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While there is widespread agreement on the importance of incorporating problem solving and reasoning into mathematics classrooms, there is limited specific advice on how this can best happen. This is a report of an aspect of a project that is examining the opportunities and constraints in initiating learning by posing challenging mathematics tasks intended to prompt problem solving and reasoning to students, not only to activate their thinking but also to develop an orientation to persistence. The results indicate that such learning is facilitated by a particular lesson structure. This article reports research on the implementation of this lesson structure and also on the finding that students’ responses to the lessons can be used to inform subsequent learning experiences.

Mathematics education is highly regarded as a research field within our region, especially when compared to other fields within the broader education discipline. The field has been relatively cohesive, well organised and internationally influential in a universally strong field. Mathematics education research has developed and evolved in challenging times— when other fields have become fragmented and lost vision—have we more to offer? This keynote paper considers the challenges we face as a field of research as we navigate our theoretical underpinnings and pedagogical practices, within both the mathematical sciences and broader education disciplines.

Linked research and development forms the central pillar of the 5-year Wits Maths Connect Secondary Project in South Africa. Our empirical data emphasised the need for teaching that mediates towards mathematics viewed as a network of scientific concepts, and the development of the notion of ‘mathematical discourse in instruction’ (MDI), as an analytic tool and discursive resource for working on research and professional development. This paper describes and reflects on MDI, its emergence in a particular education context, and what this discursive resource offers more generally as it works across different discourses and practices.

In recent years there has been an increased emphasis on integrating the teaching of arithmetic and algebra in primary school classrooms. This requires teachers to develop links between arithmetic and algebra and use pedagogical actions that facilitate algebraic reasoning. Drawing on findings from a classroom-based study, this paper provides an exemplar of one teacher’s journey in shifting her practice to integrate early algebra into her everyday mathematics lessons. The findings highlight the importance of addressing different areas including algebraic content, task development and enactment, and the classroom and mathematical practices to facilitate algebraic reasoning.

Effective lesson planning is a real challenge for many beginning teachers. This paper presents a case study of one such teacher, and the author’s efforts to support her in the planning process. Results show supporting the beginning teacher’s planning by (a) providing access to resources such as web-sites and teaching handbooks, (b) modelling, and (c) providing an explication of planning were insufficient to create substantive and necessary changes in the teacher’s planning during the period of research. Implications for supporting beginning teachers are considered.

Analysis of mathematical notations must consider both syntactical aspects of symbols and the underpinning mathematical concept(s) conveyed. We argue that the construct of syntax template provides a theoretical framework to analyse undergraduate mathematics students’ written solutions, where we have identified several types of symbol-related errors. A focus on syntax templates may address the under-developed symbol sense of many tertiary mathematics students, resulting in greater mathematics success, and with the potential to improve retention rates in mathematics.

We assume many things when considering our practice, but our assumptions limit what we do. In this theoretical/philosophical paper I consider some assumptions that relate to our work. My purpose is to stimulate a debate, a search for alternatives, and to help us improve mathematics education by influencing our future curriculum documents and practice.

The context in which mathematics is used is an important aspect of numeracy. Therefore, students’ numeracy capabilities need to be developed in subjects across the curriculum. The case study of a secondary school history teacher is presented to demonstrate how a framework for identity as an embedder-of-numeracy can be used to identify ways that this teacher might be supported to embed numeracy into the history curriculum. While the framework was generally effective for this purpose, a potential limitation was identified.

In this paper we report on two assessment tasks extracted from a larger study. The tasks involved number-line placements on two different number lines (0-to-10 and 0-to-20) and place-value understanding. Participants were 119 children from four different classes (Years 1-3). Children’s placements were more accurate on the 0-to-20 than the 0-to-10 number line but many found midpoint placements difficult. Children with good place-value understanding were better than their peers at making accurate number-line placements. The findings have implications for practitioners in making more explicit the connections between number and space.

Despite the Ministry of Education Statement of Intent 2014 – 2018 that the performance of the education system for priority students – Māori, Pāsifika, students with special education needs and students from low socio-economic areas needs to improve rapidly these groups remain a concern in the New Zealand Education System. This article explores what happens to a group of Pāsifika students and their teachers when the teachers draw on Pāsifika focused culturally responsive teaching in the mathematics classroom. Changes to the identity and mathematical disposition of the Pāsifika students are illustrated when their ethos becomes the cultural capital valued in the classroom using teacher and student voice.

We argue the importance of praxis in financial literacy education teaching practices that is, the moral and ethical nature of teaching and learning. Post the global financial crisis of 2008, the teaching of financial literacy has become a priority for many countries. Indigenous communities are often the target of broad FLE strategies and/or government policies. We present a case for praxis in financial literacy education by drawing on interview data following a financial literacy ‘train the trainer’ workshop in an Indigenous community in Canada that failed to gain traction.

This paper explores teacher’ ‘identity’ as two teachers talk about teaching mathematics in classrooms situated within two different contexts of learning – mainstream and alternative. Employing a form of discourse analysis framed within a participation approach to learning, this paper describes teacher identity in terms of the norms and practices that frame the translation of content, pedagogy and assessment in each teacher’s classroom. Differences between each context of learning are highlighted and parallels drawn between similarities.

This paper reports on a research project that examined the beliefs and attitudes of reluctant 16 to 18-year-old learners when using apps in their numeracy and literacy programmes. In particular, it considers the students’ change of attitude towards numeracy learning. The data were consistent that the use of apps in the numeracy programme was instrumental in transforming student attitudes towards numeracy.

This paper reports on a study of choices about the use of a computer algebra system (CAS) or pen-and-paper (p&p) by a class of seven Year 11 Mathematical Methods (CAS) students as they completed a calculus worksheet. Factors that influenced students’ choices are highlighted by comparing and contrasting the use of CAS and p&p between students. Teacher expectation of students’ use of CAS and p&p reveals that, even in a small class, the students’ use of CAS and p&p sometimes differed from what was expected. The analysis here indicates that there are a variety of factors that influence students’ decisions, including speed of calculation and accuracy of p&p work.

Mathematical knowledge in classrooms is mediated through the use of both technical and informal language. This paper is a report of a study of the language use of teachers as they examine students’ work and discuss teaching for the topic of fraction operations. This provides a window on their pedagogical content knowledge and also on the way in which language is used to make sense of mathematical knowledge, either personally or for students. It was found that some mathematical knowledge appeared to be taken as understood, perhaps because the expected words were used.

That the quality of teachers’ knowledge has direct impact on students’ engagement and learning outcomes in mathematics is now well established. But questions about the nature of this knowledge and how to characterise that knowledge are important for mathematics educators. In the present study, we examine a strand of Specialised Content Knowledge, SCK (Ball, Thames and Phelps, 2008) of a group of pre-service teachers in the domain of proportional reasoning. In particular, we were concerned with teachers’ knowledge of evaluation of the plausibility of students’ claims and errors. Our preliminary results indicate that the participants, as a group, had developed a sense of student error but experienced difficulty in explaining the source of these errors.

A central premise of this project is that teachers learn from the act of teaching a lesson and that this learning is evident in the planning and teaching of a subsequent lesson. In this project, the knowledge construction of mathematics teachers was examined utilising multicamera research techniques during lesson planning, classroom interactions and reflection. Our goal is a refined understanding of classroom events that create opportunities for teacher learning. This paper reports what one Year 5 teacher appeared to learn from the process.

The practices of effective primary school teachers including students with Down syndrome in their mathematics classes are largely unexplored and many teachers feel unprepared to teach students with intellectual disabilities. A study with cohorts in Victoria and the ACT is underway and here we report a subset of findings concerning the support teachers claim to require. There was an identified need for mathematics specific resources and strategies but a strong endorsement of inclusion as an appropriate practice in primary mathematics.

Fractions are a well-researched area; yet, student learning of fractions remains problematic. We outline a novel path to initial fraction learning and document its promise. Building on Freudenthal’s analysis of the fraction concept, we regard comparing, rather than fracturing, as the primary activity from which students are expected to make sense of fractions. Analysing a classroom design experiment conducted with a class of 14 fourth grade pupils, we identify two successive mathematical practices that emerged in the course of the experiment and indicate how their emergence was supported.

This paper reports an aspect of a large research and development project that aimed to promote middle years school teachers’ understanding and awareness of the pervasiveness of proportional reasoning as integral to numeracy. Teacher survey data of proportional reasoning across the curriculum were mapped on to a rich model of numeracy. Results provided evidence of extensive and creative teaching of proportional reasoning in all learning areas. The capacity of such tasks and activities for promoting student numeracy is theorised.

This study examines a teacher’s questioning strategies in mathematics classrooms in China when implementing reform-based mathematics curriculum. It explores teacher’s strategies to deal with the tensions involved in the creation of opportunities for students to express and communicate mathematics ideas while ensuring the productivity of mathematics communication and the accomplishment of the lesson goals in a limited period of time. By doing so, this study has implications for teacher education and professional development in terms of how to strengthen the links between intended mathematics curriculum reforms and teacher’s actual practices in mathematics classrooms.

A small study of active reflection was undertaken with 21 primary students in a Prep and Year 1 classroom. To provide feedback from the students on their views about their personal learning and ways they could be better supported to learn mathematics a simple survey was supplemented by one-to-one interviews. Students’ perceptions of their learning of mathematics, their identification of the mathematics they were learning; and what they felt would better cater for their learning needs. Ongoing reflections by students and the teacher throughout the year provided further data for consideration. The findings show that young students are self-aware, they understand what they are learning and they have ideas about ways their teacher could support their learning. These findings fed into the teacher reflection process and professional learning, which in turn led to some changes in classroom practice.

Lesson Study has captured the attention of many international educators with its promise of improved student learning and sustained teacher growth. Lesson Study, however, has cultural underpinnings that a simple transference model overlooks. A culturally embedded approach attends to the existing cultural orientations and values of host schools. This paper reports on the author’s implementation of Lesson Study in a Philippine public school and the growth teachers experienced as a result of their participation.

The relationship between the self-efficacy of 23 High School students with intellectual disability (ID) and their achievements in Mathematics was evaluated using a modified version of the self-efficacy instrument developed by Joet, Bressoux and Usher (2011). Four different number sense assessment tools were administered pre- and post- six months of instruction to measure their Mathematics achievement. Relevant data analyses were carried out with Minitab statistical software. While the mean self-efficacy was found to be about 65%, the correlation between self-efficacy and the mathematics achievements of students was weak.

Having students address mathematical inquiry problems that are ill-structured and ambiguous offers potential for them to develop a focus on mathematical evidence and reasoning. However, students may not necessarily focus on these aspects when responding to such problems. Argument-Based Inquiry is one way to guide students in this direction. This paper draws on an analysis of multiple primary classes to describe core elements in Argument-Based Inquiry in mathematics.

The emphasis on science, technology, engineering, and mathematics (STEM) education in recent times could be perceived as business as usual or as an opportunity for innovation and change in mathematics classrooms. Either option presents challenges for mathematics educators who are expected to contribute to the foundations of a STEM literate community. A greater understanding of the implications of a STEM education for mathematics education is needed. This paper seeks to add to conversations about the implications of STEM education for the learning and teaching of mathematics.

This paper is a reflective critique of practice within the field of mathematics education in relation to the challenges faced by non-first-language-English speaking academics when they attempt to publish in English language research outlets. Data for this study are drawn from communications between a German and an Australian academic as the Australian assisted the German in negotiating aspects of translation bound by syntactic, semiotic, cultural, and colloquial language considerations. The paper concludes by raising questions about the issue of the use of English as a universal language for the dissemination of new knowledge and offers possible solutions to the problem.

Let’s Count is an early mathematics program that has been designed by The Smith Family and the authors to assist educators in early childhood contexts in socially disadvantaged areas of Australia to work in partnership with parents and other family members to promote positive mathematical experiences for young children (3-5 years). A longitudinal evaluation of Let’s Count was undertaken in 2012-2014 involving 337 children in two treatment groups and 125 children in a comparison group. This paper shares preliminary results from the evaluation. Overall the findings demonstrate that Let’s Count was effective.

This paper compares the counting and whole number knowledge and skills of primary school children in Australia and Germany at the end of Grade 1 and Grade 2. Children’s learning was assessed using the Early Numeracy Interview and associated Growth Point Framework. The findings highlight substantial differences between the two groups that vary for the four whole number content domains that have been investigated. These variations are likely due to different curriculum emphases in the two countries.

This paper reports on a project that aims to foster interdisciplinary collaboration between mathematicians and mathematics educators in pre-service teacher education. The project involves 23 investigators from six universities. Interviews were conducted with selected project participants to identify conditions that enable or hinder collaboration, and to identify learning mechanisms at the boundaries between disciplinary communities. A hybrid narrative constructed from the interviews is used to illustrate transformation as a learning mechanism that leads to new practices.

While principals and systemic leaders have a significant role to play in leading, supporting and structuring mathematics education, their influence tends to be indirect and general. However, middle leaders such as curriculum leaders, senior teachers, and faculty heads, exercise their leadership much closer to the classroom, and as such they can have a more direct influence on the quality of teaching and learning in schools. To improve mathematics learning outcomes of student, it is crucial that educational leading is practiced by those with the greatest capacity to bring about positive practical and sustainable change – middle leaders. These school-based curriculum leaders can promote this development by engaging in forms of Critical Participatory Action Research that allows them to improve the quality of teaching and learning through an evidence-driven, site-based, collaborative approach.

Concerns regarding the dominance of the traditional written algorithms in schools have been raised by many mathematics educators, yet the teaching of these procedures remains a dominant focus in in primary schools. This paper reports on a project in one school where the staff agreed to put the teaching of the traditional written algorithm aside, replaced with computational strategies. The results reinforce a belief that I have held for many years that the traditional algorithms should be removed from the primary mathematics curriculum.

In Māori medium schools, research that investigates children’s mathematical computation with number and connections they might make to mathematical ideas in other strands is limited. This paper seeks to share ideas elicited in a task-based observation and interview with one child about the number ideas she utilises to solve a problem requiring probabilistic thinking. The explanations provided by the child demonstrate how early number and spatial patterns can impact on computation, ease of determining possible outcomes and assigning a numerical probability measure to an event.

In this paper, an examination of students’ relationships with mathematics is informed by affective research into internal mathematical structures and identity research into students’ narratives. By analysing the perceptions of a class of 31 adolescents, five interacting elements emerged: students’ views, feelings, mathematical knowledge, identities, and habits of engagement. These elements contributed to the context within which students engaged in mathematics and resulted in their unique learning experiences. This framework has potential for researching aspects of students’ mathematical journeys and can be used by teachers to get to know individual students’ unique connection to the subject of mathematics.

When viewed through a lens of embedded cognition, algorithms may enable aspects of the cognitive work of multi-digit multiplication to be ‘offloaded’ to the environmental structure created by an algorithm. This study analyses four multiplication algorithms by viewing different algorithms as enabling cognitive work to be distributed across environmental and mental resources to varying degrees. This produces a plausible framework which could allow further analysis designed to guide the pedagogical use of alternative algorithms.

This paper describes the lesson practices at one very remote school that has been highly successful in numeracy. Drawing on a significant body of diverse research that promotes quality teaching and learning, this case study describes the features of the practice that have been implemented across the school. Teachers’ voices provide both justification for the adopted practices and insights into why the practices have been effective within the context of the school. Finally, consideration is given to the on-going sustainability of changed practices within the school.

This paper explores the value of different paradigms to explain dispositions towards mathematics among primary school students from different social backgrounds. As part of a larger project designed to elicit students’ thinking and attitudes towards mathematics, we seek to develop an explanatory model for the socially-differentiated outcomes in students’ responses. The three paradigms – psychology, sociology and post-modernism – form the basis of the paper where the data we collected from three geographically close but socially different schools were analysed.

The aim of this study was to investigate the role of the instructional leader when introducing digital technology into the mathematics teaching in the Australian Curriculum. The research reported here involves the principal and five teachers from one school and is part of a larger study. Results indicated that principal-led ‘crucial conversations’ supported educational change that comprised not only curriculum change but also a transition from a pedagogy that draws on technology to a pedagogy in which technology is embedded.

As the use of mathematics apps in classrooms becomes more prevalent, robust research into their effectiveness is required to inform best practice regarding their use. This is particularly the case for Geometry apps where accurate and dynamic representations are critical in enhancing mathematical learning. This paper provides findings from an initial critique of 53 Geometry apps. Early findings indicate that the majority of these apps were limited in their ability to assist students in developing Geometrical conceptual understanding; however, all is not lost as a number of apps were highly appropriate.

Data from a pilot study concerned with pre-service teachers’ perceptions of the numeracy demands on Australian teachers are reported. The sample comprised 211 students enrolled in pre-service teacher education courses at a large Australian university. While most recognised the importance of mathematics and its applications in everyday life, less than half considered there were mathematical demands on teachers beyond their teaching domain. NAPLAN-related information data was used to examine the group’s ability to access, apply, and interpret the statistical information.

Exploring why more boys than girls continue to study higher levels of mathematics in senior school when there appear to be no gender differences in achievement in earlier years is worthy of investigation. There are potentially many reasons why this occurs including career aspirations, interest, and attitudes. One factor explored in this study was the gender composition of classes in Years 7 to 9. Data were collected from students in a single-sex boy’s school, a single-sex girl’s school and a coeducational school. Data revealed differences in attitude to mathematics with girls in the single-sex school having the most positive attitudes and girls in the coeducation setting having the least positive attitudes.

Geometric competences of students have sparked great concern in Taiwan since the release of last TIMMS assessment. Geometric argumentation is viewed as to play an important role to enhance the competences of geometry and reasoning. This study adopts Toulmin’s (2003) model to develop such indicators, including naming, supporting ideas, and transformation reasoning. It is expected that further research will provide empirical evidence in these indicators to apply to topics in mathematics other than geometry.

This position paper discusses the role of open access research data within mathematics education, a relatively new initiative across the wider research community. International and national policy documents are explored and examples from both the scientific and social science paradigms of mathematical sciences and mathematics education respectively are provided. Within these examples, some of the more well-known concerns associated with making data open and accessible are acknowledged and debated.

This article presents a snapshot of the mathematical competencies of children aged four to five years in Australian early childhood education settings, as perceived by their educators. Data are presented from a nationally-representative sample of 6511 children participating in the Longitudinal Study of Australian Children (LSAC). The results reveal that children are seen to possess a number of mathematical competencies at 4-5 years, with the majority of children displaying interest in mathematics. Moreover, differences were noted with respect to the different program types in which the children participated. These results are discussed in relation to previous research, and implications for future research, policy and practice are presented.

Teacher knowledge, including Pedagogical Content Knowledge (PCK), continues to be the focus of research, with the general consensus being that PCK impacts upon teaching and learning. Much of the current research has focused on pre-service teachers and practicing primary teachers, with few studies focused on studying senior secondary teachers’ PCK. Even rarer are studies which examine PCK from students’ perspectives. This study investigates the nature of PCK as experienced in a lesson by a class of senior secondary mathematics students. The findings indicated that there were a number of PCK elements incorporated in the lesson and that these were noticed by the students.

Developing mathematical inquiry practices requires that teachers are explicit about classroom norms that support these practices. In this study, we asked: How can a teacher scaffold the development of norms and practices in mathematical inquiry over time? Analysis of classroom video over a year showed that the teacher constantly diagnosed classroom norms and responsively used strategies to improve them. By the end of the year, there was evidence of inquiry norms and practices independent of the teacher’s presence.

Middle Years students often do not see mathematics as useful. Authentic and real mathematics tasks and artefacts are frequently advocated as arresting this situation. However, often such experiences are contrived and lack authenticity. This paper reports on how a group of Middle Years students used mathematics and technology to engage in a real community issue, of the need for a teenage safe space, to inform local Council policy. Data were collected for this case study via journal observations and reflections, semi-structured interviews, samples of students’ work and videos of students working. The data were analysed by identifying the main themes that were connected with designing and locating the space and focused on the stages of the statistical investigation cycle used. How this impacted students’ beliefs about the usefulness and value of mathematics is discussed.

Recent research findings indicate that using multiple metaphors in multimodal learning experiences are effective teaching approaches in early years mathematics. Using a social semiotic lens this paper reports on eight early years teachers’ perceptions of this approach whilst engaging in a small collaborative professional learning group. This group focussed on observing video footage of one teacher implementing multiple metaphors such as the number line and using multimodalities such as gesture, drawings and concrete materials in her classroom. Analysis of the data revealed variations in the teachers’ perceptions of this particular teaching approach.

The aim of this study was to determine the role of semiotics in assisting young Indigenous students to engage with and identify the general structure of growing patterns. The theoretical perspective of semiotics underpinned the study. Data are drawn from two Year 3 students, including analysis of pretest questions and two conjecture-driven lessons. Results indicate that particular semiotic signs (iconic signs) contribute to how young Indigenous students attend to, and identify the structure of growing patterns.

This paper presents findings as part of a wider study that investigated the professional knowledge of teachers when teaching mathematics for numeracy in the primary school classroom. This paper focuses on teachers in action as they taught two lessons on multiplication. It outlines the specific pedagogical categories the teachers used and the impact their knowledge had on student learning.

Participation in society is increasingly dependent on educational achievement. Accordingly, society as a whole is committing more resources to education to prevent the adverse outcome of students moving through the school system only to emerge without the knowledge and skills that they might be expected to attain. In this paper, we explore the application of two models developed to prevent adverse outcomes in industrial and medical settings to the issues involved in providing an optimal mathematics education for all children.

Traditionally, the domain of higher education, the ‘flipped classroom’ is gaining in popularity in secondary school settings. In the flipped classroom, digital technologies are used to shift direct instruction from the classroom to the home, providing students with increased autonomy over their learning. While advocates of the approach believe it is more engaging and effective than traditional instruction, there is little empirical research into the benefits of this approach, particularly in relation to mathematics instruction. This paper adds to the limited research by reporting on students and parents’ experiences with a flipped classroom in a senior mathematics class. The results indicated that there were five main components that influenced students’ motivation to engage with the flipped classroom approach. The study has particular implications for students and secondary mathematics teachers who have limited time to make the curriculum comprehensible for students and to prepare them for external assessment tasks.

This paper presents a preliminary study of three six year-old children’s use of functional language when engaging collaboratively on a mathematics task. The analysis is presented as an illustration of young children’s authority and agency in mathematics as evidenced in their discourse. Modality, as a function of language, was seen to indicate reasoning as a semantic process that expressed a state of knowledge as the children explored number comparison relationships. It is proposed that the children’s use of modality indicated an element of internal authority in arbiting mathematical correctness and that related to the nature of the task.

As part of a study examining how teachers in Singapore select and use examples for teaching mathematics, 121 teachers from 24 secondary schools responded to three openended questions about the use of examples in teaching. The results show that students’ abilities and the difficulty level of the examples were among the topmost considerations teachers have when introducing mathematical ideas or when selecting homework tasks. This paper also reports on teachers’ perceptions of a good example.

Growth mindsets are vital for effective lifelong learning. Students with growth mindsets are more willing to learn new things, take risks, and embrace challenges. Students with fixed mindsets have limiting beliefs about their abilities, and will attribute success in learning to factors beyond their control. Inquiry in mathematics classrooms may have the potential to facilitate growth mindsets. This paper provides an analysis of inquiry mathematics in a primary classroom and reflects upon its potential to foster growth mindsets in classrooms.

This case study narrative reports on the journey of *Sammy as her mindset as a learner of mathematics is challenged. Often students who are mathematically highly capable are viewed as being privileged, they are rarely placed with the cohort of struggling students. Children like Sammy who are mathematically highly capable or gifted, however, are simply students who learn differently and therefore require a different type of teacher support. [*Sammy is a pseudonym].

This study investigates the potential of Facebook as a medium and process for teachers’ learning about mathematical and pedagogical knowledge. Participants’ (N=117) responses towards four inter-related posts regarding division-of-fractions were captured and systematically analysed to gain insight about the participants’ engagement. The results suggested the potential of Facebook to support informal teachers’ learning. This was evidenced by the existence of the three main elements of community of practice (CoP): mutual engagement; negotiated joint enterprise; and development of a shared repertoire.

Many researchers argue that a deep understanding of fractions is important for a successful transition to algebra. Teaching, especially in the middle years, needs to focus specifically on those areas of fraction knowledge and operations that support subsequent solution processes for algebraic equations. This paper focuses on the results of Year 6 students from three tasks from a Fraction Screening Test that demonstrate clear links between algebraic thinking and students’ solutions to fractional tasks involving reverse processes.

Increasing numbers of primary pre-service teachers (PSTs) enrolled in Education degrees in Australia enter university with insufficient mathematical content knowledge (Livy & Vale, 2011) and low confidence levels about their ability to teach and do the mathematics required for their intended role as classroom teachers (Wilson, 2009). Mentoring of PSTs by highly capable and experienced classroom teachers, within the framework of a structured and well-planned mentoring programme (Hudson & Peard, 2006), has the potential for developing the confidence, and thus alleviating the mathematics anxiety exhibited by PSTs.

This study investigated potential gender differences in a sample of 807 Year 6 Singaporean students in relation to two variables: spatial visualisation ability and cognitive style. In contrast to the general trend, overall there were no significant gender differences on spatial visualisation ability. However, gender differences were prevalent among students who possessed high spatial visualisation ability, in favour of boys. In terms of cognitive style, there were significant gender differences in the spatial imagery and verbal information processing dimensions. Boys gave higher ratings to their spatial-imagery encoding and processing preferences than their verbal information processing preferences. Some of these findings are in contrast to studies undertaken in the educational-psychology literature. Implications are drawn regarding pedagogical practices in Singaporean schools.

This paper describes a pilot study investigating Teacher Aides (TAs) in primary mathematics classrooms. Three teacher/TA teams were investigated. The teachers were asked about the role of TAs in their classrooms, and the TAs were asked about their confidence in mathematics and in the desirability of professional learning. The TAs indicated a need to update their knowledge of mathematics content and terminology. It is also suggested that more research to investigate methods of assisting students with learning difficulties is required.

The research presented in this paper focuses on the cognitive diagnostic strategies that prospective elementary mathematics teachers (PTs) use in their reflections of one-on-one diagnostic interviews with children in grade one. Thereby, it responds to the detected lack of knowledge regarding qualitative facets of diagnostic proceeding in interview assessments. Results include facets of collecting data and facets of interpreting within a diagnostic micro-process. The discussion takes up the relevance of these findings for teacher education.

As part of a project that is examining how to support teachers in the use of challenging tasks and those teacher actions that encourage students to persist, we focused on the activities of students and teachers during seatwork. We describe the nature of teacher interactions with students, student behaviours when working on challenging tasks, and the relationships between the two. Interactions that seemed most beneficial were brief, and usually preceded by the teacher watching and listening to the students at work.

Programming and the use of robotics present affordances for mathematics learning with application across a broad range of ages. However, realising these affordances in the classroom requires educators to recognise and build apron these potential opportunities for learning. This paper reports one component of a larger study, examining teacher discourse in semi-structured focus group as they review engagement with robotics. Data highlights limited engagement in mathematisation and the key role of mathematical pedagogic content knowledge (PCK).

Statistics is a domain that is taught in Mathematics in all school levels. We suggest a potential in using an interdisciplinary approach with this concept. Thus the development of the understanding of a situation might mean to use both mathematical and statistical reasoning. In this paper, we present two case studies where two middle school Mathematics teacher taught a lesson in Statistics where the students had the task create a pie graph representing the data. Results show us that their procedural vision of Statistics lead them to focus more on a graphical representation and thus led to avoid all statistical reasoning development (Garfield, 2002).

This article reports the findings of research involving more than 30 teachers and their Year 5 and 6 students in 16 Victorian primary schools. The participants experienced an educational intervention where the “Money and Financial Mathematics” substrand of the “Number and Algebra” content strand was taught and learned through challenging worded mathematical problems involving realistic financial contexts. Data related to one such example, a task involving three friends sharing the cost of movie tickets and food, are discussed. Insights into the nature of student

The guiding philosophy of this theoretical work lays in the argument that mathematics teachers’ professional knowledge is the integration of various knowledge facets derived from different sources including teaching experience and research. This paper goes beyond past trends identifying what the teachers’ knowledge is about (content) by providing new perspectives, in particular, on how the knowledge is structured and organised (form), on what teachers’ draw on their knowledge (source), and whether the knowledge is stable and coherent or contextually-sensitive and fluid (nature).

This paper reports part of an ongoing investigation into aspects of pre-service teachers’ geometric knowledge. One hundred and fifty-two Australian pre-service teachers responded to a series of questions that reflect the type of knowledge teachers are expected to know and teach. Analysis of their responses shows that teacher knowledge can be understood through the interplay between individual teachers’ formal figural concepts and personal figural concepts. Errors and misconceptions of geometric properties can be addressed by strengthening the link between formal and personal knowledge through visualisation.

In this study we examine the use of cumulative and exploratory talk types in a year 5 computer supported collaborative learning environment. The focus for students in this environment was to participate in mathematical problem solving, with the intention of developing the proficiencies of problem solving and reasoning. Findings suggest that students engaged in exploratory talk may more regularly attempt the use of technical (tier 3) mathematical vocabulary.

There is an identified and growing need for a levelled diagnostic basic facts assessment tool that provides teachers with formative information about students’ mastery of a broad range of basic fact sets. The Individual Basic Facts Assessment tool has been iteratively and cumulatively developed, trialled, and refined with input from teachers and students to meet that need. The development of the tool, results from test trials, and our next steps are described in this article.

How teachers position themselves and their students can influence the development of afforded or constrained local moral orders in ability-based teacher-led mathematics lessons. Local moral orders are the negotiated discursive practices and interactions of participants in the group. In this article, the developing local moral orders of 12 teachers and their highest and lowest mathematics groups are examined with particular attention paid to teacher positioning and the patterns of differentiated positioning between the groups.

Reasoning is considered to be an important proficiency in national mathematics curricula both in Australia (ACARA, 2014) and Malaysia (MOE, 2013). However, the nature of reasoning that supports learning and problem solving in mathematics is an area that requires further study (Schoenfeld, 2013). In this study we explored the link between Scientific Reasoning Skills (SRS) and mathematics problem solving performance among a cohort of Malaysian students. As expected, there was a positive relationship but the level of correlation between these two variables was moderate. Although the High-Achievement group performed significantly better than their peers in the Low-Achievement group in their solution outcomes, overall, all students exhibited low-levels of SRS. These findings suggest that while SRS could play a role in problem solving, components of SRS need further analysis in order to better explain how reasoning in science could facilitate problem solving processes.

In the current reform of mathematics classrooms teachers are charged with the role of facilitating collaborative groups during problem-solving activity. The challenge is for teachers to engage students in making mathematical meaning during collaborative group discussions. In this paper we draw on the concept of adaptive expertise to report on teachers’ actions to engage students in co-constructing collective knowledge. We address how teachers attended to students’ cultural values and socio-mathematical norms to promote and cultivate adaptive expertise.

Responses of 223 students in grades 6 to 11 to questions related to beliefs about getting out of bed on the left side are analysed from two perspectives. On one hand the items explore subjective beliefs about chance. On the other hand the different wording and context of the items provide opportunity to show different levels of understanding of students’ explanations. Rasch analysis is used to place the items on a scale with other statistical literacy items in order to suggest potential levels of difficulty.

The phenomenon of the ‘middle-years dip’ in mathematics engagement and achievement has been a cause of concern for over a decade. This paper presents an example of one upper-primary classroom identified as having higher than average levels of student engagement, with the purpose of documenting specific teaching strategies that align with known key elements of motivation and engagement. Drawing on evidence from teacher interviews, observation notes and lesson video with recorded dialogue, we argue that particular types of one-to-one interactions between teacher and student can have a powerful influence on student engagement.

This paper presents results from a survey of 80 parents and 120 secondary school students in Australia. Many parents report that their children put in all their effort into mathematics education but they believe that their children can do better if they try harder. This paradox is more evident among parents from Asian-Australian backgrounds compared to parents from other backgrounds who also report having high expectations in mathematics education, which is not the common perception in Australian media and society.

Mathematics anxiety affects primary pre-service teachers’ engagement with and future teaching of mathematics. The study aimed to assess the level and range of mathematics anxiety in first year pre-service teachers entering their teacher education course, and to investigate the sources of this anxiety as perceived and identified by them. Data collection methods included the RMARS survey, and Critical Incident Technique. The results indicate that the most common negative impacts on pre-service teacher mathematical self-concept involved experiences with teachers. However, their current mathematics anxiety is most commonly aroused under testing or evaluation situations.

This article reports on initial findings, including the mathematics components, of a multiinstitutional Science,Technology, Engineering, and Mathematics (STEM) project, It’s part of my life: Engaging university and community to enhance science and mathematics education. This project is focussed on improving the scientific and mathematical thinking of pre-service teachers (PSTs) by aligning their pedagogy with the scientific and mathematical thinking that occurs in authentic, real-world contexts. This article discusses emotional literacy and emotional regulation as aspects of self-reflective professional development and how these measures are conceptually related to improving competence and confidence for pre-service STEM teachers. This report details how emotional feedback was used in trials of a pilot program to enable PSTs to analyse, understand, and make use of emotional information to improve their teaching confidence, particularly in mathematics.

Learning mathematics is a complex and dynamic process. In this paper, the authors adopt a semiotic framework (Yeh & Nason, 2004) and highlight programming as one of the main aspects of the semiosis or meaning-making for the learning of mathematics. During a 10 week teaching experiment, mathematical meaning-making was enriched when primary students wrote Logo programs to create 3D virtual worlds. The analysis of results found deep learning in mathematics, as well as in technology and engineering areas. This prompted a rethinking about the nature of learning mathematics and a need to employ and examine a more holistic learning approach for the learning in science, technology, engineering, and mathematics (STEM) areas.

Multiplicative thinking is required when engaging in proportional reasoning tasks. While proportional reasoning does not always develop naturally in students, providing students from a young age with tasks that require students to think multiplicatively may lay the foundation for them to do so. This paper reports the findings of Grade 3 students’ performance on tasks relating to different multiplicative structures and the influence of each structure on students strategy choice.

IMPELS is an Individualised Mathematics Planning and Evaluation of Learning Tool for Students with Intellectual Disability. IMPELS was evaluated against 3 number sense tools and subjected to standard validity and reliability assessments. Results obtained indicated that IMPELS correlated strongly with the tools, ranging from 0.70 to 0.91 and 0.45 to 0.70 for Pearson and Spearman’s Rho correlation coefficients respectively. Cronbach’s alpha and Spilt-Half Reliability (KR-20) was 0.96. IMPELS is useful for the collection of baseline data to inform the development of individual education plans (IEPs) and for monitoring the progress of learning of individual students.

This paper presents the theoretical findings from a PhD study into assessing mathematical learning in an inquiry context. The pedagogy of inquiry will continue to struggle to prove its worth, while student improvement in mathematics continues to be measured in terms of data gained through assessment designed for more traditional pedagogies. Findings from this study revealed high levels of student thinking about mathematics in inquiry when teachers artfully engineered feedback gained through formative assessment into teaching and learning experiences. Learning mathematics in inquiry reflected a complex and highly interactive journey, not easily measured using traditional school assessment practices.

Professional development for teachers utilises a significant portion of school budgets. Too often the impact on the performance of teachers, individually or collectively or on the learning outcomes of students is limited. One school principal devised a mentoring system that has been shown to bring about profound and sustainable cultural change, where all staff willingly take responsibility for their own professional learning and play a crucial role in the professional development of their peers.

This paper reports on continued research of student produced mathscasts to support learning. Teachers and pre-service teachers, enrolled in a university course, were asked to create and peer-critique mathscasts to explain concepts in middle school. This paper discusses results of students’ use of a mathscast rubric that was developed by the authors to assist in the creation and evaluation of mathscasts. Surveys, practice mathscasts with informal feedback, and students’ final mathscasts are analysed. The paper concludes with an outline of future directions.

Algebra is essential in higher mathematics and initiation into the language and conventions of algebra, and the development of algebraic thinking, are crucial in the earlier years of schooling. It is the teachers’ beliefs about the nature of mathematics and teaching and learning which underpins their approach to teaching algebra. In this paper, we explore the strategies used by four teachers to teach beginning algebra.

Information Technology (IT) plays an educational role of organising the learning environment to promote social interaction among students as well as between students and a teacher but little has been known about what underlying factors influence such social interaction within the context of statistics learning. A questionnaire-based survey was therefore conducted to gather data relevant to this issue. The data were then summarised by using Factor Analysis into factors: co-learning, teacher’s scaffolding assistance, positive working relationship linking with social interaction.

An important issue related to the current discussion about teachers’ knowledge and qualifications is to improve and enhance their preparation of numeracy skills. Further studies, including longitudinal studies designed to identify mathematical content knowledge (MCK) pre-service teachers’ gain during teacher education are important for course design and developing effective primary numeracy teachers. This paper reports on one pre-service teacher’s development of MCK but was informed by an historical overview of theoretical frameworks and the findings of a four-year longitudinal study of 17 pre-service teachers’ MCK. The results identified how and when different categories of MCK were developed and can be used to improve future course design.

With an interest in children’s learning of mathematics and ways to gain insights into this learning, we explore the possible value of an open-ended self-assessment task, Impress Me, and follow-up interview. Ten children in their first or second year of school recorded their understandings using drawing and/or writing during the period in which they were taught lessons on mass measurement and then met individually with an interviewer/researcher to discuss their portrayal and their learning. The Impress Me recording was found to be a useful initial prompt to stimulate discussion and other effective interview prompts are identified in this paper.

The Australian curriculum now recognises the importance of language in mathematics learning. However, little recognition is given to the fact that most urban schools have many students who are from families who speak a non-English first language (L1). Participants in this session will be introduced to a language-use model for teaching mathematics. This model can be used in planning mathematics lessons that will highlight important aspects of language, particularly for English as a later language ELL students’ learning. Examples will come from research carried out in Papua New Guinea with multilingual teachers.

This paper reports first results of a 3-year longitudinal study that seeks to explore the impact of early number skills and knowledge as demonstrated prior to school on achievement in school mathematics at the end of junior primary school. The study investigates the development of early numeracy understanding of 334 children from one year prior to school entry until the end of grade 2. The study identifies second graders that are vulnerable in their mathematics learning and compares their performance with their achievements over the past three years.

The issue of quality teachers has been well debated internationally. Both Ireland and England have previously flagged their concern about the lack of qualified teachers in secondary mathematics and overreliance on traditional teaching methods. The UK response to improving teaching standards has included changes to the structure of teacher training and skills testing and currently in Australia the topical education issue is the introduction of similar skills test for all trainee teachers. Despite facing similar issues, Ireland didn’t follow suit with skills testing. Instead the Irish government opted to implement a number of strategies which included the upskilling of practising teachers of mathematics. However, while this addressed one side of the issue a key aspect of the challenge still remained “challenging pre-service teachers to do more than talk the talk’ (Prendergast et al., 2013). Hence, this paper aims to present the Mathematics Education team’s (at University of Limerick) response – “Mathematical Thinking”

The aim of this paper is to examine transitions between phases of a modelling process in cases of introduction of square root using paper and electric geoboard. The method is to analyse construction by media based on McLuhan’s media theory (McLuhan, 1987; Tokitsu, 2012). As conclusions, the followings about the both cases are found; (1) transitions between phases of the modelling process are same but constructions by media are different, and (2) a new mathematical problem can be posed because of the constructions by media.

In this paper, the knowledge dimension of Revised Bloom’s taxonomy (RBT) in the context of integration in stage 1 university calculus is presented. For this purpose, eleven subcategories of the knowledge dimension of RBT are introduced and through document analysis of chapter 4 of the handbook of RBT, subcategories are defined. Then, using materials frequently employed for teaching integration, the knowledge dimension of RBT in the context of integration is explored. The study findings may enable enhanced opportunities for dialogue between teachers, lecturers, and researchers about metacognitive knowledge in relation to teaching integration and to the development of tools for designing educational objectives, teaching activities, and assessments based on RBT.

In this study, a video excerpt of two boys working on a mathematical open-ended problem is discussed. In the video, affective and social factors overrule development of logical thinking. Analysing such an episode is challenging, as appropriate tools are few. This study elaborates the video excerpt to find out what affective, cognitive and social phenomena exist in the episode, aiming to develop an analysing tool for such purpose. In addition, a framework called Patterns of Participation will be adapted to test its purposefulness to the analysis. As a result, it was found out that most of the essential features of the episode were revealed. However, it is suggested including theories of emotions, student engagement and positioning would make the tool more profound.

Forty-five Grade 7 students from a larger sample of 118 were interviewed on the thinking strategies they used in solving number sense problems. Students were categorised into high, middle and low ability groups. Students were asked a series of questions designed to assess the thinking strategies they used in solving number sense questions. The study also investigated the extent to which misconceptions and learned rules were sufficiently fixed that they continue to influence students’ responses despite having been given lessons on number sense. Results show that many students continued to apply rule-based methods in attempting to solve number sense questions.

This is a presentation on a focus question approach to teaching mathematics (FFQA) which is the title of my thesis. It is proposed to investigate the impact of the FFQA at the commencement of each mathematics lesson on the learning and motivation of students. The style of five questions that I propose to investigate has the first four questions as instrumental style questions that focus on procedural knowledge, with the final question using a relational understanding approach with some of the questions being open ended investigational style questions focusing on conceptual knowledge. The research is ongoing.

Three pre-service teachers (PST) who had no prior experience with lesson study had to use a lesson study approach to plan and teach a problem solving lesson. This paper documents how the three PSTs were initiated into the Japanese style of lesson study and then how as a team they went about planning their research lesson on problem solving for a primary three class and then teaching it. The focus is on some of the issues that surfaced when preparing this problem solving lesson on magic squares and how they addressed them.

Engaging cohorts including less quantitatively-adept students and educating them about the value of Statistics has its challenges. This talk will outline two successes: the first resulted in a first-year Statistics for Business course increasing student satisfaction scores from under 3.5 out of 5 to 4.72 whilst maintaining ‘challenge’ scores and reducing Failure rates previously exceeding 25% to 7-12%; the second is a national project-based learning activity (piloted in the Hunter Region in 2014) which facilitates boundary encounters (between secondary, tertiary, and industry sectors and students having varied backgrounds and areas of interest) and develops key communication, research and quantitative skills.

The language model of mathematics is a useful framework to conceptualise the teaching and learning of mathematics from a constructivist perspective. The model currently proposes that students move along two dimensions (visual and verbal) towards increasing levels of mathematical abstraction. We present the case for theorising the existence of a third dimension, the gestural, by drawing upon established theories of learning within mathematics and also from brain based learning. Examples will be provided on how the addition of the gestural dimension can enhance mathematics education at all levels.

Educating teachers in Indigenous communities to use collaborative mathematics is a challenge. This is particularly the case in developing countries such as Papua New Guinea. First there are the issues around the perception of authority and questioning in school. Second, there is the issue of class atmosphere and teacher pedagogical knowledge. Third is the issue of meeting different needs in large under-resourced classes. Finally there is the issue of teacher professional learning. This paper discusses one attempt that has led to an increased awareness and use of the role of questioning in the classroom. It points out some of the aspects of teacher development and what seemed to be contributing to change.

Human environmental interactions involve general conceptual connectivity processes such as categorisation, abstraction and generalisation. These are linked to the development of mathematics concepts, but research in this area is relatively new in mathematics education. A conceptual connectivity lens, however, has been used in cases where there are difficulties in mathematics learning, such as developmental dyscalculia, as well as in studies of mathematical pattern and structure with young gifted children. This presentation suggests that such studies support the determination that individual differences in processing of environmental information are an important way forward in understanding what underpins mathematics conceptual development.

This presentation examines a student’s learning of the limit concept of a sequence compatible with his strategy of making sense, through which the structural abstraction framework evolves and is further refined. The attention is focused on a student’s generic representation of the limit concept that allows him to generate meaningful components specific to particular contexts. Further, a sketch of the basic ideas of structural abstraction is given, and the use of the generic representation as a resource to reconstruct the meaning of the concept at need is discussed. Additionally, the importance of structural abstraction for learning mathematics is elaborated.

The use of iPads in education is increasing, with increasing numbers of studies focussing on teacher use of this tool in mathematics teaching and learning. As a stakeholder group, the views of students must also be investigated. As part of a larger case study, the views of Year 5 to Year 12 students from one Victorian school were sought about the use of iPads in mathematics. A number of concerns related to the perceived negative impact of iPad use in mathematics learning arose and will be further explored in the presentation.

Declining enrolments in STEM disciplines and a lack of interest in STEM careers is concerning at a time when society is becoming more reliant on complex technologies. We examine student aspirations for STEM careers by drawing on survey data from 8235 school students in Years 3 to 11 who were asked to indicate their occupational choices and give reasons for those choices. These data are also examined in relation to student SES, gender, prior achievement and educational aspirations. The analysis provides a strong empirical basis for understanding current student interest in STEM and exploring implications for educational policy and practice.

This new project explores the similarities and differences of mathematical thinking and ‘general thinking’, as well as related motivational and emotional aspects, focusing on how these differ in educational contexts. It will examine assumptions of the underlying feature of mathematics curriculum design and pedagogy, for example, that linear structure is the most efficient means of building mathematical knowledge or that number-based knowledge is a reliable indicator of mathematical skill. Insights gained will be used to improve the current paradigms in course structure and pedagogy for classroom mathematics in order to develop a structure better aligned to student capabilities and potentials.

There is a growing awareness of the important and differential influence fathers have on child lifestyle behaviours compared to mothers. This ‘paternal’ influence could potentially carry across to children’s early career aspirations. A sample of n = 8235 school students in Years 3 to 11 were asked to indicate their occupational choices, give reasons for those choices and also provide information about their parents education and occupation. Using regression analysis, associations between paternal and maternal education levels and occupations with children’s STEM career aspirations were modelled. The findings provide further evidence of the potential differential influence parents have on their child’s aspirations.

Literature suggests that homework plays an important role in mathematics learning yet, in the Australian context, there is limited related research on this issue. This exploratory study sets out to better understand pre-service teachers’ intentions and practices concerning mathematics homework. Using a survey design, we analysed data collected from a questionnaire administered to 98 (71% response rate) pre-service teachers (PSTs), all in the third year of their BEd program and completing a third course in mathematical methods as well as professional experience. Contrary to our expectation, the difference in perceptions among PSTs teaching upper and lower primary grades were not statistically significant.

The 1999 TIMSS video study highlighted a heavy reliance on the mathematics textbook in Australian classrooms (Hiebert et al., 2003). This promoted further investigation by Vincent & Stacey (2008) who have documented the differences between mathematical textbooks and concerns with regard to problem solving. However, there is much anecdotal evidence to suggest that the role of the textbook may be changing and that the emergence of digital technologies may in fact replace the mathematics textbook (Hu, 2011). Hence, this exploratory study intends to a brief insight into the current status of the mathematics textbook and its use within Australian classrooms.

Opening Real Science (ORS) is 3-year Australian Government project led by Macquarie University supported by the Office for Learning and Teaching under the Enhancing the Training of Mathematics and Science Teachers Scheme (ETMST). ORS is developing a series of modules for implementation in teacher education programs, some of which focus on financial literacy: budgeting, investing and protecting, and modelling. The modules will be designed for active learning incorporating digital literacy themes to showcase implementation of technology integration into curriculum. Currently there are several trials in progress at three partner Australian universities. Evaluation data will inform the design-based approach to program re-development aimed at building the mathematical competence, and confidence of teachers.

A feature of Linsell and Anakin’s (2013) concept of foundation content knowledge is that all pre-service teachers should have a growth oriented disposition and extend their knowledge, whether or not it is initially strong. This study reports on the use in mathematics pedagogy classes of introductory problems designed to encourage all first year primary pre-service teachers to become aware of the features of foundation content knowledge and to extend their own knowledge. Eighty-one percent of those pre-service teachers whose foundation content knowledge was not initially strong considered the introductory problems helpful, compared to 61% of those whose knowledge was strong.

This study investigated mathematics teachers’ beliefs about teachers’ knowledge of content and students (Ball, Thames, & Phelps, 2008) about particular mathematical content and its effect on teaching practice. Two teachers participated in the study. Data were collected through classroom observations and an interview. The interview was based on An, Kulm, Wu, Ma, and Wang (2002) and focused mainly on teachers’ beliefs about knowledge of students’ thinking, approach to planning the mathematics instruction, students’ homework, and importance and approach to grading homework. The study indicated both teachers believed the importance of teachers’ understanding the way students think about a certain mathematics subject or the difficulties they experience with it. Nevertheless, it is seemed the teachers’ beliefs had no effect on their teaching practice. Moreover, they had limited awareness of how to identify students’ difficulties.

Teaching out-of-field is a concern internationally, and in Australia, and is linked to social, economic and educational costs for students and teachers along with an ethical and social justice issue for the community. At the national level, out-of-field teaching is most often represented as a problem of teacher quality involving less qualified teachers. Using a critical lens, meanings and representations of government policy and stakeholder perspectives and practices are analysed. The findings show how teaching out-of-field occurs and is legitimated and reveal the opportunities for contesting these positions to improve the outcomes for students and out-of-field teachers.

The Australian Mathematics Competition (AMC) is a problem-solving competition for Primary and Secondary students. Each paper has 30 problems graded from routine to baffling, challenging and rewarding students of all abilities. The competition’s quality depends on the collective effort of dozens of Mathematics Educators (Primary to University) who write and scrutinise the papers in several stages. Our current work is to ensure the AMC provides a reliable challenge for students. Tools for calibrating the performance of questions and papers across a range of question types are improving the competition, measured by the relative performance of each question, and by each paper’s aggregate score.

The mathematical proficiencies in the Australian Curriculum—Mathematics describe the processes students are engaged in while developing mathematical concepts (ACARA, 2014). This presentation focuses on how the proficiencies: understanding, problem solving, reasoning and fluency, may work together to build patterns of thinking which can lead to generalised understandings of mathematical concepts. The authors connect the combined role of these proficiencies with a proposed Generalised Model of Patterning (McCluskey, Mitchelmore, & Mulligan, 2013), highlighting the role of patterning in the development of conceptual understandings within and beyond mathematics.

This presentation describes a research project designed to understand the relationship between teachers’ conceptual understandings of mathematics, the tasks they design for their students and their evaluation of students’ responses to tasks. Using Timperley’s (2008) Teacher Knowledge Building and Inquiry Cycle, Year 5 and 6 primary teachers and leaders at a range of career stages engaged in tasks to highlight the connection between what students need to know, what teachers need to know and what teachers need to learn. The implications for developing teachers’ understandings of mathematics will be discussed in terms of system-level professional learning.

The aim of this Round Table is to bring together a community of researchers who focus on the teaching, learning, assessment, and research of a mathematical inquiry approach. We invite those interested in the study of mathematical inquiry to discuss their work or aspects of inquiry that are in need of research. A few questions are listed below to provoke conversation. Bring your own! 1. What shared and unshared perspectives do we have of mathematical inquiry? 2. What are purposes of mathematical inquiry? 3. How can mathematical inquiry be used to assess learning? 4. What signature practices characterise inquiry pedagogy in mathematics education? 5. How is mathematical inquiry similar to or different from inquiry in other content areas, such as science? 6. How does the teaching of mathematical inquiry fit into the broader repertoire of pedagogies used by teachers in the course of a year? 7. What challenges do teachers and students face in adopting mathematical inquiry? 8. Does an inquiry approach benefit children with different backgrounds differently? 9. What are key benefits and drawbacks of learning mathematics through inquiry? 10. Do particular strands of mathematics fit better with inquiry? 11. Does mathematical inquiry improve learning in mathematics? 12. Is mathematical inquiry scalable? 13. How can different paradigms contribute to a diversity of insights into mathematical inquiry? 14. What key research areas are strongly tied to mathematical inquiry (e.g., argumentation, socio-mathematical norms, collaboration)? 15. What are possible programs of research for mathematical inquiry?

Good teaching is described as that which is “charged with positive emotion” (Hargreaves, 1998, p.835). Yet, primary pre-service teacher education programs predominantly focus on the development of knowledge and pedagogy while affective aspects, including emotions, are only implicitly treated (Gootenboer, 2008). To date, research exploring the role emotions play in the process of learning to teach mathematics has received little attention (Hogden & Askew, 2007). The round table will begin by outlining the rationale and theoretical underpinnings of a trans-Tasman research project that aims to deepen primary pre-service teachers’ [PST] emotional and intellectual engagement in learning to teach mathematics. The Mathematics Emotional Engagement [MEE] project aims to develop and assess the effectiveness of an innovative teaching approach designed to promote positive emotional engagement in learning and teaching mathematics. The study explores the impact of a three-step interventional framework, referred to as ‘AIR’, that utilises a series of research-based instructional activities involving preservice primary teachers in: (1) Attending to their existing emotional responses towards the learning and teaching of mathematics; (2) Interpreting the causes and potential impact of existing emotional responses; and (3) Responding to their emotions with strategies to ameliorate negative affects on their learning and teaching of mathematics. Data from the first stage of the project—developing and refining AIR instructional strategies—will provide the stimulus for discussion amongst participants.

There are substantial and ongoing concerns in the Australian and international secondary and tertiary education sectors about students’ transition from secondary to tertiary mathematics. Declining enrolments in advanced mathematics in secondary schools and less stringent university entry requirements are seen as a major concern for the future of STEM education in Australia. In this round table, I will present data collected from secondary school students on precalculus and calculus topics. These data were collected from two groups of students: those studying intermediate mathematics in the last two years of secondary school; and those studying both intermediate and advanced mathematics. The results suggest that there are distinct differences in students’ procedural and conceptual understanding depending on which mathematics they studied in the last two years of secondary school. Students who studied both intermediate and advanced mathematics performed considerably better in all questions, not only on the calculus questions but also on junior mathematics pre-calculus topics such as gradient of a straight line. The data also showed that both groups of students had difficulty identifying lines parallel to axes, as well as explaining the meaning of the definition of the derivative. This presentation is part of a two-year state-wide longitudinal project that is investigating the transition from secondary to tertiary mathematics.

In Australia, a suite of national projects has been funded by the Australian government to promote strategic change in mathematics and science pre-service teacher education. This round table session will share some of the interdisciplinary strategies being trialled in one project, Inspiring Mathematics and Science in Teacher Education (IMSITE), and invite feedback from participants on the transferability of strategies to other institutional contexts and the sustainability of these strategies over time. The specific objectives of the IMSITE project are: • to develop and validate a repertoire of strategies for combining knowledge of content and pedagogy in mathematics and science; and • to connect academics from different communities of practice – mathematics, science, education – in order to collaboratively design and implement these new teacher education approaches. Six universities and 23 investigators – mathematicians, scientists, and mathematics and science teacher educators – are the core participants in the project, with more universities to be added in 2015. The first half of the round table session will showcase interdisciplinary strategies such as: • Collaborative development and delivery of new content and pedagogy courses by mathematicians and mathematics educators; • Reciprocal tutoring by mathematicians and mathematics educators into each other’s courses; • Peer observation by mathematicians and mathematics educators of each other’s teaching; • Development of a mathematics specialisation in primary pre-service programs. The remainder of the session will invite discussion of challenges to interdisciplinary collaboration (“siloing” of disciplines, inflexible workload and course funding models, cultural differences between the disciplines) and ways to overcome these.