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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.

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.

Determining the most effective ways to support student-to-student talk requires some negotiating from a responsive teacher. This paper reports on a case study of two emergent multilingual students in Grade 3 (seven to eight-year-olds) who explained their strategies to each other. The transcript of their conversation was analysed using Chan and Sfard's (2020) "participation profile framework." Findings indicate that the two students learned from each other during the interaction because they revised their work to be more precise. One implication of this study is that strategic pairing may be a useful practice to eliminate inequitable power dynamics.

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.

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.

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.

This paper explores factors that contribute to increased self-efficacy in preservice teachers as they practise teaching mathematics in a primary classroom. Thirteen preservice teachers completing a Master of Primary Teaching contributed to the research, four of whom became the focus of intense examination during two professional practices conducted over a 12-month period. Findings revealed six factors. When conceptualised into a framework the factors contributed to a better understanding of ways to support preservice teachers' self-efficacy for teaching mathematics.

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.

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.

The profound advancements in technology have rendered novel forms of data and data visualisation increasingly accessible to individuals within society, thereby influencing daily decision-making processes. To address this change, this study sets out to review recent research on data-driven inquiries at the K-12 level from two perspectives: innovative data visualisation and non-traditional data sources. Our findings indicate that transnumeration of multiple data representations, along with data moves throughout the process of data visualisation, can potentially enhance the development of visual reasoning and data modelling skills.

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.

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.

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.

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.

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.

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.

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.

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 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.

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.

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.

For students to engage in mathematical thinking, a greater emphasis is needed on the expectations of students, by themselves and others, as active listeners and explainers. As student responsibility for mathematical thinking and participation increases, the roles of the teacher and learner change. A qualitative study of changing classroom expectations in a Grade 2 class was conducted. The teacher saw her role shifting to that of facilitator and the students' expectations were as active listeners and explainers. The type of questions asked by the teacher was instrumental in whether justification and mathematical reasoning was elicited from all learners.

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.

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.

Technology can play a pivotal role in mathematics education. Qualitative methods were used to report on how a Year 1-2 teacher incorporated "Conveyance technology" (iPads), to support the teaching and learning of mathematics through student reasoning and problem-solving. The study was conducted in Australia. A single case was chosen, reporting a lesson where students engaged with a 12-cube task. The findings contribute to the broader discourse on the role of technology in early mathematics education, suggesting that conveyance technology supported by effective teaching practices and open-ended problems, fosters students' reasoning and problem-solving skills.

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.

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 reports on the development of complex unfamiliar mathematics questions using conventional mathematics questions. The autoethnographic research data included retrospective reflections of two educators and review of literature. Data analysis resulted in a three-phase development process: identifying conventional questions and subject matter to be modified to enhance levels of understandings and skills, modifying conventional questions and subject matter to complex unfamiliar questions, and identifying enhanced understandings and skills in modified questions. The paper then discusses the educators' insights developing complex unfamiliar mathematics questions for the practice of teaching and learning.

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.

Research shows primary teachers report negative dispositions towards teaching mathematics, impacting their confidence and student outcomes. One approach to improve teacher and student enthusiasm is using picturebooks. While research supports the use of picturebooks in mathematics learning, specific guidance for teachers to implement this practice effectively is lacking. Using a methodology of metalogue, we developed a framework to support teachers in providing engaging mathematics activities through aesthetic perceptions. We reflect on the development of the theoretically informed framework and discuss how it might support teachers' work.

Typically, more primary students qualify for mathematics intervention support than schools have the capacity to assist. This highlights the importance of every primary mathematics teacher having the expertise to design inclusive and responsive curricula and instruction for students who may experience difficulty. Our study addresses this issue through exploring how specialist intervention teachers can support the mathematics professional learning of teachers using co-teaching cycles. The findings provide insight about the challenges experienced by classroom teachers when teaching students who experience difficulty with mathematics, and the actions of the specialist intervention teachers that assisted the teachers' professional growth.

This paper reports on a key representation, a triple number line, designed as part of the first author's doctoral study. The study sought ways to represent multiple constructs of fractions in the context of merging music and mathematics to support learners' understanding of fractions. A problem scenario was designed guided by Realistic Mathematics Education principles. Findings shared in this paper are based on the process of designing and implementing the tasks around the triple number line. Data for this qualitative, participatory dual-design experiment in task design were collected via formal and informal interviews in two micro-Communities of Practice. We conclude that the key representation of the triple number line can be a powerful tool for supporting learners in their fraction understanding.

Big Ideas in school mathematics can be seen as overarching concepts that occur in various mathematical topics in a syllabus. For teachers, this knowledge can be used to help students develop a better understanding of mathematics by making visible the central ideas, and connection across topics and across levels. For students, this knowledge can further be helpful affectively by engendering an appreciation of mathematics as a subject that is coherent and comprehensible. Although there has been much interest recently in the understanding of Big Ideas, there is little research done in the assessment of Big Ideas thinking. In this paper, we discuss our development of an instrument to measure the Big Ideas of equivalence and proportionality. Our analysis of some pilot items suggests that Big Idea thinking is a multidimensional construct within most school environments.

This paper is a brief summary of a large historic research project in Papua New Guinea (PNG). The project aimed to document and analyse the nature of mathematics education from tens of thousands of years ago to the present. Data sources varied from first contact and later records, archaeology, oral histories, language analyses, lived experiences, memoirs, government documents, field studies, and previous research especially doctoral studies. The impacts of colonisation, post-colonial aid and globalisation on mathematics education have been analysed and an understanding of the current status of mathematics education established as neocolonial. Managing neocolonial education policies may minimise the loss of cultural ways of thinking.

We explored primary pre-service teachers' beliefs about challenging mathematical tasks and the role they perceived their initial teacher education played in influencing those aspects. Fifty-seven pre-service teachers completed an online questionnaire, and four participants were individually interviewed. Results showed that most participants recognised the importance of teaching with challenging mathematical tasks even prior to exposure to such content in their teacher education program. The teacher education program was perceived to have positively impacted final year pre-service teachers' perspectives about challenging tasks. Implications for teacher education regarding challenging tasks are discussed.

In this study, we aim to investigate the role of language in small group peer collaboration. Based on the notion of symmetrical scaffolding, we draw on theories of dialogic space and functional linguistics to analyse a transcript of three six-year-old students as they explore a shared understanding of 'two more than'. Using Martin and White's (2005) engagement framework as an analytical tool, we identify how the three students used language resources in contractive and expansive ways to move each other's learning forward. These findings provide a perspective of symmetrical scaffolding closely focused on students' language choices that support engagement with each other's thinking. We suggest that a focus on use of language with young students is valuable in identifying the type of mathematical discourse that will support peer collaboration in problem solving and mathematical reasoning.

This paper explores use of a set of diagrammatic tools for representation and analysis of the moves a teacher makes implementing a mathematical modelling task. The focus here is on identifying what the teacher did so we can subsequently interrogate this, as to the why. Data include pre and post lesson teacher interviews and transcripts of a video and audio-recorded task implementation. The analytical tools developed, with one teacher and one task early in a three-year project were particularly useful in ascertaining what the teacher moves were as we subsequently sought to determine reasons for these.

This qualitative study investigates remote Australian primary school parents' attitudes towards their children's learning of mathematics and the role of technology. Using semi-structured interviews and thematic analysis, results revealed that parents aimed to provide the best mathematics learning opportunities for their children, yet they felt obsolete and isolated from their children's learning. Additionally, they valued the role of technology, but did not think school was providing adequate digital literacy skills. Discussion about what changes to the educational community are suggested to support parents in their children's learning.

In this paper, the SOLO taxonomy is used to identify different levels of student understanding of the statistical concepts associated with sampling distribution. This study was part of a research project investigating students' conceptual understanding of concepts of hypothesis testing taught with the support of simulation learning activities. The study involved eight students enrolled in a first-year tertiary introductory statistics unit and the examination of their written responses to three questions about sampling distribution concepts. The SOLO taxonomy categorisations revealed that some students had only pre- and unistructural understanding of sampling distribution, and none providing responses at the extended abstract level.

Place value is one of the 'big ideas' in number and plays a critical role in helping students develop their number sense, problem solving and computation skills. Yet, the elegant simplicity of our place value system belies the abstract nature of the construct. This paper presents data from 606 Year 3-6 students (ages 8-12) from two metropolitan Melbourne primary schools who completed the Place Value Assessment Tool (PVAT). Each student's place value knowledge was categorised according to the Place Value Developmental Progression (PVDP). The results highlight the wide range of understanding in each year level and challenge the efficacy of a number magnitude-based progression in place value.

In this paper, we explore how students' algebraic noticing's and explanations changed across a two-year period with the introduction of designed instructional material. The data in this report is drawn from n=53 Year 7-8 students' responses to a free-response assessment task across two different years. Analysis focused on how students noticed and explained algebraic relationships in pairs of equivalent equations. Findings indicate that with the introduction of designed instructional material, there was a shift in student noticing of number properties to identify equivalence between pairs of equations. However, identifying the distributive property of multiplication and developing generalisations about the algebraic relationships remained challenging for students.

Calls for high levels of participation and success in Science, Technology, Engineering and Mathematics (STEM) by all Australians exacerbates the need for research into improving participation in mathematics by students from disadvantaged backgrounds. Rogoff's three planes of analysis is used to foreground the institutional plane in a low socioeconomic status school with sustained increased enrolments in Mathematics B (now replaced by Mathematics Methods). Processes in this plane are examined by drawing on semi-structured interviews with a Deputy Principal and Head of Mathematics. Contributing factors appear to be the way that the Mathematics Program and Pastoral Care Program are delivered at the school.

This conceptual paper discusses two frameworks, developed independently by the lead author, that will provide the conceptual foundation for the identification and evaluation of mental computation strategies students demonstrate during an upcoming research project entitled Mental Computation in Year 5. These frameworks will be used by the lead author during an intervention to investigate the application of mental computation strategies in problem solving tasks involving duration of time. It is an intended outcome of the project that the two frameworks will be useful for teachers and students in upper primary school to provide feedback regarding the teaching and learning of mental computation.

It is generally understood that both clear teacher instruction and orderly classroom climates support student achievement in mathematics. However, to what extent does instructional clarity "compensate" for classroom disorder? In this exploratory study, we analyse data from 8,864 Year 8 students sampled by TIMSS 2019 to investigate the relationship between instructional clarity, classroom disorder, and mathematics achievement. The findings demonstrate the deleterious effects of classroom disorder for mathematics achievement, even in the presence of high instructional clarity. The findings contribute to an emerging international body of work and reinforce the importance of teachers having an optimal combination of classroom skills to support student learning.

This paper describes results from a case study about how a primary pre-service teacher (PST) used curriculum materials (CMs) when planning for a mathematics lesson during her final practicum. The data is drawn from a doctoral study (in progress) and results show how the PST initiated an active process of searching for and sifting through CMs on a familiar website to make selections for a lesson. Selections were based on several aspects, including the mathematics focus of her lesson, curriculum connections, her chosen teaching approach and mathematical representation for teaching multiplication. Implications for mathematics Initial Teacher Educators (ITEs) are discussed.

This paper reports on students' experiences of describing and representing variation in hypothetical data. Fifty-six students (8-9 years-old) experienced collecting and working with quantitative data for two years as part of a STEM education project. The task described here was an end-of-year survey question, with three parts about a hypothetical context for surveying students in two different Australian cities: recording the data, describing the potential variation in the data, and creating a representation of what the data might look like when only a descriptive account of the context and variables were provided. The data analysis framework utilised provides a means of determining students' readiness for further development of statistical ideas.

There has been a lot of media attention about 'out-of-field' teaching, but much of it does not capture the complexities of the term or account for the range of knowledge, experience, and attitudes relevant for teaching mathematics in the middle years. In this paper we report on a survey conducted to better understand the diversity of the profession teaching middle school mathematics (Years 7-10) in South Australia. A preliminary analysis indicates that self-identification as a teacher of mathematics is a key contributing factor to confidence in teaching mathematics. We suggest that looking through an identity lens will better inform planning and support for out-of-field teaching in mathematics.

Worldwide interest in Lesson Study (LS) and the opportunities offered for student learning through the use of a Structured Problem-Solving Approach (SPSA), as typically adopted in Japanese LS research lessons in mathematics, have left largely unanswered questions about the extent to which these can be replicated elsewhere. This paper presents a case study of one primary school teacher's learning experiences, and his views about LS and SPSA, as a result of participating in a project introducing SPSA through LS in three Fijian primary schools. The results reveal that engaging in the LS process was instrumental in supporting this teacher's implementation of SPSA in his mathematics classroom. The findings are important for teacher professional learning (PL) in Pacific cultural contexts.

Informed by teaching statistics across curriculum areas strategies, this study investigated the skills of 36 pre-service teachers (PSTs) who designed numeracy activities that focused on the statistics strand of the Australian curriculum. The data were analysed using descriptive statistics. The results showed that the PSTs designed numeracy activities focused on the science curriculum area. The results further showed that PSTs emphasised a few year levels and focused on collecting and recording data. The first stage of teaching statistics (designing effective questions) is often ignored in their activities. The approach adopted in this study can be used to identify PSTs' knowledge gaps and their professional learning requirements.

This paper reports on 73 Grades 3 to 6 students' written responses to equal groups, arrays, multiplicative comparison and Cartesian product word problems. It is part of a larger study relating to students' development of multiplicative thinking (MT). The potential of using multiplicative word problems as a diagnostic assessment to reveal students' transition barriers from additive thinking to MT was explored. The development of the assessment and some of the research findings are described here. Findings show that students experience different types of barriers during their transition from additive to MT. Some recommendations are given on how these barriers might be overcome during primary school years.