A review of the conversations and their content

This is the 2nd of a series of discussion papers (Table 1) around the pedagogy of supervision in the technology disciplines. The papers form part of an Australian Learning and Teaching Council Fellowship program conducted by ALTC Associate Fellow, Professor Christine Bruce, Queensland University of Technology.

Schools and Diversity, 2nd ed.

Schools and diversity aims to address the need for schools and teachers to provide quality education for all students in rapidly changing social contexts. Community and student voices are telling schools that traditional education is too authoritarian and restrictive. Students do not feel valued and respected in their school community. Schools are obliged to respond to this critique with more democratic and relevant policies and processes that connect all students with their learning futures. This text is about developing a more inclusive approach to education which aims to identify and dismantle actual and potential sources of exclusion that limit opportunities and outcomes for all students.

Levelling expectations across different years in an undergraduate degree to support work-related learning : evidence for a multi-pronged approach.

One of the ways in which university departments and faculties can enhance the quality of learning and assessment is to develop a ‘well thought out criterion‐referenced assessment system’ (Biggs, 2003, p. 271). In designing undergraduate degrees (courses) this entails making decisions about the levelling of expectations across different years through devising objectives and their corresponding criteria and standards: a process of alignment analogous to what happens in unit (subject) design. These decisions about levelling have important repercussions in terms of supporting students’ work‐related learning, especially in relation to their ability to cope with the increasing cognitive and skill demands made on them as they progress through their studies. They also affect the accountability of teacher judgments of students’ responses to assessment tasks, achievement of unit objectives and, ultimately, whether students are awarded their degrees and are sufficiently prepared for the world of work. Research reveals that this decision‐making process is rarely underpinned by an explicit educational rationale (Morgan et al, 2002). The decision to implement criterion referenced assessment in an undergraduate microbiology degree was the impetus for developing such a rationale because of the implications for alignment, and therefore ‘levelling’ of expectations across different years of the degree. This paper provides supporting evidence for a multi‐pronged approach to levelling, through backward mapping of two revised units (foundation and exit year). This approach adheres to the principles of alignment while combining a work‐related approach (via industry input) with the blended disciplinary and learner‐centred approaches proposed by Morgan et al. (2002). It is suggested that this multi‐pronged approach has the potential for making expectations, especially work‐related ones across different year levels of degrees, more explicit to students and future employers.

A Numerical Solution Using an Adaptively Preconditioned Lanczos Method for a Class of Linear Systems Related with the Fractional Poisson Equation

This study considers the solution of a class of linear systems related with the fractional Poisson equation (FPE) (−∇2)α/2φ=g(x,y) with nonhomogeneous boundary conditions on a bounded domain. A numerical approximation to FPE is derived using a matrix representation of the Laplacian to generate a linear system of equations with its matrix A raised to the fractional power α/2. The solution of the linear system then requires the action of the matrix function f(A)=A−α/2 on a vector b. For large, sparse, and symmetric positive definite matrices, the Lanczos approximation generates f(A)b≈β0Vmf(Tm)e1. This method works well when both the analytic grade of A with respect to b and the residual for the linear system are sufficiently small. Memory constraints often require restarting the Lanczos decomposition; however this is not straightforward in the context of matrix function approximation. In this paper, we use the idea of thick-restart and adaptive preconditioning for solving linear systems to improve convergence of the Lanczos approximation. We give an error bound for the new method and illustrate its role in solving FPE. Numerical results are provided to gauge the performance of the proposed method relative to exact analytic solutions.

A review of prostate-specific antigen screening prevalence and risk perceptions for first-degree relatives of men with prostate cancer

First-degree relatives of men with prostate cancer have a higher risk of being diagnosed with prostate cancer than men without a family history. The present review examines the prevalence and predictors of testing in first-degree relatives, perceptions of risk, prostate cancer knowledge and psychological consequences of screening. Medline, PsycInfo and Cinahl databases were searched for articles examining risk perceptions or screening practices of first-degree relatives of men with prostate cancer for the period of 1990 to August 2007. Eighteen studies were eligible for inclusion. First-degree relatives participated in prostate-specific antigen (PSA) testing more and perceived their risk of prostate cancer to be higher than men without a family history. Family history factors (e.g. being an unaffected son rather than an unaffected brother) were consistent predictors of PSA testing. Studies were characterized by sampling biases and a lack of longitudinal assessments. Prospective, longitudinal assessments with well-validated and comprehensive measures are needed to identify factors that cue the uptake of screening and from this develop an evidence base for decision support. Men with a family history may benefit from targeted communication about the risks and benefits of prostate cancer testing that responds to the implications of their heightened risk.

Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term

In this paper, we consider a modified anomalous subdiffusion equation with a nonlinear source term for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. A new implicit difference method is constructed. The stability and convergence are discussed using a new energy method. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of theoretical analysis

Numerical methods for the variable-order fractional advection-diffusion equation with a nonlinear source term

In this paper, we consider a variable-order fractional advection-diffusion equation with a nonlinear source term on a finite domain. Explicit and implicit Euler approximations for the equation are proposed. Stability and convergence of the methods are discussed. Moreover, we also present a fractional method of lines, a matrix transfer technique, and an extrapolation method for the equation. Some numerical examples are given, and the results demonstrate the effectiveness of theoretical analysis.

Numerical schemes and multivariate extrapolation of a two-dimensional anomalous sub-diffusion equation

Anomalous dynamics in complex systems have gained much interest in recent years. In this paper, a two-dimensional anomalous subdiffusion equation (2D-ASDE) is considered. Two numerical methods for solving the 2D-ASDE are presented. Their stability, convergence and solvability are discussed. A new multivariate extrapolation is introduced to improve the accuracy. Finally, numerical examples are given to demonstrate the effectiveness of the schemes and confirm the theoretical analysis.

Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation

In this paper, we consider the variable-order nonlinear fractional diffusion equation View the MathML source where xRα(x,t) is a generalized Riesz fractional derivative of variable order View the MathML source and the nonlinear reaction term f(u,x,t) satisfies the Lipschitz condition |f(u1,x,t)-f(u2,x,t)|less-than-or-equals, slantL|u1-u2|. A new explicit finite-difference approximation is introduced. The convergence and stability of this approximation are proved. Finally, some numerical examples are provided to show that this method is computationally efficient. The proposed method and techniques are applicable to other variable-order nonlinear fractional differential equations.