Stepping stones : student journal : year 2

"ORIGO Stepping Stones gives mathematics teachers the best of both worlds by delivering lessons and teacher guides on a digital platform blended with the more traditional printed student journals." -- Publisher website

Stepping stones : student guide : year 3

"ORIGO Stepping Stones gives mathematics teachers the best of both worlds by delivering lessons and teacher guides on a digital platform blended with the more traditional printed student journals." -- Publisher website

Stepping stones : student journal : year K

"ORIGO Stepping Stones gives mathematics teachers the best of both worlds by delivering lessons and teacher guides on a digital platform blended with the more traditional printed student journals." -- Publisher website

Stepping stones : teacher lesson plans : year K

"ORIGO Stepping Stones gives mathematics teachers the best of both worlds by delivering lessons and teacher guides on a digital platform blended with the more traditional printed student journals." -- Publisher website

Charting the system : the integrated master schedule as a multi-level and poly-temporal boundary object in complex projects

This paper investigates the use of visual artifacts to represent a complex adaptive system (CAS). The integrated master schedule (IMS) is one of those visuals widely used in complex projects for scheduling, budgeting, and project management. In this paper, we discuss how the IMS outperforms the traditional timelines and acts as a ‘multi-level and poly-temporal boundary object’ that visually represents the CAS. We report the findings of a case study project on the way the IMS mapped interactions, interdependencies, constraints and fractal patterns in a complex project. Finally, we discuss how the IMS was utilised as a complex boundary object by eliciting commitment and development of shared mental models, and facilitating negotiation through the layers of multiple interpretations from stakeholders.

An improved boundary layer scaling with ramp heating on a sloping plate

A scaling analysis for the natural convection boundary layer adjacent to an inclined semi-infinite plate subject to a non-instantaneous heating in the form of an imposed wall temperature which increases linearly up to a prescribed steady value over a prescribed time is reported. The development of the boundary layer flow from start-up to a steady-state has been described based on scaling analyses and verified by numerical simulations. The analysis reveals that, if the period of temperature growth on the wall is sufficiently long, the boundary layer reaches a quasi-steady mode before the growth of the temperature is completed. In this mode the thermal boundary layer at first grows in thickness and then contracts with increasing time. However, if the imposed wall temperature growth period is sufficiently short, the boundary layer develops differently, but after the wall temperature growth is completed, the boundary layer develops as though the startup had been instantaneous. The steady state values of the boundary layer for both cases are ultimately the same.

Scaling analysis of natural convection boundary layers : Application to attic space

The natural convection thermal boundary layer adjacent to an inclined flat plate and inclined walls of an attic space subject to instantaneous and ramp heating and cooling is investigated. A scaling analysis has been performed to describe the flow behaviour and heat transfer. Major scales quantifying the flow velocity, flow development time, heat transfer and the thermal and viscous boundary layer thicknesses at different stages of the flow development are established. Scaling relations of heating-up and cooling-down times and heat transfer rates have also been reported for the case of attic space. The scaling relations have been verified by numerical simulations over a wide range of parameters. Further, a periodic temperature boundary condition is also considered to show the flow features in the attic space over diurnal cycles.

Breaching the standardised assessment boundary : assessment for learning as a field of exchange

The introduction of the Australian curriculum, the use of standardised testing (e.g. NAPLAN) and the My School website are couched in a context of accountability. This circumstance has stimulated and in some cases renewed a range of boundaries in Australian Education. The consequences that arise from standardised testing have accentuated the boundaries produced by social reproduction in education which has led to an increase in the numbers of students disengaging from mainstream education and applying for enrolment at the Edmund Rice Education Australia Flexible Learning Centre Network (EREAFLCN). Boundaries are created for many young people who are denied access to credentials and certification as a result of being excluded from or in some way disengaging from standardised education and testing. Young people who participate at the EREAFLCN arrive with a variety of forms of cultural capital that are not valued in current education and employment fields. This is not to say that these young people’s different forms of cultural capital have no value, but rather that such funds of knowledge, repertoires and cultural capital are not valued by the majority of powerful agents in educational and employment fields. How then can the qualitative value of traditionally unorthodox - yet often intricate, ingenious, and astute - versions of cultural capital evident in the habitus of many young people be made to count, be recognised, be valuated? Can a process of educational assessment be a field of capital exchange and a space which breaches boundaries through a valuating process? This paper reports on the development of an innovative approach to assessment in an alternative education institution designed for the re-engagement of ‘at risk’ youth who have left formal schooling. A case study approach has been used to document the engagement of six young people, with an educational approach described as assessment for learning as a field of exchange across two sites in the EREAFLCN. In order to capture the broad range of students’ cultural and social capital, an electronic portfolio system (EPS) is under trial. The model draws on categories from sociological models of capital and reconceptualises the eportfolio as a sociocultural zone of learning and development. Results from the trial show a general tendency towards engagement with the EPS and potential for the attainment of socially valued cultural capital in the form of school credentials. In this way restrictive boundaries can be breached and a more equitable outcome achieved for many young Australians.

Scaling for the Prandtl number of the natural convection boundary layer of an inclined flat plate under uniform surface heat flux

An improved scaling analysis and direct numerical simulations are performed for the unsteady natural convection boundary layer adjacent to a downward facing inclined plate with uniform heat flux. The development of the thermal or viscous boundary layers may be classified into three distinct stages: a start-up stage, a transitional stage and a steady stage, which can be clearly identified in the analytical as well as the numerical results. Previous scaling shows that the existing scaling laws of the boundary layer thickness, velocity and steady state time scale for the natural convection flow on a heated plate of uniform heat flux provide a very poor prediction of the Prandtl number dependency of the flow. However, those scalings perform very well with Rayleigh number and aspect ratio dependency. In this study, a modified Prandtl number scaling is developed using a triple layer integral approach for Pr > 1. It is seen that in comparison to the direct numerical simulations, the modified scaling performs considerably better than the previous scaling.

A boundary preserving numerical algorithm for the Wright-Fisher model with mutation

The Wright-Fisher model is an Itô stochastic differential equation that was originally introduced to model genetic drift within finite populations and has recently been used as an approximation to ion channel dynamics within cardiac and neuronal cells. While analytic solutions to this equation remain within the interval [0,1], current numerical methods are unable to preserve such boundaries in the approximation. We present a new numerical method that guarantees approximations to a form of Wright-Fisher model, which includes mutation, remain within [0,1] for all time with probability one. Strong convergence of the method is proved and numerical experiments suggest that this new scheme converges with strong order 1/2. Extending this method to a multidimensional case, numerical tests suggest that the algorithm still converges strongly with order 1/2. Finally, numerical solutions obtained using this new method are compared to those obtained using the Euler-Maruyama method where the Wiener increment is resampled to ensure solutions remain within [0,1].

Prandtl number scaling of the unsteady natural convection boundary layer adjacent to a vertical flat plate for Pr > 1 subject to ramp surface heat flux

It is found in the literature that the existing scaling results for the boundary layer thickness, velocity and steady state time for the natural convection flow over an evenly heated plate provide a very poor prediction of the Prandtl number dependency of the flow. However, those scalings provide a good prediction of two other governing parameters’ dependency, the Rayleigh number and the aspect ratio. Therefore, an improved scaling analysis using a triple-layer integral approach and direct numerical simulations have been performed for the natural convection boundary layer along a semi-infinite flat plate with uniform surface heat flux. This heat flux is a ramp function of time, where the temperature gradient on the surface increases with time up to some specific time and then remains constant. The growth of the boundary layer strongly depends on the ramp time. If the ramp time is sufficiently long, the boundary layer reaches a quasi steady mode before the growth of the temperature gradient is completed. In this mode, the thermal boundary layer at first grows in thickness and then contracts with increasing time. However, if the ramp time is sufficiently short, the boundary layer develops differently, but after the wall temperature gradient growth is completed, the boundary layer develops as though the startup had been instantaneous.