Thinking Critically in the Land of Princesses and Giants : The Affordances and Challenges of Critical Approaches in the Early Years

During the last four decades, educators have created a range of critical literacy approaches for different contexts, including compulsory schooling (Luke & Woods, 2009) and second language education (Luke & Dooley, 2011). Despite inspirational examples of critical work with young students (e.g., O’Brien, 1994; Vasquez, 1994), Comber (2012) laments the persistent myth that critical literacy is not viable in the early years. Assumptions about childhood innocence and the priorities of the back-to-basics movement seem to limit the possibilities for early years literacy teaching and learning. Yet, teachers of young students need not face an either/or choice between the basic and critical dimensions of literacy. Systematic ways of treating literacy in all its complexity exist. We argue that the integrative imperative is especially important in schools that are under pressure to improve technical literacy outcomes. In this chapter, we document how critical literacy was addressed in a fairytales unit taught to 4.5 - 5.5 year olds in a high diversity, high poverty Australian school. We analyze the affordances and challenges of different approaches to critical literacy, concluding they are complementary rather than competing sources of possibility. Furthermore, we make the case for turning familiar classroom activities to critical ends.

Australian learning and teaching council projects in the mathematical sciences : a retrospective

Since 2004, the Australian Learning and Teaching Council (ALTC) and its predecessor, the Carrick Institute for Learning and Teaching in Higher Education, have funded numerous teaching and educational research-based projects in the Mathematical Sciences. In light of the Commonwealth Government’s decision to close the ALTC in 2011, it is appropriate to take account of the ALTCs input into the Mathe- matical Sciences in higher education. Here we present an overview of ALTC projects in the Mathematical Sciences, as well as report on the contributions they have made to the Discipline.

Leadership for creating a thinking school at Buranda State School

This article explores the role of principal leadership in creating a thinking school. It contributes to the school leadership literature by exploring the intersection of two important areas of study in education - school leadership and education for thinking - which is a particularly apt area of study, because effective school leadership is crucial if students are to learn to be critical and creative thinkers, yet this connection has not be widely investigated. We describe how one principal, Hinton, turned around an underperforming school by using critical and creative philosophical thinking as the focus for students, staff and parents. Then, drawing on the school leadership literature, the article describes seven attributes of school leadership beginning with four articulated by Leithwood and colleagues (2006) (building vision and setting direction; redesigning the organisation; understanding and developing people; managing the teaching and learning program), and adding three others (influence; self-development; and responding to context). This framework is then used in a case study format in a collaboration between practitioner and researchers to first explore evidence from empirical studies and personal reflection about Hinton's leadership of Buranda State School, and second to illuminate how these general features of school leadership apply to creating a thinking school. Based on the case study and using the general characteristics of school leadership, a framework for leading a thinking school is described. Because the framework is based on a turnaround school, this framework has wide applicability: to schools that are doing well as an indication of how to implement a contemporary approach to curriculum and pedagogy; and to schools that are underperforming and want a rigorous, high expectation and contemporary way to improve student learning.

Numerical techniques for simulating a fractional mathematical model of epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider the numerical simulation of a fractional mathematical model of epidermal wound healing (FMM-EWH), which is based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in the advection and diffusion terms belong to the intervals (0, 1) or (1, 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of Riemann-Liouville and Grünwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.

Repeating patterns : strategies to assist young students to generalise the mathematical structure

This paper focuses on very young students' ability to engage in repeating pattern tasks and identifying strategies that assist them to ascertain the structure of the pattern. It describes results of a study which is part of the Early Years Generalising Project (EYGP) and involves Australian students in Years 1 to 4 (ages 5-10). This paper reports on the results from the early years' cohort (Year 1 and 2 students). Clinical interviews were used to collect data concerning students' ability to determine elements in different positions when two units of a repeating pattern were shown. This meant that students were required to identify the multiplicative structure of the pattern. Results indicate there are particular strategies that assist students to predict these elements, and there appears to be a hierarchy of pattern activities that help students to understand the structure of repeating patterns.

Mathematical modelling of controlled drug release from polymer micro-spheres : incorporating the effects of swelling, diffusion and dissolution via moving boundary problems

Controlled drug delivery is a key topic in modern pharmacotherapy, where controlled drug delivery devices are required to prolong the period of release, maintain a constant release rate, or release the drug with a predetermined release profile. In the pharmaceutical industry, the development process of a controlled drug delivery device may be facilitated enormously by the mathematical modelling of drug release mechanisms, directly decreasing the number of necessary experiments. Such mathematical modelling is difficult because several mechanisms are involved during the drug release process. The main drug release mechanisms of a controlled release device are based on the device’s physiochemical properties, and include diffusion, swelling and erosion. In this thesis, four controlled drug delivery models are investigated. These four models selectively involve the solvent penetration into the polymeric device, the swelling of the polymer, the polymer erosion and the drug diffusion out of the device but all share two common key features. The first is that the solvent penetration into the polymer causes the transition of the polymer from a glassy state into a rubbery state. The interface between the two states of the polymer is modelled as a moving boundary and the speed of this interface is governed by a kinetic law. The second feature is that drug diffusion only happens in the rubbery region of the polymer, with a nonlinear diffusion coefficient which is dependent on the concentration of solvent. These models are analysed by using both formal asymptotics and numerical computation, where front-fixing methods and the method of lines with finite difference approximations are used to solve these models numerically. This numerical scheme is conservative, accurate and easily implemented to the moving boundary problems and is thoroughly explained in Section 3.2. From the small time asymptotic analysis in Sections 5.3.1, 6.3.1 and 7.2.1, these models exhibit the non-Fickian behaviour referred to as Case II diffusion, and an initial constant rate of drug release which is appealing to the pharmaceutical industry because this indicates zeroorder release. The numerical results of the models qualitatively confirms the experimental behaviour identified in the literature. The knowledge obtained from investigating these models can help to develop more complex multi-layered drug delivery devices in order to achieve sophisticated drug release profiles. A multi-layer matrix tablet, which consists of a number of polymer layers designed to provide sustainable and constant drug release or bimodal drug release, is also discussed in this research. The moving boundary problem describing the solvent penetration into the polymer also arises in melting and freezing problems which have been modelled as the classical onephase Stefan problem. The classical one-phase Stefan problem has unrealistic singularities existed in the problem at the complete melting time. Hence we investigate the effect of including the kinetic undercooling to the melting problem and this problem is called the one-phase Stefan problem with kinetic undercooling. Interestingly we discover the unrealistic singularities existed in the classical one-phase Stefan problem at the complete melting time are regularised and also find out the small time behaviour of the one-phase Stefan problem with kinetic undercooling is different to the classical one-phase Stefan problem from the small time asymptotic analysis in Section 3.3. In the case of melting very small particles, it is known that surface tension effects are important. The effect of including the surface tension to the melting problem for nanoparticles (no kinetic undercooling) has been investigated in the past, however the one-phase Stefan problem with surface tension exhibits finite-time blow-up. Therefore we investigate the effect of including both the surface tension and kinetic undercooling to the melting problem for nanoparticles and find out the the solution continues to exist until complete melting. The investigation of including kinetic undercooling and surface tension to the melting problems reveals more insight into the regularisations of unphysical singularities in the classical one-phase Stefan problem. This investigation gives a better understanding of melting a particle, and contributes to the current body of knowledge related to melting and freezing due to heat conduction.

Higher order thinking in chemistry curriculum and its assessment

Higher-order thinking has featured persistently in the reform agenda for science education. The intended curriculum in various countries sets out aspirational statements for the levels of higher-order thinking to be attained by students. This study reports the extent to which chemistry examinations from four Australian states align and facilitate the intended higher-order thinking skills stipulated in curriculum documents. Through content analysis, the curriculum goals were identified for each state and compared to the nature of question items in the corresponding examinations. Categories of higher-order thinking were adapted from the OECD’s PISA Science test to analyze question items. There was considerable variation in the extent to which the examinations from the states supported the curriculum intent of developing and assessing higher-order thinking. Generally, examinations that used a marks-based system tended to emphasize lower-order thinking, with a greater distribution of marks allocated for lower-order thinking questions. Examinations associated with a criterion-referenced examination tended to award greater credit for higher-order thinking questions. The level of complexity of chemistry was another factor that limited the extent to which examination questions supported higher-order thinking. Implications from these findings are drawn for the authorities responsible for designing curriculum and assessment procedures and for teachers.

Mathematical modelling of LiFePO4 cathodes

LiFePO4 is a commercially available battery material with good theoretical discharge capacity, excellent cycle life and increased safety compared with competing Li-ion chemistries. It has been the focus of considerable experimental and theoretical scrutiny in the past decade, resulting in LiFePO4 cathodes that perform well at high discharge rates. This scrutiny has raised several questions about the behaviour of LiFePO4 material during charge and discharge. In contrast to many other battery chemistries that intercalate homogeneously, LiFePO4 can phase-separate into highly and lowly lithiated phases, with intercalation proceeding by advancing an interface between these two phases. The main objective of this thesis is to construct mathematical models of LiFePO4 cathodes that can be validated against experimental discharge curves. This is in an attempt to understand some of the multi-scale dynamics of LiFePO4 cathodes that can be difficult to determine experimentally. The first section of this thesis constructs a three-scale mathematical model of LiFePO4 cathodes that uses a simple Stefan problem (which has been used previously in the literature) to describe the assumed phase-change. LiFePO4 crystals have been observed agglomerating in cathodes to form a porous collection of crystals and this morphology motivates the use of three size-scales in the model. The multi-scale model developed validates well against experimental data and this validated model is then used to examine the role of manufacturing parameters (including the agglomerate radius) on battery performance. The remainder of the thesis is concerned with investigating phase-field models as a replacement for the aforementioned Stefan problem. Phase-field models have recently been used in LiFePO4 and are a far more accurate representation of experimentally observed crystal-scale behaviour. They are based around the Cahn-Hilliard-reaction (CHR) IBVP, a fourth-order PDE with electrochemical (flux) boundary conditions that is very stiff and possesses multiple time and space scales. Numerical solutions to the CHR IBVP can be difficult to compute and hence a least-squares based Finite Volume Method (FVM) is developed for discretising both the full CHR IBVP and the more traditional Cahn-Hilliard IBVP. Phase-field models are subject to two main physicality constraints and the numerical scheme presented performs well under these constraints. This least-squares based FVM is then used to simulate the discharge of individual crystals of LiFePO4 in two dimensions. This discharge is subject to isotropic Li+ diffusion, based on experimental evidence that suggests the normally orthotropic transport of Li+ in LiFePO4 may become more isotropic in the presence of lattice defects. Numerical investigation shows that two-dimensional Li+ transport results in crystals that phase-separate, even at very high discharge rates. This is very different from results shown in the literature, where phase-separation in LiFePO4 crystals is suppressed during discharge with orthotropic Li+ transport. Finally, the three-scale cathodic model used at the beginning of the thesis is modified to simulate modern, high-rate LiFePO4 cathodes. High-rate cathodes typically do not contain (large) agglomerates and therefore a two-scale model is developed. The Stefan problem used previously is also replaced with the phase-field models examined in earlier chapters. The results from this model are then compared with experimental data and fit poorly, though a significant parameter regime could not be investigated numerically. Many-particle effects however, are evident in the simulated discharges, which match the conclusions of recent literature. These effects result in crystals that are subject to local currents very different from the discharge rate applied to the cathode, which impacts the phase-separating behaviour of the crystals and raises questions about the validity of using cathodic-scale experimental measurements in order to determine crystal-scale behaviour.

Establishing design thinking : accident, program frameworks and personal practices

Distribution through electronic media provides an avenue for promotion, recognition and an outlet of display for graphic designers. The emergence of available media technologies have enabled graphic designers to extend these boundaries of their practice. In this context the designer is constantly striving for aesthetic success and is strongly influenced by the fashion and trends of contemporary design work. The designer is always in a state of inquiry, finding pathways of discovery that lead to innovation and originality that are highly valued criteria for self-evaluation. This research is based on an analysis of the designer perspective and the processes used within an active graphic design practice specializing entirely within a digital collage domain. Contemporary design methodologies were critically examined, compared and refined to reflect the self-practice of the researcher. The refined methodology may assist designers in maintaining systematic work practices, as well as promote the importance of exploration and experimentation processes. Research findings indicate some differences in the identified methodologies and the design practice of the researcher in the sense that many contemporary designers are not confined to a client-base but are self-generating design images influenced by contemporary practitioners. As well as confirming some aspects of more conventional design processes, the researcher found that accidental discoveries and the designer’s interaction with technology plays a significant part in the design process.

Teaching design thinking : Expanding horizons in design education

The term design thinking is increasingly used to mean the human-centred 'open' problem solving process decision makers use to solve real world 'wicked' problems. Claims have been made that design thinking in this sense can radically improve not only product innovation but also decision making in other fields, such as management, public health, and organizations in general. Many design and management schools in North America and elsewhere now include course offerings in design thinking though little is known about how successful these are with students. The lack of such courses in Australia presents an opportunity to design a curriculum for design thinking, employing design thinking's own practices. This paper describes the development of a design thinking course at Swinburne University taught simultaneously in Melbourne and Hong Kong. Following a pilot of the course in Semester 1, 2011 with 90 enrolled students across the two countries, we describe lessons learned to date and future course considerations as it is being taught in its second iteration.

From concept to capability : developing design thinking within a professional services firm

Corporate business and management are embracing design thinking for its potential to deliver competitive advantage through helping them be more innovative, differentiate their brands, and bring more customer centric products and services to market (Brown, 2008). As consumers continue to expect more personalisation and customisation from their service providers, the use of design thinking for innovation within organisations is a logical progression. To date however, there is little empirical literature discussing how organisations are setting about integrating design thinking into their culture and innovation practices. This paper is a first step in initiating a scholarly discussion on the integration of design thinking within organisational culture. Deloitte Australia is a large professional services firm employing over 5700 staff in 12 offices across Australia. The company provides a range of services to clients in the areas of audit, tax, financial advisory and consulting. In early 2011 the company made a strategic commitment to introducing design thinking into the organisation’s practices. While it already maintains a strong innovation culture, to date it had largely been operating within an analytical business environment. For Deloitte, design thinking is an opportunity to create better outcomes for the people they serve – both internal and external stakeholders (Brown and Wyatt, 2010). Research was conducted using case study methodology and ethnographic methods from June to September 2011 at the Melbourne Deloitte office. It involved three methods of data collection: semi structured interviews, participant observation and artifact analysis. This paper presents preliminary case study findings of Deloitte’s approach to building awareness and a consistent understanding of design thinking, as well as large scale capability, across the firm. Deloitte’s commitment to transforming its culture to one of design thinking poses significant potential for understanding how design thinking is comprehended, enabled and integrated within a complex organisational environment.

Mathematical modelling of tumour growth and interaction with host tissue and the immune system

In this thesis, three mathematical models describing the growth of solid tumour incorporating the host tissue and the immune system response are developed and investigated. The initial model describes the dynamics of the growing tumour and immune response before being extended in the second model by introducing a time-varying dendritic cell-based treatment strategy. Finally, in the third model, we present a mathematical model of a growing tumour using a hybrid cellular automata. These models can provide information to pre-experimental work to assist in designing more effective and efficient laboratory experiments related to tumour growth and interactions with the immune system and immunotherapy.

Systems thinking : an approach for advancing workplace information literacy

As the importance of information literacy has gained increased recognition, so too have academic library professionals intensified their efforts to champion, activate, and advance these capabilities in others. To date, however, little attention has focused on advancing these essential competencies amongst practitioner advocates.This paper helps redress the paucity of professional literature on the topic of workplace information literacy among library professionals.

From solving puzzles to designing solutions : integrating design thinking into evidence based practice

Evidence based practice (EBP) focuses on solving ‘tame’ problems, where literature supports question construction toward determining a solution. What happens when there is no existing evidence, or when the need for agility precludes a full EBP implementation? How might we build a more agile and innovative practice that facilitates the design of solutions to complex and wicked problems, particularly in cases where there is no existing literature? As problem solving and innovation methods, EBP and design thinking overlap considerably. The literature indicates the potential benefits to be gained for evidence based practice from adopting a human-centred rather than literature-focused foundation. The design thinking process is social and collaborative by nature, which enables it to be more agile and produce more innovative results than evidence based practice. This paper recommends a hybrid approach to maximise the strengths and benefits of the two methods for designing solutions to wicked problems. Incorporating design thinking principles and tools into EBP has the potential to move its applicability beyond tame problems and continuous improvement, and toward wicked problem solving and innovation. The potential of this hybrid approach in practice is yet to be explored.