Kindergarten students' understanding of probability concepts

This study explored kindergarten students’ intuitive strategies and understandings in probabilities. The paper aims to provide an in depth insight into the levels of probability understanding across four constructs, as proposed by Jones (1997), for kindergarten students. Qualitative evidence from two students revealed that even before instruction pupils have a good capacity of predicting most and least likely events, of distinguishing fair probability situations from unfair ones, of comparing the probability of an event in two sample spaces, and of recognizing conditional probability events. These results contribute to the growing evidence on kindergarten students’ intuitive probabilistic reasoning. The potential of this study for improving the learning of probability, as well as suggestions for further research, are discussed.

Mixing colours : an ICT tool based on a semiotic framework for mathematical meaning-making about ratio and fractions

This paper reports on the research and development of an ICT tool to facilitate the learning of ratio and fractions by adult prisoners. The design of the ICT tool was informed by a semiotic framework for mathematical meaning-making. The ICT tool thus employed multiple semiotic resources including topological, typological, and social-actional resources. The results showed that individual semiotic resource could only represent part of the mathematical concept, while at the same time it might signify something else to create a misconception. When multiple semiotic resources were utilised the mathematical ideas could be better learnt.

Concepts of intuitive interaction

Intuition is a type of cognitive processing that is often non-conscious and utilises stored experiential knowledge. Intuitive interaction involves the use of knowledge gained from other products and/or experiences. We have developed novel approaches and techniques for studying intuitive use of interfaces, and shown that intuitive interaction is based on past experience with similar artefacts. Based on our empirical work we have developed principles and tools for designers to assist them in making interfaces more intuitive. These principles are discussed in this paper.

Can tissue engineering concepts advance tumor biology research?

Advances in tissue engineering have traditionally led to the design of scaffold- or matrix-based culture systems that better reflect the biological, physical and biochemical environment of the natural extracellular matrix. Although their clinical applications in regenerative medicine tend to receive most of the attention, it is obvious that other areas of biomedical research could be well served by the powerful tools that have already been developed in tissue engineering. In this article, we review the recent literature to demonstrate how tissue engineering platforms can enhance in vitro and in vivo models of tumorigenesis and thus hold great promise to contribute to future cancer research.

Mathematical modelling of muscle recruitment and function in the lumbar spine

Low back pain is an increasing problem in industrialised countries and although it is a major socio-economic problem in terms of medical costs and lost productivity, relatively little is known about the processes underlying the development of the condition. This is in part due to the complex interactions between bone, muscle, nerves and other soft tissues of the spine, and the fact that direct observation and/or measurement of the human spine is not possible using non-invasive techniques. Biomechanical models have been used extensively to estimate the forces and moments experienced by the spine. These models provide a means of estimating the internal parameters which can not be measured directly. However, application of most of the models currently available is restricted to tasks resembling those for which the model was designed due to the simplified representation of the anatomy. The aim of this research was to develop a biomechanical model to investigate the changes in forces and moments which are induced by muscle injury. In order to accurately simulate muscle injuries a detailed quasi-static three dimensional model representing the anatomy of the lumbar spine was developed. This model includes the nine major force generating muscles of the region (erector spinae, comprising the longissimus thoracis and iliocostalis lumborum; multifidus; quadratus lumborum; latissimus dorsi; transverse abdominis; internal oblique and external oblique), as well as the thoracolumbar fascia through which the transverse abdominis and parts of the internal oblique and latissimus dorsi muscles attach to the spine. The muscles included in the model have been represented using 170 muscle fascicles each having their own force generating characteristics and lines of action. Particular attention has been paid to ensuring the muscle lines of action are anatomically realistic, particularly for muscles which have broad attachments (e.g. internal and external obliques), muscles which attach to the spine via the thoracolumbar fascia (e.g. transverse abdominis), and muscles whose paths are altered by bony constraints such as the rib cage (e.g. iliocostalis lumborum pars thoracis and parts of the longissimus thoracis pars thoracis). In this endeavour, a separate sub-model which accounts for the shape of the torso by modelling it as a series of ellipses has been developed to model the lines of action of the oblique muscles. Likewise, a separate sub-model of the thoracolumbar fascia has also been developed which accounts for the middle and posterior layers of the fascia, and ensures that the line of action of the posterior layer is related to the size and shape of the erector spinae muscle. Published muscle activation data are used to enable the model to predict the maximum forces and moments that may be generated by the muscles. These predictions are validated against published experimental studies reporting maximum isometric moments for a variety of exertions. The model performs well for fiexion, extension and lateral bend exertions, but underpredicts the axial twist moments that may be developed. This discrepancy is most likely the result of differences between the experimental methodology and the modelled task. The application of the model is illustrated using examples of muscle injuries created by surgical procedures. The three examples used represent a posterior surgical approach to the spine, an anterior approach to the spine and uni-lateral total hip replacement surgery. Although the three examples simulate different muscle injuries, all demonstrate the production of significant asymmetrical moments and/or reduced joint compression following surgical intervention. This result has implications for patient rehabilitation and the potential for further injury to the spine. The development and application of the model has highlighted a number of areas where current knowledge is deficient. These include muscle activation levels for tasks in postures other than upright standing, changes in spinal kinematics following surgical procedures such as spinal fusion or fixation, and a general lack of understanding of how the body adjusts to muscle injuries with respect to muscle activation patterns and levels, rate of recovery from temporary injuries and compensatory actions by other muscles. Thus the comprehensive and innovative anatomical model which has been developed not only provides a tool to predict the forces and moments experienced by the intervertebral joints of the spine, but also highlights areas where further clinical research is required.

Mathematical modelling in the early school years

In this article we explore young children's development of mathematical knowledge and reasoning processes as they worked two modelling problems (the Butter Beans Problem and the Airplane Problem). The problems involve authentic situations that need to be interpreted and described in mathematical ways. Both problems include tables of data, together with background information containing specific criteria to be considered in the solution process. Four classes of third-graders (8 years of age) and their teachers participated in the 6-month program, which included preparatory modelling activities along with professional development for the teachers. In discussing our findings we address: (a) Ways in which the children applied their informal, personal knowledge to the problems; (b) How the children interpreted the tables of data, including difficulties they experienced; (c) How the children operated on the data, including aggregating and comparing data, and looking for trends and patterns; (c) How the children developed important mathematical ideas; and (d) Ways in which the children represented their mathematical understandings.

The application of the Park & Ride and TOD concepts to develop a new framework that can maximise public transport patronage

With growing concern over the use of the car in our urbanized society, there have emerged a number of lobby groups and professional bodies promoting a return to public transport, walking and cycling, with the urban village as the key driving land use, as a means of making our cities’ transportation systems more sustainable. This research has aimed at developing a framework applicable to the Australian setting that can facilitate increased passenger patronage of rail based urban transport systems from adjacent or associated land uses. The framework specifically tested the application of the Park & Ride and Transit Oriented Development (TOD) concepts and their applicability within the cultural, institutional, political and transit operational characteristics of Australian society. The researcher found that, although the application of the TOD concept had been limited to small pockets of town houses and mixed use developments around stations, the development industry and emerging groups within the community are posed to embrace the concept and bring with it increased rail patronage. The lack of a clear commitment to infrastructure and supporting land uses is a major barrier to the implementation of TODs. The research findings demonstrated significant scope for the size of a TOD to expand to a much greater radius of activity from the public transport interchange, than the commonly quoted 400 to 600 meters, thus incorporating many more residents and potential patrons. The provision of Park & Rides, and associated support facilities like Kiss & Rides, have followed worldwide trends of high patronage demands from the middle and outer car dependent suburbs of our cities. The data collection and analysis gathered by the researcher demonstrated that in many cases Park & Rides should form part of a TOD to ensure ease of access to rail stations by all modes and patron types. The question, however, remains how best to plan the incorporation of a Park & Ride within a TOD and still maintain those features that attract and promote TODs as a living entity.

‘Keep telling until someone listens’ : understanding prevention concepts in children’s picture books dealing with child sexual abuse

Children’s picture books dealing with the topic of child sexual abuse appeared in the 1980s with the aim of addressing the need for age-appropriate texts to teach sexual abuse prevention concepts and to provide support for young children who may be at risk of or have already experienced sexual abuse. Despite the apparent potential of children’s picture books to convey child sexual abuse prevention concepts, very few studies have addressed the topic of child sexual abuse in children’s literature. This article critically examines a selection of 15 picture books (published in the US, Canada and Australia) for children aged 3–8 years dealing with this theme. It makes use of an established set of evaluative criteria to conduct an audit of the books’ content and applies techniques of literary discourse analysis to explain how these picture books satisfy criteria for child sexual abuse prevention. The analysis is used as a way to understand the discourses available to readers, both adults and children, on the topic of child sexual abuse. Key themes in the books include children’s empowerment and agency, and the need for persistence and hope.

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.

Predicting active material utilisation in LiFePO4 electrodes using a multi-scale mathematical model

A mathematical model is developed to simulate the discharge of a LiFePO4 cathode. This model contains 3 size scales, which match with experimental observations present in the literature on the multi-scale nature of LiFePO4 material. A shrinking-core is used on the smallest scale to represent the phase-transition of LiFePO4 during discharge. The model is then validated against existing experimental data and this validated model is then used to investigate parameters that influence active material utilisation. Specifically the size and composition of agglomerates of LiFePO4 crystals is discussed, and we investigate and quantify the relative effects that the ionic and electronic conductivities within the oxide have on oxide utilisation. We find that agglomerates of crystals can be tolerated under low discharge rates. The role of the electrolyte in limiting (cathodic) discharge is also discussed, and we show that electrolyte transport does limit performance at high discharge rates, confirming the conclusions of recent literature.

Theory and development of GPS integrity monitoring system

This thesis discusses various aspects of the integrity monitoring of GPS applied to civil aircraft navigation in different phases of flight. These flight phases include en route, terminal, non-precision approach and precision approach. The thesis includes four major topics: probability problem of GPS navigation service, risk analysis of aircraft precision approach and landing, theoretical analysis of Receiver Autonomous Integrity Monitoring (RAIM) techniques and RAIM availability, and GPS integrity monitoring at a ground reference station. Particular attention is paid to the mathematical aspects of the GPS integrity monitoring system. The research has been built upon the stringent integrity requirements defined by civil aviation community, and concentrates on the capability and performance investigation of practical integrity monitoring systems with rigorous mathematical and statistical concepts and approaches. Major contributions of this research are: • Rigorous integrity and continuity risk analysis for aircraft precision approach. Based on the joint probability density function of the affecting components, the integrity and continuity risks of aircraft precision approach with DGPS were computed. This advanced the conventional method of allocating the risk probability. • A theoretical study of RAIM test power. This is the first time a theoretical study on RAIM test power based on the probability statistical theory has been presented, resulting in a new set of RAIM criteria. • Development of a GPS integrity monitoring and DGPS quality control system based on GPS reference station. A prototype of GPS integrity monitoring and DGPS correction prediction system has been developed and tested, based on the A USN A V GPS base station on the roof of QUT ITE Building.

The development of science concepts emergent from science museum and post-visit activity experiences : students' construction of knowledge

This research investigated students' construction of knowledge about the topics of magnetism and electricity emergent from a visit to an interactive science centre and subsequent classroom-based activities linked to the science centre exhibits. The significance of this study is that it analyses critically an aspect of school visits to informal learning centres that has been neglected by researchers in the past, namely the influence of post-visit activities in the classroom on subsequent learning and knowledge construction. Employing an interpretive methodology, the study focused on three areas of endeavour. Firstly, the establishment of a set of principles for the development of post-visit activities, from a constructivist framework, to facilitate students' learning of science. Secondly, to describe and interpret students' scientific understandings : prior t o a visit t o a science museum; following a visit t o a science museum; and following post-visit activities that were related to their museum experiences. Finally, to describe and interpret the ways in which students constructed their understandings: prior to a visit to a science museum; following a visit to a science museum; and following post-visit activities directly related to their museum experiences. The study was designed and implemented in three stages: 1) identification and establishment of the principles for design and evaluation of post-visit activities; 2) a pilot study of specific post-visit activities and data gathering strategies related to student construction of knowledge; and 3) interpretation of students' construction of knowledge from a visit to a science museum and subsequent completion of post-visit activities, which constituted the main study. Twelve students were selected from a year 7 class to participate in the study. This study provides evidence that the series of post-visit activities, related to the museum experiences, resulted in students constructing and reconstructing their personal knowledge of science concepts and principles represented in the science museum exhibits, sometimes towards the accepted scientific understanding and sometimes in different and surprising ways. Findings demonstrate the interrelationships between learning that occurs at school, at home and in informal learning settings. The study also underscores for teachers and staff of science museums and similar centres the importance of planning pre- and post-visit activities, not only to support the development of scientific conceptions, but also to detect and respond to alternative conceptions that may be produced or strengthened during a visit to an informal learning centre. Consistent with contemporary views of constructivism, the study strongly supports the views that : 1) knowledge is uniquely structured by the individual; 2) the processes of knowledge construction are gradual, incremental, and assimilative in nature; 3) changes in conceptual understanding are can be interpreted in the light of prior knowledge and understanding; and 4) knowledge and understanding develop idiosyncratically, progressing and sometimes appearing to regress when compared with contemporary science. This study has implications for teachers, students, museum educators, and the science education community given the lack of research into the processes of knowledge construction in informal contexts and the roles that post-visit activities play in the overall process of learning.