Rich and purposeful mathematical knowledge of mothers and children in a Torres Strait Islander community

This paper focuses on a pilot study that explored the situated mathematical knowledge of mothers and children in one Torres Strait Islander community in Australia. The community encouraged parental involvement in their children’s learning and schooling. The study explored parents’ understandings of mathematics and how their children came to learn about it on the island. A funds of knowledge approach was used in the study. This approach is based on the premise that people are competent and have knowledge that has been historically and culturally accumulated into a body of knowledge and skills essential for their functioning and well-being (Moll, 1992). The participants, three adults and one child are featured in this paper. Three separate events are described with epiphanic or illuminative moments analysed to ascertain the features that enabled an understanding of the nature of the mathematical events. The study found that Indigenous ways of knowing of mathematics were deeply embedded in rich cultural practices that were tied to the community. This finding has implications for teachers of children in the early years. Where school mathematics is often presented as disembodied and isolated facts with children seeing little relevance, learning a different perspective of mathematics that is tied to the resources and practices of children’s lives and facilitated through social relationships, may go a long way to improving the engagement of children and their parents in learning and schooling.

Manifestations of preoperational reasoning on similar programming tasks

In this research paper, we study a simple programming problem that only requires knowledge of variables and assignment statements, and yet we found that some early novice programmers had difficulty solving the problem. We also present data from think aloud studies which demonstrate the nature of those difficulties. We interpret our data within a neo-Piagetian framework which describes cognitive developmental stages through which students pass as they learn to program. We describe in detail think aloud sessions with novices who reason at the neo-Piagetian preoperational level. Those students exhibit two problems. First, they focus on very small parts of the code and lose sight of the "big picture". Second, they are prone to focus on superficial aspects of the task that are not functionally central to the solution. It is not until the transition into the concrete operational stage that decentration of focus occurs, and they have the cognitive ability to reason about abstract quantities that are conserved, and are equipped to adapt skills to closely related tasks. Our results, and the neo-Piagetian framework on which they are based, suggest that changes are necessary in teaching practice to better support novices who have not reached the concrete operational stage.

Mathematical investigation of the interactions between the inflammatory response and mechanical aspects of dermal wound repair

Dermal wound repair involves complex interactions between cells, cytokines and mechanics to close injuries to the skin. In particular, we investigate the contribution of fibroblasts, myofibroblasts, TGFβ, collagen and local tissue mechanics to wound repair in the human dermis. We develop a morphoelastic model where a realistic representation of tissue mechanics is key, and a fibrocontractive model that involves a reasonable approximation to the true kinetics of the important bioactive species. We use each of these descriptions to elucidate the mechanisms that generate pathologies such as hypertrophic scars, contractures and keloids. We find that for hypertrophic scar and contracture development, factors regulating the myofibroblast phenotype are critical, with heightened myofibroblast activation, reduced myofibroblast apoptosis or prolonged inflammation all predicted as mediators for scar hypertrophy and contractures. Prevention of these pathologies is predicted when myofibroblast apoptosis is induced, myofibroblast activation is blocked or TGFβ is neutralised. To investigate keloid invasion, we develop a caricature representation of the fibrocontractive model and find that TGFβ spread is the driving factor behind keloid growth. Blocking activation of TGFβ is found to cause keloid regression. Thus, we recommend myofibroblasts and TGFβ as targets for clinicians when developing intervention strategies for prevention and cure of fibrotic scars.

A multiscale road map of cancer spheroids : incorporating experimental and mathematical modelling to understand cancer progression

Computational models represent a highly suitable framework, not only for testing biological hypotheses and generating new ones but also for optimising experimental strategies. As one surveys the literature devoted to cancer modelling, it is obvious that immense progress has been made in applying simulation techniques to the study of cancer biology, although the full impact has yet to be realised. For example, there are excellent models to describe cancer incidence rates or factors for early disease detection, but these predictions are unable to explain the functional and molecular changes that are associated with tumour progression. In addition, it is crucial that interactions between mechanical effects, and intracellular and intercellular signalling are incorporated in order to understand cancer growth, its interaction with the extracellular microenvironment and invasion of secondary sites. There is a compelling need to tailor new, physiologically relevant in silico models that are specialised for particular types of cancer, such as ovarian cancer owing to its unique route of metastasis, which are capable of investigating anti-cancer therapies, and generating both qualitative and quantitative predictions. This Commentary will focus on how computational simulation approaches can advance our understanding of ovarian cancer progression and treatment, in particular, with the help of multicellular cancer spheroids, and thus, can inform biological hypothesis and experimental design.

Mathematical relationships for metal build-up on urban road surfaces based on traffic and land use characteristics

The study investigated the influence of traffic and land use parameters on metal build-up on urban road surfaces. Mathematical relationships were developed to predict metals originating from fuel combustion and vehicle wear. The analysis undertaken found that nickel and chromium originate from exhaust emissions, lead, copper and zinc from vehicle wear, cadmium from both exhaust and wear and manganese from geogenic sources. Land use does not demonstrate a clear pattern in relation to the metal build-up process, though its inherent characteristics such as traffic activities exert influence. The equation derived for fuel related metal load has high cross-validated coefficient of determination (Q2) and low Standard Error of Cross-Validation (SECV) values indicates that the model is reliable, while the equation derived for wear-related metal load has low Q2 and high SECV values suggesting its use only in preliminary investigations. Relative Prediction Error values for both equations are considered to be well within the error limits for a complex system such as an urban road surface. These equations will be beneficial for developing reliable stormwater treatment strategies in urban areas which specifically focus on mitigation of metal pollution.

From expert to tasks, expert nursing practice redefined?

Aim The aim of this paper was to explore the concept of expertise in nursing from the perspective of how it relates to current driving forces in health care in which it discusses the potential barriers to acceptance of nursing expertise in a climate in which quantification of value and cost containment run high on agendas. Background Expert nursing practice can be argued to be central to high quality, holistic, individualized patient care. However, changes in government policy which have led to the inception of comprehensive guidelines or protocols of care are in danger of relegating the ‘expert nurse’ to being an icon of the past. Indeed, it could be argued that expert nurses are an expensive commodity within the nursing workforce. Consequently, with this change to the use of clinical guidelines, it calls into question how expert nursing practice will develop within this framework of care. Method The article critically reviews the evidence related to the role of the Expert Nurse in an attempt to identify the key concepts and ideas, and how the inception of care protocols has implications for their role. Conclusion Nursing expertise which focuses on the provision of individualized, holistic care and is based largely on intuitive decision making cannot, should not be reduced to being articulated in positivist terms. However, the dominant power and decision-making focus in health care means that nurses must be confident in articulating the value of a concept which may be outside the scope of knowledge of those with whom they are debating. Relevance to clinical practice The principles of abduction or fuzzy logic may be useful in assisting nurses to explain in terms which others can comprehend, the value of nursing expertise.

Co-thought gestures : supporting students to successfully navigate map tasks

This study considers the role and nature of co-thought gestures when students process map-based mathematics tasks. These gestures are typically spontaneously produced silent gestures which do not accompany speech and are represented by small movements of the hands or arms often directed toward an artefact. The study analysed 43 students (aged 10–12 years) over a 3-year period as they solved map tasks that required spatial reasoning. The map tasks were representative of those typically found in mathematics classrooms for this age group and required route finding and coordinate knowledge. The results indicated that co-thought gestures were used to navigate the problem space and monitor movements within the spatial challenges of the respective map tasks. Gesturing was most influential when students encountered unfamiliar tasks or when they found the tasks spatially demanding. From a teaching and learning perspective, explicit co-thought gesturing highlights cognitive challenges students are experiencing since students tended to not use gesturing in tasks where the spatial demands were low.

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.

Alterations in cervical muscle activity in functional and stressful tasks in female office workers with neck pain

This study determined differences between computer workers with varying levels of neck pain in terms of work stressors, employee strain, electromyography (EMG) amplitude and heart rate response to various tasks. Participants included 85 workers (33, no pain; 38, mild pain; 14, moderate pain) and 22 non-working controls. Work stressors evaluated were job demands, decision authority, and social support. Heart rate was recorded during three tasks: copy-typing, typing with superimposed stress and a colour word task. Measures included electromyography signals from the sternocleidomastoid (SCM), anterior scalene (AS), cervical extensor (CE) and upper trapezius (UT) muscles bilaterally. Results showed no difference between groups in work stressors or employee strain measures. Workers with and without pain had higher measured levels of EMG amplitude in SCM, AS and CE muscles during the tasks than controls (all P < 0.02). In workers with neck pain, the UT had difficulty in switching off on completion of tasks compared with controls and workers without pain. There was an increase in heart rate, perceived tension and pain and decrease in accuracy for all groups during the stressful tasks with symptomatic workers producing more typing errors than controls and workers without pain. These findings suggest an altered muscle recruitment pattern in the neck flexor and extensor muscles. Whether this is a consequence or source of the musculoskeletal disorder cannot be determined from this study. It is possible that workers currently without symptoms may be at risk of developing a musculoskeletal disorder.

Do left and right asymmetries of hemispheric preference interact with attention to predict local and global performance in applied tasks?

Many cognitive neuroscience studies show that the ability to attend to and identify global or local information is lateralised between the two hemispheres in the human brain; the left hemisphere is biased towards the local level, whereas the right hemisphere is biased towards the global level. Results of two studies show attention-focused people with a right ear preference (biased towards the left hemisphere) are better at local tasks, whereas people with a left ear preference (biased towards the right hemisphere) are better at more global tasks. In a third study we determined if right hemisphere-biased followers who attend to global stimuli are likely to have a stronger relationship between attention and globally based supervisor ratings of performance. Results provide evidence in support of this hypothesis. Our research supports our model and suggests that the interaction between attention and lateral preference is an important and novel predictor of work-related outcomes.

Eldercare demands, mental health, and work performance : the moderating role of satisfaction with eldercare tasks

Due to demographic changes, a growing number of employees provide in-home care to an elderly family member. Previous research suggested a negative relationship between employees' eldercare demands and their work performance. However, the empirical nature of this relationship and its boundary conditions and mediating mechanisms have been neglected. The goal of this multisource study was to examine a mediated-moderation model of eldercare demands, mental health, and work performance. Drawing on the theory of conservation of resources (Hobfoll, 1989), it was expected that employees' satisfaction with eldercare tasks would buffer the negative relationship between eldercare demands and work performance, and that mental health would mediate this moderating effect. Data were collected from 165 employees providing in-home eldercare, as well as from one colleague and one family member of each employee. Results of mediated-moderation analyses supported the hypothesized model. The findings suggest that interventions that aim to increase employees' satisfaction with eldercare tasks may help protect employees from the negative effects of high eldercare demands on mental health and, subsequently, on work performance.

Measurement of energy expenditure of daily tasks among mothers of young children

There is currently some debate about whether the energy expenditure of domestic tasks is sufficient to confer health benefits. The aim of this study was therefore to measure the energy cost of five activities commonly undertaken by mothers of young children. Seven women with at least one child younger than five years of age spent 15 minutes in each of the following activities: sitting quietly, vacuum cleaning, washing windows, walking at moderate pace (approx 5km/hour), walking with a stroller and grocery shopping in a super-market. Each of the six 'trials' was completed on the same day, in random order. A carefully calibrated portable gas analyser was used to measure oxygen uptake during each activity, and data were converted to units of energy expenditure (METS). Vacuum cleaning, washing windows and walking with and without a stroller were found to be 'moderate intensity activities' (3 to 6 METs), but supermarket shopping did not reach this criterion. The MET values for these activities were similar to those reported in the Compendium of Physical Activities (Ainsworth et al., 2000). However, the energy expenditures of walking, both with and without a stroller, were higher than those reported in the Compendium. The findings suggest that some of the tasks associated with domestic caring duties are conducted at an intensity which is sufficient to confer some health benefit. Such benefits will only accrue however if the daily duration of these activities is sufficient to meet current guidelines.

Short-term changes in axial length during simulations of typical far, intermediate and near tasks

Purpose: To investigate the changes in axial length with the combined effect of accommodation and angle of gaze (convergence and downward gaze) over 5 minutes in groups of myopes and emmetropes. Methods: A total of 31 subjects (nine emmetropes, 10 low myopes, and 12 moderate to high myopes) aged from 18 to 31 years were recruited. To measure ocular biometrics in inferonasal gaze with accommodation, an optical biometer (Lenstar LS900) was inclined on a tilt and height adjustable stage, with the subject’s chinrest mounted on a rotary stage to induce various levels of convergence by rotation of the subject’s head in primary or downward gaze. Initially, the subjects performed a distance viewing task in primary gaze for 10 minutes to provide a ‘wash-out’ period for prior visual tasks, and then the subject’s axial length and ocular biometrics were measured in nine different combinations of gaze/accommodation over 5 minutes. These nine sessions for all gaze measurements (i.e. three levels of accommodation 9 three levels of convergence) were completed across 3 days of testing (one accommodation condition on each day).The nine combinations of gaze/accommodation were based on those required to view the centre, right and left edges of a distant TV at 6 m in primary gaze, an intermediate task (i.e. computer at 50 cm in 10° downward gaze) and a near task (i.e. reading A4 page at 20 cm in 20° downward gaze). Subjects were wearing a custom built three-axes head tracker throughout the experiment that monitored subjects’ relative head movements (roll, pitch and yaw) during measurements. Results: A significant increase in axial length occurred with the combined effect of accommodation, convergence and downward gaze (repeated measures ANOVA, p < 0.001), with the greatest axial elongation during the near task in downward gaze with convergence (i.e. downward 20°/inward 33°, with 5 D accommodation) (mean change 33 ± 13 lm, after 5 minutes task) followed by the intermediate task (i.e. downward 10°/inward 25°, with 2 D accommodation) (mean change 14 ± 11 lm, after 5 minutes task).Changes in axial length for the distance task (i.e. primary gaze/9° convergence, with 0.16 D accommodation) were not statistically significant (mean change 4 ± 8 lm, after 5 minutes task, p > 0.05). Moderate to high myopes had a greater change in the axial length (mean change 40 ± 11 lm after 5 minutes of near task) than that of emmetropes (mean change 29 ± 15 lm after 5 minutes of near task) and low myopes (mean change 29 ± 16 lm after 5 minutes of near task) associated with time (p = 0.02) and accommodation by time (p = 0.03). Conclusions: The combination of accommodation, convergence and downward angle has a significant short term effect on axial length over time. The near task in downward gaze with convergence caused a greater change in axial length than the intermediate and distant visual tasks. The greater axial elongation measured in the infero-nasal direction with accommodation is most likely associated with a combination of biomechanical factors such as, extraocular muscle forces and ciliary muscle contraction.

A comparison of mathematical models for phase separation in high-rate LiFePO4 cathodes

We construct a two-scale mathematical model for modern, high-rate LiFePO4cathodes. We attempt to validate against experimental data using two forms of the phase-field model developed recently to represent the concentration of Li+ in nano-sized LiFePO4crystals. We also compare this with the shrinking-core based model we developed previously. Validating against high-rate experimental data, in which electronic and electrolytic resistances have been reduced is an excellent test of the validity of the crystal-scale model used to represent the phase-change that may occur in LiFePO4material. We obtain poor fits with the shrinking-core based model, even with fitting based on “effective” parameter values. Surprisingly, using the more sophisticated phase-field models on the crystal-scale results in poorer fits, though a significant parameter regime could not be investigated due to numerical difficulties. Separate to the fits obtained, using phase-field based models embedded in a two-scale cathodic model results in “many-particle” effects consistent with those reported recently.