Time-dependent fractional advection–diffusion equations by an implicit MLS meshless method

Recently, many new applications in engineering and science are governed by a series of fractional partial differential equations (FPDEs). Unlike the normal partial differential equations (PDEs), the differential order in a FPDE is with a fractional order, which will lead to new challenges for numerical simulation, because most existing numerical simulation techniques are developed for the PDE with an integer differential order. The current dominant numerical method for FPDEs is Finite Difference Method (FDM), which is usually difficult to handle a complex problem domain, and also hard to use irregular nodal distribution. This paper aims to develop an implicit meshless approach based on the moving least squares (MLS) approximation for numerical simulation of fractional advection-diffusion equations (FADE), which is a typical FPDE. The discrete system of equations is obtained by using the MLS meshless shape functions and the meshless strong-forms. The stability and convergence related to the time discretization of this approach are then discussed and theoretically proven. Several numerical examples with different problem domains and different nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the FADE.

Scaffolding techniques : a teacher training for cooperative learning in Thailand primary education

In general, the benefits of using cooperative learning include academic achievement, communication skills, problem-solving, social skills and student motivation. Yet cooperative learning as a Western educational concept may be ineffective in a different learning system. The study aims to investigate scaffolding techniques for cooperative learning in Thailand primary education. The program was designed to foster Thai primary school teachers’ cooperative learning implementation that includes the basic tenets of cooperative learning and socio-cognitive based learning. Two teachers were invited to participate in this experimental teacher training program for one and a half weeks. Then the teachers implemented a cooperative learning in their mathematics class for six weeks. The data from teacher interview and classroom observation indicated that the both teachers are able to utilise questions to scaffold their students’ engagement in cooperative learning. This initiative study showed that difficulty or failure of implementing cooperative learning in Thailand education may not be derived from cultural difference. The paper discussed the techniques the participant teachers applied with proactive scaffolding, reactive scaffolding and scaffolding questions that can be used to facilitate the implementation of cooperative learning in Thai school.

An implicit RBF meshless approach for time fractional diffusion equations

This paper aims to develop an implicit meshless approach based on the radial basis function (RBF) for numerical simulation of time fractional diffusion equations. The meshless RBF interpolation is firstly briefed. The discrete equations for two-dimensional time fractional diffusion equation (FDE) are obtained by using the meshless RBF shape functions and the strong-forms of the time FDE. The stability and convergence of this meshless approach are discussed and theoretically proven. Numerical examples with different problem domains and different nodal distributions are studied to validate and investigate accuracy and efficiency of the newly developed meshless approach. It has proven that the present meshless formulation is very effective for modeling and simulation of fractional differential equations.

From classroom resistance to school reform

In the project described in this chapter, a group of educationally disengaged high school students investigated their peers' perspectives of factors related to low aspiration for and access to university. On the basis of their findings, they created an informative DVD to address the student needs.

Support teachers, learning difficulties and secondary school culture

This thesis will report on mixed method research which examined secondary Support Teachers Learning Difficulties (STLDs) and their modes of operation in New South Wales (NSW) government schools, Australia. Four modes of operation were identified in the literature as consultancy, team teaching, in-class support and withdrawal. An additional area of other duties was also included to examine the time when STLDs were not functioning in the four identified modes of operation. NSW government policy is in keeping with the literature as it recommends that STLDs should spend the majority of their time in consultancy and team teaching while in class with a minimum of withdrawal of students from their main classrooms for individual or small group instruction. STLDs, however, did not appear to be functioning in the recommended way. A number of factors identified in the literature, which may influence the modes of operation, can be grouped under the heading of school culture thus this research involved the examination of the effects of school culture on the modes of operation with the aim of expanding our understanding of the functioning of STLDs and providing suggestions for improvement. The theoretical base of social constructionism has informed this research which included survey and case study methods. Case studies of the STLDs in three secondary schools led to the conclusion that, in conjunction with factors such as flexibility and commitment, the involvement of the STLD in a sub-culture of learning support may lead to functioning in the recommended modes of operation.

Conceptions of school-based youth health nursing

The aim of this research is to explore the meaning of the experience of school-based youth health nursing in Queensland, Australia. The research follows a qualitative approach and is based on indepth interviews. The dominant experience is negative because participants feel they have to battle to gain respect and survive in the school environment. The small, positive experience of school-based youth health nursing is related to student consultations. Student consultations are a ‘golden egg’ because participants gain a sense of reward from making a difference to student wellbeing. This paper proposes operational recommendations including those related to health promotion and professional development and strategic recommendations regarding this model of school nursing. The authors conclude, first, that this ‘golden egg’ should be promoted to ensure all school nurses reap the rewards, second, that this model of school nursing is not the most effective model.

The transition to school of children with developmental disabilities : views of parents and teachers

The transition from early intervention programs to inclusive school settings presents children with developmental disabilities with a range of social challenges. In Queensland, in the year of transition to school, many children with developmental disabilities attend an Early Childhood Development Program for 2 to 3 days each week and also begin attendance in a mainstream program with the latter increasing to full-time attendance during the year. Quantitative and qualitative data were collected by parent interviews and teacher questionnaires for 62 children participating in the Transition to School Project regarding their perceptions of the success of the transition process and the benefits and challenges of inclusion. Both parents and teachers saw a range of benefits to children from their inclusion in ‘regular’ classrooms, with parents noting the helpfulness of teachers and their support for inclusion. Challenges noted by parents included the school’s lack of preparation for their child’s particular developmental needs especially in terms of the physical environment while teachers reported challenges meeting the needs of these children within the context and resources of the classroom. Parents were more likely than teachers to view the transition as easy. Correlational analyses indicated that teachers were more likely to view the transition as easy when they felt that the child was appropriately placed in a ‘regular’ classroom. Findings from this project can inform the development of effective transition-to-school programs in the early school years for children with developmental disabilities.

Mapping the language of science and science teaching practices : a case study of early childhood school science

Concerns raised in educational reports about school science in terms of students. outcomes and attitudes, as well as science teaching practices prompted investigation into science learning and teaching practices at the foundational level of school science. Without science content and process knowledge, understanding issues of modern society and active participation in decision-making is difficult. This study contended that a focus on the development of the language of science could enable learners to engage more effectively in learning science and enhance their interest and attitudes towards science. Furthermore, it argued that explicit teaching practices where science language is modelled and scaffolded would facilitate the learning of science by young children at the beginning of their formal schooling. This study aimed to investigate science language development at the foundational level of school science learning in the preparatory-school with students aged five and six years. It focussed on the language of science and science teaching practices in early childhood. In particular, the study focussed on the capacity for young students to engage with and understand science language. Previous research suggests that students have difficulty with the language of science most likely because of the complexities and ambiguities of science language. Furthermore, literature indicates that tensions transpire between traditional science teaching practices and accepted early childhood teaching practices. This contention prompted investigation into means and models of pedagogy for learning foundational science language, knowledge and processes in early childhood. This study was positioned within qualitative assumptions of research and reported via descriptive case study. It was located in a preparatory-school classroom with the class teacher, teacher-aide, and nineteen students aged four and five years who participated with the researcher in the study. Basil Bernstein.s pedagogical theory coupled with Halliday.s Systemic Functional Linguistics (SFL) framed an examination of science pedagogical practices for early childhood science learning. Students. science learning outcomes were gauged by focussing a Hallydayan lens on their oral and reflective language during 12 science-focussed episodes of teaching. Data were collected throughout the 12 episodes. Data included video and audio-taped science activities, student artefacts, journal and anecdotal records, semi-structured interviews and photographs. Data were analysed according to Bernstein.s visible and invisible pedagogies and performance and competence models. Additionally, Halliday.s SFL provided the resource to examine teacher and student language to determine teacher/student interpersonal relationships as well as specialised science and everyday language used in teacher and student science talk. Their analysis established the socio-linguistic characteristics that promoted science competencies in young children. An analysis of the data identified those teaching practices that facilitate young children.s acquisition of science meanings. Positive indications for modelling science language and science text types to young children have emerged. Teaching within the studied setting diverged from perceived notions of common early childhood practices and the benefits of dynamic shifting pedagogies were validated. Significantly, young students demonstrated use of particular specialised components of school-science language in terms of science language features and vocabulary. As well, their use of language demonstrated the students. knowledge of science concepts, processes and text types. The young students made sense of science phenomena through their incorporation of a variety of science language and text-types in explanations during both teacher-directed and independent situations. The study informs early childhood science practices as well as practices for foundational school science teaching and learning. It has exposed implications for science education policy, curriculum and practices. It supports other findings in relation to the capabilities of young students. The study contributes to Systemic Functional Linguistic theory through the development of a specific resource to determine the technicality of teacher language used in teaching young students. Furthermore, the study contributes to methodology practices relating to Bernsteinian theoretical perspectives and has demonstrated new ways of depicting and reporting teaching practices. It provides an analytical tool which couples Bernsteinian and Hallidayan theoretical perspectives. Ultimately, it defines directions for further research in terms of foundation science language learning, ongoing learning of the language of science and learning science, science teaching and learning practices, specifically in foundational school science, and relationships between home and school science language experiences.

Modelling travelling waves in spatially constrained environment solutions

In this study, we consider how Fractional Differential Equations (FDEs) can be used to study the travelling wave phenomena in parabolic equations. As our method is conducted under intracellular environments that are highly crowded, it was discovered that there is a simple relationship between the travelling wave speed and obstacle density.

Assessing students in senior science: an analysis of questions in contextualised chemistry exams

This study explores the development of a coding system for analysing test questions in two context-based chemistry exams. We describe our unique analytical procedures before contrasting the data from both tests. Our findings indicate that when a new curriculum is developed such as a context-based curriculum, teachers are required to combine the previously separate domains of context and concept to develop contextualised assessment. We argue that constructing contextualised assessment items requires teachers to view concepts and context as interconnected rather than as separate entities that may polarise scientific endeavour. Implications for practice, curriculum and assessment-development in context-based courses are proposed.

Redesigning school spaces : creating possibilities for learning

This chapter reports on a project in which university researchers’ expertise in architecture, literacy and communications enabled two teachers in one school to expand the forms of literacy that primary school children engaged in. Starting from the school community’s concerns about an urban renewal project in their neighbourhood, participants collaborated to develop a curriculum of spatial literacies with real-world goals and outcomes. We describe how the creative re-design of curriculum and pedagogy by classroom teachers, in collaboration with university academics and students, allowed students aged 8 to 12 years to appropriate semiotic resources from their local neighbourhood, home communities, and popular culture to make a difference to their material surrounds. We argue that there are productive possibilities for educators who integrate critical and place-based approaches to the design and teaching of the literacy curriculum with work in other learning areas such as society and environment, technology and design and the arts. The student production of expansive and socially significant texts enabled by such approaches may be especially necessary in contemporary neoconservative policy contexts that tend to limit and constrain what is possible in schools.

Pattern recognition using invariants defined from higher order spectra - one-dimensional inputs

A new approach to pattern recognition using invariant parameters based on higher order spectra is presented. In particular, invariant parameters derived from the bispectrum are used to classify one-dimensional shapes. The bispectrum, which is translation invariant, is integrated along straight lines passing through the origin in bifrequency space. The phase of the integrated bispectrum is shown to be scale and amplification invariant, as well. A minimal set of these invariants is selected as the feature vector for pattern classification, and a minimum distance classifier using a statistical distance measure is used to classify test patterns. The classification technique is shown to distinguish two similar, but different bolts given their one-dimensional profiles. Pattern recognition using higher order spectral invariants is fast, suited for parallel implementation, and has high immunity to additive Gaussian noise. Simulation results show very high classification accuracy, even for low signal-to-noise ratios.

Children’s strategies for making friends when starting school

Starting school is a critical and potentially stressful time for many young children, and having supportive relationships with parents, teachers and peers and friends offer better outcomes for school adjustment and social relationships. This paper explores matters of friendship when young children are starting school, and how they initiate friendships. In audio-recorded conversations with a researcher and their peers, the children proposed a number of strategies, including making requests, initiating clubs and teams, and peer intervention to support a friend. Their accounts drew on social knowledge and relational understandings, and showed that having someone, a friend, to play with was important for starting school. Children gave serious attention to developing strategies to initiate friendships.

An analytical and experimental study of the vibration response of a clamped ribbed plate

An analytical solution is presented in this paper for the vibration response of a ribbed plate clamped on all its boundary edges by employing a travelling wave solution. A clamped ribbed plate test rig is also assembled in this study for the experimental investigation of the ribbed plate response and to provide verification results to the analytical solution. The dynamic characteristics and mode shapes of the ribbed plate are measured and compared to those obtained from the analytical solution and from finite element analysis (FEA). General good agreements are found between the results. Discrepancies between the computational and experimental results at low and high frequencies are also discussed. Explanations are offered in the study to disclose the mechanism causing the discrepancies. The dependency of the dynamic response of the ribbed plate on the distance between the excitation force and the rib is also investigated experimentally. It confirms the findings disclosed in a previous analytical study [T. R. Lin and J. Pan, A closed form solution for the dynamic response of finite ribbed plates. Journal of the Acoustical Society of America 119 (2006) 917-925] that the vibration response of a clamped ribbed plate due to a point force excitation is controlled by the plate stiffness when the source is more than a quarter plate bending wavelength away from the rib and from the plate boundary. The response is largely affected by the rib stiffness when the source location is less than a quarter bending wavelength away from the rib.