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.

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).

Place value, multiplicativity, reunitizing and effective classroom teaching of decimal numeration

Student understanding of decimal number is poor (e.g., Baturo, 1998; Behr, Harel, Post & Lesh, 1992). This paper reports on a study which set out to determine the cognitive complexities inherent in decimal-number numeration and what teaching experiences need to be provided in order to facilitate an understanding of decimal-number numeration. The study gave rise to a theoretical model which incorporated three levels of knowledge. Interview tasks were developed from the model to probe 45 students’ understanding of these levels, and intervention episodes undertaken to help students construct the baseline knowledge of position and order (Level 1 knowledge) and an understanding of multiplicative structure (Level 3 knowledge). This paper describes the two interventions and reports on the results which suggest that helping students construct appropriate mental models is an efficient and effective teaching strategy.

An old language for a new landscape

Because aesthetics can have a profound effect upon the human relationship to the non-human environment the importance of aesthetics to ecologically sustainable designed landscapes has been acknowledged. However, in recognition that the physical forms of designed landscapes are an expression of the social values of the time, some design professionals have called for a new aesthetic ― one that reflects these current ecological concerns. To address this, some authors have suggested various theoretical design frameworks upon which such an aesthetic could be based. Within these frameworks there is an underlying theme that the patterns and processes of natural systems have the potential to form a new aesthetic for landscape design —an aesthetic based on fractal rather than Euclidean geometry. Perry, Reeves and Sim (2008) have shown that it is possible to differentiate between different landscape forms by fractal analysis. However, this research also shows that individual scenes from within very different landscape forms can possess the same fractal properties. Early data, revealed by transforming landscape images from the spatial to the frequency domain, using the fast Fourier transform, suggest that fractal patterning can have a significant effect within the landscape. In fact, it may be argued that any landscape design that includes living processes will include some design element whose ultimate form can only be expressed through the mathematics of fractal geometry. This paper will present ongoing research into the potential role of fractal geometry as a basis for a new form language – a language that may articulate an aesthetic for landscape design that echoes our ecological awakening.

How can flexible learning centres use social networking to improve their ongoing educational assessments?

Most online assessment systems now incorporate social networking features, and recent developments in social media spaces include protocols that allow the synchronisation and aggregation of data across multiple user profiles. In light of these advances and the concomitant fear of data sharing in secondary school education this papers provides important research findings about generic features of online social networking, which educators can use to make sound and efficient assessments in collaboration with their students and colleagues. This paper reports on a design experiment in flexible educational settings that challenges the dichotomous legacy of success and failure evident in many assessment activities for at-risk youth. Combining social networking practices with the sociology of education the paper proposes that assessment activities are best understood as a negotiable field of exchange. In this design experiment students, peers and educators engage in explicit, "front-end" assessment (Wyatt-Smith, 2008) to translate digital artefacts into institutional, and potentiality economic capital without continually referring to paper based pre-set criteria. This approach invites students and educators to use social networking functions to assess “work in progress” and final submissions in collaboration, and in doing so assessors refine their evaluative expertise and negotiate the value of student’s work from which new criteria can emerge. The mobile advantages of web-based technologies aggregate, externalise and democratise this transparent assessment model for most, if not all, student work that can be digitally represented.

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.

Implementing change within a school science department: progressive and dissonant voices

The purpose of this study was to describe the teaching and leadership experiences of a science teacher who, as head of department, was preparing to introduce changes in the science department of an independent school in response to the requirements of the new junior science syllabus in Queensland, Australia. This teacher consented to classroom observations and interviews with the researchers where his beliefs about teaching practice and change were explored. Other science teachers at the school also were interviewed about their reactions to the planned changes. Interpretive analysis of the data provides an account of the complex interactions, negotiations, compromises, concessions, and trade-offs faced by the teacher during a period of education reform. Perceived barriers existing within the school that impeded proposed change are identified

Mining patterns and factors contributing to crash severity on road curves

Road curves are an important feature of road infrastructure and many serious crashes occur on road curves. In Queensland, the number of fatalities is twice as many on curves as that on straight roads. Therefore, there is a need to reduce drivers’ exposure to crash risk on road curves. Road crashes in Australia and in the Organisation for Economic Co-operation and Development(OECD) have plateaued in the last five years (2004 to 2008) and the road safety community is desperately seeking innovative interventions to reduce the number of crashes. However, designing an innovative and effective intervention may prove to be difficult as it relies on providing theoretical foundation, coherence, understanding, and structure to both the design and validation of the efficiency of the new intervention. Researchers from multiple disciplines have developed various models to determine the contributing factors for crashes on road curves with a view towards reducing the crash rate. However, most of the existing methods are based on statistical analysis of contributing factors described in government crash reports. In order to further explore the contributing factors related to crashes on road curves, this thesis designs a novel method to analyse and validate these contributing factors. The use of crash claim reports from an insurance company is proposed for analysis using data mining techniques. To the best of our knowledge, this is the first attempt to use data mining techniques to analyse crashes on road curves. Text mining technique is employed as the reports consist of thousands of textual descriptions and hence, text mining is able to identify the contributing factors. Besides identifying the contributing factors, limited studies to date have investigated the relationships between these factors, especially for crashes on road curves. Thus, this study proposed the use of the rough set analysis technique to determine these relationships. The results from this analysis are used to assess the effect of these contributing factors on crash severity. The findings obtained through the use of data mining techniques presented in this thesis, have been found to be consistent with existing identified contributing factors. Furthermore, this thesis has identified new contributing factors towards crashes and the relationships between them. A significant pattern related with crash severity is the time of the day where severe road crashes occur more frequently in the evening or night time. Tree collision is another common pattern where crashes that occur in the morning and involves hitting a tree are likely to have a higher crash severity. Another factor that influences crash severity is the age of the driver. Most age groups face a high crash severity except for drivers between 60 and 100 years old, who have the lowest crash severity. The significant relationship identified between contributing factors consists of the time of the crash, the manufactured year of the vehicle, the age of the driver and hitting a tree. Having identified new contributing factors and relationships, a validation process is carried out using a traffic simulator in order to determine their accuracy. The validation process indicates that the results are accurate. This demonstrates that data mining techniques are a powerful tool in road safety research, and can be usefully applied within the Intelligent Transport System (ITS) domain. The research presented in this thesis provides an insight into the complexity of crashes on road curves. The findings of this research have important implications for both practitioners and academics. For road safety practitioners, the results from this research illustrate practical benefits for the design of interventions for road curves that will potentially help in decreasing related injuries and fatalities. For academics, this research opens up a new research methodology to assess crash severity, related to road crashes on curves.

The economics of the FIFA Football World Cup

The expansion of economics to ‘non-market topics’ has received increased attention in recent years. The economics of sports (football) is such a sub-field. This paper reports empirical evidence of team and referee performances in the FIFA World Cup 2002. The results reveal that being a hosting nation has a significant impact on the probability of winning a game. Furthermore, the strength of a team measured with the FIFA World Ranking does not play the important role presumed, which indicates that the element of uncertainty is working. The findings also indicate that the influence of a referee on the game result should not be neglected. Finally, the previous World Cup experiences seem to have the strongest impact on referees' performances during the game.

What are students' understandings of how digital tools contribute to learning in design disciplines?

Building Information Modelling (BIM) is evolving in the Construction Industry as a successor to CAD. CAD is mostly a technical tool that conforms to existing industry practices, however BIM has the capacity to revolutionise industry practice. Rather than producing representations of design intent, BIM produces an exact Virtual Prototype of any building that in an ideal situation is centrally stored and freely exchanged between the project team, facilitating collaboration and allowing experimentation in design. Exposing design students to this technology through their formal studies allows them to engage with cutting edge industry practices and to help shape the industry upon their graduation. Since this technology is relatively new to the construction industry, there are no accepted models for how to “teach” BIM effectively at university level. Developing learning models to enable students to make the most out of their learning with BIM presents significant challenges to those teaching in the field of design. To date there are also no studies of students experiences of using this technology. This research reports on the introduction of Building Information Modeling (BIM) software into a second year Bachelor of Design course. This software has the potential to change industry standards through its ability to revolutionise the work practices of those involved in large scale design projects. Students’ understandings and experiences of using the software in order to complete design projects as part of their assessment are reported here. In depth semi-structured interviews with 6 students revealed that students had views that ranged from novice to sophisticate about the software. They had variations in understanding of how the software could be used to complete course requirements, to assist with the design process and in the workplace. They had engaged in limited exploration of the collaborative potential of the software as a design tool. Their understanding of the significance of BIM for the workplace was also variable. The results indicate that students are beginning to develop an appreciation for how BIM could aid or constrain the work of designers, but that this appreciation is highly varied and likely to be dependent on the students’ previous experiences of working in a design studio environment. Their range of understandings of the significance of the technology is a reflection of their level of development as designers (they are “novice” designers). The results also indicate that there is a need for subjects in later years of the course that allow students to specialise in the area of digital design and to develop more sophisticated views of the role of technology in the design process. There is also a need to capitalise on the collaborative potential inherent in the software in order to realise its capability to streamline some aspects of the design process. As students become more sophisticated designers we should explore their understanding of the role of technology as a design tool in more depth in order to make recommendations for improvements to teaching and learning practice related to BIM and other digital design tools.

The relationship between HRM practices and service behaviour in South African service organizations

This paper reports on findings from research conducted in South African service organizations that frontline employees' perceptions of HRM practices have a direct influence on their service behaviour. Specific HRM practices have more impact than others and this was attributed to the influence of external factors such as the socio-political situation and national culture and to internal factors linked to the way managers implemented the HRM practices in the organization. Organizational commitment was found to play a mediating role in the relationship between frontline employees' perceptions of HRM and their service behaviour.

Using concept mapping to scaffold learning for students who experience learning difficulties in science classes

In order to develop scientific literacy students need the cognitive tools that enable them to read and evaluate science texts. One cognitive tool that has been widely used in science education to aid the development of conceptual understanding is concept mapping. However, it has been found some students experience difficulty with concept map construction. This study reports on the development and evaluation of an instructional sequence that was used to scaffold the concept-mapping process when middle school students who were experiencing difficulty with science learning used concept mapping to summarise a chapter of a science text. In this study individual differences in working memory functioning are suggested as one reason that students experience difficulty with concept map construction. The study was conducted using a design-based research methodology in the school’s learning support centre. The analysis of student work samples collected during the two-year study identified some of the difficulties and benefits associated with the use of scaffolded concept mapping with these students. The observations made during this study highlight the difficulty that some students experience with the use of concept mapping as a means of developing an understanding of science concepts and the amount of instructional support that is required for such understanding to develop. Specifically, the findings of the study support the use of multi-component, multi-modal instructional techniques to facilitate the development of conceptual understanding with students who experience difficulty with science learning. In addition, the important roles of interactive dialogue and metacognition in the development of conceptual understanding are identified.

The effect of prolonged reading on visual functions and reading performance in students with low vision

This study is the first to investigate the effect of prolonged reading on reading performance and visual functions in students with low vision. The study focuses on one of the most common modes of achieving adequate magnification for reading by students with low vision, their close reading distance (proximal or relative distance magnification). Close reading distances impose high demands on near visual functions, such as accommodation and convergence. Previous research on accommodation in children with low vision shows that their accommodative responses are reduced compared to normal vision. In addition, there is an increased lag of accommodation for higher stimulus levels as may occur at close reading distance. Reduced accommodative responses in low vision and higher lag of accommodation at close reading distances together could impact on reading performance of students with low vision especially during prolonged reading tasks. The presence of convergence anomalies could further affect reading performance. Therefore, the aims of the present study were 1) To investigate the effect of prolonged reading on reading performance in students with low vision 2) To investigate the effect of prolonged reading on visual functions in students with low vision. This study was conducted as cross-sectional research on 42 students with low vision and a comparison group of 20 students with normal vision, aged 7 to 20 years. The students with low vision had vision impairments arising from a range of causes and represented a typical group of students with low vision, with no significant developmental delays, attending school in Brisbane, Australia. All participants underwent a battery of clinical tests before and after a prolonged reading task. An initial reading-specific history and pre-task measurements that included Bailey-Lovie distance and near visual acuities, Pelli-Robson contrast sensitivity, ocular deviations, sensory fusion, ocular motility, near point of accommodation (pull-away method), accuracy of accommodation (Monocular Estimation Method (MEM)) retinoscopy and Near Point of Convergence (NPC) (push-up method) were recorded for all participants. Reading performance measures were Maximum Oral Reading Rates (MORR), Near Text Visual Acuity (NTVA) and acuity reserves using Bailey-Lovie text charts. Symptoms of visual fatigue were assessed using the Convergence Insufficiency Symptom Survey (CISS) for all participants. Pre-task measurements of reading performance and accuracy of accommodation and NPC were compared with post-task measurements, to test for any effects of prolonged reading. The prolonged reading task involved reading a storybook silently for at least 30 minutes. The task was controlled for print size, contrast, difficulty level and content of the reading material. Silent Reading Rate (SRR) was recorded every 2 minutes during prolonged reading. Symptom scores and visual fatigue scores were also obtained for all participants. A visual fatigue analogue scale (VAS) was used to assess visual fatigue during the task, once at the beginning, once at the middle and once at the end of the task. In addition to the subjective assessments of visual fatigue, tonic accommodation was monitored using a photorefractor (PlusoptiX CR03™) every 6 minutes during the task, as an objective assessment of visual fatigue. Reading measures were done at the habitual reading distance of students with low vision and at 25 cms for students with normal vision. The initial history showed that the students with low vision read for significantly shorter periods at home compared to the students with normal vision. The working distances of participants with low vision ranged from 3-25 cms and half of them were not using any optical devices for magnification. Nearly half of the participants with low vision were able to resolve 8-point print (1M) at 25 cms. Half of the participants in the low vision group had ocular deviations and suppression at near. Reading rates were significantly reduced in students with low vision compared to those of students with normal vision. In addition, there were a significantly larger number of participants in the low vision group who could not sustain the 30-minute task compared to the normal vision group. However, there were no significant changes in reading rates during or following prolonged reading in either the low vision or normal vision groups. Individual changes in reading rates were independent of their baseline reading rates, indicating that the changes in reading rates during prolonged reading cannot be predicted from a typical clinical assessment of reading using brief reading tasks. Contrary to previous reports the silent reading rates of the students with low vision were significantly lower than their oral reading rates, although oral and silent reading was assessed using different methods. Although the visual acuity, contrast sensitivity, near point of convergence and accuracy of accommodation were significantly poorer for the low vision group compared to those of the normal vision group, there were no significant changes in any of these visual functions following prolonged reading in either group. Interestingly, a few students with low vision (n =10) were found to be reading at a distance closer than their near point of accommodation. This suggests a decreased sensitivity to blur. Further evaluation revealed that the equivalent intrinsic refractive errors (an estimate of the spherical dioptirc defocus which would be expected to yield a patient’s visual acuity in normal subjects) were significantly larger for the low vision group compared to those of the normal vision group. As expected, accommodative responses were significantly reduced for the low vision group compared to the expected norms, which is consistent with their close reading distances, reduced visual acuity and contrast sensitivity. For those in the low vision group who had an accommodative error exceeding their equivalent intrinsic refractive errors, a significant decrease in MORR was found following prolonged reading. The silent reading rates however were not significantly affected by accommodative errors in the present study. Suppression also had a significant impact on the changes in reading rates during prolonged reading. The participants who did not have suppression at near showed significant decreases in silent reading rates during and following prolonged reading. This impact of binocular vision at near on prolonged reading was possibly due to the high demands on convergence. The significant predictors of MORR in the low vision group were age, NTVA, reading interest and reading comprehension, accounting for 61.7% of the variances in MORR. SRR was not significantly influenced by any factors, except for the duration of the reading task sustained; participants with higher reading rates were able to sustain a longer reading duration. In students with normal vision, age was the only predictor of MORR. Participants with low vision also reported significantly greater visual fatigue compared to the normal vision group. Measures of tonic accommodation however were little influenced by visual fatigue in the present study. Visual fatigue analogue scores were found to be significantly associated with reading rates in students with low vision and normal vision. However, the patterns of association between visual fatigue and reading rates were different for SRR and MORR. The participants with low vision with higher symptom scores had lower SRRs and participants with higher visual fatigue had lower MORRs. As hypothesized, visual functions such as accuracy of accommodation and convergence did have an impact on prolonged reading in students with low vision, for students whose accommodative errors were greater than their equivalent intrinsic refractive errors, and for those who did not suppress one eye. Those students with low vision who have accommodative errors higher than their equivalent intrinsic refractive errors might significantly benefit from reading glasses. Similarly, considering prisms or occlusion for those without suppression might reduce the convergence demands in these students while using their close reading distances. The impact of these prescriptions on reading rates, reading interest and visual fatigue is an area of promising future research. Most importantly, it is evident from the present study that a combination of factors such as accommodative errors, near point of convergence and suppression should be considered when prescribing reading devices for students with low vision. Considering these factors would also assist rehabilitation specialists in identifying those students who are likely to experience difficulty in prolonged reading, which is otherwise not reflected during typical clinical reading assessments.

The Australian nonprofit sector legal almanac 2009, ACPNS Working Paper 49

There are a number of publications in Australian which summarises annual developments n the law for business or various industries, but little is available in accessible form for nonprofit staff, boards or volunteers. This publication seeks to fill that gap by bringing together in one place case reports and significant legislative initiatives.