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).

Visual impairment, postural stability and falls among older adults with glaucoma

Purpose: To investigate the impact of glaucomatous visual impairment on postural sway and falls among older adults.Methods: The sample comprised 72 community-dwelling older adults with open-angle glaucoma, aged 74.0 5.8 years (range 62 to 90 years). Measures of visual function included binocular visual acuity (high-contrast), binocular contrast sensitivity (Pelli- Robson) and binocular visual fields (merged monocular HFA 24-2 SITA-Std). Postural stability was assessed under four conditions: eyes open and closed, on a firm and on a foam surface. Falls were monitored for six months with prospective falls diaries. Regression models, adjusting for age and gender, examined the association between vision measures and postural stability (linear regression) and the number of falls (negative binomial regression). Results: Greater visual field loss was significantly associated with poorer postural stability with eyes open, both on firm (r = 0.34, p < 0.01) and foam (r = 0.45, p < 0.001) surfaces. Eighteen (25 per cent) participants experienced at least one fall: 12 (17 per cent) participants fell only once and six (eight per cent) participants fell two or more times (up to five falls). Visual field loss was significantly associated with falling; the rate of falls doubled for every 10 dB reduction in field sensitivity (rate ratio = 1.08, 95% CI = 1.02–1.13). Importantly, in a model comprising upper and lower field sensitivity, only lower field loss was significantly associated with the number of falls (rate ratio = 1.17, 95% CI = 1.04–1.33). Conclusions: Binocular visual field loss was significantly associated with postural instability and falls among older adults with glaucoma. These findings provide valuable directions for developing falls risk assessment and falls prevention strategies for this population.

Critical analysis of high particle number emissions from accelerating compressed natural gas buses

Compressed natural gas (CNG) engines are thought to be less harmful to the environment than conventional diesel engines, especially in terms of particle emissions. Although, this is true with respect to particulate matter (PM) emissions, results of particle number (PN) emission comparisons have been inconclusive. In this study, results of on-road and dynamometer studies of buses were used to derive several important conclusions. We show that, although PN emissions from CNG buses are significantly lower than from diesel buses at low engine power, they become comparable at high power. For diesel buses, PN emissions are not significantly different between acceleration and operation at steady maximum power. However, the corresponding PN emissions from CNG buses when accelerating are an order of magnitude greater than when operating at steady maximum power. During acceleration under heavy load, PN emissions from CNG buses are an order of magnitude higher than from diesel buses. The particles emitted from CNG buses are too small to contribute to PM10 emissions or contribute to a reduction of visibility, and may consist of semivolatile nanoparticles.

Characterization of particle number concentrations and PM2.5 in a school : influence of outdoor air pollution on indoor air

Background, Aim and Scope The impact of air pollution on school children’s health is currently one of the key foci of international and national agencies. Of particular concern are ultrafine particles which are emitted in large quantities, contain large concentrations of toxins and are deposited deeply in the respiratory tract. Materials and methods In this study, an intensive sampling campaign of indoor and outdoor airborne particulate matter was carried out in a primary school in February 2006 to investigate indoor and outdoor particle number (PN) and mass concentrations (PM2.5), and particle size distribution, and to evaluate the influence of outdoor air pollution on the indoor air. Results For outdoor PN and PM2.5, early morning and late afternoon peaks were observed on weekdays, which are consistent with traffic rush hours, indicating the predominant effect of vehicular emissions. However, the temporal variations of outdoor PM2.5 and PN concentrations occasionally showed extremely high peaks, mainly due to human activities such as cigarette smoking and the operation of mower near the sampling site. The indoor PM2.5 level was mainly affected by the outdoor PM2.5 (r = 0.68, p<0.01), whereas the indoor PN concentration had some association with outdoor PN values (r = 0.66, p<0.01) even though the indoor PN concentration was occasionally influenced by indoor sources, such as cooking, cleaning and floor polishing activities. Correlation analysis indicated that the outdoor PM2.5 was inversely correlated with the indoor to outdoor PM2.5 ratio (I/O ratio) (r = -0.49, p<0.01), while the indoor PN had a weak correlation with the I/O ratio for PN (r = 0.34, p<0.01). Discussion and Conclusions The results showed that occupancy did not cause any major changes to the modal structure of particle number and size distribution, even though the I/O ratio was different for different size classes. The I/O curves had a maximum value for particles with diameters of 100 – 400 nm under both occupied and unoccupied scenarios, whereas no significant difference in I/O ratio for PM2.5 was observed between occupied and unoccupied conditions. Inspection of the size-resolved I/O ratios in the preschool centre and the classroom suggested that the I/O ratio in the preschool centre was the highest for accumulation mode particles at 600 nm after school hours, whereas the average I/O ratios of both nucleation mode and accumulation mode particles in the classroom were much lower than those of Aitken mode particles. Recommendations and Perspectives The findings obtained in this study are useful for epidemiological studies to estimate the total personal exposure of children, and to develop appropriate control strategies for minimizing the adverse health effects on school children.

Ions in motor vehicle exhaust and their dispersion near busy roads

Measurements in the exhaust plume of a petrol-driven motor car showed that molecular cluster ions of both signs were present in approximately equal amounts. The emission rate increased sharply with engine speed while the charge symmetry remained unchanged. Measurements at the kerbside of nine motorways and five city roads showed that the mean total cluster ion concentration near city roads (603 cm-3) was about one-half of that near motorways (1211 cm-3) and about twice as high as that in the urban background (269 cm-3). Both positive and negative ion concentrations near a motorway showed a significant linear increase with traffic density (R2=0.3 at p<0.05) and correlated well with each other in real time (R2=0.87 at p<0.01). Heavy duty diesel vehicles comprised the main source of ions near busy roads. Measurements were conducted as a function of downwind distance from two motorways carrying around 120-150 vehicles per minute. Total traffic-related cluster ion concentrations decreased rapidly with distance, falling by one-half from the closest approach of 2m to 5m of the kerb. Measured concentrations decreased to background at about 15m from the kerb when the wind speed was 1.3 m s-1, this distance being greater at higher wind speed. The number and net charge concentrations of aerosol particles were also measured. Unlike particles that were carried downwind to distances of a few hundred metres, cluster ions emitted by motor vehicles were not present at more than a few tens of metres from the road.

Exposure to particle number, surface area and PM concentrations in pizzerias

The aim of this work was to quantify exposure to particles emitted by wood-fired ovens in pizzerias. Overall, 15 microenvironments were chosen and analyzed in a 14-month experimental campaign. Particle number concentration and distribution were measured simultaneously using a Condensation Particle Counter (CPC), a Scanning Mobility Particle Sizer (SMPS), an Aerodynamic Particle Sizer (APS). The surface area and mass distributions and concentrations, as well as the estimation of lung deposition surface area and PM1 were evaluated using the SMPS-APS system with dosimetric models, by taking into account the presence of aggregates on the basis of the Idealized Aggregate (IA) theory. The fraction of inhaled particles deposited in the respiratory system and different fractions of particulate matter were also measured by means of a Nanoparticle Surface Area Monitor (NSAM) and a photometer (DustTrak DRX), respectively. In this way, supplementary data were obtained during the monitoring of trends inside the pizzerias. We found that surface area and PM1 particle concentrations in pizzerias can be very high, especially when compared to other critical microenvironments, such as the transport hubs. During pizza cooking under normal ventilation conditions, concentrations were found up to 74, 70 and 23 times higher than background levels for number, surface area and PM1, respectively. A key parameter is the oven shape factor, defined as the ratio between the size of the face opening in respect

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.

Functional status, postural stability and falls among older adults with glaucoma

Visual impairment is an important contributing factor in falls among older adults, which is one of the leading causes of injury and injury-related death in this population. Visual impairment is also associated with greater disability among older adults, including poorer health-related quality of life, increased frailty and reduced postural stability. The majority of this evidence, however, is based on measures of central visual function, rather than peripheral visual function. As such, there is comparatively limited research on the associations between peripheral visual function, disability and falls, and even fewer studies involving older adults with specific diseases which affect peripheral visual function, the most common of which is glaucoma. Glaucoma is one of the leading causes of irreversible vision loss among older adults, affecting around 3 per cent of adults aged over 60 years. The condition is characterised by retinal nerve fibre loss, primarily affecting peripheral visual function. Importantly, the number of older adults with glaucomatous visual impairment is projected to increase as the ageing population grows. The first component of the thesis examined the cross-sectional association between glaucomatous visual impairment and health-related quality of life (Study 1a), functional status (Study 1b) and postural stability (Study 1c) among older adults. A cohort of 74 community-dwelling adults with glaucoma (mean age 74.2 ± 5.9 years) was recruited and completed a baseline assessment. A number of visual function measures was assessed, including central visual function (visual acuity and contrast sensitivity), motion sensitivity, retinal nerve fibre analysis and monocular and binocular visual field measures (monocular 24-2 and binocular integrated visual fields (IVF): IVF-60 and IVF-120). The analyses focused on the associations between the outcomes measures and severity and location of visual field loss, as this is the primary visual function affected by glaucoma. In Study 1a, we examined the association between visual field loss and health-related quality of life, measured by the Short Form 36-item Health Survey (SF-36). Greater binocular visual field loss, on both IVF measures, was associated with lower SF-36 physical component scores, adjusted for age and gender (Pearson's r =|0.32| to |0.36|, p<0.001). Furthermore, inferior visual field loss was more strongly associated with the SF-36 physical component than superior field loss. No association was found between visual field loss and SF-36 mental component scores. The association between visual field loss and functional status was examined in Study 1b. Functional status outcomes measures included a physical activity questionnaire (Physical Activity Scale for the Elderly, PASE), performance tests (six-minute walk test, timed up and go test and lower leg strength) and an overall functional status score. Significant, but weak, correlations were found between binocular visual field loss and PASE and overall functional status scores, adjusted for age and gender (Pearson's r =|0.24| to |0.33|, p<0.05). Greater inferior visual field loss, independent of superior visual field loss, was significantly associated with poorer physical performance results and lower overall functional status scores. In Study 1c, we examined the association between visual field loss and postural stability, using a swaymeter device which recorded body movement during four conditions: eyes open and closed, on a firm and foam surface. Greater binocular visual field loss was associated with increased postural sway, both on firm and foam surfaces, independent of age and gender (Pearson’s r =|0.44| to |0.46|, p <0.001). Furthermore, inferior visual field was a stronger contributor to postural stability, more so than the superior visual field, particularly on the foam condition with the eyes open. Greater visual field loss was associated with a reduction in the visual contribution to postural sway, which underlies the observed association with postural sway. The second component of the thesis examined the association between severity and location of visual field loss and falls during a 12-month longitudinal follow-up. The number of falls was assessed prospectively using monthly fall calendars. Of the 71 participants who successfully completed the follow up (mean age 73.9 ± 5.7 years), 44% reported one or more falls, and around 20% reported two or more falls. After adjusting for age and gender, every 10 points missed on the IVF-120 increased the rate of falls by 25% (rate ratio 1.25, 95% confidence interval 1.08 - 1.44) or every 5dB reduction in IVF-60 increased the rate of falls by 47% (rate ratio 1.47, 95% confidence interval 1.16 - 1.87). Inferior visual field loss was a significant predictor of falls, more so than superior field loss, highlighting the importance of the inferior visual field area in safe and efficient navigation. Further analyses indicated that postural stability, more so than functional status, may be a potential mediating factor in the relationship between visual field loss and falls. Future research is required to confirm this causal pathway. In addition, the use of topical beta-blocker medications was not associated with an increased rate of falls in this cohort, compared with the use of other topical anti-glaucoma medications. In summary, greater binocular visual field loss among older adults with glaucoma was associated with poorer health-related quality of life in the physical domain, reduced functional status, greater postural instability and higher rates of falling. When the location of visual field loss was examined, inferior visual field loss was consistently more strongly associated with these outcomes than superior visual field loss. Insights gained from this research improve our understanding of the association between glaucomatous visual field loss and disability, and its link with falls among older adults. The clinical implications of this research include the need to include visual field screening in falls risk assessments among older adults and to raise awareness of these findings to eye care practitioners and adults with glaucoma. The findings also assist in developing further research to examine strategies to reduce disability and prevent falls among older adults with glaucoma to promote healthy ageing and independence for these individuals.

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.

Shifting the technology context : career-change entrants’ transition into teaching

Becoming a teacher in technology-rich classrooms is a complex and challenging transition for career-change entrants. Those with generic or specialist Information and Communication Technology (ICT) expertise bring a mindset about purposeful uses of ICT that enrich student learning and school communities. The transition process from a non-education environment is both enhanced and constrained by shifting the technology context of generic or specialist ICT expertise, developed through a former career as well as general life experience. In developing an understanding of the complexity of classrooms and creating a learner centred way of working, perceptions about learners and learning evolve and shift. Shifts in thinking about how ICT expertise supports learners and enhances learning preceded shifts in perceptions about being a teacher, working with colleagues, and functioning in schools that have varying degrees of intensity and impact on evolving professional identities. Current teacher education and school induction programs are seen to be falling short of meeting the needs of career-change entrants and, as a flow on, the students they nurture. Research (see, for example, Tigchelaar, Brouwer, & Korthagen, 2008; Williams & Forgasz, 2009) highlights the value of generic and specialist expertise career-change teachers bring to the profession and draws attention to the challenges such expertise begets (Anthony & Ord, 2008; Priyadharshini & Robinson-Pant, 2003). As such, the study described in this thesis investigated perceptions of career-change entrants, who have generic (Mishra & Koehler, 2006) or specialist expertise, that is, ICT qualifications and work experience in the use of ICT. The career-change entrants‘ perceptions were sought as they shifted the technology context and transitioned into teaching in technology-rich classrooms. The research involved an interpretive analysis of qualitative data and quantitative data. The study used the explanatory case study (Yin, 1994) methodology enriched through grounded theory processes (Strauss & Corbin, 1998), to develop a theory about professional identity transition from the perceptions of the participants in the study. The study provided insights into the expertise and experiences of career change entrants, particularly in relation to how professional identities that include generic and specialist ICT knowledge and expertise were reconfigured while transitioning into the teaching profession. This thesis presents the Professional Identity Transition Theory that encapsulates perceptions about teaching in technology-rich classrooms amongst a selection of the increasing number of career-change entrants. The theory, grounded in the data, (Strauss & Corbin, 1998) proposes that career-change entrants experience transition phases of varying intensity that impact on professional identity, retention and development as a teacher. These phases are linked to a shift in perceptions rather than time as a teacher. Generic and specialist expertise in the use of ICT is a weight of the past and an asset that makes the transition process more challenging for career-change entrants. The study showed that career-change entrants used their experiences and perceptions to develop a way of working in a school community. Their way of working initially had an adaptive orientation focussed on immediate needs as their teaching practice developed. Following a shift of thinking, more generative ways of working focussed on the future emerged to enable continual enhancement and development of practice. Sustaining such learning is a personal, school and systemic challenge for the teaching profession.

Natural balancing of flying capacitor voltages in multicell inverter under PD carrier-based PWM

The flying capacitor multicell inverter (FCMI) possesses natural balancing property. With the phase-shifted (PS) carrier-based scheme, natural balancing can be achieved in a straightforward manner. However, to achieve natural balancing with the harmonically optimal phase-disposition (PD) carrierbased scheme, the conventional approaches require (n-1) x (n-1) trapezoidal carrier signals for an n-level inverter, which is (n-1) x (n-2) times more than that in the standard PD scheme. This paper proposes two improved natural balancing strategies for FMI under PD scheme, which use the same (n-1) carrier signals as used in the standard PD scheme. In the first scheme, on-line detection is performed of the band in which the modulation signal is located, corresponding period number of the carrier, and rising or falling half cycle of the carrier waveform to generate the switching signals based on certain rules. In the second strategy, the output voltage level selection is first processed and the switching signals are then generated according to a rule based on preferential cell selection algorithm. These methods are easy to use and can be simply implemented as compared to the other available methods. Simulation and experimental results are presented for a five-level inverter to verify these proposed schemes.