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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]