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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.

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.

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.