Early childhood teachers' mathematical content knowledge

The process of becoming numerate begins in the early years. According to Vygotskian theory (1978), teachers are More Knowledgeable Others who provide and support learning experiences that influence children’s mathematical learning. This paper reports on research that investigates three early childhood teachers mathematics content knowledge. An exploratory, single case study utilised data collected from interviews, and email correspondence to investigate the teachers’ mathematics content knowledge. The data was reviewed according to three analytical strategies: content analysis, pattern matching, and comparative analysis. Findings indicated there was variation in teachers’ content knowledge across the five mathematical strands and that teachers might not demonstrate the depth of content knowledge that is expected of four year specially trained early years’ teachers. A significant factor that appeared to influence these teachers’ content knowledge was their teaching experience. Therefore, an avenue for future research is the investigation of factors that influence teachers’ content numeracy knowledge.

Doing justice : young people’s representations of the Murray-Darling Basin

The business of helping children to grow up as ‘custodians’, or ‘future managers’ of the Murray-Darling Basin is not simple, and that single sources of information and ways of seeing the environment are not enough. Children (and adults) need to be able to relate individually, emotionally and aesthetically to their places if they are to learn to love them. However, they also need access to a variety of ways of thinking and seeing those same places if they are to be able to take action to sustain them – action that inevitably involves forms of communication with their fellow citizens. This chapter documents the writing and art program Special Forever, with its focus on communications, as an important intervention into promoting eco-social sustainability.

Reliable representations for association rules

Association rule mining has contributed to many advances in the area of knowledge discovery. However, the quality of the discovered association rules is a big concern and has drawn more and more attention recently. One problem with the quality of the discovered association rules is the huge size of the extracted rule set. Often for a dataset, a huge number of rules can be extracted, but many of them can be redundant to other rules and thus useless in practice. Mining non-redundant rules is a promising approach to solve this problem. In this paper, we first propose a definition for redundancy, then propose a concise representation, called a Reliable basis, for representing non-redundant association rules. The Reliable basis contains a set of non-redundant rules which are derived using frequent closed itemsets and their generators instead of using frequent itemsets that are usually used by traditional association rule mining approaches. An important contribution of this paper is that we propose to use the certainty factor as the criterion to measure the strength of the discovered association rules. Using this criterion, we can ensure the elimination of as many redundant rules as possible without reducing the inference capacity of the remaining extracted non-redundant rules. We prove that the redundancy elimination, based on the proposed Reliable basis, does not reduce the strength of belief in the extracted rules. We also prove that all association rules, their supports and confidences, can be retrieved from the Reliable basis without accessing the dataset. Therefore the Reliable basis is a lossless representation of association rules. Experimental results show that the proposed Reliable basis can significantly reduce the number of extracted rules. We also conduct experiments on the application of association rules to the area of product recommendation. The experimental results show that the non-redundant association rules extracted using the proposed method retain the same inference capacity as the entire rule set. This result indicates that using non-redundant rules only is sufficient to solve real problems needless using the entire rule set.

Australian queer student activists' media representations of queer

Queer student activists are a visible aspect of Australian tertiary communities. Institutionally there are a number of organisations and tools representing and serving gay, lesbian, bisexual, transgender, intersex and ‘otherwise queer identifying’ (GLBTIQ) students. ‘Queer’ is a contentious term with meanings ranging from a complex deconstructive academic theory to a term for ‘gay’. Despite the institutional applications, the definition remains unclear and under debate. In this thesis I examine queer student activists’ production of print media, a previously under-researched area. In queer communities, print media provides crucial grounding for a model of queer. Central to identity formation and activism, this media is a site of textuality for the construction and circulation of discourses of queer student media. Thus, I investigate the various ways Australian queer student activists construct queer, queer identity, and queer activism in their print media. I use discourse analysis, participant observation and semi-structured interviews to enable a thorough investigation of both the process and the products of queer student media. My findings demonstrate that queer student activists’ politics are grounded in a range of ideologies drawing from Marxism, Feminism, Gay Liberation, Anti-assimilation and Queer Theory. Grounded in queer theoretical perspectives of performativity this research makes relatively new links between Queer Theory and Media Studies in its study of the production contexts of queer student media. In doing so, I show how the university context informs student articulations of queer, proving the necessity to locate research within its social-cultural setting. My research reveals that, much like Queer Theory, these representations of queer are rich with paradox. I argue that queer student activists are actually theorising queer. I call for a reconceptualisation of Queer Theory and question the current barriers between who is considered a ‘theorist’ of queer and who is an ‘activist’. If we can think about ‘theory’ as encompassing the work of activists, what implications might this have for politics and analysis?

Flagging spaces : exploring representations of ownership on the Australian beach

The Australian beach is a significant element of our national identity. Since the majority of the population lives on the coastlines of the continent, the beach (rather than the Bush) plays an important role to many Australians. Yet the beach can also be a complex setting because of the often complicated concepts of ownership that surround it. ‘Flagging Spaces’ examines the layers of complexity surrounding textual representations of ownership of the beach space. In particular, this paper explores the Indigenous representation on the beach moving through to the role of multiculturalism on the beach space in the wake of the 2005 Cronulla riots, using specific textual examples such as Sacred Cows (Heiss 1996), Australia (dir. Baz Luhrmann 2008), Heaven (dir. Tracey Moffatt 1997), Radiance (dir. Rachel Perkins 1998), Butterfly Song (Jenkins 2005), and Bra Boys (dir. Sonny Abberton 2006).

A mathematical model of chlamydial infection incorporating movement of chlamydial particles

We present a spatiotemporal mathematical model of chlamydial infection, host immune response and spatial movement of infectious particles. The re- sulting partial differential equations model both the dynamics of the infection and changes in infection profile observed spatially along the length of the host genital tract. This model advances previous chlamydia modelling by incorporating spatial change, which we also demonstrate to be essential when the timescale for movement of infectious particles is equal to, or shorter than, the developmental cycle timescale. Numerical solutions and model analysis are carried out, and we present a hypothesis regarding the potential for treatment and prevention of infection by increasing chlamydial particle motility.

Towards a model for the analysis and description of mathematical knowledge and understanding

Mathematics education literature has called for an abandonment of ontological and epistemological ideologies that have often divided theory-based practice. Instead, a consilience of theories has been sought which would leverage the strengths of each learning theory and so positively impact upon contemporary educational practice. This research activity is based upon Popper’s notion of three knowledge worlds which differentiates the knowledge shared in a community from the personal knowledge of the individual, and Bereiter’s characterisation of understanding as the individual’s relationship to tool-like knowledge. Using these notions, a re-conceptualisation of knowledge and understanding and a subsequent re-consideration of learning theories are proposed as a way to address the challenge set by literature. Referred to as the alternative theoretical framework, the proposed theory accounts for the scaffolded transformation of each individual’s unique understanding, whilst acknowledging the existence of a body of domain knowledge shared amongst participants in a scientific community of practice. The alternative theoretical framework is embodied within an operational model that is accompanied by a visual nomenclature with which to describe consensually developed shared knowledge and personal understanding. This research activity has sought to iteratively evaluate this proposed theory through the practical application of the operational model and visual nomenclature to the domain of early-number counting, addition and subtraction. This domain of mathematical knowledge has been comprehensively analysed and described. Through this process, the viability of the proposed theory as a tool with which to discuss and thus improve the knowledge and understanding with the domain of mathematics has been validated. Putting of the proposed theory into practice has lead to the theory’s refinement and the subsequent achievement of a solid theoretical base for the future development of educational tools to support teaching and learning practice, including computer-mediated learning environments. Such future activity, using the proposed theory, will advance contemporary mathematics educational practice by bringing together the strengths of cognitivist, constructivist and post-constructivist learning theories.

Machine recognition of hand-drawn circuit diagrams

An application of image processing techniques to recognition of hand-drawn circuit diagrams is presented. The scanned image of a diagram is pre-processed to remove noise and converted to bilevel. Morphological operations are applied to obtain a clean, connected representation using thinned lines. The diagram comprises of nodes, connections and components. Nodes and components are segmented using appropriate thresholds on a spatially varying object pixel density. Connection paths are traced using a pixel-stack. Nodes are classified using syntactic analysis. Components are classified using a combination of invariant moments, scalar pixel-distribution features, and vector relationships between straight lines in polygonal representations. A node recognition accuracy of 82% and a component recognition accuracy of 86% was achieved on a database comprising 107 nodes and 449 components. This recogniser can be used for layout “beautification” or to generate input code for circuit analysis and simulation packages

The African Institute for Mathematical Sciences

Its mission is to promote Mathematics and Science in Africa and to provide a focal point for Mathematics university training in Africa. It offers scholarships for up to 50 students to come and study for a period of nine months. Of the 50 students, about 15 positions are reserved for females. In the 2006/2007 intake there were over 250 applicants. The students are housed and fed and their return travel from their home town is fully funded. Lecturers also stay at AIMS and share their meals with the students, so that a rapport quickly develops. The students are away from their families and friends for nine months and are absolutely committed to the discipline of Mathematics. When they first arrive, some of them have little ability in English but since all tuition is in English they quickly learn. Some find the transitions difficult but they all support one another and at the end of their time their English skills are very good. The students do a series of subjects that last for about three weeks each, consisting of 30 contact hours, as well as a thesis/project. Each course has a number of assignments associated with it and these get evaluated. AIMS has seven or eight teaching assistants who help with the tutorials, marking, advice, and who are a vital component of AIMS.

A mathematical model for genetic regulation of the lactose operon

In this paper we construct a mathematical model for the genetic regulatory network of the lactose operon. This mathematical model contains transcription and translation of the lactose permease (LacY) and a reporter gene GFP. The probability of transcription of LacY is determined by 14 binding states out of all 50 possible binding states of the lactose operon based on the quasi-steady-state assumption for the binding reactions, while we calculate the probability of transcription for the reporter gene GFP based on 5 binding states out of 19 possible binding states because the binding site O2 is missing for this reporter gene. We have tested different mechanisms for the transport of thio-methylgalactoside (TMG) and the effect of different Hill coefficients on the simulated LacY expression levels. Using this mathematical model we have realized one of the experimental results with different LacY concentrations, which are induced by different concentrations of TMG.

Sparse temporal representations for facial expression recognition

In automatic facial expression recognition, an increasing number of techniques had been proposed for in the literature that exploits the temporal nature of facial expressions. As all facial expressions are known to evolve over time, it is crucially important for a classifier to be capable of modelling their dynamics. We establish that the method of sparse representation (SR) classifiers proves to be a suitable candidate for this purpose, and subsequently propose a framework for expression dynamics to be efficiently incorporated into its current formulation. We additionally show that for the SR method to be applied effectively, then a certain threshold on image dimensionality must be enforced (unlike in facial recognition problems). Thirdly, we determined that recognition rates may be significantly influenced by the size of the projection matrix \Phi. To demonstrate these, a battery of experiments had been conducted on the CK+ dataset for the recognition of the seven prototypic expressions - anger, contempt, disgust, fear, happiness, sadness and surprise - and comparisons have been made between the proposed temporal-SR against the static-SR framework and state-of-the-art support vector machine.