Constructive development of the solutions of linear equations in introductory ordinary differential equations

The solution of linear ordinary differential equations (ODEs) is commonly taught in first year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognising what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to tables of solutions, is an important skill for students to carry with them to advanced studies in mathematics. In this study we describe a teaching and learning strategy that replaces the traditional algorithmic, transmission presentation style for solving ODEs with a constructive, discovery based approach where students employ their existing skills as a framework for constructing the solutions of first and second order linear ODEs. We elaborate on how the strategy was implemented and discuss the resulting impact on a first year undergraduate class. Finally we propose further improvements to the strategy as well as suggesting other topics which could be taught in a similar manner.

Formative and Summative Assessment and the Notion of Constructive Allignment

This paper discusses perceptions of first year accounting students about their tutorial activities and their engagements in assessment. As the literature suggests, unless participation in learning activities forms part of graded assessment it is often difficult to engage students in these activities. Using an action research model, this paper reports the study of first year accounting students' responses to action-orientated learning tasks in tutorials. The paper focuses on the importance of aligning curriculum objectives, learning and teaching activities and assessment,i.e. the notion of constructive alignment. However, as the research findings indicate, without support at institutional level, applying constructive alignment to facilitate quality student learning outcomes is a difficult task. Thus, the impacts of policy constraints on curriculum issues are also discussed, focusing on the limitations faced by tutors and their lack of involvement in curriculum development.

Australia - taxation of trusts – the problem of aligning concepts of income

The Australian government is currently considering options for the rewrite and reform of the current provisions which apply to the taxation of trust income. This article provides a discussion of the current regime and the proposed reforms. It is suggested that a major revamp of taxation of trust income in Australia is problematic and a simpler approach may be to leave the law as is, with modification where necessary to address key issues as and when they arise.

Equity and Trusts in Principle [3rd ed.]

Equity and Trusts : in Principle, 3rd edition is updated and revised throughout. It addresses the principles of equity and trusts and provides a clear analysis of this area.

A hybrid constructive heuristic and simulated annealing for railway crew scheduling

Railway crew scheduling problem is the process of allocating train services to the crew duties based on the published train timetable while satisfying operational and contractual requirements. The problem is restricted by many constraints and it belongs to the class of NP-hard. In this paper, we develop a mathematical model for railway crew scheduling with the aim of minimising the number of crew duties by reducing idle transition times. Duties are generated by arranging scheduled trips over a set of duties and sequentially ordering the set of trips within each of duties. The optimisation model includes the time period of relief opportunities within which a train crew can be relieved at any relief point. Existing models and algorithms usually only consider relieving a crew at the beginning of the interval of relief opportunities which may be impractical. This model involves a large number of decision variables and constraints, and therefore a hybrid constructive heuristic with the simulated annealing search algorithm is applied to yield an optimal or near-optimal schedule. The performance of the proposed algorithms is evaluated by applying computational experiments on randomly generated test instances. The results show that the proposed approaches obtain near-optimal solutions in a reasonable computational time for large-sized problems.

Thin single-walled carbon nanotubes with narrow chirality distribution : constructive interplay of plasma and Gibbs–Thomson effects

Multiscale, multiphase numerical modeling is used to explain the mechanisms of effective control of chirality distributions of single-walled carbon nanotubes in direct plasma growth and suggest effective approaches to further improvement. The model includes an unprecedented combination of the plasma sheath, ion/radical transport, species creation/loss, plasma–surface interaction, heat transfer, surface/bulk diffusion, graphene layer nucleation, and bending/lift-off modules. It is shown that the constructive interplay between the plasma and the Gibbs–Thomson effect can lead to the effective nucleation and lift-off of small graphene layers on small metal catalyst nanoparticles. As a result, much thinner nanotubes with narrower chirality distributions can nucleate at much lower process temperatures and pressures compared to thermal CVD. This approach is validated by a host of experimental results, substantially reduces the amounts of energy and atomic matter required for the nanotube growth, and can be extended to other nanoscale structures and materials systems, thereby nearing the ultimate goal of energy- and matter-efficient nanotechnology.

Equity in Australian estate litigation

Equitable claims are increasingly arising in Australian estate litigation, particularly in conjunction with family provision applications. Since the leading decision in Bridgewater v Leahy, in addition to undue influence and unconscionable bargain claims, actions based on equitable estoppel, constructive and resulting trusts, breach of fiduciary duty, and breach of legislative duties that mirror equitable obligations are increasingly being brought in contemporary estate litigation. Such litigation often raises challenging issues for claimants, including evidentiary hurdles and allegations of undue delay, especially when claims are made post-mortem in relation to inter vivos dealings with property. Accordingly, solicitors need to ensure that they fully understand the nature and potential application of equitable claims in estate litigation, or face the prospect of incurring liability to clients for professional negligence. This article explores recent trends in Australian estate litigation involving equitable claims.

First Literacies: Art, Creativity, Play, Constructive Meaning-Making

In this chapter art and play are considered children’s ‘first languages’, and therefore are placed at the centre of a curriculum for young children. Through art and play, children represent thought and action, which underpins their later understanding of the ‘second languages’ of reading, writing and numbering. Key issues such as image-making, graphic action, imagination, narrative, empathetic engagement and internalised thought are analysed as evidence of children’s construction of knowledge through art and play. Symbol making is the essence of being human. In children’s art and play, their symbol use captures their sensory modes in emotional and embodied ways, as children know their worlds and their place. The chapter addresses how children’s creation, manipulation and meaning making through engaged interaction with art materials are precursors to learning to read and write and, as first languages, should not be discarded nor replaced. The notion of creativity is explored in relation to pedagogical approaches. In a climate of testing regimes that emphasise ‘academic’ achievements, teachers are encouraged to not lose sight of imagination, pretence, constructive meaning making, holistic teaching and being a co-player and co-artist.

Constructive Perspectives on Inductive Logic

Constructive (intuitionist, anti-realist) semantics has thus far been lacking an adequate concept of truth in infinity concerning factual (i.e., empirical, non-mathematical) sentences. One consequence of this problem is the difficulty of incorporating inductive reasoning in constructive semantics. It is not possible to formulate a notion for probable truth in infinity if there is no adequate notion of what truth in infinity is. One needs a notion of a constructive possible world based on sensory experience. Moreover, a constructive probability measure must be defined over these constructively possible empirical worlds. This study defines a particular kind of approach to the concept of truth in infinity for Rudolf Carnap's inductive logic. The new approach is based on truth in the consecutive finite domains of individuals. This concept will be given a constructive interpretation. What can be verifiably said about an empirical statement with respect to this concept of truth, will be explained, for which purpose a constructive notion of epistemic probability will be introduced. The aim of this study is also to improve Carnap's inductive logic. The study addresses the problem of justifying the use of an "inductivist" method in Carnap's lambda-continuum. A correction rule for adjusting the inductive method itself in the course of obtaining evidence will be introduced. Together with the constructive interpretation of probability, the correction rule yields positive prior probabilities for universal generalizations in infinite domains.

Constructive deviance as a driver for performance in retail

A growing body of research is concerned with deviance in the workplace. While much research has explored negative forms of deviance, we examine constructive deviance: behaviour that deviates from salient norms and benefits the reference group. We empirically explore manifestations, determinants and performance outcomes of constructive deviance in standardised work processes. We do this through a mixed-methods study in bakery trading departments of an Australian retailer. We illustrate that constructive deviance occurs in these settings and show that some manifestations of constructive deviance improve organisational performance and pave the way for applying constructive deviance as a strategic tool in retail.

Constructive alignment: A journey for new eyes

The needs of students engaged in enterprise education programs are of ever growing importance. This paper considers the pedagogical challenges that confront the designers of such-programs. It is argued that it is the designer's mindset that will most likely determine the program's outcomes. That, regardless of where such programs reside, their development should be guided by a learner-centred approach. The recently developed hic et nunc framework, provides an example of such a student-centred approach. The process through which student learning outcomes occur is argued to be essentially Darwinian in nature. Taking into account both knowledge and skills, it is also argued that assessment of desirable learning outcomes should occur in visible interaction spaces. That the failure to eliminate invisible interaction spaces from such programs is an invitation for criticism from those who favour a more traditional lecturer-centred approach to teaching and learning.