Reconceptualizing Early Mathematics Learning : The Fundamental Role of Pattern and Structure

The Pattern and Structure Mathematics Awareness Program (PASMAP) was developed concurrently with the studies of AMPS and the development of the Pattern and Structure Assessment (PASA) interview. We summarize some early classroom-based teaching studies and describe the PASMAP that resulted. A large-scale two-year longitudinal study, Reconceptualizing Early Mathematics Learning (REML) resulted. We provide an overview of the REML study and discuss the consequences for our view of early mathematics learning. A purposive sample of four large primary schools, two in Sydney and two in Brisbane, representing 316 students from diverse socio-economic and cultural contexts, participated in an evaluation of the PASMAP intervention throughout the 2009 school year and a follow-up assessment in 2010. Two different mathematics programs were implemented: in each school, two Kindergarten teachers implemented the PASMAP and another two implemented their regular program. The study shows that both groups of students made substantial gains on the ‘I Can Do Maths’ standardized assessment and the PASA interview, but highly significant differences were found on the latter with PASMAP students outperforming the regular group on PASA scores. Qualitative analysis of students’ responses for structural development showed increased levels for the PASMAP students. Implications for pedagogy and curriculum are discussed.

Exploring the fundamental theorem of arithmetic in excel 2007

This paper discusses how fundamentals of number theory, such as unique prime factorization and greatest common divisor can be made accessible to secondary school students through spreadsheets. In addition, the three basic multiplicative functions of number theory are defined and illustrated through a spreadsheet environment. Primes are defined simply as those natural numbers with just two divisors. One focus of the paper is to show the ease with which spreadsheets can be used to introduce students to some basics of elementary number theory. Complete instructions are given to build a spreadsheet to enable the user to input a positive integer, either with a slider or manually, and see the prime decomposition. The spreadsheet environment allows students to observe patterns, gain structural insight, form and test conjectures, and solve problems in elementary number theory.

Exploration of the fundamental equilibrium behaviour of calcium exchange with weak acid cation resins

This study evaluated the complexity of calcium ion exchange with sodium exchanged weak acid cation resin (DOW MAC-3). Exchange equilibria recorded for a range of different solution normalities revealed profiles which were represented by conventional “L” or “H” type isotherms at low values of equilibrium concentration (Ce) of calcium ions, plus a superimposed region of increasing calcium uptake was observed at high Ce values. The loading of calcium ions was determined to be ca. 53.5 to 58.7 g/kg of resin when modelling only the sorption curve created at low Ce values,which exhibited a well-defined plateau. The calculated calcium ion loading capacity for DOWMAC-3 resin appeared to correlate with the manufacturer's recommendation. The phenomenon of super equivalent ion exchange (SEIX) was observed when the “driving force” for the exchange process was increased in excess of 2.25 mmol calcium ions per gram of resin in the starting solution. This latter event was explained in terms of displacement of sodium ions from sodium hydroxide solution which remained in the resin bead following the initial conversion of the as supplied “H+” exchanged resin sites to the “Na+” version required for softening studies. Evidence for hydrolysis of a small fraction of the sites on the sodium exchanged resin surface was noted. The importance of carefully choosing experimental parameters was discussed especially in relation to application of the Langmuir–Vageler expression. This latter model which compared the ratio of the initial calcium ion concentration in solution to resin mass, versus final equilibrium loading of the calcium ions on the resin; was discovered to be an excellent means of identifying the progress of the calcium–sodium ion exchange process. Moreover, the Langmuir–Vageler model facilitated standardization of various calcium–sodium ion exchange experiments which allowed systematic experimental design.

The 4C spectrum of fundamental behavioral relations for concurrent systems

The design of concurrent software systems, in particular process-aware information systems, involves behavioral modeling at various stages. Recently, approaches to behavioral analysis of such systems have been based on declarative abstractions defined as sets of behavioral relations. However, these relations are typically defined in an ad-hoc manner. In this paper, we address the lack of a systematic exploration of the fundamental relations that can be used to capture the behavior of concurrent systems, i.e., co-occurrence, conflict, causality, and concurrency. Besides the definition of the spectrum of behavioral relations, which we refer to as the 4C spectrum, we also show that our relations give rise to implication lattices. We further provide operationalizations of the proposed relations, starting by proposing techniques for computing relations in unlabeled systems, which are then lifted to become applicable in the context of labeled systems, i.e., systems in which state transitions have semantic annotations. Finally, we report on experimental results on efficiency of the proposed computations.

The Coming of Post-reflexive Society: Commodification and Language in Digital Capitalism

Language is a unique aspect of human communication because it can be used to discuss itself in its own terms. For this reason, human societies potentially have superior capacities of co-ordination, reflexive self-correction, and innovation than other animal, physical or cybernetic systems. However, this analysis also reveals that language is interconnected with the economically and technologically mediated social sphere and hence is vulnerable to abstraction, objectification, reification, and therefore ideology – all of which are antithetical to its reflexive function, whilst paradoxically being a fundamental part of it. In particular, in capitalism, language is increasingly commodified within the social domains created and affected by ubiquitous communication technologies. The advent of the so-called ‘knowledge economy’ implicates exchangeable forms of thought (language) as the fundamental commodities of this emerging system. The historical point at which a ‘knowledge economy’ emerges, then, is the critical point at which thought itself becomes a commodified ‘thing’, and language becomes its “objective” means of exchange. However, the processes by which such commodification and objectification occurs obscures the unique social relations within which these language commodities are produced. The latest economic phase of capitalism – the knowledge economy – and the obfuscating trajectory which accompanies it, we argue, is destroying the reflexive capacity of language particularly through the process of commodification. This can be seen in that the language practices that have emerged in conjunction with digital technologies are increasingly non-reflexive and therefore less capable of self-critical, conscious change.

Risk-assessment practices in the private rental sector : implications for low-income renters (Final Report)

This report focuses on risk-assessment practices in the private rental market, with particular consideration of their impact on low-income renters. It is based on the fieldwork undertaken in the second stage of the research process that followed completion of the Positioning Paper. The key research question this study addressed was: What are the various factors included in ‘risk-assessments’ by real estate agents in allocating ‘affordable’ tenancies? How are these risks quantified and managed? What are the key outcomes of their decision-making? The study builds on previous research demonstrating that a relatively large proportion of low-cost private rental accommodation is occupied by moderate- to high-income households (Wulff and Yates 2001; Seelig 2001; Yates et al. 2004). This is occurring in an environment where the private rental sector is now the de facto main provider of rental housing for lower-income households across Australia (Seelig et al. 2005) and where a number of factors are implicated in patterns of ‘income–rent mismatching’. These include ongoing shifts in public housing assistance; issues concerning eligibility for rent assistance; ‘supply’ factors, such as loss of low-cost rental stock through upgrading and/or transfer to owner-occupied housing; patterns of supply and demand driven largely by middle- to high-income owner-investors and renters; and patterns of housing need among low-income households for whom affordable housing is not appropriate. In formulating a way of approaching the analysis of ‘risk-assessment’ in rental housing management, this study has applied three sociological perspectives on risk: Beck’s (1992) formulation of risk society as entailing processes of ‘individualisation’; a socio-cultural perspective which emphasises the situated nature of perceptions of risk; and a perspective which has drawn attention to different modes of institutional governance of subjects, as ‘carriers of specific indicators of risk’. The private rental market was viewed as a social institution, and the research strategy was informed by ‘institutional ethnography’ as a method of enquiry. The study was based on interviews with property managers, real estate industry representatives, tenant advocates and community housing providers. The primary focus of inquiry was on ‘the moment of allocation’. Six local areas across metropolitan and regional Queensland, New South Wales, and South Australia were selected as case study localities. In terms of the main findings, it is evident that access to private rental housing is not just a matter of ‘supply and demand’. It is also about assessment of risk among applicants. Risk – perceived or actual – is thus a critical factor in deciding who gets housed, and how. Risk and its assessment matter in the context of housing provision and in the development of policy responses. The outcomes from this study also highlight a number of salient points: 1.There are two principal forms of risk associated with property management: financial risk and risk of litigation. 2. Certain tenant characteristics and/or circumstances – ability to pay and ability to care for the rented property – are the main factors focused on in assessing risk among applicants for rental housing. Signals of either ‘(in)ability to pay’ and/or ‘(in)ability to care for the property’ are almost always interpreted as markers of high levels of risk. 3. The processing of tenancy applications entails a complex and variable mix of formal and informal strategies of risk-assessment and allocation where sorting (out), ranking, discriminating and handing over characterise the process. 4. In the eyes of property managers, ‘suitable’ tenants can be conceptualised as those who are resourceful, reputable, competent, strategic and presentable. 5. Property managers clearly articulated concern about risks entailed in a number of characteristics or situations. Being on a low income was the principal and overarching factor which agents considered. Others included: - unemployment - ‘big’ families; sole parent families - domestic violence - marital breakdown - shift from home ownership to private rental - Aboriginality and specific ethnicities - physical incapacity - aspects of ‘presentation’. The financial vulnerability of applicants in these groups can be invoked, alongside expressed concerns about compromised capacities to manage income and/or ‘care for’ the property, as legitimate grounds for rejection or a lower ranking. 6. At the level of face-to-face interaction between the property manager and applicants, more intuitive assessments of risk based upon past experience or ‘gut feelings’ come into play. These judgements are interwoven with more systematic procedures of tenant selection. The findings suggest that considerable ‘risk’ is associated with low-income status, either directly or insofar as it is associated with other forms of perceived risk, and that such risks are likely to impede access to the professionally managed private rental market. Detailed analysis suggests that opportunities for access to housing by low-income householders also arise where, for example: - the ‘local experience’ of an agency and/or property manager works in favour of particular applicants - applicants can demonstrate available social support and financial guarantors - an applicant’s preference or need for longer-term rental is seen to provide a level of financial security for the landlord - applicants are prepared to agree to specific, more stringent conditions for inspection of properties and review of contracts - the particular circumstances and motivations of landlords lead them to consider a wider range of applicants - In particular circumstances, property managers are prepared to give special consideration to applicants who appear worthy, albeit ‘risky’. The strategic actions of demonstrating and documenting on the part of vulnerable (low-income) tenant applicants can improve their chances of being perceived as resourceful, capable and ‘savvy’. Such actions are significant because they help to persuade property managers not only that the applicant may have sufficient resources (personal and material) but that they accept that the onus is on themselves to show they are reputable, and that they have valued ‘competencies’ and understand ‘how the system works’. The parameters of the market do shape the processes of risk-assessment and, ultimately, the strategic relation of power between property manager and the tenant applicant. Low vacancy rates and limited supply of lower-cost rental stock, in all areas, mean that there are many more tenant applicants than available properties, creating a highly competitive environment for applicants. The fundamental problem of supply is an aspect of the market that severely limits the chances of access to appropriate and affordable housing for low-income rental housing applicants. There is recognition of the impact of this problem of supply. The study indicates three main directions for future focus in policy and program development: providing appropriate supports to tenants to access and sustain private rental housing, addressing issues of discrimination and privacy arising in the processes of selecting suitable tenants, and addressing problems of supply.

Corona discharges on the surfaces of high voltage composite insulators

The degradation of high voltage electrical insulation is a prime factor that can significantly influence the reliability performance and the costs of maintaining high voltage electricity networks. Little information is known about the system of localized degradation from corona discharges on the relatively new silicone rubber sheathed composite insulators that are now being widely used in high voltage applications. This current work focuses on the fundamental principles of electrical corona discharge phenomena to provide further insights to where damaging surface discharges may localize and examines how these discharges may degrade the silicone rubber material. Although water drop corona has been identified by many authors as a major cause of deterioration of silicone rubber high voltage insulation until now no thorough studies have been made of this phenomenon. Results from systematic measurements taken using modern digital instrumentation to simultaneously record the discharge current pulses and visible images associated with corona discharges from between metal electrodes, metal electrodes and water drops, and between waters drops on the surface of silicone rubber insulation, using a range of 50 Hz voltages are inter compared. Visual images of wet electrodes show how water drops can play a part in encouraging flashover, and the first reproducible visual images of water drop corona at the triple junction of water air and silicone rubber insulation are presented. A study of the atomic emission spectra of the corona produced by the discharge from its onset up to and including spark-over, using a high resolution digital spectrometer with a fiber optic probe, provides further understanding of the roles of the active species of atoms and molecules produced by the discharge that may be responsible for not only for chemical changes of insulator surfaces, but may also contribute to the degradation of the metal fittings that support the high voltage insulators. Examples of real insulators and further work specific to the electrical power industry are discussed. A new design concept to prevent/reduce the damaging effects of water drop corona is also presented.

The neuro-muscular and musculo-skeletal characterization of children with joint hypermobility

In children, joint hypermobility (typified by structural instability of joints) manifests clinically as neuro-muscular and musculo-skeletal conditions and conditions associated with development and organization of control of posture and gait (Finkelstein, 1916; Jahss, 1919; Sobel, 1926; Larsson, Mudholkar, Baum and Srivastava, 1995; Murray and Woo, 2001; Hakim and Grahame, 2003; Adib, Davies, Grahame, Woo and Murray, 2005:). The process of control of the relative proportions of joint mobility and stability, whilst maintaining equilibrium in standing posture and gait, is dependent upon the complex interrelationship between skeletal, muscular and neurological function (Massion, 1998; Gurfinkel, Ivanenko, Levik and Babakova, 1995; Shumway-Cook and Woollacott, 1995). The efficiency of this relies upon the integrity of neuro-muscular and musculo-skeletal components (ligaments, muscles, nerves), and the Central Nervous System’s capacity to interpret, process and integrate sensory information from visual, vestibular and proprioceptive sources (Crotts, Thompson, Nahom, Ryan and Newton, 1996; Riemann, Guskiewicz and Shields, 1999; Schmitz and Arnold, 1998) and development and incorporation of this into a representational scheme (postural reference frame) of body orientation with respect to internal and external environments (Gurfinkel et al., 1995; Roll and Roll, 1988). Sensory information from the base of support (feet) makes significant contribution to the development of reference frameworks (Kavounoudias, Roll and Roll, 1998). Problems with the structure and/ or function of any one, or combination of these components or systems, may result in partial loss of equilibrium and, therefore ineffectiveness or significant reduction in the capacity to interact with the environment, which may result in disability and/ or injury (Crotts et al., 1996; Rozzi, Lephart, Sterner and Kuligowski, 1999b). Whilst literature focusing upon clinical associations between joint hypermobility and conditions requiring therapeutic intervention has been abundant (Crego and Ford, 1952; Powell and Cantab, 1983; Dockery, in Jay, 1999; Grahame, 1971; Childs, 1986; Barton, Bird, Lindsay, Newton and Wright, 1995a; Rozzi, et al., 1999b; Kerr, Macmillan, Uttley and Luqmani, 2000; Grahame, 2001), there has been a deficit in controlled studies in which the neuro-muscular and musculo-skeletal characteristics of children with joint hypermobility have been quantified and considered within the context of organization of postural control in standing balance and gait. This was the aim of this project, undertaken as three studies. The major study (Study One) compared the fundamental neuro-muscular and musculo-skeletal characteristics of 15 children with joint hypermobility, and 15 age (8 and 9 years), gender, height and weight matched non-hypermobile controls. Significant differences were identified between previously undiagnosed hypermobile (n=15) and non-hypermobile children (n=15) in passive joint ranges of motion of the lower limbs and lumbar spine, muscle tone of the lower leg and foot, barefoot CoP displacement and in parameters of barefoot gait. Clinically relevant differences were also noted in barefoot single leg balance time. There were no differences between groups in isometric muscle strength in ankle dorsiflexion, knee flexion or extension. The second comparative study investigated foot morphology in non-weight bearing and weight bearing load conditions of the same children with and without joint hypermobility using three dimensional images (plaster casts) of their feet. The preliminary phase of this study evaluated the casting technique against direct measures of foot length, forefoot width, RCSP and forefoot to rearfoot angle. Results indicated accurate representation of elementary foot morphology within the plaster images. The comparative study examined the between and within group differences in measures of foot length and width, and in measures above the support surface (heel inclination angle, forefoot to rearfoot angle, normalized arch height, height of the widest point of the heel) in the two load conditions. Results of measures from plaster images identified that hypermobile children have different barefoot weight bearing foot morphology above the support surface than non-hypermobile children, despite no differences in measures of foot length or width. Based upon the differences in components of control of posture and gait in the hypermobile group, identified in Study One and Study Two, the final study (Study Three), using the same subjects, tested the immediate effect of specifically designed custom-made foot orthoses upon balance and gait of hypermobile children. The design of the orthoses was evaluated against the direct measures and the measures from plaster images of the feet. This ascertained the differences in morphology of the modified casts used to mould the orthoses and the original image of the foot. The orthoses were fitted into standardized running shoes. The effect of the shoe alone was tested upon the non-hypermobile children as the non-therapeutic equivalent condition. Immediate improvement in balance was noted in single leg stance and CoP displacement in the hypermobile group together with significant immediate improvement in the percentage of gait phases and in the percentage of the gait cycle at which maximum plantar flexion of the ankle occurred in gait. The neuro-muscular and musculo-skeletal characteristics of children with joint hypermobility are different from those of non-hypermobile children. The Beighton, Solomon and Soskolne (1973) screening criteria successfully classified joint hypermobility in children. As a result of this study joint hypermobility has been identified as a variable which must be controlled in studies of foot morphology and function in children. The outcomes of this study provide a basis upon which to further explore the association between joint hypermobility and neuro-muscular and musculo-skeletal conditions, and, have relevance for the physical education of children with joint hypermobility, for footwear and orthotic design processes, and, in particular, for clinical identification and treatment of children with joint hypermobility.