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This conceptual paper proposes a model to describe the quality of student dialogue during participative collaborative problem solving. Drawing on the participation metaphor of learning, we argue that the construct of mathematical sophistication is useful to describe the quality. We then present two frameworks, mathematical competencies and mathematical practices, as ways to operationalise the construct in the collaborative problem-solving setting. We argue that by using a networking theories approach, the two frameworks will provide nuances of levels of mathematical sophistication that can be observed in student interaction. In addition, they could provide an analysis of both individual and group contributions to mathematical sophistication in a collaborative task setting. Implications of using two approaches for conceptualizing mathematical sophistication for future mathematics education research and teaching practices are provided.

Students in secondary school often find mathematics abstract and irrelevant, frequently questioning its usefulness and purpose. The discourse around STEM education has encouraged secondary teachers to attempt connecting mathematics with other STEM disciplines, most commonly with science. By making connections between content and skills through applications, it is anticipated that secondary school students will engage more in class that may result in improved mathematics achievement. This paper explores the rationale for making connections with science, examines the impact on student achievement in mathematics from previous research and discusses challenges for schools and teachers.

Place value is a foundational competency for primary school mathematics and for this reason we have sought to investigate what the recent and current academic conversations are around this important concept. In this paper we present a survey of literature presented in the Australasian, European and Southern African contexts through a review of purposively selected conference proceedings and journals to establish what the conversations have been about the teaching and learning of place value in these research communities from 2013 to 2022.

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.

From 2011-2013 the VCAA conducted a trial aligning the use of computers in curriculum, pedagogy and assessment culminating in a group of 62 volunteer students sitting their end of Year 12 technology-active Mathematical Methods (CAS) Examination 2 as a computer-based examination. This paper reports on statistical modelling undertaken to compare the distribution of results for this group with the standard cohort, and any differences in student response between the two groups at the item level.

This paper reports changes in the extent to which a group of Year 11 students used a Computer Algebra System (CAS), pen-and-paper (P&P), or a combination of both, when solving routine problems across seven months in four different topics. Comparing the frequency of CAS use across topics shows students made greater use of CAS in the topics of "Linear, quadratic, and cubic functions" and "Exponential and logarithmic functions" than in the topics of "Trigonometry and circular functions" and "Calculus." These differences suggest that students either made different choices about the use of CAS in these topics or used CAS less frequently as they gained experience with CAS.

This paper reports on a section of a larger study, investigating the mathematics experiences of Down syndrome (DS) learners in Australian Primary Schools. Developing the numeracy skills to experience independence in post school settings is crucial for individuals with DS. The aim of this paper is to share the school mathematics experiences of six DS adults and their parents/carers to ascertain if their experiences (DS adults) with mathematics when they were at school have had consequences for how they engage and participate in society as adults. Initial findings suggest that DS adults' mathematics experiences have impacted on their quality of life in a post-school setting.

In this position paper we highlight language as a perennial factor contributing to compromised meaning-making in multilingual primary school mathematics classrooms. We note use of the term 'translanguaging' in discussions around mitigating this meaning-making challenge. The paper argues that, while much work remains to be done towards clarifying the pedagogical insights, skills, and resources needed to ensure that translanguaging practices achieve their intended goals, potentially important parallels may be found between horizontal and vertical forms of translanguaging and horizontal and vertical mathematisation.

Research has shown that many primary students experience transition barriers between additive and multiplicative thinking. This paper analysed responses from 253 Years 3 to 6 students to a diagnostic assessment which consists of whole number multiplication and division problems involving equal groups, arrays, multiplicative comparison and Cartesian product situations. Based on the Rasch analysis, item responses were differentiated into five developmental Stages indicating a wide range of understanding and pointing to different transition barriers that students experience. The reasons for these are discussed in the paper and some advice is presented for teachers.

In this study, the evaluation of mathematical proficiency (MP) in one NSW Year 12 standardised exam paper was investigated. By considering the multi-strand model of MP, a literature-based criteria for scoring the assessment of MP in individual exam questions was first developed. The criteria were then applied to quantitatively evaluate the 2023 HSC Advanced Mathematics exam paper. The findings revealed a generally balanced assessment of all MP strands in the short-response exam questions. This study has methodological implications for evaluating the assessment of MP in external mathematics assessments, and the designing mathematics exams.

This paper is part of a broader study which explores South African pre-service teachers' use of the jump strategy on the empty number line for enhancing their confidence to do and teach mental mathematics computation strategies. The focus of this paper is the use of micro-teaching in the form of video recordings by pre-service teachers. Forty videos were analysed thematically indicating that most pre-service teachers could implement the strategy with some level of fidelity. Three micro-teaching videos are shared in this paper to exemplify the range of strong, medium, and poor implementation fidelity.

This paper reports on part of a longitudinal project investigating the formation of preservice secondary mathematics teachers' identities at one Australian university. Given that school-based placement experiences impact teacher identity development, the Flourishing Mathematics Teacher (FMT) project focuses on this experience and aims to identify features of placement experiences that enable beginning secondary mathematics teachers to flourish, and remain, in their teaching careers. In this paper, we report on preliminary data exploring changes to 23 preservice secondary mathematics teachers anticipated job enjoyment after their first teaching placement.

This paper explores the complex problem of project sustainability, focusing on the leadership of three primary school mathematics leaders. Using cultural-historical activity theory (CHAT), the leaders' efforts are reported, highlighting their contribution to project sustainability. The CHAT-informed research design supported the generation of findings, revealing how the mathematics leaders enacted a form of resourceful practice. This paper contributes new knowledge about mathematics leaders, characterising how they acted as agents of project sustainability. Implications for mathematics education project design are also offered.

In this paper we explored primary school teachers preference for different game modes to support mathematics teaching and learning. Eighty-four teachers played digital and non-digital addition and subtraction games that were functionally equivalent during professional learning workshops. Most teachers indicated that they would be more likely to use the non-digital mode; despite more mixed views around perceived effectiveness for supporting learning and anticipated student preferences. Key reasons as to why teachers tended to prefer non-digital or digital games are examined.

Mathematical thinking is a complex, multi-faceted process that has been described as messy and difficult but can also show growth and insights into conceptual understanding and knowing. This paper explores the application of Edward de Bono's practical thinking, in particular, the occurrence of porridge words to examine the mathematical thinking of primary school students. The research employed qualitative research techniques using participant's drawings, their written descriptions, and interviews about their drawings. Employing discourse analysis uncovered patterns in how students used porridge words to communicate their mathematical thinking.

Fractions are among the most problematic concepts that children encounter in their primary school years because of the many different conceptions of fractions. Textbook analyses have tried to provide insights into how fractions are introduced, focusing on the different concepts and representations of fractions. In this paper, we contribute to these efforts by investigating the way fractions are first introduced using the notion of potential concept images as afforded by the textbooks. Analyses of two textbooks, one from Northern Ireland and the other from Singapore, will be presented to highlight these potential concept images and their implications for practice.

The current paper overviews a nine-month PhD study that investigated the impact of learning mathematics through sequences of challenging tasks on the mathematical competence and attitudes of Year 2 students (n = 59). Adopting a Self-Determination Theory lens, a pragmatist paradigm and a mixed-method design, the study found that at all levels of investigation and analysis, the experience of learning through sequences of connected, cumulative, and challenging tasks had positive benefits for Year 2 students.

The Queensland Certificate of Education (QCE) system is Queensland's senior school qualification. To support the introduction of the system in 2019, existing senior syllabuses were redeveloped and a new senior assessment model was established, this included the implementation of a mandatory high-stakes assessment task, the Problem-solving and Modelling Task (PSMT) in all four mathematics syllabi. The PSMT required new skills from both students and teachers to manage complex, open-ended investigations. In this paper, we reflect on our school's approach to build teacher capability in designing PSMTs and supporting student engagement with PSMTs.

The revised Australian curriculum presents a new emphasis in primary schools on the process of Mathematical Modelling. A modelling focus brings close attention to confidence and capability with a potentially new problem-solving process, associated language, and pedagogical processes. This paper presents a Year 4 classroom modelling experience that arose as students planned their end-of-year party through Guided Mathematical Inquiry. Classroom video data captured two students working on vertical whiteboards as they formulated and solved a problem involving carrot sticks and dip. Findings reflect the students as doers of mathematics, engaged in productive struggle.

This paper presents an analysis of how resources were designed to support implementation of the new Queensland senior secondary mathematics syllabuses. The analysis draws on the concept of educative curriculum materials that build teachers' subject matter knowledge and pedagogical content knowledge. Such resources are intended to help teachers "learn how to learn" to teach mathematical content that is new or unfamiliar to them.

This paper provides evidence that a short, fully online, well-constructed diagnostic test based on research literature can give teachers information about their students' thinking and strategies that is sufficiently accurate to use for formative assessment purposes. The example is a test for students beginning to learn to solve equations. The main goal is to inform their teacher of the solving strategies each can use. Accuracy data from 3010 students is analysed to judge how well the overall performance of each group matches predictions. Alongside a previous analysis of misconceptions and common errors, we show this test gives teachers a good picture of most students to plan their lessons.

Concern regarding the prevalence of out-of-field teaching continues to grow, as does the body of literature calling for a better understanding of the nuanced complexities associated with out-of-field teaching. In this paper, we extend our previous analysis of data from a survey of the profession teaching Years 7-10 mathematics in South Australia. Analysing the data through an identity lens indicates that out-of-field teachers who self-identify as mathematics teachers and express a preference for teaching mathematics are more likely to exhibit levels of interest, enjoyment, confidence, and commitment that align with those of in-field teachers.

Progressing from additive to multiplicative thinking is a key outcome of school mathematics, making ratios an essential topic of study in junior secondary. In this study, 15 Australian Year 8 students were administered a ratio test followed by semi-structured interviews to explore their conceptions of ratio prior to formal instruction. In this paper, students' responses to one of the ratio questions are analysed in detail. Analysis of incorrect responses was conducted using a modified version of Radatz's (1979) framework. Analysis of correct responses revealed that some students worked proficiently with ratio without formal instruction.

This paper investigates the expectations that a group of preservice secondary mathematics teachers had for how students would approach four particular algebra problems. Their responses to a set of open-ended items were content analysed. Findings show that the teachers ranged in the expectations that they held for their students. Some teachers expected their students would approach the problems with more sophisticated problem-solving strategies, but many of the teachers expected that the students would only use less desirable "guess-and-check" strategies. We believe teachers' expectations for student strategies for problem-solving is a topic that warrants further investigation.

Research on mathematics learner identity often relies on interview data and presents case studies of individuals. This method allows an in-depth understanding of the person and their relationship with mathematics, but fails to generate a larger picture of identity with more breadth. In this paper we propose a method that blurs the boundaries of fiction and fact by creating fictional characters and a playscript derived from questionnaire response data of senior secondary mathematics students. We argue that this method allows for a wide representation of learner identity without sacrificing the individual voice that may resonate for various stakeholders within mathematics education.

Problems presented in mathematics classrooms often focus on routine tasks with students practicing mathematical techniques demonstrated by the teacher. However, this does not reflect the problem-solving process in the real world, and students often find it difficult to connect school mathematics with authentic contexts. This paper discusses findings from a study of Year 5 student perceptions of problem-posing during a two-week open mathematical inquiry. While the semi-structured interviews indicated the students perceived themselves to be skilled at problem-posing, triangulation of the video observations and work samples told a different story.

In this paper, we present research on New Zealand secondary teachers' perspectives of teaching and learning mathematics during the COVID-19 pandemic of 2020--2023. We use narrative analyses of interviews to explore the perspectives of eight participant teachers. COVID-19, and its resulting restrictions, were found to impact student-teacher relationships, teachers' ability to provide mathematical explanations and support students' learning, and students' engagement and participation.

Little research is evident about integration of mathematics in sustainability tasks to raise students' awareness and actions to solve a sustainability challenge. In this paper, we explore how a teacher designed and implemented a sustainability project, which included mathematics to raise Year 10 students' (aged 15-16) awareness and actions about sustainability. Data, including classroom observations and interviews, were analysed based on one characteristic of the green mathematics framework: "projection." We report on how students used mathematics to project future situations and how the projection may raise students' awareness and actions to address sustainability.

Despite substantial research exploring multiplicative thinking and students' difficulty in the domain, the topic of multi-digit multiplication is under-researched. In this paper, I share a learning trajectory for multi-digit multiplication that combined social and cognitive perspectives of learning. Using Design Research methods and involving 45 Year 5 (9-11-year-olds) students from two different schools, an instructional sequence based on the trajectory was implemented. Findings led to the refinement of a trajectory that has implications for teaching practice.

Mathematics anxiety and examination anxiety affect student well-being, engagement, and performance in the mathematics classroom. An increase in confidence in the mathematics classroom leads to a decrease in anxiety. This paper reports on the Five Question Approach (FQA) to teaching mathematics which provides teachers with a method of reducing these anxieties. This case study draws on data collected in three Australian secondary classrooms using the FQA as an intervention. Findings indicate that when added to normal classroom practice, the Five Question Approach alleviated these anxieties to some extent and increased engagement and academic performance.

In Ireland, Initial Teacher Education [ITE] standards require all teachers to possess an adequate level of numeracy themselves in order to teach for numeracy learning across the school curriculum. This paper reports on a study that investigated 204 pre-service post-primary teachers' numeracy capabilities. Analysis of questionnaire data from participants in three universities showed that pre-service teachers tend to struggle to complete the numeracy tasks correctly, especially tasks related to ratio and proportional reasoning. If pre-service teachers of all disciplines are not capable of completing core numeracy concepts, then they will struggle to teach for numeracy learning.

This paper examines the mathematical experiences of students with additional and diverse needs in multi-year classes within the educational context of small regional South Australian (SA) schools. Qualitative research methods were used to collect data about how students communicate their mathematical thinking. Opportunities for students to communicate their mathematical thinking were categorised using Bruner's experiential stages of learning. Findings suggest that the collaborative nature of multi-year classes fosters peer learning and cooperation, enabling students to share and build upon each other's mathematical thinking.

Differentiated Instruction (DI) is a philosophical and pedagogical approach supporting diverse student engagement in learning, but limited research exists in DI in senior-secondary mathematics. Using semi-structured interviews, the perceived use of DI of two senior secondary mathematics teachers was investigated. One of three themes is discussed in this paper; using strategies to enable student choice and voice. Results indicated teachers used various DI strategies to support students to understand their current levels of need, allowing student choice in their tasks, and supporting student reflective practice. DI in senior-secondary mathematics is complex, but achievable.

Primary mathematics leaders work together both with and between school leadership and teachers as middle leaders, balancing expectations and responsibilities of themselves, school leadership, and teachers. This paper presents a case study of mathematics leaders in a school with a diverse community and frequently changing staff. It explores the tensions in this school and the supports that help the mathematics leaders find opportunities to respond. Findings show that building relationships and trust with staff were essential to address challenges and meet the needs of the school.

Big Ideas can be seen as overarching concepts that occur in various mathematical topics and strands within a syllabus. Within our project on Big Ideas in School Mathematics, we developed instruments to measure two Big Ideas: Equivalence and Proportionality. The instruments we developed seek to assess students' ability to see these Big Ideas as common ideas connecting within and across topics, and their ability to apply these Big Ideas in solving problems. In this paper, we discuss the development of items for these instruments.

This paper reports on a study that seeks new insight into how the expertise of specialist mathematics intervention teachers might be harnessed to support classroom teachers to assist students who experience difficulty learning mathematics. Findings show that the classroom teachers' confidence increased after engaging in co-teaching cycles led by the specialists. The most highly ranked helpful actions of the specialist intervention teachers were 'suggesting appropriate tasks for a given topic,' 'team teaching with me,' and 'suggestions about content for the next lesson.' The findings suggest that teachers' professional learning needs vary and require a personalised response.

Curriculum change affords middle leaders opportunities for pedagogical and planning renewal. This paper reports case studies of two schools engaged in preparing for implementation of Version 9 of the Australian Curriculum: Mathematics. Drawing on interview data from a middle leader from each school, Bacchi's question, "What's the problem represented to be?" was used to explore factors underpinning how these leaders identified a "problem" to be addressed. Findings revealed that even when shown alternative interpretations of their perceived problem, these middle leaders were still "driven" by their own interpretation of the problem.

The study reported in this paper is on the professional development (PD) of primary school mathematics teachers. Teachers from two primary schools participated in the PD for two years. High-stakes mathematics examination tasks were used to kick start awareness and thinking about teaching for big ideas. Teachers did the tasks and discussed their solutions focusing on how their instruction could facilitate the acquisition of mathematical ideas as a body of connected knowledge. Data presented in this paper show that the tasks teachers worked with at the start of the PD did impact their understanding and instructional practice specific to big ideas in mathematics. Some challenges the teachers faced during the PD are also noted.

In this paper we report on an aspect of the findings of a larger three-phase study exploring the factors that influence teachers implementing pedagogies that cultivate students' STEM capabilities and 21st century skills. Data were collected through an online questionnaire, semi-structured interviews, focus groups and case studies. This paper will focus on the findings from the first phase of this study and initial analysis of focus groups and semi-structured interviews data. Preliminary findings show that participants hold mixed beliefs concerning student proficiency in mathematics and there are common factors that influence decisions concerning the use of pedagogical practices that support students' mathematical proficiency and the development of students' 21st century skills. These factors include teachers' personal beliefs and attitudes, perceived time and curriculum constraints, student behaviour and students' academic ability.

The interactional role of language use in the mathematics classroom is explored in the last few decades. This paper adds to the knowledge base by exploring different ways of talking that children and their teacher use in a New Zealand primary geometry English-medium classroom. Bakhtin's concept of speech genres is used for an analysing transcript of one audiovisually recorded whole-class interaction episode from a geometry lesson in a Year 5/6 classroom. The analysis suggests that the teacher and children use various genres to participate in classroom interactions. The use of several genres provides insights into what children and the teacher construct as mathematical in the real sense. The paper finished with a few implications for teaching and research.

Probability requires teaching approaches that allow children to predict, observe and experiment with concreate materials, games and simulations. In this study, we explored one teacher's beliefs and practices of teaching probability using game-based approaches. We employed a design-based research approach to explore how our case study teacher engaged with an hour-long professional learning on using a game-based probability teaching sequence. We found that our case study teacher's espoused beliefs and self-reported practices aligned with knowledge of teaching probability demonstrated during the professional learning activity.

At the end of Primary 6, students in Singapore schools take a national examination, the Primary School Leaving Examination (PSLE). Society at large view the PSLE as a highstakes examination. In addition to out-of-class work assigned by mathematics teachers for students to prepare for the PSLE mathematics, parents may also draw on out-ofschool practice books to further support their children's preparation for the examination. A study of two main types of such books show that these books do generally support students in reviewing content knowledge for the examination and test preparation.

Young children often explore partitioning as the idea of fair sharing in contexts where equal parts are created and distributed based on spatial constructs of the objects, rather than enumerating parts or collections. However, the presence of spatial reasoning in children's early fraction experiences is implicit within much of the literature and has not been explored pedagogically in a range of early schooling contexts. This study reports on a selection of data from a larger Design Based Research study that demonstrates the power spatial reasoning plays in developing early partitioning. Implications for teaching and learning are discussed.

Creativity is a task-specific construct that exhibits diverse characteristics depending on the context it operates in. Currently, there is little consensus on how creativity can be defined and taught within STEM education. In this study, mathematics teachers' beliefs about STEM creativity and their pedagogical approaches to teaching creativity within a novel STEM creativity framework have been explored. Results show that mathematics teachers have a variety of beliefs and practices about creativity that can be grouped into four pedagogical themes: exposure, exploration, experimentation, and execution.

Prior to the COVID-19 pandemic, the university educational system in Nigeria largely employed traditional, face-to-face classroom approaches for teaching. This study examines how mathematics lecturers adapted to online teaching in response to COVID-19 restrictions. A mixed methods approach was used to obtain both qualitative and quantitative data from ten mathematics and mathematics education lecturers, using questionnaires and semi-structured interviews. The results highlight mathematics and mathematics education lecturers' use of virtual boards, writing pads, and WhatsApp to improve interactions while teaching online via Zoom.

This study was conducted in Maharashtra, India with children studying in a regional medium (Marathi) government school. In Marathi, the translation of the word 'about' is not very commonly used. The aim of the study was to see how the children used uncertain language about prediction while engaged in a statistical investigation and how children would respond to the uncertain language introduced by the researcher. The findings suggest that children did not use the equivalent word for 'about' without prompting from the researcher. The study has the potential of exploring and impacting the influences of language on the learning of statistics in a non-Western culture.

Teaching resources and professional development based on mathematics education research have the potential to support teachers to develop and sustain improved pedagogies. The Queensland Department of Education provided online professional learning modules for teachers of Prep (Foundation) to Year 10 mathematics. To support implementation of the Australian Curriculum: Mathematics this evidence-based resource would assist teachers in understanding the curriculum and providing support for quality teaching and learning. This resource exemplifies the partnerships between the department, researchers and teachers in building capability in mathematics teaching.

The exploratory study combined an online survey and interviews with Australian primary and secondary mathematics teachers to examine their views on "Active, Bodily experience Mathematics learning activities." The research sought to identify teachers' expectations, challenges, and limitation for their implementation. Initial results indicate teachers recognise the value of such activities in deepening students' understanding and increasing engagement but encounter obstacles such as time constraints, insufficient resources, and difficulties in managing the classroom, underscoring the need for further investigation into effectively incorporating these activities into teaching practices.

Semi-structured interviews are used to gain insights into participants' lived experiences and perspectives on issues, but they are open to subjectivity. To address this issue our study explored the combination of timeline graphic elicitation tools with semistructured interviews as an approach to gain insights into teachers' experiences of mathematics teaching and professional learning. A qualitative study was conducted with ten participants from two schools who took part in professional learning activities for mathematics teaching. Findings indicated that combining these instruments can support researchers in gathering deeper insights into teachers' lived experiences.