts, new statistical literacies in a new open data and big data era, the increasing need of research tools that affords opportunities to: 1) study classroom practices in sophisticated ways provided the access to "big data" and the open-access nature of information, and 2) ways of visualising data. I invite those interested in big data" and the increasingly open-access information to discuss their work or aspects of big data" and the increasingly open-access data in Mathematics/Statistics Education that are in need of research. A few questions are listed below to provoke conversation. Bring your own! 1. What is the role of open-access information (open data) and big data in Australian Mathematics classrooms? 2. What is the role of open-access information (open data) and big data in Mathematics research? 3. How can open-access information (open data) and big data be used in Mathematics (or Statistics) teaching and learning? 4. How do we need to change the way we think in terms of the nature of data and its availability, the ways in which data is displayed and used, and the skills that are required for its interpretation in order to take into account the full complexity of data? 5. What views must be included in a framework for teaching mathematical/Statistical literacy or data literacy in a new open data and big data era? 6. What the instructional and research dilemmas in data revolution era?

Mathematics Support Teacher (MST): What has been the impact on the students?
Deborah Gibbs & Fiona Fox

The Mathematics Support Teacher (MST) intervention was designed for students who have been identified as having severe learning difficulties in mathematics. The MSTs provide intensive mathematics teaching support with the aim to accelerate the students’ progress. The students were provided with four to five additional half hour lessons per week over a 15 to 20 week period. Initial involvement in the intervention has resulted in accelerated gains for the majority of these students. This case study involved interviewing past students who had maintained their learning gains after participating in the intervention in either 2011 or 2012. The students’ past teachers were also interviewed. Interviews were conducted using three schools from different regions across New Zealand. This round table forum presents impact stories of students, teachers and family after involvement in a mathematics intervention. It will provide an opportunity for participants to discuss the findings and consider the conditions and implications for students and their mathematics learning.

Provoking Contingent Moments: A New Model of Knowledge for Powerful Teaching at the Mathematical Horizon
Chris Hurst

Teacher knowledge continues to be a topic of debate in Australasia and in other parts of the world. There have been many attempts by mathematics educators and researchers to define knowledge needed by teachers to effectively teach mathematics, and a plethora of terms such 681 as mathematical content knowledge, pedagogical content knowledge, horizon content knowledge and specialised content knowledge have been used to describe aspects of such knowledge. Here, I put forward a new model for teacher knowledge that embraces aspects of earlier models and which focuses on the notions of contingent knowledge and the connectedness of ‘big ideas’ of mathematics to enact what is described as ‘powerful teaching’. Its power lies in the teacher’s ability to set up and provoke contingent moments to extend children’s mathematical horizons. The new model proposed here considers the various cognitive and affective components and domains that teachers require to enact ‘powerful teaching’. Contingency is described in Rowland’s Knowledge Quartet as the ability to respond to children’s questions, misconceptions and actions and to be able to deviate from a teaching plan as needed. It follows that a deeper level of knowledge might enable a teacher to respond better and indeed to plan and anticipate contingent moments. Taking this further and considering teacher knowledge as ‘dynamic’, I suggest that instead of responding to contingent events, powerful teaching is about provoking contingent events. In order to place genuine problem solving at the heart of learning, the idea is to actually plan for contingent events, to provoke them, and ‘set them up’. The proposed model attempts to represent that process.

Secondary teachers’ participation in STEM professional development: Challenges and opportunities
Judy Anderson & Gaye Williams

Governments and school systems are investing resources into science, technology, engineering and mathematics (STEM) education to address perceived shortages in these fields in university enrolments as well as in the workforce. Many initiatives have been implemented to capitalise on the increased focus on the STEM subjects in schools with universities frequently leading the way by offering engaging and worthwhile programs for students and teachers to promote the STEM subjects. However, many of these programs are ‘one off’ or ‘once a year’ events for small numbers of students in participating schools, potentially having little ongoing impact on the larger cohort of students in each school. A different initiative provides ongoing professional learning for teams of teachers of all STEM subjects from a small number of schools and focuses not just on improving pedagogy in each of the subject areas but encourages teachers to work in teams to design integrated approaches to curriculum. Our experiences with this professional development program has raised many questions about secondary teachers’ engagement and participation in working together in multidisciplinary teams to design integrated units of work. This roundtable will seek to explore the challenges in bringing such teams together, the challenges in implementing integrated approaches in secondary school contexts, and the opportunities afforded by integrating curriculum to enhance connections for students.

Teachers Collaborating to Accelerate Learning for Students Struggling in Mathematics
Jill Peterson, Anne Milburn, & Gaynor Terrill

Some mathematics learners need additional support to enable them to achieve at their expected level in relation to the New Zealand curriculum and the mathematics standards. Effective mathematics teachers can accelerate the learning of small groups of students in a relatively short period of time when they provide targeted support within their daily classroom programmes. This roundtable will begin by outlining the Accelerated Learning in Mathematics intervention model where teachers are given an opportunity to design an intervention response to accelerate the learning of students struggling in mathematics. We will discuss the early findings of a research project that examined the conditions in twelve schools that enabled a successful and sustainable intervention. Effective collaboration across a small group of teachers was identified as a common feature that promoted changed teacher practice and accelerated learning for targeted students. We will consider the different models of collaboration that lead to a successful intervention for these schools. Results showed that the collaborative nature developed in these schools led to an increased derivatisation of practice, a shared responsibility for accelerated outcomes, a greater willingness to take risks, and teachers became more reflective in their practice which led to deeper conversations around teaching and learning.

What is the Evidence for Best Practice in Mathematics Education?
Rosemary Callingham, Judy Anderson, Kim Beswick, Colin Carmichael, Vince Geiger, Merrilyn Goos, Derek Hurrell, Christopher Hurst, Tracey Muir, & Helen Watt

A recent national study aimed to provide an evidence base for best practice in mathematics education in Australia. Schools were included in the study on the basis of growth in NAPLAN 680 numeracy from 2011 to 2013, and 2012 to 2014, in Years 3 to 5 and Years 7 to 9. Using Bronfenbrenner’s (1989) Ecological Systems Theory as a structural framework, the study aimed to identify goal orientations and costs associated with achieving these goals at system, school, classroom, and individual level. Mastery goal orientations were defined as having a focus on connections within mathematics, relevance, and cooperation, whereas performance goal orientations were defined as having a focus on skill development, achievement, and competition. Findings suggest that successful schools, regardless of their social context, were consistent in their focus on mathematics across the school, in classrooms and among individuals. Mastery approaches were associated with reduced costs in terms of students’ perceptions of effort, social costs and mathematics difficulty. Teacher enthusiasm for mathematics teaching emerged as a key factor. Issues that arose from the study will provide starting point for discussion.