An evaluation of the Australian ‘reconceptualising early mathematics learning’ project : key findings and implications

The Pattern and Structure Mathematics Awareness Project (PASMAP) has investigated the development of patterning and early algebraic reasoning among 4 to 8 year olds over a series of related studies. We assert that an awareness of mathematical pattern and structure (AMPS) enables mathematical thinking and simple forms of generalization from an early age. This paper provides an overview of key findings of the Reconceptualizing Early Mathematics Learning empirical evaluation study involving 316 Kindergarten students from 4 schools. The study found highly significant differences on PASA scores for PASMAP students. Analysis of structural development showed increased levels for the PASMAP students; those categorised as low ability developed improved structural responses over a short period of time.

Recasting the theory of mosquito-borne pathogen transmission dynamics and control

Mosquito-borne diseases pose some of the greatest challenges in public health, especially in tropical and sub-tropical regions of theworld. Efforts to control these diseases have been underpinned by a theoretical framework developed for malaria by Ross and Macdonald, including models, metrics for measuring transmission, and theory of control that identifies key vulnerabilities in the transmission cycle. That framework, especially Macdonald’s formula for R0 and its entomological derivative, vectorial capacity, are nowused to study dynamics and design interventions for many mosquito-borne diseases. A systematic review of 388 models published between 1970 and 2010 found that the vast majority adopted the Ross–Macdonald assumption of homogeneous transmission in a well-mixed population. Studies comparing models and data question these assumptions and point to the capacity to model heterogeneous, focal transmission as the most important but relatively unexplored component in current theory. Fine-scale heterogeneity causes transmission dynamics to be nonlinear, and poses problems for modeling, epidemiology and measurement. Novel mathematical approaches show how heterogeneity arises from the biology and the landscape on which the processes of mosquito biting and pathogen transmission unfold. Emerging theory focuses attention on the ecological and social context formosquito blood feeding, themovement of both hosts and mosquitoes, and the relevant spatial scales for measuring transmission and for modeling dynamics and control.

The implementation of a guideline of care for patients with a Sengstaken-Blakemore tube in situ in a general intensive care unit using transitional change theory

The use of the Sengstaken–Blakemore tube as a life-saving treatment for bleeding oesophageal varices is slowly becoming the least preferred method possibly due to the potential complications associated with its placement. Nursing practice pertaining to the care of this patient group appears ad hoc and reliant on local knowledge and experience as opposed to recognised evidence of best practice. Therefore, this paper focuses on the application of Lewin's transitional change theory used to introduce a change in nursing practice with the application of a guideline to enhance the care of patients with a Sengstaken–Blakemore tube in situ within a general intensive care unit. This method identified some of the complexities surrounding the change process including the driving and restraining forces that must be harnessed and minimised in order for the adoption of change to be successful.

Context-resonant systems perspectives in career theory

"The focus of this chapter is on context-resonant systems perspectives in career theory and their implications for practice in diverse cultural and contextual settings. For over two decades, the potential of systems theory to offer a context-resonant approach to career development has been acknowledged. Career development theory and practice, however, have been dominated for most of their history by more narrowly defined theories informed by a trait-and-factor tradition of matching the characteristics of individuals to occupations. In contrast, systems theory challenges this parts-in-isolation approach and offers a response that can accommodate the complexity of both the lives of individuals and the world of the 21st century by taking a more holistic approach that considers individuals in context. These differences in theory and practice may be attributed to the underlying philosophies that inform them. For example, the philosophy informing the trait-and-factor theoretical position, logical positivism, places value on: studying individuals in isolation from their environments; content over process; facts over feelings; objectivity over subjectivity; and views individual behavior as observable, measurable, and linear. In practice, this theory base manifests in expert-driven practices founded on the assessment of personal traits such as interests, personality, values, or beliefs which may be matched to particular occupations. The philosophy informing more recent theoretical positions, constructivism, places value on: studying individuals in their contexts; making meaning of experience through the use of subjective narrative accounts; and a belief in the capacity of individuals known as agency. In practice, this theory base manifests in practices founded on collaborative relationships with clients, narrative approaches, and a reduced emphasis on expert-driven linear processes. Thus, the tenets of constructivism which inform the systems perspectives in career theory are context-resonant. Systems theory stresses holism where the interconnectedness of all elements of a system is considered. Systems may be open or closed. Closed systems have no relationship with their external environment whereas open systems interact with their external environment and are open to external influence which is necessary for regeneration. Congruent with general systems theory, the systems perspectives emerging within career theory are based on open systems. Such systems are complex and dynamic and comprise many elements and subsystems which recursively interact with each other as well as with influences from the surrounding environment. As elements of a system should not be considered in isolation, a systems approach is holistic. Patterns of behavior are found in the relationships between the elements of dynamic systems. Because of the multiplicity of relationships within and between elements of subsystems, the possibility of linear causal explanations is reduced. Story is the mechanism through which the relationships and patterns within systems are recounted by individuals. Thus the career guidance practices emanating from theories informed by systems perspectives are inherently narrative in orientation. Narrative career counseling encourages career development to be understood from the subjective perspective of clients. The application of systemic thinking in practice takes greater account of context. In so doing, practices informed by systems theory may facilitate relevance to a diverse client group in diverse settings. In a world that has become increasingly global and diverse it seems that context-resonant systems perspectives in career theory are essential to ensure the future of career development. Translating context-resonant systems perspectives into practice offers important possibilities for methods and approaches that are respectful of diversity."--publisher website

Potential interstellar molecules : Formation of neutral C6CO from C6CO- in the gas phase

Computations at the RCCSD(T)/aug-cc-pVDZ//B3LYP/6-31G* level of theory indicate that neutral C6CO is a stable species. The ground state of this neutral is the singlet cumulene oxide :C=C=C=C=C=C=C=O. The adiabatic electron affinity and dipole moment of singlet C6CO are 2.47 eV and 4.13 D, respectively, at this level of theory. The anion (C6CO)(-.) should be a possible precursor to this neutral. It has been formed by an unequivocal synthesis in the ion source of a mass spectrometer by the S(N)2(Si) reaction between (CH3)(3)Si-C=C-C=C-C=C-CO-CMe3 and F- to form C-=C-C=C-C=C-CO-CMe3 which loses Me3C in the source to form C6CO-.. Charge stripping of this anion by vertical Franck-Condon oxidation forms C6CO, characterised by the neutralisation-reionisation spectrum (-NR+) of C6CO-., which is stable during the timeframe of this experiment (10(-6) s), Copyright (C) 2000 John Wiley & Sons, Ltd.

Database relation watermarking resilient against secondary watermarking attacks

There has been tremendous interest in watermarking multimedia content during the past two decades, mainly for proving ownership and detecting tamper. Digital fingerprinting, that deals with identifying malicious user(s), has also received significant attention. While extensive work has been carried out in watermarking of images, other multimedia objects still have enormous research potential. Watermarking database relations is one of the several areas which demand research focus owing to the commercial implications of database theft. Recently, there has been little progress in database watermarking, with most of the watermarking schemes modeled after the irreversible database watermarking scheme proposed by Agrawal and Kiernan. Reversibility is the ability to re-generate the original (unmarked) relation from the watermarked relation using a secret key. As explained in our paper, reversible watermarking schemes provide greater security against secondary watermarking attacks, where an attacker watermarks an already marked relation in an attempt to erase the original watermark. This paper proposes an improvement over the reversible and blind watermarking scheme presented in [5], identifying and eliminating a critical problem with the previous model. Experiments showing that the average watermark detection rate is around 91% even with attacker distorting half of the attributes. The current scheme provides security against secondary watermarking attacks.

‘Doing’ social justice in early childhood : the potential of leadership

Early childhood education has long been connected with objectives related to social justice. Australian Early Childhood Education and Care (ECEC) has its roots in philanthropic and educational reform movements prevalent at the turn of the 20th century. More recently, with the introduction of the National Early Childhood Reform Agenda, early childhood education has once more been linked to the achievement of aims associated with redressing inequality and disadvantage. According to Jean-Marie, Normore and Brooks (2009), educational leaders have a moral and social obligation to foster equitable practices through advocating for traditionally marginalised and poorly served students while creating a new social order “...that subverts the long standing system that has privileged certain students while oppressing or neglecting others” (p.4). Drawing on extant literature, including data from two previously reported Australian studies in which leadership emerged as having a transformational impact on service delivery, this paper examines the potential of early childhood leadership to generate ‘socially just’ educational communities. With reference to critical theory, we argue that critically informed, intentional and strategic organisational leadership can play a pivotal role in creating changed circumstances and opportunities for children and families. Such leadership includes positional and distributed elements, articulation of values and beliefs, and collective action that is mindful and informed.

Conversion of neutral C2COC2 to C4CO. potential interstellar molecules

Both [C4CO]−· and [C2COC2]−· are formed in the ion source of a VG ZAB 2HF mass spectrometer by the respective processes HO− + Me3Si–CC–CC–CO–CMe3 → [C4CO]−· + Me3SiOH + Me3C·, and Me3Si–CC–CO–CC–SiMe3 + SF6 + e → [C2COC2]−· + 2Me3SiF + SF4. The second synthetic pathway involves a double desilylation reaction similar to that first reported by Squires. The two radical anion isomers produce different and characteristic charge reversal spectra upon collisional activation. In contrast, following collision induced charge stripping, both radical anions produce neutral C4CO as evidenced by the identical neutralisation reionisation (−NR+) spectra. The exclusive rearrangement of C213COC2 to C413CO indicates that 12C–O bond formation is not involved in the reaction. Ab initio calculations (at the RCCSD(T)/aug-cc-pVDZ//B3LYP/6-31G∗ level of theory) have been used to investigate the reaction coordinates on the potential surfaces for both singlet and triplet rearrangements of neutral C2COC2. Singlet C2COC2 is less stable than singlet C4CO by 78.8 kcal mol−1 and requires only 8.5 kcal mol−1 of additional energy to effect conversion to C4CO by a rearrangement sequence involving three C–C ring opening/cyclisation steps.

Letters & Numbers : a vehicle to illustrate mathematical and computing fundamentals

The television quiz program Letters and Numbers, broadcast on the SBS network, has recently become quite popular in Australia. This paper explores the potential of this game to illustrate and engage student interest in a range of fundamental concepts of computer science and mathematics. The Numbers Game in particular has a rich mathematical structure whose analysis and solution involves concepts of counting and problem size, discrete (tree) structures, language theory, recurrences, computational complexity, and even advanced memory management. This paper presents an analysis of these games and their teaching applications, and presents some initial results of use in student assignments.

Formation of neutral molecules of potential stellar interest by neutralisation of negative ions in a mass spectrometer - The application of experiment and molecular modelling in concert

This paper is a modified version of a lecture which describes the synthesis, structure and reactivity of some neutral molecules of stellar significance. The neutrals are formed in the collision cell of a mass spectrometer following vertical Franck-Condon one electron oxidation of anions of known bond connectivity. Neutrals are characterised by conversion to positive ions and by extensive theoretical studies at the CCSD(T)/aug-cc-pVDZ//B3LYP/6-31G(d) level of theory. Four systems are considered in detail, viz (i) the formation of linear C-4 and its conversion to the rhombus C-4, (ii) linear C-5 and the atom scrambling of this system when energised, (iii) the stable cumulene oxide CCCCCO, and (iv) the elusive species O2C-CO. This paper is not intended to be a review of interstellar chemistry: examples are selected from our own work in this area. (C) 2002 Elsevier Science Inc. All rights reserved.

Aspects of elementary number theory illustrated in the spreadsheet environment

Number theory has in recent decades assumed a great practical importance, due primarily to its application to cryptography. This chapter discusses how elementary concepts of number theory may be illuminated and made accessible to upper secondary school students via appropriate spreadsheet models. In such environments, students can observe patterns, gain structural insight, form and test conjectures, and solve problems. The chapter begins by reviewing literature on the use of spreadsheets in general and the use of spreadsheets in number theory in particular. Two sample applications are then discussed. The first, factoring factorials, is presented and instructions are given to construct a model in Excel 2007. The second application, the RSA cryptosystem, is included because of its importance to Science, Technology, Engineering, and Mathematics (STEM) students. Number theoretic concepts relevant to RSA are discussed, and an outline of RSA. is given, with example. The chapter ends with instructions on how to construct a simple spreadsheet illustrating RSA.

A survey in mathematics for industry: Two-timing and matched asymptotic expansions for singular perturbation problems

Following the derivation of amplitude equations through a new two-time-scale method [O'Malley, R. E., Jr. & Kirkinis, E (2010) A combined renormalization group-multiple scale method for singularly perturbed problems. Stud. Appl. Math. 124, 383-410], we show that a multi-scale method may often be preferable for solving singularly perturbed problems than the method of matched asymptotic expansions. We illustrate this approach with 10 singularly perturbed ordinary and partial differential equations. © 2011 Cambridge University Press.

Serial explant culture provides novel insights into the potential location and phenotype of corneal endothelial progenitor cells

The routine cultivation of human corneal endothelial cells, with the view to treating patients with endothelial dysfunction, remains a challenging task. While progress in this field has been buoyed by the proposed existence of progenitor cells for the corneal endothelium at the corneal limbus, strategies for exploiting this concept remain unclear. In the course of evaluating methods for growing corneal endothelial cells, we have noted a case where remarkable growth was achieved using a serial explant culture technique. Over the course of 7 months, a single explant of corneal endothelium, acquired from cadaveric human tissue, was sequentially seeded into 7 culture plates and on each occasion produced a confluent cell monolayer. Sample cultures were confirmed as endothelial in origin by positive staining for glypican-4. On each occasion, small cells, closest to the tissue explant, developed into a highly compact layer with an almost homogenous structure. This layer was resistant to removal with trypsin and produced continuous cell outgrowth during multiple culture periods. The small cells gave rise to larger cells with phase-bright cell boundaries and prominent immunostaining for both nestin and telomerase. Nestin and telomerase were also strongly expressed in small cells immediately adjacent to the wound site, following transfer of the explant to another culture plate. These findings are consistent with the theory that progenitor cells for the corneal endothelium reside within the limbus and provide new insights into expected expression patterns for nestin and telomerase within the differentiation pathway.

Examining the predictive value of combining the theory of planned behaviour and the volunteer functions inventory

The functions of the volunteer functions inventory were combined with the constructs of the theory of planned behaviour (i.e., attitudes, subjective norms, and perceived behavioural control) to establish whether a stronger, single explanatory model prevailed. Undertaken in the context of episodic, skilled volunteering by individuals who were retired or approaching retirement (N = 186), the research advances on prior studies which either examined the predictive capacity of each model independently or compared their explanatory value. Using hierarchical regression analysis, the functions of the volunteer functions inventory (when controlling for demographic variables) explained an additional 7.0% of variability in individuals’ willingness to volunteer over and above that accounted for by the theory of planned behaviour. Significant predictors in the final model included attitudes, subjective norms and perceived behavioural control from the theory of planned behaviour and the understanding function from the volunteer functions inventory. It is proposed that the items comprising the understanding function may represent a deeper psychological construct (e.g., self-actualisation) not accounted for by the theory of planned behaviour. The findings highlight the potential benefit of combining these two prominent models in terms of improving understanding of volunteerism and providing a single parsimonious model for raising rates of this important behaviour.

Developing young students’ meta-representational competence through integrated mathematics and science investigations

This paper describes students’ developing meta-representational competence, drawn from the second phase of a longitudinal study, Transforming Children’s Mathematical and Scientific Development. A group of 21 highly able Grade 1 students was engaged in mathematics/science investigations as part of a data modelling program. A pedagogical approach focused on students’ interpretation of categorical and continuous data was implemented through researcher-directed weekly sessions over a 2-year period. Fine-grained analysis of the developmental features and explanations of their graphs showed that explicit pedagogical attention to conceptual differences between categorical and continuous data was critical to development of inferential reasoning.