Critical timescales and time intervals for coupled linear processes

In 1991, McNabb introduced the concept of mean action time (MAT) as a finite measure of the time required for a diffusive process to effectively reach steady state. Although this concept was initially adopted by others within the Australian and New Zealand applied mathematics community, it appears to have had little use outside this region until very recently, when in 2010 Berezhkovskii and coworkers rediscovered the concept of MAT in their study of morphogen gradient formation. All previous work in this area has been limited to studying single–species differential equations, such as the linear advection–diffusion–reaction equation. Here we generalise the concept of MAT by showing how the theory can be applied to coupled linear processes. We begin by studying coupled ordinary differential equations and extend our approach to coupled partial differential equations. Our new results have broad applications including the analysis of models describing coupled chemical decay and cell differentiation processes, amongst others.

Students’ approaches to learning a new mathematical model

In this article, we report on the findings of an exploratory study into the experience of undergraduate students as they learn new mathematical models. Qualitative and quanti- tative data based around the students’ approaches to learning new mathematical models were collected. The data revealed that students actively adopt three approaches to under- standing a new mathematical model: gathering information for the task of understanding the model, practising with and using the model, and finding interrelationships between elements of the model. We found that the students appreciate mathematical models that have a real world application and that this can be used to engage students in higher level learning approaches.

Does teaching sequence matter when teaching high school chemistry with scientific visualisations?

Five Canadian high school Chemistry classes in one school, taught by three different teachers, studied the concepts of dynamic chemical equilibria and Le Chatelier’s Principle. Some students received traditional teacher-led explanations of the concept first and used an interactive scientific visualisation second, while others worked with the visualisation first and received the teacher-led explanation second. Students completed a test of their conceptual understanding of the relevant concepts prior to instruction, after the first instructional session and at the end of instruction. Data on students’ academic achievement (highest, middle or lowest third of the class on the mid-term exam) and gender were also collected to explore the relationship between these factors, conceptual development and instructional sequencing. Results show, within this context at least, that teaching sequence is not important in terms of students’ conceptual learning gains.

Responding to national curriculum goals for English language learners : enhancing reading strategies in high school content areas

The official need for content teachers to teach the language features of their fields has never been greater in Australia than now. In 2012, the recently formed national curriculum board announced that all teachers are responsible for the English language development of students whose first language or dialect is not Standard Australian English (SAE). This formal endorsement is an important juncture regarding the way expertise might be developed, perceived and exchanged between content and language teachers through collaboration, in order for the goals of English language learners in content areas to be realised. To that end, we conducted an action research project to explore and extend the reading strategies pedagogy of one English language teacher who teaches English language learners in a parallel junior high school Geography program. Such pedagogy will be valuable for all teachers as they seek to contribute to English language development goals as outlined in national curricula.

'These are my photos of when I was little' : Locating Media Arts in the Primary School Curriculum

‘Media Arts’ has been included as a fifth area of the Arts for the Australian Curriculum which will become mandatory learning for all Australian children from pre-school to Year Six (Y6) from 2014. The current curriculum design is underpinned by an approach familiar to media educators who combine creative practice and critical response to develop students’ media literacies. Media Arts within the Australian Curriculum will place Australia at the forefront of international efforts to promote media education as an entitlement for all children. Even with this mandated endorsement, however, there remains ongoing debate about where to locate media education in school curricula. Historically, media education in Australia has been approached through diverse curriculum activities at the secondary school level. These include subject English’s critical literacy objectives; vocationally oriented media and technology education or ICTs education; and Arts courses using new media technologies for creativity. In this chapter we consider the possibilities and challenges for Media Arts, specifically for primary school student learning. We draw on empirical evidence from a research project that has trialled a Media Arts curriculum with students attending a primary school in a low socio-economic status and culturally diverse community on the outskirts of Brisbane, Queensland.

Funds of knowledge of sorting and patterning : networks of exchange in a Torres Strait Island community

The purpose of this article is to describe a project with one Torres Strait Islander Community. It provides some insights into parents’ funds of knowledge that are mathematical in nature, such as sorting shells and giving fish. The idea of funds of knowledge is based the premise that people are competent and have knowledge that has been historically and culturally accumulated into a body of knowledge and skills essential for their functioning and well-being. This knowledge is then practised throughout their lives and passed onto the next generation of children. Through using a community research approach, funds of knowledge that can be used to validate the community’s identities as knowledgeable people, can be used as foundations for future learnings for teachers, parents and children in the early years of school. They can be the bridge that joins a community’s funds of knowledge with schools validating that knowledge.

Practical insights into curricula integration for primary science

As indicated in a previous Teaching Science article, effective planning for curricula integration requires using standards from two (or more) subject areas (e.g., science and English, science and art or science and mathematics), which also becomes the assessment foci for teaching and learning. Curricula integration of standards into an activity necessitates pedagogical knowledge for developing students’ learning in both subject areas. For science education, the skills and tools for curricula integration include the use of other key learning areas (KLAs). A balance between teacher and student-centred science education programs that draw on democratic processes (e.g., Beane, 1997) can be used to make real-world links to target students’ individual needs. This article presents practical ways to commence thinking about curricula integration towards using Australian curriculum standards.

Self-proxy agreement and weekly school travel behaviour in a sectarian divided society

Proxy reports from parents and self-reported data from pupils have often been used interchangeably to identify factors influencing school travel behaviour. However, few studies have examined the validity of proxy reports as an alternative to self-reported data. In addition, despite research that has been conducted in a different context, little is known to date about the impact of different factors on school travel behaviour in a sectarian divided society. This research examines these issues using 1624 questionnaires collected from four independent samples (e.g. primary pupils, parent of primary pupils, secondary pupils, and parent of secondary pupils) across Northern Ireland. An independent sample t test was conducted to identify the differences in data reporting between pupils and parents for different age groups using the reported number of trips for different modes as dependent variables. Multivariate multiple regression analyses were conducted to then identify the impacts of different factors (e.g. gender, rural–urban context, multiple deprivations, and school management type, net residential density, land use diversity, intersection density) on mode choice behaviour in this context. Results show that proxy report is a valid alternative to self-reported data, but only for primary pupils. Land use diversity and rural–urban context were found to be the most important factors in influencing mode choice behaviour.

Combinatorial design of key distribution mechanisms for wireless sensor networks

Secure communications in wireless sensor networks operating under adversarial conditions require providing pairwise (symmetric) keys to sensor nodes. In large scale deployment scenarios, there is no prior knowledge of post deployment network configuration since nodes may be randomly scattered over a hostile territory. Thus, shared keys must be distributed before deployment to provide each node a key-chain. For large sensor networks it is infeasible to store a unique key for all other nodes in the key-chain of a sensor node. Consequently, for secure communication either two nodes have a key in common in their key-chains and they have a wireless link between them, or there is a path, called key-path, among these two nodes where each pair of neighboring nodes on this path have a key in common. Length of the key-path is the key factor for efficiency of the design. This paper presents novel deterministic and hybrid approaches based on Combinatorial Design for deciding how many and which keys to assign to each key-chain before the sensor network deployment. In particular, Balanced Incomplete Block Designs (BIBD) and Generalized Quadrangles (GQ) are mapped to obtain efficient key distribution schemes. Performance and security properties of the proposed schemes are studied both analytically and computationally. Comparison to related work shows that the combinatorial approach produces better connectivity with smaller key-chain sizes.

Nambour : the model rural school

This paper examines the Rural Schools of Queensland. Starting with Nambour in 1917, the scheme incorporated thirty schools, and operated for over forty years. The rhetoric of the day was that boys and girls from the senior classes of primary school would be provided with elementary instruction of a practical character. In reality, the subjects taught were specifically tailored to provide farm skills to children in rural centres engaged in farming, dairying or fruit growing. Linked to each Rural School was a number of smaller surrounding schools, students from which travelled to the Rural School for special agricultural or domestic instruction. Through this action, the Queensland Department of Public Instruction left no doubt it intended to provide educational support for agrarian change and development within the state; in effect, they had set in motion the creation of a Queensland yeoman class. The Department’s intention was to arrest or reverse the trend toward urbanisation — whilst increasing agricultural productivity — through the making of a farmer born of the land and accepting of the new scientific advances in agriculture.

School-based programs for increasing connectedness and reducing risk behavior : a systematic review

School connectedness has a significant impact on adolescent outcomes, including reducing risk taking behavior. This paper critically examines the literature on school-based programs targeting increased connectedness for reductions in risk taking. Fourteen articles describing seven different school-based programs were reviewed. Programs drew on a range of theories to increase school connectedness, and evaluations conducted for the majority of programs demonstrated positive changes in school connectedness, risk behavior, or a combination of the two. Many of the reviewed programs involved widespread school system change, however, which is frequently a complex and time consuming task. Future research is needed to examine the extent of intervention complexity required to result in change. This review also showed a lack of consistency in definitions and measurement of connectedness as well as few mediation analyses testing assumptions of impact on risk taking behavior through increases in school connectedness. Additionally, this review revealed very limited evaluation of the elements of multi-component programs that are most effective in increasing school connectedness and reducing adolescent risk taking.

Does 'habitus' count in Chinese Australians' mathematics achievement?

Large-scale international comparative studies and cross-ethnic studies have revealed that Chinese students, whether living in China or overseas, consistently outperform their counterparts in mathematics achievement. These studies tended to explain this result from psychological, educational, or cultural perspectives. However, there is scant sociological investigation addressing Chinese students’ better mathematics achievement. Drawing on Bourdieu’s sociological theory, this study conceptualises Chinese Australians’ “Chineseness” by the notion of ‘habitus’ and considers this “Chineseness” generating but not determinating mechanism that underpins Chinese Australians’ mathematics learning. Two hundred and thirty complete responses from Chinese Australian participants were collected by an online questionnaire. Simple regression model statistically significantly well predicted mathematics achievement by “Chineseness” (F = 141.90, R = .62, t = 11.91, p < .001). Taking account of “Chineseness” as a sociological mechanism for Chinese Australians’ mathematics learning, this study complements psychological and educational impacts on better mathematics achievement of Chinese students revealed by previous studies. This study also challenges the cultural superiority discourse that attributes better mathematics achievement of Chinese students to cultural factors.