Fractions, reunitisation and the number-line representation

Centre for Mathematics and Science Education, QUT, Brisbane, Australia This paper reports on a study in which Years 6 and 10 students were individually interviewed to determine their ability to unitise and reunitise number lines used to represent mixed numbers and improper fractions. Only 16.7% of the students (all Year 6) were successful on all three tasks and, in general, Year 6 students outperformed Year 8 students. The interviews revealed that the remaining students had incomplete, fragmented or non-existent structural knowledge of mixed numbers and improper fractions, and were unable to unitise or reunitise number lines. The implication for teaching is that instruction should focus on providing students with a variety of fraction representations in order to develop rich and flexible schema for all fraction types (mixed numbers, and proper and improper fractions).

Primary students' success on the structured number line

Number lines are part of our everyday life (e.g., thermometers, kitchen scales) and are frequently used in primary mathematics as instructional aids, in texts and for assessment purposes on mathematics tests. There are two major types of number lines; structured number lines, which are the focus of this paper, and empty number lines. Structured number lines represent mathematical information by the placement of marks on a horizontal or vertical line which has been marked into proportional segments (Figure 1). Empty number lines are blank lines which students can use for calculations (Figure 2) and are not discussed further here (see van den Heuvel-Panhuizen, 2008, on the role of empty number lines). In this article, we will focus on how students’ knowledge of the structured number line develops and how they become successful users of this mathematical tool.

Representational change and strategy use in children's number line estimation during the first years of primary school

Background: The objective of this study was to scrutinize number line estimation behaviors displayed by children in mathematics classrooms during the first three years of schooling. We extend existing research by not only mapping potential logarithmic-linear shifts but also provide a new perspective by studying in detail the estimation strategies of individual target digits within a number range familiar to children. Methods: Typically developing children (n = 67) from Years 1 – 3 completed a number-to-position numerical estimation task (0-20 number line). Estimation behaviors were first analyzed via logarithmic and linear regression modeling. Subsequently, using an analysis of variance we compared the estimation accuracy of each digit, thus identifying target digits that were estimated with the assistance of arithmetic strategy. Results: Our results further confirm a developmental logarithmic-linear shift when utilizing regression modeling; however, uniquely we have identified that children employ variable strategies when completing numerical estimation, with levels of strategy advancing with development. Conclusion: In terms of the existing cognitive research, this strategy factor highlights the limitations of any regression modeling approach, or alternatively, it could underpin the developmental time course of the logarithmic-linear shift. Future studies need to systematically investigate this relationship and also consider the implications for educational practice.

Early mathematical learning: Number processing skills and executive function at 5 and 8 years of age

This research investigated differences and associations in performance in number processing and executive function for children attending primary school in a large Australian metropolitan city. In a cross-sectional study, performance of 25 children in the first full-time year of school, (Prep; mean age = 5.5 years) and 21 children in Year 3 (mean age = 8.5 years) completed three number processing tasks and three executive function tasks. Year 3 children consistently outperformed the Prep year children on measures of accuracy and reaction time, on the tasks of number comparison, calculation, shifting, and inhibition but not on number line estimation. The components of executive function (shifting, inhibition, and working memory) showed different patterns of correlation to performance on number processing tasks across the early years of school. Findings could be used to enhance teachers’ understanding about the role of the cognitive processes employed by children in numeracy learning, and so inform teachers’ classroom practices.

Close-quarters Quadrotor flying for a pole inspection with position based visual servoing and high-speed vision

This paper presents a 100 Hz monocular position based visual servoing system to control a quadrotor flying in close proximity to vertical structures approximating a narrow, locally linear shape. Assuming the object boundaries are represented by parallel vertical lines in the image, detection and tracking is achieved using Plücker line representation and a line tracker. The visual information is fused with IMU data in an EKF framework to provide fast and accurate state estimation. A nested control design provides position and velocity control with respect to the object. Our approach is aimed at high performance on-board control for applications allowing only small error margins and without a motion capture system, as required for real world infrastructure inspection. Simulated and ground-truthed experimental results are presented.

A model eliciting framework for integrating mathematics and robotics learning

Robotics is taught in many Australian ICT classrooms, in both primary and secondary schools. Robotics activities, including those developed using the LEGO Mindstorms NXT technology, are mathematics-rich and provide a fertile round for learners to develop and extend their mathematical thinking. However, this context for learning mathematics is often under-exploited. In this paper a variant of the model construction sequence (Lesh, Cramer, Doerr, Post, & Zawojewski, 2003) is proposed, with the purpose of explicitly integrating robotics and mathematics teaching and learning. Lesh et al.’s model construction sequence and the model eliciting activities it embeds were initially researched in primary mathematics classrooms and more recently in university engineering courses. The model construction sequence involves learners working collaboratively upon product-focussed tasks, through which they develop and expose their conceptual understanding. The integrating model proposed in this paper has been used to design and analyse a sequence of activities in an Australian Year 4 classroom. In that sequence more traditional classroom learning was complemented by the programming of LEGO-based robots to ‘act out’ the addition and subtraction of simple fractions (tenths) on a number-line. The framework was found to be useful for planning the sequence of learning and, more importantly, provided the participating teacher with the ability to critically reflect upon robotics technology as a tool to scaffold the learning of mathematics.

Development of a composite line source emission model for traffic interrupted microenvironments and its application in particle number emissions at a bus station

A composite line source emission (CLSE) model was developed to specifically quantify exposure levels and describe the spatial variability of vehicle emissions in traffic interrupted microenvironments. This model took into account the complexity of vehicle movements in the queue, as well as different emission rates relevant to various driving conditions (cruise, decelerate, idle and accelerate), and it utilised multi-representative segments to capture the accurate emission distribution for real vehicle flow. Hence, this model was able to quickly quantify the time spent in each segment within the considered zone, as well as the composition and position of the requisite segments based on the vehicle fleet information, which not only helped to quantify the enhanced emissions at critical locations, but it also helped to define the emission source distribution of the disrupted steady flow for further dispersion modelling. The model then was applied to estimate particle number emissions at a bi-directional bus station used by diesel and compressed natural gas fuelled buses. It was found that the acceleration distance was of critical importance when estimating particle number emission, since the highest emissions occurred in sections where most of the buses were accelerating and no significant increases were observed at locations where they idled. It was also shown that emissions at the front end of the platform were 43 times greater than at the rear of the platform. Although the CLSE model is intended to be applied in traffic management and transport analysis systems for the evaluation of exposure, as well as the simulation of vehicle emissions in traffic interrupted microenvironments, the bus station model can also be used for the input of initial source definitions in future dispersion models.

Rural and remote road safety study : final report

• Introduction: Concern and action for rural road safety is relatively new in Australia in comparison to the field of traffic safety as a whole. In 2003, a program of research was begun by the Centre for Accident Research and Road Safety - Queensland (CARRS-Q) and the Rural Health Research Unit (RHRU) at James Cook University to investigate factors contributing to serious rural road crashes in the North Queensland region. This project was funded by the Premier’s Department, Main Roads Department, Queensland Transport, QFleet, Queensland Rail, Queensland Ambulance Service, Department of Natural Resources and Queensland Police Service. Additional funding was provided by NRMA Insurance for a PhD scholarship. In-kind support was provided through the four hospitals used for data collection, namely Cairns Base Hospital, The Townsville Hospital, Mount Isa Hospital and Atherton Hospital.----- The primary aim of the project was to: Identify human factors related to the occurrence of serious traffic incidents in rural and remote areas of Australia, and to the trauma suffered by persons as a result of these incidents, using a sample drawn from a rural and remote area in North Queensland.----- The data and analyses presented in this report are the core findings from two broad studies: a general examination of fatalities and casualties from rural and remote crashes for the period 1 March 2004 until 30 June 2007, and a further linked case-comparison study of hospitalised patients compared with a sample of non-crash-involved drivers.----- • Method: The study was undertaken in rural North Queensland, as defined by the Australian Bureau of Statistics (ABS) statistical divisions of North Queensland, Far North Queensland and North-West Queensland. Urban areas surrounding Townsville, Thuringowa and Cairns were not included. The study methodology was centred on serious crashes, as defined by a resulting hospitalisation for 24 hours or more and/or a fatality. Crashes meeting this criteria within the North Queensland region between 1 March 2004 and 30 June 2007 were identified through hospital records and interviewed where possible. Additional data was sourced from coroner’s reports, the Queensland Transport road crash database, the Queensland Ambulance Service and the study hospitals in the region.----- This report is divided into chapters corresponding to analyses conducted on the collected crash and casualty data.----- Chapter 3 presents an overview of all crashes and casualties identified during the study period. Details are presented in regard to the demographics and road user types of casualties; the locations, times, types, and circumstances of crashes; along with the contributing circumstances of crashes.----- Chapter 4 presents the results of summary statistics for all casualties for which an interview was able to be conducted. Statistics are presented separately for drivers and riders, passengers, pedestrians and cyclists. Details are also presented separately for drivers and riders crashing in off-road and on-road settings. Results from questionnaire data are presented in relation to demographics; the experience of the crash in narrative form; vehicle characteristics and maintenance; trip characteristics (e.g. purpose and length of journey; periods of fatigue and monotony; distractions from driving task); driving history; alcohol and drug use; medical history; driving attitudes, intentions and behaviour; attitudes to enforcement; and experience of road safety advertising.----- Chapter 5 compares the above-listed questionnaire results between on-road crash-involved casualties and interviews conducted in the region with non-crash-involved persons. Direct comparisons as well as age and sex adjusted comparisons are presented.----- Chapter 6 presents information on those casualties who were admitted to one of the study hospitals during the study period. Brief information is given regarding the demographic characteristics of these casualties. Emergency services’ data is used to highlight the characteristics of patient retrieval and transport to and between hospitals. The major injuries resulting from the crashes are presented for each region of the body and analysed by vehicle type, occupant type, seatbelt status, helmet status, alcohol involvement and nature of crash. Estimates are provided of the costs associated with in-hospital treatment and retrieval.----- Chapter 7 describes the characteristics of the fatal casualties and the nature and circumstances of the crashes. Demographics, road user types, licence status, crash type and contributing factors for crashes are presented. Coronial data is provided in regard to contributing circumstances (including alcohol, drugs and medical conditions), cause of death, resulting injuries, and restraint and helmet use.----- Chapter 8 presents the results of a comparison between casualties’ crash descriptions and police-attributed crash circumstances. The relative frequency of contributing circumstances are compared both broadly within the categories of behavioural, environmental, vehicle related, medical and other groupings and specifically for circumstances within these groups.----- Chapter 9 reports on the associated research projects which have been undertaken on specific topics related to rural road safety.----- Finally, Chapter 10 reports on the conclusions and recommendations made from the program of research.---- • Major Recommendations : From the findings of these analyses, a number of major recommendations were made: + Male drivers and riders - Male drivers and riders should continue to be the focus of interventions, given their very high representation among rural and remote road crash fatalities and serious injuries.----- - The group of males aged between 30 and 50 years comprised the largest number of casualties and must also be targeted for change if there is to be a meaningful improvement in rural and remote road safety.----- + Motorcyclists - Single vehicle motorcycle crashes constitute over 80% of serious, on-road rural motorcycle crashes and need particular attention in development of policy and infrastructure.----- - The motorcycle safety consultation process currently being undertaken by Queensland Transport (via the "Motorbike Safety in Queensland - Consultation Paper") is strongly endorsed. As part of this process, particular attention needs to be given to initiatives designed to reduce rural and single vehicle motorcycle crashes.----- - The safety of off-road riders is a serious problem that falls outside the direct responsibility of either Transport or Health departments. Responsibility for this issue needs to be attributed to develop appropriate policy, regulations and countermeasures.----- + Road safety for Indigenous people - Continued resourcing and expansion of The Queensland Aboriginal Peoples and Torres Strait Islander Peoples Driver Licensing Program to meet the needs of remote and Indigenous communities with significantly lower licence ownership levels.----- - Increased attention needs to focus on the contribution of geographic disadvantage (remoteness) factors to remote and Indigenous road trauma.----- + Road environment - Speed is the ‘final common pathway’ in determining the severity of rural and remote crashes and rural speed limits should be reduced to 90km/hr for sealed off-highway roads and 80km/hr for all unsealed roads as recommended in the Austroads review and in line with the current Tasmanian government trial.----- - The Department of Main Roads should monitor rural crash clusters and where appropriate work with local authorities to conduct relevant audits and take mitigating action. - The international experts at the workshop reviewed the data and identified the need to focus particular attention on road design management for dangerous curves. They also indicated the need to maximise the use of audio-tactile linemarking (audible lines) and rumble strips to alert drivers to dangerous conditions and behaviours.----- + Trauma costs - In accordance with Queensland Health priorities, recognition should be given to the substantial financial costs associated with acute management of trauma resulting from serious rural and remote crashes.----- - Efforts should be made to develop a comprehensive, regionally specific costing formula for road trauma that incorporates the pre-hospital, hospital and post-hospital phases of care. This would inform health resource allocation and facilitate the evaluation of interventions.----- - The commitment of funds to the development of preventive strategies to reduce rural and remote crashes should take into account the potential cost savings associated with trauma.----- - A dedicated study of the rehabilitation needs and associated personal and healthcare costs arising from rural and remote road crashes should be undertaken.----- + Emergency services - While the study has demonstrated considerable efficiency in the response and retrieval systems of rural and remote North Queensland, relevant Intelligent Transport Systems technologies (such as vehicle alarm systems) to improve crash notification should be both developed and evaluated.----- + Enforcement - Alcohol and speed enforcement programs should target the period between 2 and 6pm because of the high numbers of crashes in the afternoon period throughout the rural region.----- + Drink driving - Courtesy buses should be advocated and schemes such as the Skipper project promoted as local drink driving countermeasures in line with the very high levels of community support for these measures identified in the hospital study.------ - Programs should be developed to target the high levels of alcohol consumption identified in rural and remote areas and related involvement in crashes.----- - Referrals to drink driving rehabilitation programs should be mandated for recidivist offenders.----- + Data requirements - Rural and remote road crashes should receive the same quality of attention as urban crashes. As such, it is strongly recommended that increased resources be committed to enable dedicated Forensic Crash Units to investigate rural and remote fatal and serious injury crashes.----- - Transport department records of rural and remote crashes should record the crash location using the national ARIA area classifications used by health departments as a means to better identifying rural crashes.----- - Rural and remote crashes tend to be unnoticed except in relatively infrequent rural reviews. They should receive the same level of attention and this could be achieved if fatalities and fatal crashes were coded by the ARIA classification system and included in regular crash reporting.----- - Health, Transport and Police agencies should collect a common, minimal set of data relating to road crashes and injuries, including presentations to small rural and remote health facilities.----- + Media and community education programmes - Interventions seeking to highlight the human contribution to crashes should be prioritised. Driver distraction, alcohol and inappropriate speed for the road conditions are key examples of such behaviours.----- - Promotion of basic safety behaviours such as the use of seatbelts and helmets should be given a renewed focus.----- - Knowledge, attitude and behavioural factors that have been identified for the hospital Brief Intervention Trial should be considered in developing safety campaigns for rural and remote people. For example challenging the myth of the dangerous ‘other’ or ‘non-local’ driver.----- - Special educational initiatives on the issues involved in rural and remote driving should be undertaken. For example the material used by Main Roads, the Australian Defence Force and local initiatives.

Increase in particle number emissions from motor vehicles due to interruption of steady traffic flow

We assess the increase in particle number emissions from motor vehicles driving at steady speed when forced to stop and accelerate from rest. Considering the example of a signalized pedestrian crossing on a two-way single-lane urban road, we use a complex line source method to calculate the total emissions produced by a specific number and mix of light petrol cars and diesel passenger buses and show that the total emissions during a red light is significantly higher than during the time when the light remains green. Replacing two cars with one bus increased the emissions by over an order of magnitude. Considering these large differences, we conclude that the importance attached to particle number emissions in traffic management policies be reassessed in the future.

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.

Evaluation of aerial remote sensing techniques for vegetation management in power line corridors

The following paper presents an evaluation of airborne sensors for use in vegetation management in powerline corridors. Three integral stages in the management process are addressed including, the detection of trees, relative positioning with respect to the nearest powerline and vegetation height estimation. Image data, including multi-spectral and high resolution, are analyzed along with LiDAR data captured from fixed wing aircraft. Ground truth data is then used to establish the accuracy and reliability of each sensor thus providing a quantitative comparison of sensor options. Tree detection was achieved through crown delineation using a Pulse-Coupled Neural Network (PCNN) and morphologic reconstruction applied to multi-spectral imagery. Through testing it was shown to achieve a detection rate of 96%, while the accuracy in segmenting groups of trees and single trees correctly was shown to be 75%. Relative positioning using LiDAR achieved a RMSE of 1.4m and 2.1m for cross track distance and along track position respectively, while Direct Georeferencing achieved RMSE of 3.1m in both instances. The estimation of pole and tree heights measured with LiDAR had a RMSE of 0.4m and 0.9m respectively, while Stereo Matching achieved 1.5m and 2.9m. Overall a small number of poles were missed with detection rates of 98% and 95% for LiDAR and Stereo Matching.

Getting it [on]line : sociological implications of e-dating

This article explores the role of sociology in understanding the phenomenon of online dating. Based on an examination of our qualitative study of 23 online daters, combined with the findings of the small number of other empirical studies available, we argue that further sociological consideration of the online dating phenomenon is required to: illuminate the social conditions informing these activities; enhance knowledge of if, and how, online technologies mediate intimate connections; and advance a critically informed understanding of the nature of intimacy in a global era.

RatSLAM on the edge : revealing a coherent representation from an overloaded rat brain

The RatSLAM system can perform vision based SLAM using a computational model of the rodent hippocampus. When the number of pose cells used to represent space in RatSLAM is reduced, artifacts are introduced that hinder its use for goal directed navigation. This paper describes a new component for the RatSLAM system called an experience map, which provides a coherent representation for goal directed navigation. Results are presented for two sets of real world experiments, including comparison with the original goal memory system's performance in the same environment. Preliminary results are also presented demonstrating the ability of the experience map to adapt to simple short term changes in the environment.

The development of an on-line module for students on “Working in Inter-cultural Teams”

Since 2005 QUT through a number of large Teaching and Learning Grants has sponsored a range of teamwork learning initiatives to assist students to develop the teamwork skills demanded by industry. After a suite of six online team learning modules was developed, first year unit coordinators requested an additional module to address the challenges of working with the diverse range of social, cultural and personal values that students from different backgrounds bring to student teams. The Intercultural Teams module asks students to map themselves against a Cultural Orientations Framework so they can understand their own cultural beliefs. By learning about other cultural orientations and comparing and analysing their effects, team members can develop communication and team process management strategies to leverage their differences to realise effective and creative outcomes. The interactive session will demonstrate the elements of the Intercultural Teams module and ask participants to consider ways the module can be integrated into classroom learning to support the development of students’ intercultural competencies.