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In this paper, we study the following fractional Choquard equation with weight (−Δ)su=1|x|N−α∗h(x)|u|ph(x)|u|p−2uinℝN,$$ {\left(-\Delta \right)}&#x0005E;su&#x0003D;\left(\frac{1}{{\left&#x0007C;x\right&#x0007C;}&#x0005E;{N-\alpha }}\ast h(x){\left&#x0007C;u\right&#x0007C;}&#x0005E;p\right)h(x){\left&#x0007C;u\right&#x0007C;}&#x0005E;{p-2}u\kern0.5em \mathrm{in}\kern0.5em {\mathrm{\mathbb{R}}}&#x0005E;N, $$where 02s,p>2,α>0$$ 02s,p>2,\alpha >0 $$ and h$$ h $$ is a positive weight function satisfying h(x)≥C|x|a$$ h(x)\ge C{\left&#x0007C;x\right&#x0007C;}&#x0005E;a $$ at infinity, for some a≥0$$ a\ge 0 $$. We establish, in this paper, a Liouville type theorem saying that if maxN−4s−2a,0<α

In Australia, there have been a growing number of nature-based early childhood education initiatives [Alme, H., and M. A. Reime. 2021. "Nature Kindergartens: A Space for Children's Participation." Journal of Outdoor and Environmental Education 24: 113–131]. Research into early years' nature education internationally remains under-theorised particularly in STEM teaching and learning. The nature or bush kindergarten programme (often referred to as 'bush kinders' in the Australian context), is one such programme where nature play and education occur. This paper considers how children's mathematical thinking develops through their time spent in bush kinder settings. Using an ethnographic lens, this longitudinal study is the first of its type in Australia with a focus on STEM in bush kinders. In this paper, eight 'powerful mathematical ideas' are used to analyse how educators can approach teaching mathematics with only what nature provides. The paper reports one main finding, that bush kinders provide opportunities for children through educator support to build mathematical understandings through nature play. Drawing on fieldwork data and the analysis of research literature, this paper contributes to the conceptualisation of mathematics in early childhood nature play and bush kinder programmes. [ABSTRACT FROM AUTHOR]

Background: Computer‐based assessment allows for the monitoring of reader behaviour. The identification of patterns in this behaviour can provide insights that may be useful in informing educational interventions. Objectives: Our study aims to explore what different patterns of reading activity exist, and investigates their interpretation and consistency across different task sets (units), countries, and languages. Three patterns were expected: on‐task, exploring and disengaged. Methods: Using log data from the PISA 2012 digital reading assessment (9226 students from seven countries), we conducted hierarchical cluster analyses with typical process indicators of digital reading assessments. We identified different patterns and explored whether they remained consistent across different units. To validate the interpretation of the identified patterns, we examined their relationship to performance and student characteristics (gender, socio‐economic status, print reading skills). Results and Conclusions: The results indicate a small number of transnational clusters, with unit‐specific differences. Cluster interpretation is supported by associations with student characteristics—for example, students with low print reading skills were more likely to show a disengaged pattern than proficient readers. Exploring behaviour tended to be exhibited only once across the three units: It occurred in the first unit for proficient readers and in later units for less skilled readers. Major Takeaways: Behavioural patterns can be identified in digital reading tasks that may prove useful for educational monitoring and intervention. Although task situations are designed to evoke certain behaviours, the interpretation of observed behavioural patterns requires validation based on task requirements, assessment context and relationships to other available information. Lay Description: What is already known about the subject matter?: Students differ in how they read, comprehend and use digital information.Indicators from process data provide insight about how students engage with digital reading tasks. What does this paper add to the subject matter?: Based on multiple process indicators, a small number of clusters indicating different behavioural activity can be distinguished.These clusters can be described as on‐task, passive, hasty, exploring, disengaged, persistent and lost interest.A meaningful interpretation of the clusters must consider the requirements of the underlying tasks. Implications for practice and/or policy: Knowledge of how students engage with digital resources may provide useful feedback for teachers to guide students' learning or intervene when they struggle.Educational monitoring: The high comparability of country‐specific results suggests an invariant set of solution strategies in the digital reading assessment. [ABSTRACT FROM AUTHOR]

This paper is intended to provide a source of critical and theoretical reflection on the current mathematics educational objectives for Indigenous students in Australia, which are premised on acceptance of underlying concepts of 'equity'. It is not the intention of this paper to identify 'how' Indigenous knowledge can be positioned within mathematics curricula, as this would entail a philosophical inquiry much deeper than has been afforded thus far. The intent here is a consideration, facilitated through the lens of key concepts of Foucault, of some of the boundaries currently shaping the ways in which this positioning is being influenced in the mathematics, albeit neoliberal education context. Acknowledging the interplay between the social, and unconsciously shaped adoptions of what can be considered truth; knowledge; and therefore power, is a first step toward developing the openness of heart and mind needed to make real and transformative changes to education for future societies. [ABSTRACT FROM AUTHOR]

While international research has demonstrated that ability grouping is inequitable, Australian research has often overlooked equity concerns, predominantly focusing on studying the benefits of grouping for students perceived to have high ability, especially in mathematics. This paper investigates the effect that mathematics ability grouping has on senior secondary mathematics participation for low and middle grouped students in New South Wales, Australia. We drew on interviews about mathematics participation with 85 students and 22 mathematics teachers from 11 government high schools. Our thematic analysis of these data identified that secondary school grouping practices often serve to entrench student interest and/or performance from primary school. This has consequences for many students, with a differentiated curriculum in Years 9 and 10 precluding low and middle grouped students from participating in high-level mathematics when they reach senior secondary school. These findings raise serious equity questions about the current push in Australia for universities to re-introduce high-level mathematics as a prerequisite to entering certain degrees. We argue that stakeholders need greater awareness of the consequences of ability grouping and that those seeking to lift post-compulsory mathematics participation should be targeting primary and early secondary school. [ABSTRACT FROM AUTHOR]

This paper explores analysis of feedback data collected from student consultations at two mathematics support centres at universities in Australia and Ireland. Unstructured text data was collected over six years and includes qualitative data on student queries collected during the consultations from mathematics and statistics related subjects. Topic modelling and clustering algorithms are used to uncover key themes in the data across stages. Common areas of difficulty experienced by undergraduate students at both universities are investigated and a comparison between them is shown. The results suggest that, despite institutional differences, there is considerable overlap in the types of mathematical and statistical difficulties experienced by students in their first and second year of university at these institutions. We discuss how the ability to uncover such common mathematical and statistical themes with the aid of text mining techniques can be used to improve the support provided by mathematics support centres in terms of providing an efficient and effective service. The code for analyses at both institutions is provided in a GitHub repository so other academic support centres may use it. Outcomes of this analysis have implications for mainstream mathematics and statistics instructors who wish to gain further insights into their students' learning. [ABSTRACT FROM AUTHOR]

With more and more political candidates using social media for campaigning, researchers are looking at measuring the effectiveness of this medium. Most research, however, concentrates on the bare count of likes (or twitter mentions) in an attempt to correlate social media presence and winning. In this paper, we propose a novel method, Interaction Strength Plot (IntS) to measure the passive interactions between a candidate’s posts on Facebook and the users (liking the posts). Using this method on original Malaysian General Election (MGE13) and Australian Federal Elections (AFE13) Facebook Pages (FP) campaign data, we label an FP as performing well if both the posting frequency and the likes gathered are above average. Our method shows that over 60% of the MGE13 candidates and 85% of the AFE13 candidates studied in this paper had under-performing FP. Some of these FP owners would have been identified as popular based on bare count. Thus our performance chart is a vital step forward in measuring the effectiveness of online campaigning. [ABSTRACT FROM AUTHOR]

This paper focuses on the contribution of Australian Football League (AFL) players to their team's on-field network by simulating player interactions within a chosen team list and estimating the net effect on final score margin. A Visual Basic computer program was written, firstly, to isolate the effective interactions between players from a particular team in all 2011 season matches and, secondly, to generate a symmetric interaction matrix for each match. Negative binomial distributions were fitted to each player pairing in the Geelong Football Club for the 2011 season, enabling an interactive match simulation model given the 22 chosen players. Dynamic player ratings were calculated from the simulated network using eigenvector centrality, a method that recognises and rewards interactions with more prominent players in the team network. The centrality ratings were recorded after every network simulation and then applied in final score margin predictions so that each player's match contribution-and, hence, an optimal team-could be estimated. The paper ultimately demonstrates that the presence of highly rated players, such as Geelong's Jimmy Bartel, provides the most utility within a simulated team network. It is anticipated that these findings will facilitate optimal AFL team selection and player substitutions, which are key areas of interest to coaches. Network simulations are also attractive for use within betting markets, specifically to provide information on the likelihood of a chosen AFL team list "covering the line". [ABSTRACT FROM AUTHOR]

After the invasion and occupation of their land by Europeans, Indigenous Australians were expected to benefit from a Western education system based on that of the dominant Europeans. Gradually educators realized that Aboriginal children learn differently and that Indigenous culture and pedagogy has validity and strength. Of course, educators also need to be acutely aware of the diversity of Indigenous cultures in Australia and that there is not a monolithic sense of Aboriginal identity or Aboriginal pedagogy. Dispossession and alienation, poor health and few employment opportunities must also affect educational interest, attendance, application and performance. In this paper the characteristics of Indigenous learners are examined and pedagogical strategies to assist in both students' learning and teachers' delivery are explored. The message conveyed in this paper has particular relevance for teaching mathematics to Aboriginal learners. It is also of considerable value in teaching mathematics to nonAboriginal students, in Australia and elsewhere. [ABSTRACT FROM AUTHOR]

Materials and Methods: In this paper, we propose a theoretical model based upon previous studies about personal and social network dynamics of job performance. We provide empirical support for this model using real-world data within the context of the Australian radiology profession. An examination of radiologists’ professional network topology through structural-positional and relational dimensions and radiologists’ personal characteristics in terms of knowledge, experience and self-esteem is provided. Thirty one breast imaging radiologists completed a purpose designed questionnaire regarding their network characteristics and personal attributes. These radiologists also independently read a test set of 60 mammographic cases: 20 cases with cancer and 40 normal cases. A Jackknife free response operating characteristic (JAFROC) method was used to measure the performance of the radiologists’ in detecting breast cancers. Results: Correlational analyses showed that reader performance was positively correlated with the social network variables of degree centrality and effective size, but negatively correlated with constraint and hierarchy. For personal characteristics, the number of mammograms read per year and self-esteem (self-evaluation) positively correlated with reader performance. Hierarchical multiple regression analysis indicated that the combination of number of mammograms read per year and network’s effective size, hierarchy and tie strength was the best fitting model, explaining 63.4% of the variance in reader performance. The results from this study indicate the positive relationship between reading high volumes of cases by radiologists and expertise development, but also strongly emphasise the association between effective social/professional interactions and informal knowledge sharing with high performance. [ABSTRACT FROM AUTHOR]

Much research has been conducted on children's self-talk and its use to regulate thinking and behaviour, but research has typically been conducted on audible self-talk when undertaking specific tasks designed by researchers and in laboratory situations. Addressing the need to study self-talk in the classroom and by students of an age when self-talk is largely internalised, this study investigated the association of self-talk with children's self-regulatory behaviour and academic performance. The findings reported in this paper are based on the data from self-report questionnaires on self-talk completed by eight-to-nine-year-olds, national mathematics achievement test results, and a teacher-completed behaviour rating scale. Based on the previous research, results were somewhat unexpected, including that self-talk may not have a very strong role in children's behavioural self-regulation and calling into question an effect of self-talk on children's learning in the classroom. Possible reasons are provided and the need for future research is acknowledged. [ABSTRACT FROM PUBLISHER]

For over a decade, the Australian Bureau of Statistics (ABS) has been measuring the progress of our nation against a set of seventeen headline social, economic and environmental dimensions. Developed in the early 2000's by the ABS, important aspects of life were chosen after extensive consultation and debate about what should be the key headline dimensions of progress for Australia. Ten years on, and in recognition of the wide spread national and international interest in measuring the wellbeing and progress of societies, the ABS embarked on a journey to have a new conversation with Australians about what matters. The Measures of Australia's Progress consultation, or MAP 2.0, was a national conversation on Australia's progress. A major part of the project was the use of an online blog to collect comments from the general public about what aspects of life matter most to them, and what aspirations they hold for Australia's progress. Video and written contributions from prominent Australians were used to raise the profile of the blog and encourage input from people who might not otherwise have engaged. The use of social media as an engagement and consultation mechanism by a national statistical organisation was a new and challenging undertaking, but was a huge success - over 140 quality comments were received and discussions on several other websites were generated. This paper focuses on the rationale for using social media, the experience of the ABS in hosting a blog, lessons learnt, and future plans for measuring progress in Australia. [ABSTRACT FROM AUTHOR]

There is general agreement in Australia and beyond that quantitative skills (QS) in science, the ability to use mathematics and statistics in context, are important for science. QS in the life sciences are becoming ever more important as these sciences become more quantitative. Consequently, undergraduates studying the life sciences require better QS than at any time in the past. Ways in which mathematics and science academics are working together to build the QS of their undergraduate science students, together with the mathematics and statistics needed or desired in a science degree, are reported on in this paper. The emphasis is on the life sciences. Forty-eight academics from eleven Australian and two USA universities were interviewed about QS in science. Information is presented on: what QS academics want in their undergraduate science students; who is teaching QS; how mathematics and science departments work together to build QS in science and implications for building the QS of science students. This information leads to suggestions for improvement in QS within a science curriculum. [ABSTRACT FROM PUBLISHER]

Inquiries into the state of mathematics and science education in Australia express the need to make the curriculum more relevant and meaningful to students' lives. However, such a vision requires that teachers understand how relevance can enter mathematics and science classrooms in a meaningful and appropriate way. This paper asks, how is relevance thought of in mathematics as compared with science, and what problems might this pose for teachers moving between mathematics and science? [ABSTRACT FROM AUTHOR]

This paper reviews Fisher's research program, showing how it constituted a theoretical basis for Darwin's evolutionary, genetical and experimental work, and identifies those fields where Fisher, through his influence on colleagues and students, caused some of his aims to be carried through in Australia, particularly in experimental design and evolutionary genetics. [ABSTRACT FROM AUTHOR]

Many students are unsuccessful in the study of school mathematics, not because of some innate ability, but because of pedagogical practices. Bernstein (1996) has argued that pedagogy serves as a mechanism for cultural reproduction, so that for those students whose cultures are different from that represented in and through pedagogy, the task of constructing school mathematics is made more difficult. The paper explores the ways in which a teacher changes the pedagogic relay in order to be more inclusive of her students. Her practice is informed by understanding the ways in which pedagogy is a subtle tool for marginalization in mathematics. [ABSTRACT FROM AUTHOR]

Service industries are becoming an increasingly important part of our economies. Not surprisingly there is a corresponding interest in statistics about service industries. The challenges in compiling statistics are often very different to other industries. This paper describes the programme for service industry statistics in the Australian Bureau of Statistics. It also describes some of the more interesting developments in Australia – new presentations in statistics such as satellite accounts; globalisation statistics including the activities of foreign affiliates; knowledge based economy and society statistics; direct volume measurement particularly for largely non-market industries such as health and education services; and price statistics for service industries such as finance, telecommunications and computer software services. These statistics are very important for measuring productivity for example. [ABSTRACT FROM AUTHOR]

This paper reports selected findings from a study of number sense proficiency of students aged 8 to 14 years in Australia, Sweden, United States, and Taiwan. It comments on the meaning and importance of number sense, the development of the assessment instruments, and student responses to the items. Some implications for classrooms of the findings are then discussed. [ABSTRACT FROM AUTHOR]