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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 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.

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.

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.

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 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.

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.

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 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 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 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.

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.

In this paper we reflect on our combined work in some of the most marginalised educational contexts in the Southern Hemisphere. We draw on the work of Bourdieu to frame the paper. We propose the working in marginalised education settings requires a particular habitus or way of being to be able to play the research game. Underpinning our approach is the South African construct of Ubuntu, which is very much about collaboration--I am because we are--so that there is a move away from doing research "on" participants and contexts to one which is very much about doing research "with" participants and contexts. We find Bourdieu's notion of game as a powerful construct to theorise ways of thinking about the field of educational research.

School Mathematics Leaders seek to improve the mathematical learning outcomes of the students in their schools. Recognising that improved learning is dependent on high quality teaching, leaders are often keen to support teachers' knowledge of mathematics content and pedagogy. This paper reports ways in which School Mathematics Leaders support and lead the professional development of teachers in team meetings. Results from survey data and case study research are reported in this paper to describe and highlight the supportive actions undertaken by School Mathematics Leaders as they provide professional learning opportunities for teachers.

This paper examines the types of teacher questions that assist young students to interpret and explain their critical mathematical thinking (CMT). Focusing on students who enter their first year of formal schooling (aged 5-6 years), this paper draws on data from a one-on-one task based clinical interview conducted with 16 students. Teacher questioning data were analysed for question type (probing, factual, guiding) and further analysed against the conceptualized critical mathematical thinking framework for young students. Findings indicated that when teachers used clarifying, noting relationships, and offering opinions style probing questions, young students were supported to interpret and explain their critical mathematical thinking.

In Australia, all teachers are expected to explicitly attend to numeracy in the subjects they teach. Pre-service teachers, therefore, need to begin to develop effective numeracy teaching strategies but there is a limited research base to inform the design of courses that address this need. This paper reports on findings from a study investigating the impact of one such course. The paper draws on data from two pre-service teachers: two course tasks completed at the beginning of the course and interviews conducted at the end of the course. Data were analysed using the 21st Century Numeracy Model. Findings suggest there were changes to the pre-service teachers' understanding of numeracy and their capacity to embed numeracy in the subjects they will teach.

Engagement in mathematics education is an important factor in a successful student experience. This paper reports findings from a study of Year 5 student perceptions of engagement during a two-week, inquiry-based learning (IBL), problem-posing investigation. The study triangulated data from semistructured interviews, video observations and student work samples to understand the student's perspectives of IBL; however, this paper reports the interview data. The findings indicate that most of the students were behaviourally, emotionally, and cognitively engaged during the IBL investigation, and that the investigation provided an opportunity for students to experience levels of competence, relatedness, and autonomy need satisfaction.

Mathematics self-efficacy is considered an important variable in mathematics education because of its links to mathematics achievement. This paper reports on the development of the "Self-efficacy-effort in Mathematics Scale" (SEEMS), an instrument that has strong theoretical and psychometric properties. Based on a sample of n = 224 Australian primary students and n =133 secondary students, the instrument demonstrated positive correlations with related measures of mathematics achievement and mathematics self-concept. Girls had higher mathematics achievement within the primary and secondary school data. There were no significant gender difference in mathematic self-concept scores for the primary and the secondary school students. For mathematics self-efficacy, a gender difference was only identified in the high school data. The implications of this research to mathematics education practices are reviewed in the paper.

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.

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.

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.

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.

In this paper we compare the early years mathematics curricula of Germany, South Africa, and Australia in relation to the place value concept. Place value is an important topic as it underpins much of the number work completed by learners in the early years of schooling. We found that there were differences between the three curricula that could be summarised using five themes: namely, number range, place value structure, role of the zero, influence of language, and use of materials. We argue that how the different curricula deal with these five themes influences the quality of learning provided and we highlight key areas of concern. In concluding we identify three important implications for our future research project.

Providing opportunities for students to demonstrate their mathematical thinking can be challenging. This paper reports on a case study conducted with a teacher and her class of Grade 3/4 students which investigated this phenomenon. Following collection of baseline data that showed her students were not demonstrating evidence of mathematical thinking, the teacher implemented teaching approaches designed to address this. The findings indicated the teaching approaches were effective and led to changes in the teacher's practice and professional growth. The study has implications for teachers who are looking to make changes to their practice based on evidence-informed teaching approaches.

This paper reports on early years teachers and how often they should devote planning time to anticipating student responses in advance of the lesson. Sixty-five Foundation to Year 2 teachers (students 5-8 years of age) completed questionnaires at the beginning and end of a year-long research-based professional development program. Participants were learning to teach with sequences of challenging tasks. Post-program data showed a shift in the frequency of time participants believed teachers should devote to anticipating student responses prior to teaching. Supporting teachers' mathematical knowledge for teaching with an emphasis on how they plan and anticipate student responses has implications for improving practice and student outcomes.

There is an educational expectation that children's natural drawing will develop into proficient mathematical representations and formal diagrams, yet there is little research available to guide the assessment and development of children's mathematical drawing skills. The aim of this paper is to explore how Year 2 children (approx. 7 years) chose to represent their interpretations of a simple story that is suggestive of the take-away subtraction process, and what changes occurred when the drawing task was repeated 6 months later. Analysis of 13 pairs of drawings revealed changes in what the children drew (categories of number representations) and how they drew it (style). The findings suggest that substantial change in children's representational ability can occur in within 6 months.

It is well accepted and understood amongst the mathematics education community that numeracy is the responsibility of all teachers, across all levels of schooling. However, the way numeracy is understood and actioned across the Early Childhood, Primary and Secondary contexts is different. This paper reports on a case study of secondary school teachers seeking to be more intentional in embedding numeracy across the curriculum. The findings indicate that dialogue and support to see, and make, numeracy connections result in greater cohesion in terms of understanding numeracy and making numeracy more visible for students.

Teachers often perceive barriers to integrating technology with Mathematics. In the study, teachers participated in professional development about considerations for and examples of integrating Digital Technologies into Mathematics learning in primary schools meeting the "Australian Curriculum: Mathematics and Digital Technologies" requirements. This exploratory multiple case study included preand post-surveys, mentoring conversations and interviews to explore their beliefs and perceived barriers to integrating mathematics and digital technologies. This paper provides insights into their perceived barriers to integrating digital technologies.

South Australia's PISA performance has been in constant decline since 2003 with the proportion of PISA participants meeting the Australian national proficient standard dropping from 73% (in 2003) to 50% (in 2018). In contrast, Singapore is a consistently strong performer. To better understand student readiness in answering PISA questions, this paper reports a curriculum comparison between Australia and Singapore for Years 9 and 10 in Measurement and Geometry. The findings highlight the similarities and differences in the topics covered in both countries' curricula and raise questions about potential implications for student outcomes in PISA.

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.

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.

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.

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.

Mathematical self-concept refers to the perceived ability that one has in being able to do mathematics. While it has been shown to be a significant predictor for how students learn and apply mathematics, little research has been conducted into the relationship between the mathematical self-concept of teachers and their pedagogical practices in the mathematics classroom. This paper reports on a section of the findings from a small mixed methods study that sought to ascertain the nature of primary teachers' mathematical self-concept and how it is related to their teaching practices. Findings suggest that a teachers' mathematical self-concept does not necessarily reflect the mathematics practices evident in their classroom.

The description "primary mathematics specialist" has become more frequently used in Australia in the past 10 years, suggesting sustained interest in deepening teacher expertise. Despite this, there is limited contextual research about how to prepare in-service teachers for such roles, and the organising structures needed to facilitate their progress. This paper describes background and emerging insights from a project offering sustained and supported learning experiences for in-service teachers to become primary mathematics specialist teachers in and across their school. Curriculum and contextual experiences designed around a theoretical framework of leadership development implemented over 2 years are described. Early insights include the "priming" influence of an extended focus on mathematical content and pedagogical knowledge on participants' confidence to lead others, and the benefits of being explicit about enabling structures that promote sustainable growth and change.

Primary mathematics leadership has become a focus for improving the teaching of mathematics within Australian primary schools. Much of the training and support for those in the role have concentrated on content knowledge, rather than leadership training. There are currently no guidelines or standards in place to support the complex and multi-faceted roles and responsibilities of primary mathematics leaders. This paper reports on the initial stage of a research project examining how primary mathematics leadership is conceptualised and experienced. It reports on survey findings regarding teachers and leaders' understanding of primary mathematics leadership.

All teachers of mathematics aim to provide productive learning experiences that cater for students in their care. The planning of effective and engaging mathematics lessons is complex and requires expertise. In a larger study survey data, observations and interviews were used to investigate the ways in which School Mathematics Leaders supported teachers to learn. This paper reports results from case study research and focuses on the actions of one School Mathematics Leader during planning meetings. Findings highlight a range of supportive actions, which included developing constructive working relationships with teachers, fostering knowledge of mathematical content and curriculum and facilitating collaborative team planning.

This paper focuses on the time teachers take to adapt to a student-centred inquiry approach to teaching mathematics, the nature of those changes and the reasons for variations in both these aspects among teachers within and across schools. Five numeracy experts, who worked with 200 Foundation to Year 2 teachers to facilitate the implementation of the approach, were individually interviewed at the end of the year to obtain their perspectives on teachers' adaptation. Thematic analysis of the data revealed two overarching themes--context and teacher agency. The findings reinforce recommendations that professional learning providers acknowledge and take account of individual teacher learning trajectories to maximise potential change in practices.

This paper outlines the rationale for, and some elements of, a particular approach to teaching and learning mathematics in the early years. The researchers worked with two school systems to offer both centrally delivered and school-based teacher professional learning, which included the application of illustrative teaching resources. The project gathered a range of data from teachers and leaders on their dispositions and knowledge, as well as the opportunities and constraints they experienced, and the influence these variables had on planning, teaching and student learning outcomes.

While interdisciplinary approaches in the STEM subjects are widely advocated there are concerns that disciplinary learning can be compromised, especially in mathematics. The Interdisciplinary Mathematics and Science (IMS) project is a three-year longitudinal study in four Victorian primary schools that has developed a pedagogical approach to mathematics and science learning where data modelling and representation are common to each. Investigations include astronomy, ecology, chemistry, fast plant growth, force and motion, water use, heat and temperature, body height, light and microorganisms. The paper describes the role of mathematics in the IMS pedagogical model and design of learning sequences.

Prospective secondary mathematics teachers in Australia are typically taught by mathematics educators and mathematicians who work in different faculties and seldom collaborate--a situation that can lead to conflicting views about how to teach mathematics. This paper reports on findings from semi-structured interviews with three mathematics teacher educators in a hybrid mathematics/mathematics education department. Valsiner's zone theory is used to analyse how their beliefs, institutional context and professional learning opportunities shape their identities as MTEs. Findings reveal that the MTEs had developed similar beliefs within supportive institutional context but drew on different sources of professional learning.

The intangible concept of data, as part of statistical literacy, can be complex for young children to grasp. Inquiry as a pedagogy has potential for supporting student development of statistical literacy as the investigation process is driven by the inquiry question. The aim of this paper is to gain insight into how a teacher's communication processes with her students supported their emerging understandings about the abstract concept of data. In this exploratory case study, we present data from a Year 4 classroom (age 9) in a guided mathematical inquiry within the STEM context of agricultural science. The inquiry question the students addressed was, "How big is a leaf?" The inquiry focused on linking data to the real-life context the data represented.

In this paper we report on an aspect of a larger study and explore whether a framework for teacher STEM Capability Sets (SCS) enhanced teacher planning and the implementation of mathematics active STEM tasks. A case study approach was employed to understand how a classroom teacher used the digital resource, Gapminder, to teach a Year 5/6 cohort of students to interpret data as the basis for a STEM assessment. The research found that using the SCS as a guide, and emphasising mathematics in STEM learning and assessment, allowed the teacher to: reflect on existing STEM capabilities; observe the enhancement of other capabilities; and identify areas for future development.