Assessment in tertiary mathematics

There is a growing consensus among many educators that the goals of teaching and learning mathematics are to help students solve real-life problems, participate intelligently in daily affairs, and prepare them for jobs (Gardiner, 1994; Roeber, 1995). These goals suggest that the role of routine procedural skills should be diminished while more emphasis ought to be placed on learners gaining conceptual insights and analytical skills that appear essential in real-life mathematical problem solving (Schoenfeld, 1993; Stenmark, 1989).

Implementation of an integrated, technology-based, discovery mode assessment item involving an incubation period to enhance learning outcomes for engineering maths students

In this paper we discuss our current efforts to develop and implement an exploratory, discovery mode assessment item into the total learning and assessment profile for a target group of about 100 second level engineering mathematics students. The assessment item under development is composed of 2 parts, namely, a set of "pre-lab" homework problems (which focus on relevant prior mathematical knowledge, concepts and skills), and complementary computing laboratory exercises which are undertaken within a fixed (1 hour) time frame. In particular, the computing exercises exploit the algebraic manipulation and visualisation capabilities of the symbolic algebra package MAPLE, with the aim of promoting understanding of certain mathematical concepts and skills via visual and intuitive reasoning, rather than a formal or rigorous approach. The assessment task we are developing is aimed at providing students with a significant learning experience, in addition to providing feedback on their individual knowledge and skills. To this end, a noteworthy feature of the scheme is that marks awarded for the laboratory work are primarily based on the extent to which reflective, critical thinking is demonstrated, rather than the amount of CBE-style tasks completed by the student within the allowed time. With regard to student learning outcomes, a novel and potentially critical feature of our scheme is that the assessment task is designed to be intimately linked to the overall course content, in that it aims to introduce important concepts and skills (via individual student exploration) which will be revisited somewhat later in the pedagogically more restrictive formal lecture component of the course (typically a large group plenary format). Furthermore, the time delay involved, or "incubation period", is also a deliberate design feature: it is intended to allow students the opportunity to undergo potentially important internal re-adjustments in their understanding, before being exposed to lectures on related course content which are invariably delivered in a more condensed, formal and mathematically rigorous manner. In our presentation, we will discuss in more detail our motivation and rationale for trailing such a scheme for the targeted student group. Some of the advantages and disadvantages of our approach (as we perceived them at the initial stages) will also be enumerated. In a companion paper, the theoretical framework for our approach will be more fully elaborated, and measures of student learning outcomes (as obtained from eg. student provided feedback) will be discussed.

Ethnic differences in body composition and anthropometric characteristics in Australian Caucasian and urban Indigenous children

The objective was to compare ethnic differences in anthropometry, including size, proportions and fat distribution, and body composition in a cohort of seventy Caucasian (forty-four boys, twenty-six girls) and seventy-four urban Indigenous (thirty-six boys, thirty-eight girls) children (aged 9–15 years). Anthropometric measures (stature, body mass, eight skinfolds, thirteen girths, six bone lengths and five bone breadths) and body composition assessment using dual-energy X-ray absorptiometry were conducted. Body composition variables including total body fat percentage and percentage abdominal fat were determined and together with anthropometric indices, including BMI (kg/m2), abdominal:height ratio (AHtR) and sum of skinfolds, ethnic differences were compared for each sex. After adjustment for age, Indigenous girls showed significantly (P < 0·05) greater trunk circumferences and proportion of overweight and obesity than their Caucasian counterparts. In addition, Indigenous children had a significantly greater proportion (P < 0·05) of trunk fat. The best model for total and android fat prediction included sum of skinfolds and age in both sexes (>93 % of variation). Ethnicity was only important in girls where abdominal circumference and AHtR were included and Indigenous girls showed significantly (P < 0·05) smaller total/android fat deposition than Caucasian girls at the given abdominal circumference or AHtR values. Differences in anthropometric and fat distribution patterns in Caucasian and Indigenous children may justify the need for more appropriate screening criteria for obesity in Australian children relevant to ethnic origin.

Early detection : a strategy to reduce risk and severity?

Despite changes in surgical techniques, radiotherapy targeting and the apparent earlier detection of cancers, secondary lymphoedema is still a significant problem for about 20–30% of those who receive treatment for cancer, although the incidence and prevalence does seem to be falling. The figures above generally relate to detection of an enlarged limb or other area, but it seems that about 60% of all patients also suffer other problems with how the limb feels, what can or cannot be done with it and a range of social or psychological issues. Often these ‘subjective’ changes occur before the objective ones, such as a change in arm volume or circumference. For most of those treated for cancer lymphoedema does not develop immediately, and, while about 60–70% develop it in the first few years, some do not develop lymphoedema for up to 15 or 20 years. Those who will develop clinically manifest lymphoedema in the future are, for some time, in a latent or hidden phase of lymphoedema. There also seems to be some risk factors which are indicators for a higher likelihood of lymphoedema post treatment, including oedema at the surgical site, arm dominance, age, skin conditions, and body mass index (BMI).

Deepening our understanding about school leadership : learning from educators and non-educators

Increasingly, leadership is argued as a way forward to improve performance and practice in a variety of contexts. School leadership is no different. There is little doubt that in the current globalised world characterized by change and complexity, effective school leadership is a key requirement. The contribution of this chapter is framed around a synthesis of current research, writing and theoretical insights regarding leadership. It draws upon three bodies of writing, Firstly, it begins by distilling several key themes and trends regarding educational leadership from the current research and writing. Secondly, it reports on the findings of a current research project carried out by the authors that explored the leadership stories of ten outstanding leaders from non-educational settings in Australia. Finally, it concludes by referring to some of the paradoxes and tensions inherent in the work of school leaders. It is argued that understanding and endeavouring to reconcile these dilemmas is a pre-requisite for school leaders as they continue to operate in an environment fraught with change and complexity.

Beneficial effects of exercise : shifting the focus from body weight to other markers of health

Background: Exercise is widely promoted as a method of weight management, while the other health benefits are often ignored. The purpose of this study was to examine whether exercise-induced improvements in health are influenced by changes in body weight. Methods: Fifty-eight sedentary overweight/obese men and women (BMI 31.8 (SD 4.5) kg/m2) participated in a 12-week supervised aerobic exercise intervention (70% heart rate max, five times a week, 500 kcal per session). Body composition, anthropometric parameters, aerobic capacity, blood pressure and acute psychological response to exercise were measured at weeks 0 and 12. Results: The mean reduction in body weight was −3.3 (3.63) kg (p<0.01). However, 26 of the 58 participants failed to attain the predicted weight loss estimated from individuals’ exercise-induced energy expenditure. Their mean weight loss was only −0.9 (1.8) kg (p<0.01). Despite attaining a lower-than-predicted weight reduction, these individuals experienced significant increases in aerobic capacity (6.3 (6.0) ml/kg/min; p<0.01), and a decreased systolic (−6.00 (11.5) mm Hg; p<0.05) and diastolic blood pressure (−3.9 (5.8) mm Hg; p<0.01), waist circumference (−3.7 (2.7) cm; p<0.01) and resting heart rate (−4.8 (8.9) bpm, p<0.001). In addition, these individuals experienced an acute exercise-induced increase in positive mood. Conclusions: These data demonstrate that significant and meaningful health benefits can be achieved even in the presence of lower-than-expected exercise-induced weight loss. A less successful reduction in body weight does not undermine the beneficial effects of aerobic exercise. From a public health perspective, exercise should be encouraged and the emphasis on weight loss reduced.

Decentred optical axes and aberrations along principal visual field meridians

Suggestions that peripheral imagery may affect the development of refractive error have led to interest in the variation in refraction and aberration across the visual field. It is shown that, if the optical system of the eye is rotationally symmetric about an optical axis which does not coincide with the visual axis, measurements of refraction and aberration made along the horizontal and vertical meridians of the visual field will show asymmetry about the visual axis. The departures from symmetry are modelled for second-order aberrations, refractive components and third-order coma. These theoretical results are compared with practical measurements from the literature. The experimental data support the concept that departures from symmetry about the visual axis in the measurements of crossed-cylinder astigmatism J45 and J180 are largely explicable in terms of a decentred optical axis. Measurements of the mean sphere M suggest, however, that the retinal curvature must differ in the horizontal and vertical meridians.

Blur limits for defocus, astigmatism and trefoil

We investigated the limits at which blur due to defocus, crossed-cylinder astigmatism, and trefoil became noticeable, troublesome or objectionable. Black letter targets (0.1, 0.35 and 0.6 logMAR) were presented on white backgrounds. Subjects were cyclopleged and had effectively 5 mm pupils. Blur was induced with a deformable, adaptive-optics mirror operating under open-loop conditions. Mean defocus blur limits of six subjects with uncorrected intrinsic higher-order ocular aberrations ranged from 0.18 ± 0.08 D (noticeable blur criterion, 0.1 logMAR) to 1.01 ± 0.27 D (objectionable blur criterion, 0.6 logMAR. Crossed-cylinder astigmatic blur limits were approximately 90% of those for defocus, but with considerable meridional influences. In two of the subjects, the intrinsic aberrations of the eye were subsequently corrected before the defocus and astigmatic blur were added. This resulted in only minor reductions in their blur limits. When assessed with trefoil blur and corrected intrinsic ocular aberrations, the ratio of objectionable to noticeable blur limits in these two subjects was much higher for trefoil (3.5) than for defocus (2.5) and astigmatism (2.2).

Exercise alone is not enough : weight loss also needs a healthy (Mediterranean) diet?

Objective: In the majority of exercise intervention studies, the aggregate reported weight loss is often small. The efficacy of exercise as a weight loss tool remains in question. The aim of the present study was to investigate the variability in appetite and body weight when participants engaged in a supervised and monitored exercise programme. ---------- Design: Fifty-eight obese men and women (BMI = 31·8 ± 4·5 kg/m2) were prescribed exercise to expend approximately 2092 kJ (500 kcal) per session, five times a week at an intensity of 70 % maximum heart rate for 12 weeks under supervised conditions in the research unit. Body weight and composition, total daily energy intake and various health markers were measured at weeks 0, 4, 8 and 12. ---------- Results: Mean reduction in body weight (3·2 ± 1·98 kg) was significant (P < 0·001); however, there was large individual variability (−14·7 to +2·7 kg). This large variability could be largely attributed to the differences in energy intake over the 12-week intervention. Those participants who failed to lose meaningful weight increased their food intake and reduced intake of fruits and vegetables. ---------- Conclusion: These data have demonstrated that even when exercise energy expenditure is high, a healthy diet is still required for weight loss to occur in many people.

Dual-process action of exercise on appetite control : increase in orexigenic drive but improvement in meal-induced satiety

Background: Exercise could contribute to weight loss by altering the sensitivity of the appetite regulatory system. Objective: The aim of this study was to assess the effects of 12 wk of mandatory exercise on appetite control. Design: Fifty-eight overweight and obese men and women [mean (±SD) body mass index (in kg/m2) = 31.8 ± 4.5, age = 39.6 ± 9.8 y, and maximal oxygen intake = 29.1 ± 5.7 mL · kg–1 · min–1] completed 12 wk of supervised exercise in the laboratory. The exercise sessions were designed to expend 2500 kcal/wk. Subjective appetite sensations and the satiating efficiency of a fixed breakfast were compared at baseline (week 0) and at week 12. An Electronic Appetite Rating System was used to measure subjective appetite sensations immediately before and after the fixed breakfast in the immediate postprandial period and across the whole day. The satiety quotient of the breakfast was determined by calculating the change in appetite scores relative to the breakfast's energy content. Results: Despite large variability, there was a significant reduction in mean body weight (3.2 ± 3.6 kg), fat mass (3.2 ± 2.2 kg), and waist circumference (5.0 ± 3.2 cm) after 12 wk. The analysis showed that a reduction in body weight and body composition was accompanied by an increase in fasting hunger and in average hunger across the day (P < 0.0001). Paradoxically, the immediate and delayed satiety quotient of the breakfast also increased significantly (P < 0.05). Conclusions: These data show that the effect of exercise on appetite regulation involves at least 2 processes: an increase in the overall (orexigenic) drive to eat and a concomitant increase in the satiating efficiency of a fixed meal.

Acute compensatory eating following exercise is associated with implicit hedonic wanting for food

The efficacy of exercise to promote weight loss could potentially be undermined by its influence on explicit or implicit processes of liking and wanting for food which in turn alter food preference. The present study was designed to examine hedonic and homeostatic mechanisms involved in the acute effects of exercise on food intake. 24 healthy female subjects were recruited to take part in two counterbalanced activity sessions; 50 min of high intensity (70% max heart rate) exercise (Ex) or no exercise (NEx). Subjective appetite sensations, explicit and implicit hedonic processes, food preference and energy intake (EI) were measured immediately before and after each activity session and an ad libitum test meal. Two groups of subjects were identified in which exercise exerted different effects on compensatory EI and food preference. After exercise, compensators (C) increased their EI, rated the food to be more palatable, and demonstrated increased implicit wanting. Compensators also showed a preference for high-fat sweet food compared with non-compensators (NC), independent of the exercise intervention. Exercise-induced changes in the hedonic response to food could be an important consideration in the efficacy of using exercise as a means to lose weight. An enhanced implicit wanting for food after exercise may help to explain why some people overcompensate during acute eating episodes. Some individuals could be resistant to the beneficial effects of exercise due to a predisposition to compensate for exercise-induced energy expenditure as a result of implicit changes in food preferences.

Resistance training for obese, type 2 diabetic adults: A review of the evidence

In both developed and developing countries, increased prevalence of obesity has been strongly associated with increased incidence of type 2 diabetes mellitus (T2DM) in the adult population. Previous research has emphasized the importance of physical activity in the prevention and management of obesity and T2DM, and generic exercise guidelines originally developed for the wider population have been adapted for these specific populations. However, the guidelines traditionally focus on aerobic training without due consideration to other exercise modalities. Recent reviews on resistance training in the T2DM population have not compared this modality with others including aerobic training, or considered the implications of resistance training for individuals suffering from both obesity and T2DM. In short, the optimal mix of exercise modalities in the prescription of exercise has not been identified for it benefits to the metabolic, body composition and muscular health markers common in obesity and T2DM. Similarly, the underlying physical, social and psychological barriers to adopting and maintaining exercise, with the potential to undermine the efficacy of exercise interventions, have not been addressed in earlier reviews. Because it is well established that aerobic exercise has profound effects on obesity and T2DM risk, the purpose of this review was to address the importance of resistance training to obese adults with T2DM.

The relationship between subjective appetite sensations, markers of inflammation and appetite in dialysis patients

Background: Poor appetite is a marker of morbidity and mortality in hemodialysis patients, making it an important area for research. Visual analog scales (VAS) can capture a range of subjective sensations related to appetite (such as hunger, desire to eat or fullness), but have not been commonly used to measure appetite in dialysis patients. The aim of this study was to explore the association between retrospective ratings of appetite using VAS and a range of clinical variables as well as biomarkers of appetite in hemodialysis patients.----- Methods: 28 hemodialysis patients (mean age 61±17y, 50% male, median dialysis vintage 19.5(4-101) months) rated their appetite using VAS for hunger, fullness and desire to eat and a 5-point categorical scale measuring general appetite. Blood levels of the appetite peptides leptin, ghrelin and peptide YY were also measured.----- Results: Hunger ratings measured by VAS were significantly (p<0.05) correlated with a range of clinical, nutritional and inflammatory markers: age (r=-0.376), co-morbidities, (r=-0.380) PG-SGA score (r=-0.451), weight (r=-0.375), fat-free mass (r=-0.435), C-Reactive Protein (CRP) (r=-0.383) and Intercellular adhesion molecule (sICAM-1) (r=-0.387). There was a consistent relationship between VAS and appetite on a 5-point categorical scale for questions of hunger, and a similar trend for desire to eat, but not for fullness. Neither method of measuring subjective appetite correlated with appetite peptides.----- Conclusions: Retrospective ratings of hunger on a VAS are associated with a range of clinical variables and further studies are warranted to support their use as a method of measuring appetite in dialysis patients.