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At MERGA1, I presented a paper entitled Mathematics in the Pre-School, which was a summary of tentative ventures into this emerging field. The role of the prior-to-school years in children’s mathematics learning was not yet under serious consideration but an understanding of the importance of play in children’s experiences was building. Forty years on, early childhood mathematics education is perceived as a critical frontier for mathematics education and other (e.g., psychology, sociology, childhood and family studies) research. Early intervention is seen as the Holy Grail. In this brief paper, I identify some of the achievements and some of the side effects of this changing context.

This presentation reflects on over three decades of research focused on the development of mathematical structure. ‘Looking back’, it traces the key theoretical influences that informed a series of studies on children’s imagery, patterns and relationships including multiplicative reasoning and spatial structuring. ‘Looking beneath’, the development of Awareness of Mathematical Pattern and Structure is highlighted through development of an interview-based assessment and pedagogical program. ‘Looking beyond’, it raises key questions about the importance of developing deep mathematical thinking leading to generalisation, and realising this possibility for young children.

Mathematics enables us to investigate, explain, and make sense of the world in which we live (Ministry of Education, 2007). Many people, however, are unable to do this fully because of their affective views and responses to mathematics. In this paper, a review of affective research in mathematics education is presented to provide a context for exploring research that includes affective aspects at MERGA conferences over the last 25 years, and to position my own research. Researchers of affect are challenged to maintain a focus on mathematics, and researchers working in the broader field of mathematics education are challenged to incorporate affective aspects into their research.

An understanding of time which goes beyond the reading of clocks and calendars is crucial to full participation in society. This paper reports on classroom experiences and pedagogies that assisted Year 3/4 children’s development when learning about time, drawing upon a Framework for the Learning and Teaching of Time, interview data, an eight-lesson intervention and student improved performance on the interview following the intervention.

The Australian Curriculum: Mathematics calls for the concurrent development of mathematical skills and mathematical reasoning. What are the big ideas of mathematical reasoning and is it possible to map their learning trajectories? Using rich assessment tasks designed for middle-years students of mathematics, this symposium reports on the preliminary phase of a large national study designed to move beyond the hypothetical and to provide an evidence-based foundation for learning progressions in mathematical reasoning in three key areas of the curriculum: Algebraic Reasoning, Geometrical and Spatial Reasoning, and Statistical Reasoning.

While measures of research quality are widely accepted in the education research community, there may be less agreement on what constitutes evidence of impact and on where to look for it. The aims of this symposium are to consider some key issues in undertaking the Australian government’s national assessment of research engagement and impact, and to propose some approaches to evidencing engagement and impact in the context of mathematics education research. Each of the four symposium papers draws on our Numeracy Across the Curriculum (NAC) research program in order to ground our discussion in specific cases of research that have been reported at previous MERGA conferences. In the first paper, Evidencing research engagement and impact, Merrilyn Goos establishes the theoretical and policy context for the symposium in terms of the apparent lack of connection between educational research and practice. She analyses aspects of the NAC research program to trace rich connections between her own teaching, research and service roles that led to beneficial knowledge exchanges (engagement), and intricate links between research activities, outputs and outcomes across multiple projects (impact). Such an analysis can suggest “where to look” for evidence of engagement and impact. In the second paper, The convoluted nature of a research impact pathway, Vince Geiger develops a case study of an aspect of his own research within the NAC program to illustrate the complexity of the journey from research origin through to potential impact. The documentation of this research progress allows for reflection on how future impact can be “read” while research is taking place. In the third paper, Engagement and impact through research participation and resource development, Anne Bennison and Shelley Dole illustrate how knowledge exchange and uptake of resources developed through research can provide evidence of research engagement and impact, respectively. The analysis suggests ways in which collaborative research (an ARC Linkage Project on proportional reasoning and numeracy) and contract research (funded by the Queensland College of Teachers) can be translated for economic and social benefits. In the fourth paper, “Numeracy for learners and teachers”: Impact on MTeach students, Helen Forgasz evaluates the impact of a compulsory unit taken by all primary and secondary pre-service teachers in the Monash University Master of Teaching. The unit design incorporates elements of the Numeracy Across the Curriculum model to address AITSL standards for knowledge and understanding of literacy and numeracy teaching strategies, and interpreting student data. The evaluation reveals substantial impact on students’ understanding of numeracy and confidence in incorporating numeracy in their teaching, thus highlighting the contribution of research to improving teacher education.

The symposium provides an overview of the Early Years STEM Australia (ELSA) program. The conceptual underpinnings of the program are framed within STEM practices, rather than traditional thinking concerning the integration of discipline content knowledge. We will argue that our focus on practices is more aligned with the play-based and intentional teaching objectives of the Early Years Learning Framework (EYLF). The symposium describes the approach we have undertaken, the extent to which some of the practices align well to mathematics thinking, and the pedagogical framework used to stimulate play and create activities for the six learning apps that form part of the program.

Presenters: Caroline Bardini, Abi Brooker, Robyn Pierce The Merriam-Webster dictionary defines transition as: (a) the passage from one state, stage, subject, or place to another: change; or (b) a movement, development, or evolution from one form, stage, or style to another. The word transition can refer to an active shift of the person in space and time or status, for example; it can also refer to developments taking place within the person. Transitions may be anticipated by those involved, and hence planned for, or they may result from unexpected changes in people’s lives. Transitions can occur at various points throughout a person’s educational trajectory, and here we include student development across primary, secondary, and tertiary sectors; also, the transitions made between cultural contexts in schools. Beach (1999) noted that (consequential) transitions consist of “changing relations between persons and their social activities represented in signs, symbols, texts, and technologies” (p. 119). In this symposium, we will be considering transitions in mathematics education affecting both students and teachers, specifically in relation to representations in the first two papers and to values in the third. In Transitions in Language Use in Primary School Online Mathematical Problem Solving, Duncan Symons and Robyn Pierce adopt a Bakhtinian lens to examine upper primary school students’ use of informal and formal language registers in CSCL mathematical problem solving. They argue that online discussion assists in the development of mathematical language as demonstrated by students’ use of a transitional mathematical register combining new mathematical words with their own natural language. In Mathematical Writing and Writing Mathematics: The Transition from Secondary to University Mathematics, Caroline Bardini and Robyn Pierce present a framework based on their research on students’ use and understanding of mathematical symbols, recognised as crucial in students’ successful transition from school to university mathematics. In particular, the framework supports a fine-grained analysis allowing better appreciation and understanding of the subtle differences in students’ experiences with symbolic expressions. In The Valuing of Deep Learning Strategies in Mathematics by Immigrant, Firstgeneration, and Australia-born Students: Transitions Between Cultural Worlds, Abi Brooker, Marian Mahat, and Wee Tiong Seah draw on an ecological systems model of students’ learning experiences to take an intercultural approach towards transitions in mathematics education. Their focus is on the many school students in Australia who move between cultures on a daily basis, particularly those who achieve well in international assessments. They consider that the multicultural nature of many Australian classrooms provides an opportunity for students to learn from different values and perspectives to enhance their learning. Identifying the values that students have for deep learning (and their preferred strategies for learning) might offer valuable insights into how students’ engagement with and abilities in mathematics can be better supported on a wider scale.

In this study, we investigated students’ thinking about the use of letters in algebra. Responses from over 1,400 Australian secondary school students to a set of three algebra items were analysed to determine the prevalence of the “letter as object” misconception. We estimate that 50% to 80% of Year 7 students bring this misconception to their initial learning of algebra. Over 50% of Year 8 students and over 40% of Year 9 students in the sample also selected responses consistent with this misconception.

The four papers presented in this symposium report on the evaluation strategies and feedback from teachers as they embarked on designing and implementing STEM approaches to learning in secondary school contexts. The STEM professional learning program was designed to provide time and expert support so that cross-disciplinary school teams of up to six teachers from science, mathematics and technology/engineering could develop new school-based initiatives. A range of evaluation strategies were used in the first two STEM Academy programs to identify factors and approaches that supported teachers’ and students’ needs, and to further enhance the STEM Academy program. This symposium addresses ways in which the progressive evaluations have informed this change process.

The aim of this qualitative study is to embed ICT in the teaching and learning of A-level vectors. Initially, students’ learning difficulties and misconceptions in A-level vectors were diagnosed. Then, based on the difficulties identified, concepts in vectors together with interactive tools were developed and integrated in a webpage to enhance the teaching and learning of vectors at A-level. Finally, the tools developed were exposed to trainees for feedback and evaluated using the framework proposed by Pillay and Clarke (2008). The tools met the following criteria: learner focus, integrity, usability, and accessibility.

Many teachers and pre-service teachers of mathematics lack experience with teaching methods, such as mathematical modelling, that require a conceptual learning and problem solving approach. To address this problem, this paper presents a study of a method – the Enhancement, Learning, Reflection (ELR) process – that has been designed to improve preservice students’ confidence in teaching mathematics, with a particular focus on the use of modelling as a teaching method. Results from the case study show that the PST participants involved in the ELR process did indeed experience an increase in confidence in their ability to present the modelling concept to a classroom of high school students.

Research interest in numeracy is growing as a result of increased understanding of the impact of low levels of numeracy. However, there has been little research on factors that influence how teachers implement learning from professional development interventions to support teachers to promote numeracy learning. This paper reports on how a theoretically developed framework for identity as an embedder-of-numeracy was re-examined through empirical research. Additional factors were added to the framework and each factor included in the framework was explicitly defined. The framework seems to capture the complexity of a teacher’s identity in this context and is amenable to empirical research.

This paper focuses on using sociocultural theory to support a context-based approach to teaching mathematics. A goal of the research was to explore the opportunities-to-learn of using a context-based approach to enrich student engagement with mathematics. This paper focuses on the practice of one female secondary school teacher as expressed through an interview transcript. Data were analysed using a participation framework. Findings suggest that aspects of a context-based approach to teaching mathematics can be used by teachers to promote student engagement with mathematics in the secondary classroom.

Multiple-choice items are used in large-scale assessments of mathematical achievement for secondary students in many countries. Research findings can be implemented to improve the quality of the items and hence increase the amount of information gathered about student learning from each item. One way to achieve this is to create items for which partial credit can be given when students select particular incorrect options. To improve the items in this way requires a critical analysis of how the items contribute to the measure of student achievement as well as extensive knowledge of the test construct.

In this paper, we report on primary-school students’ views of their learning experiences when they engaged with mathematical phenomena through apps. The students commented on how they used a range of digital tools within the apps to solve problems, and we consider how the affordances of the mobile technologies, including multi-representation, dynamic and haptic, might influence the learning experiences. In particular, we focus on the interplay between the affordances of the mobile technologies with other social and pedagogical aspects, and ask how the assemblage of social and technological entities might influence mathematical learning experiences.

This paper reports a study conducted in a laboratory classroom with the capability to record classroom social interactions in great detail using advanced video technology. The social interactions of student groups during collaborative problem solving were analysed based on transcript data. This analysis suggests that meaning negotiation in mathematics classrooms can be usefully distinguished as social, sociomathematical, or mathematical. We suggest that all three modes coexist in an entangled form in the negotiative interactions documented in the mathematics classroom and we envisage all three as constitutive of learning.

Differentiating students’ learning needs in primary mathematics classrooms is an issue faced by many teachers. One technique designed to differentiate the level of challenge in mathematics tasks is the use of enabling prompts and extending prompts. We report on survey data pertaining to enabling and extending prompts, and teacher noticing of 37 Year 3 to 6 teachers participating in a project investigating the use of challenging tasks. Data were coded and categorised using grounded theory. The teachers valued enabling and extending prompts when implementing challenging mathematical tasks, and using these prompts stimulated them to notice students’ reasoning and mathematical communication.

Children form mathematical concepts at an early age, and many of these concepts are linked to informal measurement experiences. However, mathematics education at school is often focused on counting and numbers. A mathematics intervention using a measurementfocused program replaced the usual mathematics program for 40 children entering their first year of school. The results of Counting and Place Value interviews held at the beginning and end of the school year are reported. Findings indicate that a “student-active” measurement-focused program can stimulate the development of children’s number knowledge; however, additional counting may benefit children’s number skill development.

In this paper, we re-examine the commonly-held notion that typical problems, such as textbook exercises and examination questions, are not useful for orchestrating mathematically-rich learning experiences. Drawing from a larger design-based research project, we present a case study of Alice, a secondary school teacher, who orchestrated a productive discussion by using examination questions. We describe how she perceived and harnessed the affordances of such typical problems before and during her lesson. Findings suggest teacher noticing as a key mechanism to enable teachers to unlock the mathematical potential of such problems.

In this paper, we analyse data from the University of Melbourne’s Matriculation examinations around 1900. The analyses reveal that many schools cleverly developed and applied strategies so that their Matriculation results would appear to be more impressive than they really were. After “excellent” results had been achieved, the schools advertised their Matriculation “successes” in ways which suggested that the schools’ “outstanding” results derived from high-class teaching. In this paper, we argue that these tactics generated artificially high “standards”, and that throughout the twentieth century there was a tendency to try to maintain those standards.

Many resources have been created with the aim of helping children and adults overcome difficulties with mathematics and to develop or improve their numeracy. However, these are only used once the individual has decided to act – to do something to improve their mathematics and numeracy. Unfortunately, someone who knows that they need to improve their mathematics or strengthen their numeracy is not always accessing these resources. In this theoretical paper, I explore reasons why individuals may not engage with resources designed to help them develop their mathematical understandings and numeracy and identify the need to address how to get individuals to take that first step.

In this paper, we provide an overview of the “Maths Inside” project, funded by the Australian Maths and Science Partnership Program (AMSPP). The overall aim of the AMSPP is to improve uptake and participation of students in mathematics and science at secondary and tertiary levels. In this research project, we aim to improve student interest in mathematics and support mathematics teachers in their professional learning, through provision of rich and investigative learning resources, including video case studies of CSIRO scientists and mathematicians. Data collection on the outcomes of the project is ongoing and will be reported in subsequent papers.

In this paper, we report on developments in the Mastery Learning (ML) curriculum and assessment model that has been successfully implemented in a metropolitan university for teaching first-year mathematics. Initial responses to ML were positive; however, we ask whether the nature of the ML tests encourages a focus on shallow learning of procedures, and whether the structure of the assessment regime provides sufficient motivation for learning more complex problem solving. We analysed assessment data, as well as student reports and survey responses in an attempt to answer these questions.

Pre-service teachers (PSTs), like practising teachers, enact their mathematical content knowledge (MCK) in pursuit of instructional goals during lessons. In this study, I explored the relationship between six secondary mathematics pre-service teachers’ goals and the MCK that they chose to enact in 10 lower secondary algebra lessons. The findings indicate that PSTs enact stronger aspects of their MCK when they pursue goals that pertain to making mathematical connections rather than procedural mastery. Also, live classroom interactions with confused students can positively impact the instructional goals that preservice teachers form and the quality of MCK that they enact.

The process of planning mathematics lessons is complex and presents challenges for teachers, specifically in their Mathematical Knowledge for Teaching (MKT). In this paper, I describe findings from case study research in which a Year 1 teaching team engaged in professional reading and used a specific planning proforma to enhance their MKT. Teachers reported feeling more informed in their planning decisions and overall, reported positive changes to their team planning practices which impacted their classroom teaching.

School mathematics leaders play a significant role in leading improvement in mathematics education in schools. An online survey was administered to obtain an overview of the current nature of the role of the school mathematics leader. Responses were received from 56 primary school mathematics leaders from Victorian government schools. Findings based on leaders’ views contributed to building a picture of the complex nature of the role. Survey responses suggested the impact of school mathematics leaders was often compromised by lack of time, confidence, expertise and funding. The extent of classroom teaching, teacher content knowledge and principal support also impacted on effectiveness of the role.

In this paper, we identify, from historical vantage points, the following six purposes of school algebra: (a) algebra as a body of knowledge essential to higher mathematical and scientific studies, (b) algebra as generalised arithmetic, (c) algebra as a prerequisite for entry to higher studies, (d) algebra as offering a language and set of procedures for modelling real-life problems, (e) algebra as an aid to describing structural properties in elementary mathematics, and (f) algebra as a study of variables. We conclude with brief commentary on the question whether school algebra is a unidimensional field of study.

This paper addresses the initial components of an activity in which 4th-grade students engaged in meta-questioning as they created and refined survey questions with the aim of comparing life across two Australian cities. We propose the term, meta-questioning, as a core, underrepresented feature of statistical investigations in the primary school. We report on the nature of the students’ initial posed questions and their subsequent refined questions, students’ justifications for their question refinements, their anticipated data collection, and developments in their question posing skills. Results include a hierarchy of question types posed by the students and how their question types changed with subsequent refinements.

In this preliminary study, to inform a larger study where Year 8 students create an online module for peers, I surveyed mathematics teachers (n = 30) on essential mathematics topics: (a) most critical for students’ success, (b) most conceptually challenging for students, and (c) in which more fluency is needed, as well as (d) their likelihood of considering an online course as an intervention. Fractions concepts, times tables, and equation solving were most critical for success; students need more understanding of fractions concepts, and more fluency in both fractions concepts and times tables. Online course use addressed teachers’ concerns for students in essential mathematics topics.

In this paper, the hypothesis that Developmental Dyscalculia (DD) is a characteristic of Down syndrome (DS) is proposed. Implications for the hypothesis are addressed: If it were to be confirmed that DS implies DD, what would be the consequences for the mathematics education of learners with DS? The use of prosthetic devices to overcome the impaired calculation capabilities of the brain is essential. Fortunately, electronic calculating devices are readily available. Their routine use opens the possibility of studying areas of mathematics that were once inaccessible.

Declining enrolments in advanced level mathematics at the school level are noted with concern. Whether school type (single-sex school or co-education) affects participation in mathematics continues to be debated. In this article we examine, by school type and gender, statistical data from 2001 to 2015 on Victorian Certificate of Education enrolments in the three mathematics subjects offered at that level. Also explored are the choice of, and reasons for, the school setting assumed to promote STEM studies for girls and boys.

Excellent mathematics teachers establish learning environments that encourage students to actively engage with mathematics and foster co-operative and collaborative learning. Whiteboarding, using an erasable surface on which to work and share ideas, has been shown to increase student engagement, collaboration, and higher-order thinking. We report on one teacher’s experiences as she introduces whiteboarding into her secondary mathematics classroom. The teacher reports increased student confidence and collaboration and we see a shift in her focus from concerns about classroom management, to a passionate recommendation to use whiteboarding in mathematics instruction.

This paper provides insight about the development of addition and subtraction strategies for nearly 22,000 Australian primary school children in 2016. The children were each assessed by their teacher using a task-based assessment interview that identified the strategies they used to mentally perform addition and subtraction, and matched these to a growth point framework. The findings highlight the broad distribution of strategies used by children in each grade level and suggest that few children, including those in Grade 6, reach Growth Point 6 that involves the mental calculation of two-digit and three-digit numbers. These findings have important implications for classroom teaching and professional learning.

The concept of fractions is perceived as one of the most difficult areas in school mathematics to learn and teach. The most frequently mentioned factors contributing to the complexity is fractions having five interrelated constructs: part-whole, ratio, operator, quotient, and measure. In this study, we used this framework to investigate the practices in a New Zealand Year 7 classroom. Video recordings and transcribed audio-recordings were analysed through the lenses of the five integrated concepts of fraction. The findings showed that students often initiated unexpected uses of fractions as quotient and as operator, drawing on part-whole understanding when solving fraction problems.

In this paper, we examine junior secondary mathematics teachers’ understanding of mathematical structure, and how they promote structural thinking in their teaching. Five teachers were surveyed, and three were interviewed and the observed teaching a junior secondary mathematics class. Results showed that teachers have conflicting understandings of structure, and their perceived understandings, obtained from survey data, were not reinforced by their interview responses or observations of their teaching. Analysis of connections, recognising patterns, identifying similarities and differences, and generalising (CRIG) components from observation data showed a lack of attention to structural thinking.

A current issue in initial teacher education (ITE) in Aotearoa, New Zealand is how students can best be supported to use digital technologies for mathematics teaching. While many ITE students are familiar with digital technologies for personal use, they are less likely to know how to incorporate them into the mathematics learning process. Supporting ITE students to become more critical, knowledgeable, skilled, and confident about using digital technologies was the main aim of the study. Forty second-year ITE students were surveyed about the Digital Learning Objects promoted by the Ministry of Education that they would choose to use to teach area measurement. Several different reasons were reported.

Mathematical reasoning features in curriculum documents around the world, but is understood and enacted poorly by teachers in classrooms. We explore teachers’ noticing of reasoning during observed lessons. Two teams of primary teachers in Canada and Australia worked to plan, deliver, and observe lessons intended to include reasoning. They observed each other teaching a lesson that was planned with the assistance of a researcher, and later, a researcher observed each post-lesson discussion. Given the reported benefits of teachers’ noticing of reasoning during peer-observed lessons, targeted professional learning support is required to further enact teachers’ peer discourse to facilitate mathematical reasoning.

In this research paper, I present the reasons why senior secondary students elect not to enrol in a higher mathematics course. All Year 11 and Year 12 mathematics students within Western Australian secondary schools were invited to participate in an online survey comprised chiefly of qualitative items. The key reasons espoused by students include an expressed dissatisfaction with mathematics, the opinion that there are other more viable courses of study to pursue, and that the Australian Tertiary Admissions Ranking (ATAR) can be maximised by taking a lower mathematics course. In addition, student testimony suggests that there are few incentives offered for undertaking a higher mathematics course.

The current study compared the rate at which problem-based practice increased the use of retrieval-based strategies for students identified as displaying accurate min-counting with students identified as displaying almost proficient performance. The findings supported the prediction that the rate at which problem-based practice promoted retrieval use was lower for students in the accurate min-counting group; in fact, it had no effect on their retrieval development. Implications for teaching practice are discussed, in particular, the notion that such students may require exposure to different problem representations (e.g., visual imagery) to move them away from conceptualising addition as counting.

Multiplicative thinking is a critical stage of mathematical understanding upon which many mathematical ideas are built. The myriad aspects of multiplicative thinking and the connections between them need to be explicitly developed. One such connection is the relationship between place value partitioning and the distributive property of multiplication. In this paper, we explore the extent to which students understand partitioning and relate it to the distributive property and whether they understand how the property is used in the standard multiplication algorithm.

This study aims to explore undergraduate mathematics students’ difficulties in their initial encounter with the subgroup test, and in particular in the proof of closure under operation. Subgroup test is one of the first results in an introductory course of Group Theory where students need to cope with the characteristic, for novice students, high level of abstraction. For the purposes of this study, the researcher has used the Commognitive Theoretical Framework. Analysis suggests that students’ difficulties are due to various reasons, including the formalism of the definition of group, incomplete metaphors from other mathematical discourses, confusion of the involved structures, and the proof process per se.

Public discourse concerning STEM has an increasing influence on mathematics education, yet the exact role that mathematics plays in STEM is hard to define. I compare STEM to numeracy to investigate how mathematics is repositioned in these two discourses. Each is analysed in terms of rhetorics that argue for the worth of mathematics education. While numeracy viewed mathematics as worthy for critical citizenship, STEM argues that mathematics has worth due to its support of the innovation required for productivity growth. Analysis of the rhetorics is argued to support the mathematics education research community response to changes in public and policy discourses regarding mathematics.

In this study, we examined students’ mathematical understanding and retention in a problem-based learning (PBL) classroom. The participants were 48 Grade 10 students, and the data were collected in December of 2016. After the end of the PBL lessons, the Mathematical Understanding of Function Test (MUFT) and the Retention Test (RT) were administered. The findings showed that most students demonstrated mathematical understanding of functions in all components and more than 50 percent of the students could pass both tests by the overall mean scores. Moreover, the overall mean difference between the MUFT and the RT was low, which means that the students had retention.

The use of multiuser virtual environments for educational purposes is in its infancy but offers potential for exploration of spatial contexts that could not otherwise be experienced. We report on pre-service teachers’ experiences in designing learning activities as a result of immersion in the CAVE2TM, a 320-degree, cylindrical 3D virtual environment. Observation of student actions and analysis of student-developed artefacts indicated that 3D and 2D interference impacted the design of immersive learning experiences. We hypothesise that pre-service teachers’ capacity to recognise and seize the potential of the CAVE2TM for promoting spatial reasoning is predicated on their own spatial reasoning capabilities.

Members of the Australian mathematics education research community and experienced teachers of mathematics participated in the process of documenting the professional vocabulary of middle school mathematics teachers. This vocabulary, the Australian Lexicon, captures the language in use by Australian mathematics teachers when describing the phenomena of the middle school mathematics classroom. In this paper, we examine the structure of the Australian Lexicon with particular attention given to content, connection, and characteristics of the professional vocabulary available to middle school mathematics teachers in Australia.

In this paper, we present data from a study exploring the use of coding to promote mathematical thinking. A teaching experiment was undertaken with 40 Year 2 students participating in six 45-minute lessons of coding (one lesson per week for six weeks). All lessons were video-recorded and analysed to determine students’ mathematical thinking. Insights from the study reveal that coding contexts promoted higher levels of mathematical thinking for Year 2 students including measuring angles, orientation and perspectivetaking, and deducing repeating patterns.

Flipped learning is gaining in popularity as a teaching approach in secondary mathematics classrooms. Traditionally seen as the domain of tertiary teaching, flipped learning has a number of affordances that address the challenging demands of teaching secondary mathematics. Enacting this approach requires a reconceptualization of traditional secondary mathematics instruction in that instructional content is assigned as homework before class, providing for more targeted in-class teaching. I describe three different enactments of the flipped learning approach and report on the teachers’ and students’ experiences of such an approach and the affordances it offers.

Recent research has supported and extended earlier research on how and for how long Indigenous people of Australasia have been counting. This history values the long history of Indigenous knowledge and re-writes the limited and sometimes false history that many Australian teachers accept and teach about number systems. The current views on the spread and innovation of number systems are critiqued in terms of how oral cultures used and represented large numbers.

In this paper, we report on how Year 5 and 6 students (10 to 13 years old) solve reverse fraction problems; that is, where students are required to find the quantity of an unknown whole given a known partial quantity and its equivalent fraction of the unknown whole. To what extent do students’ solutions generalise fraction structures that indicate algebraic thinking? Which solution strategies to reverse fraction problems seem to promote generalisation and which appear to hold students back?

School and university mathematics: Do they speak the same language? Our university mathematics students come from amongst the successful school mathematics students, but what difficulties with symbols do their lecturers and tutors observe? In this paper, we report on data from interviews with 21 first-year lecturers and tutors from four universities. Key emerging themes focused on mathematical communication: the importance of comprehending mathematical symbols and of composing a mathematical narrative consisting of both explanatory words as well as symbols.

We proposed to study self-regulated learning (SRL) of 11th grade students in a PBL classroom (n = 36). The data were collected in November 2016 using Students’ Self- Regulation Strategy Inventory (Students’ SRSI), Teachers’ Self-Regulation Strategy Inventory (Teachers’ SRSI), students’ interviews forms, students’ reflections, and the teachers’ notes. Descriptive statistics (percentages, means, and standard deviations) and descriptive analysis were used to analyse the data. We found that in the PBL classroom, the students demonstrated self-regulated learning in three phases – the forethought phase, the performance phase, and the self-reflection phase – at high levels.

It is well known that students of inferential statistics find the hypothetical, probabilistic reasoning used in hypothesis tests difficult to understand. Consequently, they will also have difficulties in understanding p-values. It is not unusual for these students to hold misconceptions about p-values that are difficult to remove. In this study, 19 Australian tertiary statistics educators were surveyed about their beliefs about p-values, and it was found that some of these instructors held misconceptions about the nature of p-values. These findings suggest that professional learning of statistics instructors is urgently required so that instructors may have their beliefs challenged and corrected.

This paper provides historical insights and educational background of Froebel’s Gifts, hands-on materials developed in the early 19th century. Based on an explorative study with 54 German children (aged 5 to 10) in 2016, we first took steps to explore how these materials meet the demands for early mathematics learning of primary children. Starting with a brief introduction into the work and life of Friedrich Froebel, we outline how using Froebel’s Gifts can stimulate the acquisition of mathematical knowledge and abilities, then conclude by considering future research directions within Australian schools.

Thirty primary classroom teachers quantified perceived changes in their practice and knowledge attributed to their school leaders’ participation in a six-day course focused on leaders designing and implementing a whole-school reform of mathematics teaching and learning, and the school-based professional learning that followed. The project and framework underpinning the reform are outlined, and the teachers’ reported changes in pedagogical practices are described. Teachers identified many changes in pedagogy and growth in knowledge. Not surprisingly, changes in pedagogical practices were even greater for specialist mathematics teachers who had also participated in a separate six-day course.

The current investigation systematically contrasted teaching with cognitively demanding (challenging) tasks using a task-first lesson structure with that of a teach-first lesson structure in a primary school setting (Year 1 and 2). The findings indicate that there is more than one way of incorporating challenge tasks into mathematics lessons to produce sizeable learning gains. Analyses of interviews with teachers and students regarding their perceptions of learning with challenging tasks suggest that each type of lesson structure has distinct strengths. It is concluded that teachers should consider varying the structure of the lesson to provide a range of learning experiences for students.

In this paper, I explore data collected from more than 300 Year 5 and 6 students in four government primary schools in urban Darwin. Students were asked to respond to real-world problem contexts involving fundraising as an example of an enterprise activity. The findings reveal that familiarity with the problem context, personal values, and language and literacy skills influenced students’ decisions how to price goods for sale. It is argued that contextualised learning tasks that require students to apply mathematical, financial, and entrepreneurial thinking can provide insights into students’ family backgrounds, personal values, and learning needs while guiding and informing culturally responsive teaching.

Despite the significance of the role, little is known about mathematics leaders in schools. Rachel, a mathematics leader, was observed leading planning meetings with junior primary teachers. Using activity theory, three of Rachel’s motivations were identified: influencing teacher affect, developing shared understandings, and avoiding conflict. Observation and interview data analysis revealed the use of pedagogical content knowledge (PCK) as a tool far more than subject matter knowledge. We posit that the dominant use of knowledge types associated with PCK was due mostly to Rachel’s object of avoiding conflict.

In this study, we explored the critical thinking of 47 eleventh-grade students in a mathematics problem-based learning (PBL) classroom in November 2016. A critical thinking test was used along with classroom observations to gather the critical thinking data in five dimensions according to the Association of American Colleges & Universities (2009). The findings indicate that students’ critical thinking scores in all dimensions are at an average level. The students demonstrated strength in explaining issues and analyzing influence of context and assumptions. However, students had greater difficulty in stating their positions and drawing conclusions.

This paper presents an analysis of pre-service teachers’ reflections on the consequences of their perceived public humiliation in school mathematics classrooms, based on Torres and Bergner’s (2010) model of the stages of humiliation. It analyses two examples of preservice teachers’ critical incident reflections from studies at two Australian universities. This research contributes to the frameworks through which primary pre-service teachers’ mathematics anxiety, and its implications for their identity development, might be understood.

In this paper, we undertake a content analysis of mathematics assessment tasks to understand how often graphical representations are embedded within high-stakes national and international tests. A total of 274 items were analysed, consisting of 160 Grade 9 UN items, 88 Grade 8 TIMSS items, and 26 PISA items. Analysis showed that all items in the PISA test were embedded with graphics, with far fewer graphical items in the TIMMS and national UN tests (47% and 33% respectively). We also found that graphical items in UN tests are distinct from PISA and TIMSS, suggesting a misalignment between what is represented in UN tests and international instruments.

Talk moves simulations were used in tutorials for a mathematics education unit. Pre-service teachers (PSTs) and tutors were surveyed about their perceptions of the purposes, benefits, and drawbacks of the simulations. There was strong support from both groups for the benefits of talk moves in developing PSTs’ ability to manage discussions, ask good questions, and understand students’ thinking. Tutors were more inclined than PSTs to note improvements to PSTs’ mathematical knowledge. Challenges to implementation were authentic engagement in the simulations, PSTs’ lack of experience with children, the cognitive load associated with managing discussions, and limited mathematical knowledge.

In this paper, I report on doctoral research in which I studied the changes in mathematical knowledge and beliefs of two Year 5/6 teachers as they implemented a four-week innovative curriculum unit. Such immersion experiences have the potential to develop teachers’ understanding of mathematics in the context of the classroom. Year 6 case study teacher Debbi’s experience is discussed in relation to curriculum fidelity and opportunity to learn, in particular the foregrounding of higher achieving students. Debbi’s firmly entrenched practices, related beliefs, and affective response to the curriculum presented as the dominant filters for reflection and enaction.

For Indigenous students in minority education contexts, it is important that teachers have strategies to combine both cultural knowledge and mathematical knowledge in appropriate ways. This paper presents the results from analysing preservice teachers´ statistical enquiry assignment linked to a cultural context, in a Māori-medium teacher education programme. The results indicate that there are many tensions in trying to honour both the learning of cultural and statistical understandings. The findings provide insights to teacher educators about what may be needed to reduce some of these tensions and the implications for teachers working in Māori-medium schools.

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.

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.

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.

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.

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).

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.

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.

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.

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.

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.

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.

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.

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

Despite willingness, South African mathematics teachers teaching through a second language (L2) often struggle to get their learners engaging in exploratory talk. Using transcripts of talk in one South African teacher’s Grade 4 mathematics lessons, plus interview data, we will examine and share some effects that children’s diminished access to their strongest source of linguistic capital, mother tongue (L1), appears to have on their epistemological access to mathematical sense-making. Our findings suggest that use of L2 exacerbates existing inequalities in mathematics achievement across South Africa’s socioeconomic sectors (sectors which, due to the legacy of apartheid, generally coincide with “race”).

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.

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

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.

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.

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 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 vis-à-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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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

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.

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.