## MERGA Conference Proceedings 2017

Full Proceedings |

Keynote Addresses |

The "M" in STEM: National PerspectivesAlan Finkel |

We are Still Learning to Integrate Affect (and Mathematics) into our Research |

Clements-Foyster Lecture |

In Search of Mathematical Structure: Looking Back, Beneath, and Beyond - 40 Years OnJoanne Mulligan |

Invited Panel: MERGA1 to MERGA40 |

Progressing Along a "Road Less Traveled": The History of School MathematicsM.A. (Ken) Clements |

Forty Years On: Mathematical Modelling in and for EducationPeter Galbraith |

Mathematics Performance and Future Occupation: Are They (Still) Related?Gilah C. Leder |

"Does This Mean That Kindergarten Will Be a Remedial Year?" |

Forty Years of Teaching Problem SolvingKaye Stacey |

Beth Southwell Practical Implication Award |

Framing, Assessing and Developing Children's Understanding of Time |

Symposia |

Reframing Mathematical Futures: Using Learning Progressions to Support Mathematical Thinking in the Middle Years |

Research Engagement and Impact in Mathematics Education |

STEM Practices: A Reconceptualization of STEM in the Early Years |

Transitions in Mathematics Education |

STEM Professional Learning: Evaluating Secondary School Teachers' and Students' Experiences |

Research Papers |

The Prevalence of the Letter as Object Misconception in Junior Secondary Students |

Developing Interactive ICT Tools for the Teaching and Learning of Vectors at A-Level |

Re-Examining a Framework for Teacher Identity as an Embedder-of-Numeracy |

Privileging a Contextual Approach to Teaching Mathematics: A Secondary Teacher's Perspective |

Partial Credit in Multiple-Choice Items How Might the Use of Apps Influence Students' Learning Experiences? Exploring a Socio-Technological Assemblage |

Entangled Modes: Social Interaction in Collaborative Problem Solving in Mathematics |

Investigating Teachers Perceptions of Enabling and Extending Prompts |

The Impact of a Measurement-Focused Program on Young Childrens Number Learning |

Snapshots of Productive Noticing: Orchestrating Learning Experiences Using Typical Problems |

The Argument from Matriculation Used by Proprietors of Victorian Secondary Schools Around 1900 |

That First Step: Engaging with Mathematics and Developing Numeracy |

"Maths Inside": A Project to Raise Interest in Mathematics |

Mastery Learning: Improving the Model |

The Interplay Between Pre-service Teachers' Intentions and Enacted Mathematical Content Knowledge in the Classroom |

Exploring Ways to Improve Teachers' Mathematical Knowledge for Teaching with Effective Team Planning Practices |

Primary School Mathematics Leaders' Views of their Mathematics Leadership Role |

Historical Perspectives on the Purposes of School Algebra |

Fourth-Graders' Meta-Questioning in Statistical Investigations |

Essential Topics for Secondary Mathematics Success: What Mathematics Teachers Think |

Hypothesis of Developmental Dyscalculia and Down Syndrome: Implications for Mathematics Education |

Gender and VCE Mathematics Subject Enrolments 2001-2015 in Co-Educational and Single-Sex Schools |

A Secondary Mathematics Teachers Perceptions of her Initial Attempts at Utilising Whiteboarding in her Classes |

The Development of Addition and Subtractions Strategies for Children in Kindergarten to Grade 6: Insights and Implications |

Teaching Fractions for Understanding: Addressing Interrelated Concepts |

Teachers' Understanding and Use of Mathematical Structure |

Initial Teacher Education Students' Reasons for Using Digital Learning Objects When Teaching Mathematics |

Peer Observation as Professional Learning about Mathematical Reasoning |

Exploring Reasons Why Australian Senior Secondary Students Do Not Enrol in Higher-Level Mathematics Courses |

Does (Problem-Based) Practice Always Make Proficient? |

Explicitly Connecting Mathematical Ideas: How Well Is It Done? |

Exploring Undergraduate Mathematics Students’ Difficulties with the Proof of Subgroup’s Closure under Operation |

Is Mathematics Education Worthy? From Mathematics for Critical Citizenship to Productivity Growth |

Grade 10 Students' Mathematical Understanding and Retention in a Problem-Based Learning (PBL) Classroom |

Engaging Pre-Service Mathematics Teachers in Creating Spatially- Based Problems in a 3D Virtual Environment: A CAVE2TM Experience |

Structure in the Professional Vocabulary of Middle School Mathematics Teachers in Australia |

Using Coding to Promote Mathematical Thinking with Year 2 Students: Alignment with the Australian Curriculum |

Online, Anytime, Anywhere: Enacting Flipped Learning in Three Different Secondary Mathematics Classes |

Learning from our Neighbours: The Value of Knowing Their Number History |

Generalising Fraction Structures as a Means for Engaging in Algebraic Thinking |

First-Year University Students' Difficulties with Mathematical Symbols: The Lecturer/Tutor Perspective |

11th Grade Students' Self-Regulated Learning in a Mathematics Problem-Based Learning (PBL) Classroom |

Statistics Instructors' Beliefs and Misconceptions About p-values |

Revisiting Friedrich Froebel and his Gifts for Kindergarten: What are the Benefits for Primary Mathematics Education? |

Perceived Changes in Teachers' Knowledge and Practice: The Impact on Classroom Teachers from Leader Participation in Whole-School Reform of Mathematics Teaching and Learning |

Examining the Impact of Lesson Structure when Teaching with Cognitively Demanding Tasks in the Early Primary Years |

Pricing: Exploring the Intersection Between Values, Maths, Finance, and Entrepreneurship |

Using Activity Theory to Understand a Mathematics Leader's Motivations and Use of Mathematical Knowledge for Teaching |

Exploring Critical Thinking in a Mathematics Problem-Based Learning Classroom |

Maths Anxiety: The Nature and Consequences of Shame in Mathematics Classrooms |

Graphic-Rich Items within High-Stakes Tests: Indonesia National Exam (UN), PISA, and TIMSS |

Pre-Service Teachers' and Tutors' Perceptions about the Value of Talk Moves |

Knowledge, Beliefs, and Innovative Curriculum |

Indigenous Teacher Education: When Cultural Enquiry Meets Statistical Enquiry |

Short Communications (Abstract Only) |

A Developing Framework for Identifying Young Children's Engagement with the Spatial Features of Play Spaces In this presentation, we report on our initial analysis of preschool children's engagement with spatial features of play spaces. The analysis focusses on noticing an awareness of mathematical pattern and structure (AMPS) evident in their play. The notion of spatial structure in play contexts will distinguish features of dynamic action such as children's movement through play spaces and the comparison, transformation, and navigation of 3D objects. The pattern and structure of mathematical concepts identified in this analysis will be compared with those evident in the Pattern and Structural Awareness Program (PASMAP, Mulligan & Mitchelmore, 2016). Future areas for research will be discussed. |

A Five Question Approach to the Teaching of Mathematics According to Clements (2003), Dinham (2012), and Sullivan (2013), there is an urgent need to change the way that mathematics is taught in Australian schools. The Five Question Approach (FQA) to teaching mathematics, developed during my 30 years of secondary mathematics teaching, occurs at the commencement of every lesson. It is the subject of my doctoral research, in which I am investigating if the FQA results in an increase in students' academic achievement, perceived and/or actual, and engagement. I will discuss the final data analysis and completion stage and some of the results and implications in this session. |

Challenging Teacher Perceptions: Those Children will Struggle No Matter What You Do to Them Teachers' perceptions of students' capabilities are particularly important in efforts to support instructional reforms. In this presentation, we explore the efforts of one teacher to resolve conflicts and tensions as she engaged with new practices associated with ambitious mathematics teaching. We look in particular at the influence of her diagnostic framing of students' mathematical capabilities and her beliefs about knowledge acquisition on her introduction of collaborative mixed-ability group work. |

Evaluating Learning Analytics of an Online System to Improve Teacher Education Students' Numeracy Skills Development Since 2015, all teacher education students in Australia are required to pass the Literacy and Numeracy Test for Initial Teacher Education (LANTITE) in order to meet accreditation requirements. The purpose of the test is to ensure that graduate teachers meet a satisfactory level of personal literacy and numeracy, roughly equivalent to the top 30% of the adult population. To support and help students prepare for this test, we created an online Literacy and Numeracy Practice System through the university's learning management system, Blackboard. In this short communication, we will report our initial findings from evaluating the learning analytics available with this system and discuss its impact on students' numeracy skills development. |

Exploring Mathematics Pedagogy in Collaborative Teaching Environments There is an increasing number of collaborative teaching environments in primary schools. A collaborative teaching environment is a teaching situation in which two or more teachers are responsible for the learning outcomes of a number of students commensurate with the ratio of the number of teachers. What might traditionally have been two single classrooms now have two teachers who are responsible for all students in a linked physical environment. We share initial results of a study in which we explore the ways that mathematics is taught in five collaborative environments, and compare these with best practice (Anthony & Walshaw, 2007). |

Exploring Primary Teachers' Conceptions of Mathematical Fluency: Are We Speaking the Same Language? Fluency in mathematics is defined in various forms, such as computational fluency, procedural fluency, and mathematical fluency. However, terms like "procedural" and "computational" often leave teachers interpreting fluency as simply being able to follow a set formula or to compute quickly. In this study, I explore practising primary teachers' conceptions of mathematical fluency, including how they define mathematical fluency, what features they associate with the term, and what relationship, if any, understanding plays within mathematical fluency. In this presentation, I will report some initial findings from the questionnaire used in Phase 1 of the data collection for this research project. |

Factors Influencing Student Selection of Senior Secondary School Mathematics Subjects Declining numbers of Advanced Mathematics (AM) students at secondary school are seen as a major issue for the future of STEM in Australia and internationally (Noyes, Wake, & Drake, 2011; Office of the Chief Scientist, 2014). Few large-scale research studies have investigated why students choose particular mathematics subjects. The aim of this empirical study was to identify the reasons why students choose or do not choose AM in the last two years of secondary school. Quantitative data were collected via surveys from secondary school mathematics students and teachers, and university mathematics lecturers. The surveys contained 20 statements on reasons for choosing/not choosing AM, covering intrinsic and extrinsic motivational factors. |

Fitness for Purpose of Tertiary Algebra Textbooks: An Arabic Case Study I will outline my PhD research into fitness for purpose of tertiary algebra textbooks used in Iraq in the education of pre-service teachers. I will consider (a) broad discourses and the use of introductions, examples, and explanations in light of cross-cultural studies such as the Japanese-U.S.A. comparison by Mayer et al., (b) pedagogies and assumptions about knowledge that can be inferred from the presentation style, referencing Magolda's theory linking forms to assessment to underlying theories of knowledge, (c) types of proof used in light of the theories of Harel and Sowder, and Stacey and Vincent, and (d) multilingual issues, given that some texts are translations and others are written in Arabic. |

High-Potential Mathematics Students and Their Mathematics-Related Activities Outside School Two decades ago, Csikszentmihalyi, Rathunde, and Whalen (1997) investigated what motivates young people to devote themselves to developing their potential. Studying mathematics offers long-term extrinsic rewards, but school mathematics may not be enjoyable or challenging. Hersh and John-Steiner (2011) suggested that supportive families can make a substantial difference to mathematics talent development. During a recent Australia-wide online survey of parents of school-aged children with high mathematical potential, data were gathered on the outside-of-school mathematics activities engaged in by the children. The data were examined by age and gender. The survey findings will be discussed in this presentation. |

Impact of Culture in Parental Control and Mathematics Achievement of their Children The presentation is based on a study guided by a conceptual framework developed on attributes of parental perceptions such as attitudes, beliefs, expectations, aspirations, values, and standards; parental involvement; and academic achievement of children. The participants were students (n = 128) and their parents (n = 85) from three secondary schools in Melbourne, Australia. The data were gathered by means of questionnaires and semi-structured interviews. The nature of research questions was both quantitative and qualitative, requiring a mixed-methods approach. It was found that there were significant differences in parental control between parents from European-Australian and Asian- Australian backgrounds. |

Improving Mathematics Curriculum Support for Indigenous Language Speaking Students A resource to support teaching the Australian Curriculum: Mathematics to students who speak English as an additional language or dialect (Australian Curriculum, Assessment and Reporting Authority, 2014), including Indigenous language speaking (ILS) students, provides language and cultural considerations and suggested teaching strategies linked to content descriptions. Critical analysis of this resource shows much scope for improvement. There is inconsistency between the language expectations of the resource and curriculum and the English language learning progressions of ILS students (Northern Territory Department of Education and Training, 2009). Few suggestions are specific for ILS students. I provide recommendations to improve the resource for teachers of ILS students, drawing on substantial prior research. |

Influential Factors for Effective Problem Solving Practice in Primary Mathematics Teachers Problem solving is described in Australian Curriculum as one of four proficiency strands (understanding, fluency, problem solving, and reasoning), and an integral component of mathematics teaching and learning. In this presentation, I discuss the preliminary stages of a study in which I am exploring teacher knowledge and dispositions of primary educators who effectively integrate problem solving to improve student mathematics learning, as well as identify any constraints and opportunities including the Australian Curriculum and professional learning experiences. Using a mixed methods approach, in this study, I am examining past survey data from the Encouraging Persistence Maintaining Challenge (EPMC) project to identify participants for subsequent case studies. |

Interbreeding Paradigms in Research on Mathematics Knowing and Learning Often, structuralism and constructivism are framed as competing paradigms in mathematics education from which one seems to have to choose. Here, we present emerging theoretical insights that recognize, rather than deny, individuals in the creation of the meaning of a mathematical concept, acknowledging the complex interaction between individual and subject matter: An individualâ€™s knowledge system is shaped by the meaning of a mathematical concept, but the knowledge system also shapes the meaning of a mathematical concept. These recent advances in research on mathematics knowing and learning allow interbreeding of seemingly contradicting paradigms. |

Linguistic Obstacles to Second Language Learners' Access to Mathematical Talk for Individualised Sense-Making Despite willingness, South African mathematics teachers teaching through a second language (L2) often struggle to get their learners engaging in exploratory talk. Using transcripts of talk in one South African teacher's Grade 4 mathematics lessons, plus interview data, we will examine and share some effects that children's diminished access to their strongest source of linguistic capital, mother tongue (L1), appears to have on their epistemological access to mathematical sense-making. Our findings suggest that use of L2 exacerbates existing inequalities in mathematics achievement across South Africaâ€™s socioeconomic sectors (sectors which, due to the legacy of apartheid, generally coincide with "race). |

Looking Inside the Black Box of Mathematics Teacher Noticing Research in mathematics teacher noticing, an important component of teaching expertise, has gained traction in recent years (Hunter, Hunter, Jorgensen, & Choy, 2016). Despite the advances in our understanding of teacher noticing as a high leverage practice (Sherin, Jacobs, & Philipp, 2011) and its application across a wide variety of contexts (Amador, 2016; Choy, 2016; Seto & Loh, 2015; Simpson & Haltiwanger, 2016; Wager, 2014), the "complex interactions of cognitive and perceptual processes and activities in dynamic situations (such as classrooms) have never been fully described in research on teacher noticing" (Scheiner, 2016, p. 234). Many of these processes remain hidden in the "black box" of noticing (Scheiner, 2016). This begs the question: How do we look inside the black box of teacher noticing? Scheiner (2016) suggests that researchers should draw on the perceptual cycle model (Neisser, 1976) and blend insights from cognitive sciences and human factors studies. In this short communication, we will present our initial idea of using wearable eye trackers to investigate teacher noticing. More importantly, we will invite feedback from the participants to explore how different video technologies could be used with the FOCUS Framework (Choy, 2015), developed for characterising productive noticing, to build a more comprehensive model of teacher noticing. |

Numeracy in Action in Family Shopping Experiences: A View from the Trolley In this short communication, we will introduce a current pilot study in which we are documenting the ways in which children and their families engage in everyday numeracy as they participate in shopping experiences. The study is underpinned by the notion that mathematical learning opportunities exist in the everyday activities of families, outside of the home, childcare centre, or school. Six families, with children ranging from 18 months to 10 years, were recorded whilst undertaking their shopping using a trolley mounted with a custom-built Go-ProÂ© camera rig (nicknamed "trolley-cam"). In this presentation, we will share selected "trolley-cam" data and vignettes of family numeracy engagement in action. |

Numeracy of Undergraduate Business School Students There is growing concern of a mismatch between the numeracy of students upon entry to university and the expectations of mathematical competence by university teachers (Marr & Grove, 2010). Poor numeracy has been identified as an issue for undergraduate students across a range of disciplines (Galligan & Hobohm, 2014; Hodgen, McAlinden, & Tomei, 2014; Linsell & Anakin, 2012). In this study, we investigated student numeracy in a compulsory 100-level business school statistics paper and found that 25% of students had numeracy levels below that expected of a competent Year 9 student (13-year-old). There was a highly significant relationship between low numeracy and failing quantitative papers. Students with low numeracy were not necessarily low ability students but lacked specific skills needed for quantitative work at university level. |

Practitioner Inquiry: Developing Capabilities in Mathematics Teachers The 21st century has seen a definite shift from teacher training towards teacher education in initial teacher education programmes. As a tertiary educator in a postgraduate initial teacher education program, I have seen the dichotomous thinking in which some of my education students embrace the idea of an inquiry-based mathematics approach with multiple solutions, while others, for whom mathematics has always been about finding a solution through learned steps of reasoning, face insurmountable challenges. While mathematics educators continue to advocate for a constructivist approach to learning, current practice has not overwhelmingly shifted from the symbol manipulation procedural approach. Could this be attributed to the notion that how we teach mathematics may be an internally learned habit from the way we were taught and that change is difficult because it requires that habit to be broken? Through the lived experiences of first-year teachers as inquiring practitioners, I explore the concept of practitioner inquiry and its implication for mathematics practitioners, and I consider how practitioner inquiry could be a catalyst for transforming mathematics education practices. |

South African Vocational Engineering Students' Conceptual
Understandings of Area, Surface Area, Volume, and Flow Rate Measurement:
A Case Study Measurement is particularly important for vocational Engineering students, for whom this is a key skill required in the workplace. It is also a skill that many students find extremely challenging. In this research, I explored, through task-based interviews, 35 South African vocational Engineering students' measurement conceptualisations of area, surface area, volume, and flow rate, in order to identify the specific learning needs of these students. The amount, degree, and type of mediation required were used to map the structure of the students' measurement conceptualisations. In this presentation, I reflect on these students' conceptual understandings and the implications that these hold for mathematics educators and researchers. |

Student Engagement in Mathematics Student engagement in mathematics and mathematics learning has been a concern for educators for many years (Attard, 2011). There have been many studies and reports that have suggested ways to improve student engagement in mathematics lessons, and these seem to offer some useful approaches. In this presentation, we discuss some of the key factors related to student engagement in primary mathematics learning as have been identified in the literature reviewed. In particular, pedagogical approaches will be explored, including the use of textbooks and investigations (Langer-Osuna, 2015), and classroom factors including teacher rapport (Attard, 2011) and peer interactions (Way, Reese, Bobis, Anderson, & Martin, 2016). Finally, we will discuss issues of student engagement visa-a -vis other variables including gender, previous achievement, and socio-economic status. The initial findings presented here will underpin some empirical work that is to be subsequently undertaken. |

Student Errors in a Mathematical Literacy Examination and the Correlated English Language Features Much research has established that when students have a poor command of the language of learning, teaching, and assessment, they experience a complex and deep learning disadvantage. This is the case for the majority of students in South African vocational colleges. In this study, I analysed the errors made by English language learners when writing a mathematical literacy examination in English, to determine whether the linguistic complexity of items influenced their responses. A statistically significant correlation was found between the linguistic complexity of items and certain errors, and it was possible to isolate which features of the language contributed to these errors. |

Students' Espoused and Enacted Theories in an Inquiry Mathematics Classroom Although inquiry classrooms as learning environments for mathematics have existed for many years, only recently has literature emerged on what it means from the perspective of students to learn mathematics in these contexts. Many researchers (e.g., Attard, 2011; Fraivillig, Murphy, & Fuson, 1999; Grootenboer & Marshman, 2016; Hunter & Anthony, 2011; McDonough & Sullivan, 2014) argue the importance of listening to students' views about their experiences in inquiry environments so that mathematics educators can better meet students' learning needs. At the same time, there is a need for recognition that what students say is important about learning mathematics may not connect to what they do while learning mathematics. Previous research studies either focus on students' perspectives about classroom practices in mathematics lessons (e.g., Cobb, Gresalfi, & Hodge, 2009; Hodge, 2008; Hunter, 2006) or their theory-in-use, through classroom observations, as they engage in mathematical activity (e.g., McCrone, 2005; Perger, 2007; Pratt, 2006). In contrast, in this presentation, I report on a group of students' (aged 9-10 years old) views and attitudes towards learning mathematics and their actions within the classroom while an inquiry mathematics community was being developed. |

Students' Reflections on Portfolio Assessment in Mathematics We discuss findings from a study that utilized students' portfolio entries to provide initial insights into students' views about portfolio assessment. Two Fijian Year 9 mathematics teachers implemented portfolios as a means of assessing student learning in measurement. While students in Jenny's class noted advantages in terms of learning new content and skills, their difficulties with portfolio assessment were often bounded by the various mathematical content. Students in Gavin's class provided insight into students' perspectives on value of portfolio assessment. Apart from discussing the various areas of content, students in Gavin's class pointed out many other benefits of portfolio assessment. |

Task Modification to Facilitate Creativity by Korean Prospective Mathematics Teachers Mathematical tasks play a critical role in the teaching and learning of mathematics. Tasks with different natures can provide different opportunities to promote studentsâ€™ mathematical thinking and understanding (Henningsen & Stein, 1997). Teachers can read and evaluate curriculum material focusing on tasks in order to modify them based on current reforms in mathematics education. Creativity is the essence of mathematics (Mann, 2006) and has been one of the main emphases of the Korean mathematics curriculum for decades. Various attempts in the curriculum to enhance student creativity in mathematics have been made. Attempts to promote creativity education have been made by leading mathematics teachers, and their approaches have been shared for several years in Korea (Lee, 2015). Some of these approaches to promote creativity have included promoting communication among students, practicing activity-based instruction, having students grasp fundamental ideas and knowledge in advance and focus on discussions in class, and planning and implementing storytelling lessons. Textbooks have also been redeveloped to include opportunities for creativity cultivation. When looking back over the past few years of creativity education in Korean mathematics classrooms, one of the biggest concerns has been that we have not paid much attention to the development of tasks that are appropriate for creativity development. The majority of the tasks for cultivating creativity used in textbooks and classes have not been suitable for cultivating creativity. This is because textbook authors and teachers have attempted to design tasks without fully understanding what to consider in developing a task suitable for creativity education. In this paper, I aim to determine what points need to be considered in the design of tasks for nurturing creativity. The definition of creativity varies, but I will discuss common and meaningful pursuits for creativity in school mathematics by analyzing some empirical data from the prospective teacher education course I ran in 2016. In order to maintain consistency with the curriculum, task design was aimed at increasing opportunities for creativity while retaining the learning objectives and content of existing textbooks. I will report the patterns that Korean prospective mathematics teachers tend to follow when they modify mathematical tasks in textbooks to facilitate creativity. |

Teachers Choosing Mathematics The basis for teacher confidence, or the lack of it, in teaching mathematics varies across the teaching cohort, with many reporting a range of degrees of comfort with their own mathematical abilities. Through the CHOOSEMATHS Project, we have found some interesting connections in the preliminary data and suggest some explanations for it. CHOOSEMATHS is a national project aimed at getting more girls and young women into mathematics through targeted teacher professional development, career awareness, and mentoring and support across mathematics. |

The Road to Transformative Healing of Mathematics Anxiety: A Case Study in Progress Significant proportions of pre-service teachers in Australia are having their enthusiasm to become capable and successful primary school teachers significantly dampened by their inability to work confidently and capably with mathematical content. Wilson and Gurney (2011) defined mathematics anxiety as "a learned emotional response characterised by a feeling that mathematics cannot make sense, of helplessness, tension and lack of control over one's learning" (p. 805). In an ongoing study into the mathematics anxiety experienced by pre-service primary teachers at an Australian university, one significant case study is explored in depth to highlight the mathematical journey of one participant in the study who has had a transformational experience through mentoring. |

The Use of Contextual Patterning Tasks with Young Pasifika and Maori Students in New Zealand Mathematics Classrooms Mathematical achievement of culturally diverse students is a challenge in many countries. Teaching in ways responsive to the cultures of our students is vital towards enhancing equity of access to mathematics achievement and putting educational policy (e.g., Ministry of Education, 2011) into practice. Similar to other countries, New Zealand has a changing student population that is increasingly culturally diverse. This population includes a large number of Pāsifika and Maori students whose educational results are characterised by unenviable statistics in which a large percentage are under-achieving compared to their peers. Educators frequently attribute this under-achievement to the learners themselves and position Pāsifika and Maori cultures as being mathematically deficient (Hunter et al., 2016). However, both Pāsifika and Maori cultures have a rich background of mathematics, including a strong emphasis on patterns used within craft design (Finau & Stillman, 1995). In this presentation, we report on the preliminary findings of a study in which we are investigating how contextual Pāsifika and Maori patterning tasks can potentially support young children to develop their understanding of growing patterns. |

Unidoodle Audience responses systems, commonly referred to as "clickers", are common in many university classes. Typically the clicker allows a student to enter an answer to a multiplechoice question. The teacher then displays the responses before (usually) either leading students in a discussion of the merits of each answer choice or asking students to discuss the question in pairs or small groups. The benefits of using clickers are well documented in the research literature and include improved classroom interaction, motivation and attendance, and improved student understanding. Unidoodle takes clickers one-step further as it enables students to submit freehand drawing and sketch-style answers. Students can write equations, draw graphs, or show their working. This allows teachers to receive much richer feedback from their students. In this short communication I will briefly present the Unidoodle system and the way in which I have used it in two first-year mathematics classes. I will then pose some discussion questions on the use of clickers. |

Use of Social Media in Preservice Mathematics Education Courses Facebook was used in preservice primary and secondary mathematics education units to provide a forum for students. The innovation was readily received by most of the students, but not all. Facebook was mainly used to share resources, but there was some discussion suggestive of a community of enquiry. In this presentation, I explain how to set up and run a closed Facebook group and explore the advantages and disadvantages of the system. These include the immediacy, access, and continuity Facebook provides, and the problems that inappropriate interactions generate. The research reported does not support the idea that Facebook constitutes a distraction for tertiary students. |

Using Peer-Reflection to Develop Self-Regulated Learning Strategies in Year 10 Mathematics Recent reforms to the Australian Curriculum and the Victorian Curriculum provide a framework for developing students' awareness of metacognition and self-regulated learning strategies. In this study, I use educational design research to develop and implement a class-based intervention that aims to improve students' self-regulated learning strategies. This educational intervention structures an approach to critical peer-reflection as part of Year 10 mathematics lessons whereby students reflect, discuss, observe, and model learning strategies. In this presentation, I will explore preliminary data that have informed the development of the intervention. |

Round Tables (Abstract Only) |

Exploring Emotional Aspects of Pre-Service Mathematics Learning Environments Preparing primary teachers for mathematics teaching typically includes attention to their existing beliefs and attitudes towards mathematics as a discipline. The potential of the pre-service learning environment to enhance emotional engagement with mathematics learning and teaching is a developing field of research. In the session, I will provide an opportunity to discuss issues around initial teacher education learning environments in terms of introducing structures to promote positive experiences in learning to teach mathematics. I will examine emerging theories of emotions from a sociological perspective that are useful for analyzing the emotional aspect of learning environments. In the round table session, I will draw on survey data about emotional dispositions and beliefs in mathematics as well as emotions associated with teaching mathematics. I will also draw on case studies of individual students who were excited and enthusiastic about teaching mathematics despite having had negative learning experiences themselves. The session will provide an opportunity for participants to discuss (a) increased awareness of emotional reactions to classroom events, (b) the connection between innovative teaching approaches and mathematics teaching and learning, and (c) the potential of games to impact the emotional aspects of learning environments. |

Mathematics Leadership in Primary Schools In response to the recent Teacher Education Ministerial Advisory Group (TEMAG) report (2014), teacher education providers are developing new units of study and pathways of study within existing programs to cater for pre-service teachers (PSTs) who elect to undertake a specialization in mathematics. Entry requirements for students electing such a pathway are not specified; however, it is expected that when they graduate, they will have demonstrated competence in mathematics and perhaps taken one or more additional units in mathematics pedagogy. Teacher education providers currently know little about the background experiences, aspirations, and expectations of primary school PSTs who might elect and be accepted into a primary mathematics specialization pathway. This gap in our knowledge is partly due to prior research foci on primary PSTs who lack the mathematical content knowledge required as a basis for teaching mathematics well (Callingham & Beswick, 2011). Teacher education providers also know little about what potential employers are expecting of PSTs who will graduate with a specialization in mathematics. This knowledge is necessary for teacher education providers to be able to select appropriate candidates for a mathematics specialization pathway and plan units of study for them. In the round table, we will begin by presenting the aim of our research, some preliminary data concerning the PSTs who have elected to undertake a new primary mathematics specialisation at The University of Sydney, and the skills and characteristics that some potential employers have identified as being essential or desirable for mathematics leadership in primary |

Rethinking Mathematical Tasks Mathematics teachers invariably use a multitude of tasks in their day-to-day practice. Indeed, "mathematical tasks provide tools for promoting learning of particular mathematical concepts and are, therefore, a key part of the instructional process" (Simon & Tzur, 2004, p. 93) Further, the National Council of Teachers of Mathematics (NCTM, 1991) postulated that tasks "convey messages about what mathematics is and what doing mathematics entails" (p. 24). Over the years, several terms have been used to describe mathematical tasks, such as worthwhile mathematical tasks (NCTM, 1991), challenging tasks (Sullivan et al., 2014), high-level tasks (Henningsen & Stein, 1997), open-ended tasks (Zaslavsky, 1995), and rich mathematical tasks (Grootenboer, 2009). While acknowledging the benefits of using such tasks, research has also surfaced some shortcomings. Stein, Grover, and Henningsen (1996) cautioned that "When employing the construct of mathematical task, however, one needs to be constantly vigilant about the possibility that the tasks with which students actually engage may or may not be the same task that the teacher announced at the outset"(p. 462). In this round table presentation, we will discuss the affordances that mathematical tasks such as those stated above offer to teachers, as well as other alternatives that are available to teachers for enhancing students' learning of mathematics. We will provide some examples from one of our on-going projects for further discussion. |

Scaling Up and Sustaining Successful Interventions in Mathematics Teaching Education research journals regularly report on small-scale studies that have been successful in changing mathematics teachers' classroom practices. However, it is rare to find large-scale transfer of research knowledge into practice in mathematics education (Begg, Davis, & Bramald, 2003). In this round table discussion, we will share some early findings from research into an established, large-scale professional development project initiated and sustained by a state education system at a regional level and involving a large number of schools and teachers. In this project, we have developed a cluster model for bringing primary and secondary school teachers and principals together to analyse student performance data, create diagnostic tasks that reveal students' current mathematical understanding, and promote teaching practices that address students' learning difficulties in mathematics. The effectiveness of this approach is evidenced by reported improvements in teacher confidence and knowledge and in student achievement and enjoyment of mathematics, changes to mathematics teaching and assessment practices, and an everincreasing number of schools volunteering to join the project and commit professional development funding. In our research, we seek to identify critical factors that support these mathematics teachers in instructional improvement on a large scale. The round table will begin with an overview of the cluster model and then we will present some insights from interviews that we have conducted with teachers and principals. We invite MERGA members to join us and share their own experiences and ideas in response to the following research questions that are guiding our study (based on Cobb & Jackson, 2011): 1. What practices are effective in establishing a coherent instructional system supporting mathematics teachers' development of ambitious teaching practices? 2. To what extent do teacher networks and mathematics coaching of teachers support changes in mathematics teaching practice? 3. What features of school and district or regional leadership contribute to the scalability and sustainability of a cluster-based professional development model? We also invite colleagues to suggest new lines of inquiry that could contribute to a theoretical rationale for sustained, scalable professional development. |