Supporting exceptional students to thrive mathematically

Providing an appropriate education for exceptional students in mathematics is mandated in educational policy in Australasia (Australian Curriculum, Assessment and Reporting Agency (ACARA), 2010; Ministry of Education, 2009, 2011) but a challenge for teachers and schools. ‘Exceptional students’ refer to two distinct populations, namely those who are gifted in mathematics and have the capability to perform very highly compared to age peers and those who experience learning difficulties in mathematics and may underperform (Diezmann, Lowrie, Bicknell, Faragher, & Putt, 2004).

Leadership practices of Kuwaiti Secondary School Principals for embedding ICT

Globalisation and the emergence of knowledge-based economies have forced many countries to reform their education system. The enhancement of human capital to meet modern day demands of a knowledge economy, and equip the new generation with the capacity to meet the challenges of the 21st Century has become a priority. This change is particularly necessary in economies typical of countries, such as Kuwait, which have been dependent on the exploitation of non-renewable natural resources. Transiting from a resource-based economy to an economy based on knowledge and intellectual skills poses a key challenge for an education system. Significant in the development of this new economy has been the expansion of Information Communication Technology (ICT). In education, in particular, ICT is a tool for transforming the education setting. However, transformation is only successful where there are effective change management strategies and appropriate leadership. At the school level, rapid changes have affected the role that principals take particularly in relation to leading the change process. Therefore, this study investigated the leadership practices of school principals for embedding ICT into schools. The case study assessed two Kuwaiti secondary schools; both schools had well established ICT programs. The mode of data collection used a mixed-methods design, to address the purpose of the study, namely, to examine the leadership practices of school principals when managing the change processes associated with embedding ICT in the context of Kuwait. A theoretical model of principal leadership, developed, from the literature, documented and analysed the practices of the respective school principals. The study used the following five data sources: (a) face to face interviews (with each school principal), and two focus group interviews (with five teachers and five students, from each school); (b) school documents (related to the implementation and embedding of ICT); (c) one survey (of all teachers in each school); (d) an open-ended questionnaire (of participating principals and teachers); and (e) the observation of ICT activities (PD ICT activities and instruction meetings). The study revealed a range of strategies used by the principals and aligned with the theoretical perspective. However, these strategies needed to be refined and selectively used to fit the Kuwait context, both culturally and organisationally. The principals of Schools A and B employed three key strategies to maximise the impact on the teaching staff incorporating ICT into their teaching and learning practices. These strategies were: (a) encouragement for teaching staff to implement ICT in their teaching; (b) support to meet the material and human needs of teaching staff using ICT; and (c) provision of instructions and guidance for teaching staff in how and why such behaviours and practices should be performed. The strategies provided the basic leadership practices required to construct a successful ICT embedded implementation process. Hence, a revised model of leadership that has applicability in the adoption of ICT in Kuwait was developed. The findings provide a better understanding of how a school principal’s leadership practices impact upon the ICT embedding process. Hence, the outcome of this study informs emerging countries, which are also undergoing major change related to ICT, for example, other members of the Cooperation Council for the Arab States of the Gulf. From an educational perspective, this knowledge has the potential to support ICT-based learning environments that will help educational practitioners to effectively integrate ICT into teaching and learning that will facilitate students’ ICT engagement, and prepare them for the ICT development challenges that are associated with the new economy; this is achieved by increasing students’ knowledge and performance. Further, the study offers practical strategies that have been shown to work for school principals leading ICT implementation in Kuwait. These strategies include how to deal with the shortage in schools’ budgets, and the promotion of the ICT vision, as well as developing approaches to build collaborative culture in the schools.

A least squares based finite volume method for the Cahn-Hilliard and Cahn-Hilliard-reaction equations

A vertex-centred finite volume method (FVM) for the Cahn-Hilliard (CH) and recently proposed Cahn-Hilliard-reaction (CHR) equations is presented. Information at control volume faces is computed using a high-order least-squares approach based on Taylor series approximations. This least-squares problem explicitly includes the variational boundary condition (VBC) that ensures that the discrete equations satisfy all of the boundary conditions. We use this approach to solve the CH and CHR equations in one and two dimensions and show that our scheme satisfies the VBC to at least second order. For the CH equation we show evidence of conservative, gradient stable solutions, however for the CHR equation, strict gradient-stability is more challenging to achieve.

Solution methods for advection-diffusion-reaction equations on growing domains and subdomains, with application to modelling skin substitutes

Problems involving the solution of advection-diffusion-reaction equations on domains and subdomains whose growth affects and is affected by these equations, commonly arise in developmental biology. Here, a mathematical framework for these situations, together with methods for obtaining spatio-temporal solutions and steady states of models built from this framework, is presented. The framework and methods are applied to a recently published model of epidermal skin substitutes. Despite the use of Eulerian schemes, excellent agreement is obtained between the numerical spatio-temporal, numerical steady state, and analytical solutions of the model.

…Where did I lose you? Accessing the literacy demands of assessment

In this study we sought to find out how teachers could make assessment fairer for Indigenous students in learning mathematics, given the context of the high stakes of the National Assessment Program Literacy and Numeracy (NAPLAN). Today, teachers are experiencing the full range of demands from their own students who require individual attention, through to system level expectations of improved performances for all students. Many staff experience reform fatigue with limited time for critical reflection and a reduction in support for the use and the analysis of the overwhelming amount of data that has become available in recent years. Over the past three years we worked with teachers in seven schools to gradually refine our research focus to centre on how we might best support teachers in this demanding context with the important outcome of improved teaching and learning of mathematics with particular consideration of how to respond to the cultural needs of Indigenous (Aboriginal and Torres Strait Islander) students.

Serious playground : using Second Life to engage high school students in urban planning

Virtual world platforms such as Second Life have been successfully used in educational contexts to motivate and engage learners. This article reports on an exploratory workshop involving a group of high school students using Second Life for an urban planning project. Young people are traditionally an under-represented demographic when it comes to participating in urban planning and decision making processes. The research team developed activities that combined technology with a constructivist approach to learning. Real world experiences and purposes ensured that the workshop enabled students to see the relevance of their learning. Our design also ensured that play remained an important part of the learning. By conceiving of the workshop as a ‘serious playground’ we investigated the ludic potential of learning in a virtual world.

Visualising mathematical knowledge and understanding

Contemporary mathematics education attempts to instil within learners the conceptualization of mathematics as a highly organized and inter-connected set of ideas. To support this, a means to graphically represent this organization of ideas is presented which reflects the cognitive mechanisms that shape a learner’s understanding. This organisation of information may then be analysed, with the view to informing the design of mathematics instruction in face-to-face and/or computer-mediated learning environments. However, this analysis requires significant work to develop both theory and practice.

Moments of action provide insight into critical times for advection–diffusion–reaction processes

In 2010 Berezhkovskii and coworkers introduced the concept of local accumulation time (LAT) as a finite measure of the time required for the transient solution of a reaction diffusion equation to effectively reach steady state(Biophys J. 99, L59 (2010); Phys Rev E. 83, 051906 (2011)). Berezhkovskii’s approach is a particular application of the concept of mean action time (MAT) that was introduced previously by McNabb (IMA J Appl Math. 47, 193 (1991)). Here, we generalize these previous results by presenting a framework to calculate the MAT, as well as the higher moments, which we call the moments of action. The second moment is the variance of action time; the third moment is related to the skew of action time, and so on. We consider a general transition from some initial condition to an associated steady state for a one–dimensional linear advection–diffusion–reaction partial differential equation(PDE). Our results indicate that it is possible to solve for the moments of action exactly without requiring the transient solution of the PDE. We present specific examples that highlight potential weaknesses of previous studies that have considered the MAT alone without considering higher moments. Finally, we also provide a meaningful interpretation of the moments of action by presenting simulation results from a discrete random walk model together with some analysis of the particle lifetime distribution. This work shows that the moments of action are identical to the moments of the particle lifetime distribution for certain transitions.

Explicit, latent and meta-criteria : types of criteria at play in professional judgement practice

This paper engages with debates about whether comprehensive prior specification of criteria and standards is sufficient for informed professional judgement. A preoccupation has emerged with the specificity and explication of criteria intended to regulate judgement. This has resulted in criteria-compliance in the use of defined standards to validate judgements and improve reliability and consistency. Compliance has become a priority, the consequence being the prominence of explicit criteria, to the lack of acknowledgement of the operation of latent and meta-criteria within judgement practice. This paper examines judgement as a process involving three categories of assessment criteria in the context of standards-referenced systems: explicit, latent and meta-criteria. These are understood to be wholly interrelated and interdependent. A conceptualisation of judgement involving the interplay of the three criteria types is presented with an exploration of how they function to focus or alter assessments of quality in judgements of achievement in English and Mathematics.

The persistence of phase-separation in LiFePO4 with two-dimensional Li+ transport : the Cahn-Hilliard-reaction equation and the role of defects

We examine the solution of the two-dimensional Cahn-Hilliard-reaction (CHR) equation in the xy plane as a model of Li+ intercalation into LiFePO4 material. We validate our numerical solution against the solution of the depth-averaged equation, which has been used to model intercalation in the limit of highly orthotropic diffusivity and gradient penalty tensors. We then examine the phase-change behaviour in the full CHR system as these parameters become more isotropic, and find that as the Li+ diffusivity is increased in the x direction, phase separation persists at high currents, even in small crystals with averaged coherency strain included. The resulting voltage curves decrease monotonically, which has previously been considered a hallmark of crystals that fill homogeneously.

School-aged workers : industrial citizens in waiting?

While the literature points to significant shifts in young peoples’ labour market participation and the social, economic and political context in which this has occurred, it tells us little about whether and in what sense young people can be considered as industrial citizens. We explored the notion of youth citizenship using data derived from 48 focus groups conducted with 216 young people (13-16 years of age) at 19 high schools in Australia. The findings reveal the ways in which several key dimensions of industrial citizenship come to be shaped and have implications for addressing the vulnerability of youth in employment and informing policy and action.

How research findings can inform legislation and school policy on cyberbullying.

Recent empirical research has found that the psychological consequences for young people involved in cyberbullying are more severe than in the case of traditional bullying (Campbell, Spears, Slee, Butler, & Kift, 2012; Perren, Dooley, Shaw, & Cross, 2010). Cybervictimisation has been found to be a significant predictor of depressive symptoms over and above that of being victimised by traditional bullying (Perren et al., 2010). Cybervictims also have reported higher anxiety scores and social difficulties than traditional victims, with those students who had been bullied by both forms showing similar anxiety and depression scores to cyberbullying victims (Campbell et al., 2012). This is supported by the subjective views of many young people, not involved in bullying, who believed that cyberbullying is far more harmful than traditional bullying (Cross et al., 2009). However, students who were traditionally bullied thought the consequences of traditional bullying were harsher than did those students who were cyberbullied (Campbell, et al., 2012). In Slonje and Smith’s study (2008), students reported that text messaging and email bullying had less of an impact than traditional bullying, but that bullying by pictures or video clips had more negative impact than traditional bullying.

A hybrid model for studying spatial aspects of infectious diseases

We consider a hybrid model, created by coupling a continuum and an agent-based model of infectious disease. The framework of the hybrid model provides a mechanism to study the spread of infection at both the individual and population levels. This approach captures the stochastic spatial heterogeneity at the individual level, which is directly related to deterministic population level properties. This facilitates the study of spatial aspects of the epidemic process. A spatial analysis, involving counting the number of infectious agents in equally sized bins, reveals when the spatial domain is nonhomogeneous.

Educational stress among Chinese adolescents : individual, family, school and peer influences

Educational stress is common among school children and adolescents, especially in Asian countries. This study aims to identify factors associated with perceived educational stress among students in China. A cross-sectional questionnaire survey was conducted with 1627 students (Grades 7–12) from six secondary schools in rural and urban areas of Shandong Province. A wide range of individual, family, school and peer factors were associated with stress measured using the Educational Stress Scale for Adolescents (ESSA). Rural school location, low school connectedness, perceived poor academic grades, female gender, older age and frequent emotional conflicts with teachers and peers were among the strongest correlates, and most of them are school- or study-related. Unexpectedly, family and parental factors were found to have little or no association with children’s perceived educational stress. These findings may offer directions for interventions in secondary school settings.

Teaching in Inclusive School Communities

"Teaching in Inclusive School Communities, 1st Edition is the essential resource to provide pre-service teachers with the most contemporary, ethical and useful framework for incorporating diversity and inclusive practices in today’s classroom. Fourteen concise chapters compose a focused picture of the values and beliefs that inform the inclusive education approach, with the most up-to-date connections to curriculum and pedagogy throughout. Complemented by the latest research in the field, this text provides the practical knowledge and skills needed for inclusive classroom teaching in Australia and New Zealand, as well as a thorough analysis of exactly what is required to build respectful relationships in modern school communities."--publisher website