Reunitising hundredths: prototypic and nonprototypic representations

This paper reports on a study in which 29 Year 6 students (selected from the top 30% of 176 Year 6 students) were individually interviewed to explore their ability to reunitise hundredths as tenths (Behr, Harel, Post & Lesh, 1992) when represented by prototypic (PRO) and nonprototypic (NPRO) models. The results showed that 55.2% of the students were able to unitise both models and that reunitising was more successful with the PRO model. The interviews revealed that many of these students had incomplete, fragmented or non-existent structural knowledge of the reunitising process and often relied on syntactic clues to complete the tasks. The implication for teaching is that instruction should not be limited to PRO representations of the part/whole notion of fraction and that the basic structures (equal parts, link between name and number of equal parts) of the part/whole notion needs to be revisited often.

Skydweller and representations of the adolescent crisis : group identity versus alienation

This document contains a creative work – the text of a young adult novel, Skydweller – and an exegesis discussing the ways in which identity and the adolescent crisis of group identity versus alienation are represented in young adult science fiction/fantasy novels.

Combining Cartesian and polar coordinates in IBVS

Image-based visual servo (IBVS) is a simple, efficient and robust technique for vision-based control. Although technically a local method in practice it demonstrates almost global convergence. However IBVS performs very poorly for cases that involve large rotations about the optical axis. It is well known that re-parameterizing the problem by using polar, instead of Cartesian coordinates, of feature points overcomes this limitation. First, simulation and experimental results are presented to show the complementarity of these two parameter-izations. We then describe a new hybrid visual servo strategy based on combining polar and Cartesian image Jacobians. © 2009 IEEE.

Learning spatial concepts from RatSLAM representations

RatSLAM is a biologically-inspired visual SLAM and navigation system that has been shown to be effective indoors and outdoors on real robots. The spatial representation at the core of RatSLAM, the experience map, forms in a distributed fashion as the robot learns the environment. The activity in RatSLAM’s experience map possesses some geometric properties, but still does not represent the world in a human readable form. A new system, dubbed RatChat, has been introduced to enable meaningful communication with the robot. The intention is to use the “language games” paradigm to build spatial concepts that can be used as the basis for communication. This paper describes the first step in the language game experiments, showing the potential for meaningful categorization of the spatial representations in RatSLAM.

Experience mapping : producing spatially continuous environment representations using RatSLAM

RatSLAM is a system for vision-based Simultaneous Localisation and Mapping (SLAM) inspired by models of the rodent hippocampus. The system can produce stable representations of large complex environments during robot experiments in both indoor and outdoor environments. These representations are both topological and metric in nature, and can involve multiple representations of the same place as well as discontinuities. In this paper we describe a new technique known as experience mapping that can be used online with the RatSLAM system to produce world representations known as experience maps. These maps group together multiple place representations and are spatially continuous. A number of experiments have been conducted in simulation and a real world office environment. These experiments demonstrate the high degree to which experience maps are representative of the spatial arrangement of the environment.

Exploring visual features through Gabor representations for facial expression detection

Gabor representations have been widely used in facial analysis (face recognition, face detection and facial expression detection) due to their biological relevance and computational properties. Two popular Gabor representations used in literature are: 1) Log-Gabor and 2) Gabor energy filters. Even though these representations are somewhat similar, they also have distinct differences as the Log-Gabor filters mimic the simple cells in the visual cortex while the Gabor energy filters emulate the complex cells, which causes subtle differences in the responses. In this paper, we analyze the difference between these two Gabor representations and quantify these differences on the task of facial action unit (AU) detection. In our experiments conducted on the Cohn-Kanade dataset, we report an average area underneath the ROC curve (A`) of 92.60% across 17 AUs for the Gabor energy filters, while the Log-Gabor representation achieved an average A` of 96.11%. This result suggests that small spatial differences that the Log-Gabor filters pick up on are more useful for AU detection than the differences in contours and edges that the Gabor energy filters extract.

Photographic representations of Asylum seekers in Australian media

This paper introduces three approaches to unlocking the degrees of “truth” within photographs published in newspapers by exploring the genres of Press photography, Photojournalism and Documentary photography. This is brought into context through a study of photographs appearing in The Australian newspaper during 2001 when the Norwegian freighter, the MV Tampa, rescued boat people whose vessel had sunk off the West Australian coast in 2001, and two months later the Children Overboard incident occurred.

Transnational business masculinities : media representations of gender and management in global mining corporations

This paper examines Australian media representations of the male managers of two global mining corporations, Rio Tinto and BHP Billiton. These organizations are transnational (or multinational) corporations with assets and/or operations across national boundaries (Dunning and Lundan, 2008), and indeed their respective Chief Executive Officers, Tom Albanese and Marius Kloppers are two of the most economically (and arguably politically) powerful in the world overseeing 37 000 and 39 000 employees internationally. With a 2008 profit of US$15.962 billion and assets of US$ 75.889 Billion BHP Billiton is the world's largest mining company. In terms of its profits and assets Rio Tinto ranks fourth in the world, but with operations in six countries (mainly Canada and Australia) and a 2008 profit of US$10.3 billion it is also emblematic of the transnational in that its ‘budget is larger than that of all but a few nations’ (Giddens, 2003, p. 62).

Years 2 to 6 students' ability to generalise : models, representations and theory for teaching and learning

Over the last three years, in our Early Algebra Thinking Project, we have been studying Years 3 to 5 students’ ability to generalise in a variety of situations, namely, compensation principles in computation, the balance principle in equivalence and equations, change and inverse change rules with function machines, and pattern rules with growing patterns. In these studies, we have attempted to involve a variety of models and representations and to build students’ abilities to switch between them (in line with the theories of Dreyfus, 1991, and Duval, 1999). The results have shown the negative effect of closure on generalisation in symbolic representations, the predominance of single variance generalisation over covariant generalisation in tabular representations, and the reduced ability to readily identify commonalities and relationships in enactive and iconic representations. This chapter uses the results to explore the interrelation between generalisation and verbal and visual comprehension of context. The studies evidence the importance of understanding and communicating aspects of representational forms which allowed commonalities to be seen across or between representations. Finally the chapter explores the implications of the studies for a theory that describes a growth in integration of models and representations that leads to generalisation.

Cognitive processes and strategies employed by children to learn spatial representations

Children often have difficulties in learning spatial representations. This study investigated the effect of four different instructional formats on learning outcomes and strategies used when dealing with spatial tasks such as assembly procedures. It was hypothesised that instructional material that imposed least extraneous cognitive load would facilitate enhanced learning. Forty secondary students were presented with four types of instruction; orthographic drawing, isometric drawing, physical model and, isometric and physical model together. The findings provide evidence to suggest that working from physical models caused least extraneous cognitive load compared to the isometric and orthographic groups. The model group took less time, had more correctly completed models, required fewer extra looks, spent less time studying the instruction and made fewer errors. Problem decomposition, forward working and attending to information in the foreground of the graphical representation strategies were analysed.

Processing load and the use of concrete representations and strategies for solving linear equations

This paper is a report of students' responses to instruction which was based on the use of concrete representations to solve linear equations. The sample consisted of 21 Grade 8 students from a middle-class suburban state secondary school with a reputation for high academic standards and innovative mathematics teaching. The students were interviewed before and after instruction. Interviews and classroom interactions were observed and videotaped. A qualitative analysis of the responses revealed that students did not use the materials in solving problems. The increased processing load caused by concrete representations is hypothesised as a reason.