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Traditionally Australian primary school teachers have been viewed as generalists responsible for instruction across all content areas. Adopting self-determination theory as a lens, the aim of the study was to explore the extent to which generalist primary school teachers are interested in becoming subject matter specialists. Questionnaire data were collected from 104 early years primary school teachers. Findings suggest that two-thirds of these generalist teachers expressed an interest in specialising in either English, mathematics, and to a far lesser extent, science, such that they would be responsible for exclusively teaching this subject. Preferences for specialisation were based on teachers' self-perceived content and pedagogical expertise and/ or their enjoyment of teaching in this content area. By contrast, the one-third of teachers who would choose to remain generalists referred to the value in a variety of teaching experiences, teaching from a whole child perspective and content integration. Implications for educational policy are discussed.

Just as students experience productive struggle or spend time in the 'zone of confusion' when engaging with challenging tasks, teachers also experience similar difficulties and periods of confusion when engaging with new pedagogical approaches. Prior to a 19-week lockdown due to Coronavirus (COVID-19) during 2020, two Foundation teachers implemented a student-centred pedagogical approach when teaching with challenging tasks. While they had some initial success implementing the pedagogical approach and a three-phase lesson structure, they struggled to do so online during the lockdown. It is the experiences of these teachers, in particular their experience of confusion relating to aspects of the pedagogical approach, and how this confusion was overcome, that is reported in this paper. Central to our findings is the importance of teachers reflecting on their own experiences of struggle and the impact this had on their professional learning, as well as the notion that adversity can be a catalyst for change.

Purpose: The purpose of this paper is to explore whether the four value alignment strategies available to educators (Scaffolding, Balancing, Intervention, and Refuge) previously identified in the mathematics education literature comprehensively capture educator value alignment strategies in an intervention context. Design/Approach/Methods: To this end, we analyse semi-structured interview data with two teacher-leaders involved in the Getting Ready in Numeracy (G.R.I.N.) intervention program through a value alignment lens. Findings: We ascertain that a fifth strategy, the Beacon strategy, is needed to describe the range of value alignment strategies employed by educators in the G.R.I.N. program. The Beacon strategy involves the educator digging in and reasserting their expectations until the student behaves in a manner that aligns with the educator's values. In part it involves the educator being able to recognize their own values and clearly communicating these values to students. Originality/Value: This article further explores strategies that educators have at their disposal for aligning their values with those of their students. The uncovering of the Beacon strategy is particularly valuable as it suggests that educators could be purposefully pursuing value alignment even when they do not appear to take any active steps to move further towards their students' sets of values.

SARS coronavirus 2 (SARS-CoV-2) has caused an ongoing global pandemic with significant mortality and morbidity. At this time, the only FDA-approved therapeutic for COVID-19 is remdesivir, a broad-spectrum antiviral nucleoside analog. Efficacy is only moderate, and improved treatment strategies are urgently needed. To accomplish this goal, we devised a strategy to identify compounds that act synergistically with remdesivir in preventing SARS-CoV-2 replication. We conducted combinatorial high-throughput screening in the presence of submaximal remdesivir concentrations, using a human lung epithelial cell line infected with a clinical isolate of SARS-CoV-2. This identified 20 approved drugs that act synergistically with remdesivir, many with favorable pharmacokinetic and safety profiles. Strongest effects were observed with established antivirals, Hepatitis C virus nonstructural protein 5A (HCV NS5A) inhibitors velpatasvir and elbasvir. Combination with their partner drugs sofosbuvir and grazoprevir further increased efficacy, increasing remdesivir's apparent potency > 25-fold. We report that HCV NS5A inhibitors act on the SARS-CoV-2 exonuclease proofreader, providing a possible explanation for the synergy observed with nucleoside analog remdesivir. FDA-approved Hepatitis C therapeutics Epclusa® (velpatasvir/sofosbuvir) and Zepatier® (elbasvir/grazoprevir) could be further optimized to achieve potency and pharmacokinetic properties that support clinical evaluation in combination with remdesivir.

Mathematical games are widely employed by Australian primary school teachers to support mathematics instruction. Despite broad usage, prior research has not focused on the how and why games are employed from a teacher perspective. Australian primary school teachers (n = 248) completed a questionnaire designed to probe their experience with mathematical games in the classroom, specifically; motivation for and frequency of game usage, game execution within lesson routines and structures, and, perceptions of the efficacy of games to achieve pedagogical objectives. Almost all the primary teachers self-reported playing mathematical games in their classrooms a minimum of once a week. Games were utilised in differing pedagogical capacities, for example, as a 'warm-up' exercise, to introduce new mathematical concepts, to consolidate skills and knowledge, and for fluency practice. Consistent with prior research, teachers viewed games as highly effective for engaging students in mathematics. Teachers also viewed games as being effective for developing all four proficiencies highlighted in the Australian Curriculum: Mathematics (ACARA, 2019); fluency, understanding, problem-solving, and reasoning. Interestingly, despite the burgeoning use of digital games, only two out of the 248 teachers surveyed mentioned a computer game or digital application as their favourite game to use in a mathematics lesson. A substantial majority of teachers nominated favourite games that involved minimal or no materials, in particular, playing cards and/ or dice, pen and paper, and oral games. Implications of these findings are discussed and future research directions are recommended. This study has taken steps towards deepening our mathematics educational community's understanding of primary teachers' use and experience of games.

Given what is known about the importance of productive struggle for supporting student learning of mathematics at all levels, the current study sought to examine teacher attitudes towards student struggle when students learn mathematics in remote learning settings compared with classroom settings. Eighty-two Australian early years primary teachers involved in a professional learning initiative focused on teaching mathematics through sequences of challenging tasks completed a questionnaire inviting them to compare the two settings. Drawing on a mixed-methods approach, we found that teachers were more positive about the value of student struggle in classroom-based settings compared with remote learning settings. Qualitative analysis of open-ended responses revealed four themes capturing why teachers viewed efforts to support productive struggle in a remote learning setting as potentially problematic: absence of a teacher-facilitated, synchronous, learning environment; parents' negative attitudes towards struggle when learning mathematics; lack of social connection and peer-to-peer collaboration; and difficulties accessing learning materials. Suggestions for mitigating some of these challenges in the future are put forward.

In early 2020, due to the COVD-19 pandemic, Australian schools were closed and students began an unprecedented time of remote learning. The current study aimed to understand how teachers planned and implemented mathematics learning programs for their students, the challenges they encountered, as well as the degree to which their students were motivated or engaged when learning mathematics at home. Two teachers from two Australian primary schools who shared a similar contemporary teaching and learning philosophy emphasising inquiry-based learning were interviewed, and students were surveyed anonymously about their engagement (cognitive, emotional, social and behavioural) when learning mathematics from home. Findings indicated that both teachers were concerned about effectively catering for all students and assessing student progress and engagement with the tasks. Survey data revealed most students displayed positive engagement with remote learning experiences, except for the lack of opportunity to learn mathematics with and from their peers.

Using children's literature to support mathematics instruction has been connected to positive academic outcomes and learning dispositions; however, less is known about the use of audiovisual based narrative mediums to support student mathematical learning experiences. The current exploratory, qualitative study involved teaching three lessons based on challenging, problem solving tasks to two classes of Australian Year (Grade) 5 students (10 and 11 year olds). These tasks were developed from various narratives, each portrayed through a different medium (movie clip, short film, picture story book). Post lesson interviews were undertaken with 24 students inviting them to compare and contrast this lesson sequence with their usual mathematics instruction. Drawing on a self-determination theory lens, our analysis revealed that these lessons were experienced by students as both highly enjoyable and mathematically challenging. More specifically, it was found that presenting mathematics tasks based on rich and familiar contexts and providing meaningful choices about how to approach their mathematical work supported student autonomy. In addition, there was evidence that the narrative presentation supported student understanding of the mathematics through making the tasks clearer and more accessible, whilst the audiovisual mediums (movie clip, short film) in particular provided a dynamic representation of key mathematical ideas (e.g., transformation and scale). Students indicated an eclectic range of preferences in terms of their preferred narrative mediums for exploring mathematical ideas. Our findings support the conclusion that educators and researchers focused on the benefits of teaching mathematics through picture story books consider extending their definition of narrative to encompass other mediums, such as movie clips and short films.

Despite teacher enjoyment of teaching being associated with a range of benefits for teachers and their students, little research exploring the characteristics of teachers who enjoy teaching mathematics exists. Semi-structured interviews were conducted with ten teachers who scored in the top third in terms of their enjoyment of teaching mathematics from a sample of 118 generalist, early-year primary school teachers. Thematic analysis of interview data revealed that negative-to-positive turning point experiences were commonplace amongst high-enjoyment primary teachers, but so too were reports of consistently positive feelings towards mathematics throughout their entire lives. While most articulated a passion for teaching mathematics, all teachers considered instances when students experienced 'light bulb' moments in their mathematical understanding that made a mathematics lesson enjoyable to teach. An important implication of our research is that one need not be a 'maths person' to come to love teaching mathematics. Rather, positive experiences in one's pre-service teacher education, or in-service teacher professional learning, have the potential to transform one's attitude towards teaching mathematics.

There is evidence that student attitudes towards mathematics become more negative as students move through their schooling. However, less is known about the different factors that shape student attitudes at various stages. This qualitative study sought to shed light on this issue and consider how stage of schooling influenced self-perceived supports for what helped underperforming students to learn mathematics. One hundred and seventy-nine students in Grades 2/3 and 5/6 completed a questionnaire before they participated in a mathematics intervention program, targeting students who had fallen behind in mathematics. Participating students were asked to complete the sentence stem. The best thing about learning mathematics in my classroom is…and answered the question: What helps you learn mathematics in the classroom? Thematic analysis revealed that the majority of younger students emphasized specific tasks (e.g. games) and mathematical content areas (e.g. counting) when describing the best thing about learning mathematics at school and were twice as likely to highlight such aspects compared with older students. By contrast, older students were far more likely to indicate the importance of being supported directly by their teacher or peers when learning mathematics, compared with younger students.

This article is based upon Peter Sullivan's (2021) structured inquiry approach to teaching mathematics, in which the authors take a deep dive into the technique of "Spotlighting" in the "Explore" phase of this model to assist in optimal learning experiences for students. Working from the premise that students are best placed to connect with instruction after a powerful and sometimes confusing learning experience, Sullivan et al.'s (2021) model provides three distinct phases to structure a mathematics lesson. They are: (1) The Launch phase--poses the task to students without any further instruction about the strategies required to solve the task; (2) The Explore phase--where collaboration and peer learning is encouraged as a support for students to consider multiple solutions and solution pathways; and (3) The Summarise/Review phase--provides an opportunity for the teacher to orchestrate class discussions by presenting various student solutions that reflect the mathematical focus of the lesson. The authors conclude they have been pleasantly surprised at how particular student explanations, derived from real time spotlight moments, were critical in shaping successful learning opportunities for the rest of the class.

There has been considerable research into how children solve single-digit addition problems for more than a century now, which has brought about significant changes to the ways teachers' support children to retrieve single-digit addition facts. In this project, we examine what makes an addition problem difficult to retrieve in light of contemporary teaching approaches, based on both student performance and teacher perceptions. Australian primary school students in Years 3 and 4 (n = 166) solved 36 single-digit addition problems under two different conditions during a structured interview. These data were then used to create the Difficulty Retrieving Addition Facts (DRAF) measure, which we propose as a contemporary measure of single-digit addition problem difficulty to supersede older measures developed in a different era of instruction. We then invited Australian primary school teachers (n = 49) to complete a questionnaire asking them to estimate the percentage of students who would be able to rapidly retrieve these same 36 single-digit addition problems to facilitate comparison between student performance and teacher perceptions. We found that although teachers were generally accurate in discerning which addition problems students would find relatively easy to retrieve and which they would find more difficult, they tended to overestimate student capacity to retrieve addition facts in general, particularly when the addition fact was comparatively difficult. We suggest that this overestimation resulted from teacher responses being shaped by curriculum expectations, which states that students should be able to recall single-digit addition facts by the end of Year 3.

Despite a focus on teaching mathematics through challenging, problem solving tasks, there has been limited research into student attitudes towards these learning experiences. To address this gap in the literature, we asked 52 Australian primary students who had recently experienced mathematics taught in this manner to convey their feelings about learning through problem solving. Adopting a qualitative, exploratory, research design, student participants completed a brief questionnaire, and a sub-set also contributed to follow-up focus groups. Thematic analysis of the questionnaire data revealed that three-quarters of students reported unambiguously positive attitudes towards problem solving, most others were ambivalent, and no students expressed negative attitudes. Younger students (Year 3/4) were more likely to express positive attitudes than older students (Year 5/6) and boys more likely to express positive attitudes than girls. Positive attitudes arose from students enjoying learning through problem solving, the perception that it supported their learning, and students thriving on challenge. Follow-up focus groups also reinforced the power of working collaboratively, particularly the importance of learning through discussions with peers, and opportunities to explore authentic and purposeful tasks. The findings help explain why students frequently have positive reactions to learning mathematics through problem solving.

This paper outlines a tutoring initiative intended to re-engage students who have become alienated from mathematics class at school. The initiative is focused on priming students for their subsequent mathematics lessons, and is referred to as "Getting Ready in Numeracy" (G.R.I.N.). Following a discussion outlining the principles of G.R.I.N., data from interviews with G.R.I.N. tutors and classroom teachers are presented. Findings suggest that participating in G.R.I.N. enhanced student engagement in mathematics and helped foster a growth mindset. Analysis of interviews also revealed some of the challenges associated with the initiative, in particular, issues relating to communication and coordination, such as: understanding the purpose of G.R.I.N., timetabling, planning and having sufficient students in the target group. In addition, in some instances, tensions between the professional and pedagogical expertise of the G.R.I.N. tutor and classroom teacher required navigation. Recommendations for mitigating these challenges and tensions are put forward, all of which are reliant on strong leadership and support for the program at the school level.

Teaching assistants are not always utilised effectively in mathematics classrooms. Moreover, there is limited research examining instructional models that might more meaningfully incorporate teaching assistants into the teaching and learning of mathematics. To address this gap in the literature, the current study explored three distinct teacher-tutor dyads involved in a particular intervention program, Getting Ready in Numeracy (G.R.I.N.), from a single Australian primary school. All three tutors currently operated as teaching assistants in the classrooms of their G.R.I.N. teacher counterparts. The professional working relationships between G.R.I.N. teachers and their respective tutors were investigated through interviews. We outline common themes between the different dyads' approaches to G.R.I.N., and argue that all three dyads' practices are consistent with principles outlined in the literature around the effective utilisation of teaching assistants. We conclude by synthesising our findings, and presenting an embedded tutor model for the G.R.I.N. program. This model is presented as a prototype of good practice in a context where G.R.I.N. has been implemented successfully, whilst also serving as a more general model for how teaching assistants can be meaningfully incorporated into mathematics intervention programs.

There is frequently a substantial disconnect reported between educational research and classroom practice. It has been proposed that individuals operating at the intersection of research and practice can potentially strengthen the relationship between the two communities through transcending institutional boundaries. The current study involved semi-structured interviews with three such 'hybrid professionals', who were all currently working as teachers in Australian primary schools and had completed PhDs in mathematics education. The purpose of the interviews was to gain insight into their experiences, and associated professional identity structures. Thematic analysis revealed that all participants were motivated to pursue higher-degree research to enhance their practice through the opportunity to specialise and work with an expert in their field. Consequently, rather than the proposed disconnect, there was evidence that at least some researchers within primary mathematics education were viewed as exemplifying expert practice. By contrast, participant professional identity structures did not converge, but remained idiosyncratic. In particular, participants varied in relation to the complexity of their researcher identity when in the classroom teacher role. Several possible directions for future research are outlined.

Teaching mathematics through problem solving is central to contemporary approaches to mathematics instruction, whilst augmenting problem-solving tasks through enabling and extending prompts ensures that a diverse community of learners are provided with opportunities to be optimally challenged, supporting an inclusive classroom environment. However, it has been frequently assumed that teachers should determine when a student should access an enabling prompt, perhaps in part due to concerns that students might be reluctant to seek prompts themselves because of social stigma associated with help seeking. In this paper, we argue that getting students to access prompts of their own volition should be central to teaching mathematics in this manner. One hundred and thirty-two Year 3-6 students completed a questionnaire disclosing their attitudes towards enabling prompts in classroom environments where they were expected to access prompts themselves. Most students consistently reported that enabling prompts empowered them as learners, allowing them to both take responsibility for, and have success with, their mathematics learning. In particular, students valued being able to access prompts when they were stuck on a task, felt that prompts had the power to increase their understanding, and to approach mathematical tasks with more confidence. Students generally did not associate accessing enabling prompts with being 'bad' at mathematics and acknowledged that even strong mathematicians might use a prompt sometimes. There was almost no evidence of any stigma or embarrassment associated with accessing enabling prompts. The implication is that classroom teachers can rapidly establish a culture where students access enabling prompts themselves to support learning mathematics through problem solving.

Little is known about primary school mathematics middle leaders' aspirations for mathematics learning. We sought to give mathematics middle leaders a voice to articulate their desires for mathematics learning based on what was most salient to them. Statements collected from 149 primary school mathematics middle leaders through an online survey were categorised using an ecological approach to determine the system level (i.e., mathematics middle leader, classroom, school, education system, or cultural norm) in which their aspirations for mathematics learning mostly presided. The mathematics middle leaders' aspirations were situated across the full range of ecological systems. However, more mathematics middle leaders focused their aspirations within the classroom level, compared with any other level, and around 15% focused on their own knowledge and capacity to lead.

Building on recent research into the importance of positive teacher emotions for student learning experiences, the current study involved five upper primary teachers at a Victorian government school developing inquiry mathematics units built around topic areas of personal interest or passion. Respective students (n=88) elected to participate in one of five structured inquires developed by these teachers. Despite being given a mandate to let their own passion drive their topic choice, interviews with teachers indicated that they invariably anticipated the interests of students when selecting their topic. Moreover, although teachers enjoyed the experience of developing and delivering the inquiry units, their emotional responses were inextricably linked to the perceived student learning experience. Student questionnaire data revealed that participation in the inquiry units was associated with increases in students' intrinsic motivation to learn mathematics. Students attributed positive evaluations to the opportunity to learn mathematics in a context in which they were personally engaged. Possible future research directions are discussed.

Building on the rich tradition of 'teacher as researcher' in mathematics education, I describe a study undertaken whilst working as a mathematics specialist in an Australian primary school. The focus of the study was on examining whether explicitly teaching students test-taking strategies ('test-wiseness') improved their performance on a standardised numeracy assessment; specifically, a practice version of the Year 3 National Assessment Program -- Literacy and Numeracy (NAPLAN). The study was unusual for teacher-research in that it adopted an experimental design. Thirty-eight Year 2 students (7 and 8 year olds) were randomly allocated to either an intervention condition (n=19) focused on developing test wiseness, or a 'business as usual' control condition (n=19). It was found that exposure to test-taking strategies improved student numeracy performance, with the intervention group significantly out-performing the control group. Implications of the findings are discussed, with a particular focus on what they mean in an environment where schools are increasingly held to account through the use of 'value-add' metrics.

Estimation supports the development of higher level mathematical thinking and reasoning; however, has received relatively little research attention. We examined whether making predictions influences the accuracy of numerosity estimates in elementary-aged children, and whether the amount of information available to the estimator determines the accuracy of their subsequent estimate. The study was conceptualized on the basis of five different conditions for estimating, based on the contention that estimates will become more accurate as additional information becomes available to the estimator. To test this idea, the study utilized two tasks to examine the responses of year 2 (grade 2) and year 6 (grade 6) students (n = 110) when using prediction-first and estimation-only strategies. Across both tasks, we found a direct linear relationship between the accuracy of students' estimates and the amount of information available. Moreover, there was some evidence that being given an opportunity to make an initial prediction improved the accuracy of final estimates; however, these conclusions were tempered by task and age. Overall, our findings support a strategy sophistication effect, whereby the amount of information available to the estimator, and the ability to use that information effectively, increases the accuracy of the estimate.

How can we engage all primary school students in rich mathematical learning, support them to make connections, and develop their mathematical language and reasoning? In this article, we draw on one school's experience in considering an approach to mathematics instruction that could support teachers in addressing this question, specifically pursuing structured inquiry in a multi-age setting.