Knowledge and writing in school mathematics : a communicational approach

This thesis is about young students’ writing in school mathematics and the ways in which this writing is designed, interpreted and understood. Students’ communication can act as a source from which teachers can make inferences regarding students’ mathematical knowledge and understanding. In mathematics education previous research indicates that teachers assume that the process of interpreting and judging students’ writing is unproblematic. The relationship between what students’ write, and what they know or understand, is theoretical as well as empirical. In an era of increased focus on assessment and measurement in education it is necessary for teachers to know more about the relationship between communication and achievement. To add to this knowledge, the thesis has adopted a broad approach, and the thesis consists of four studies. The aim of these studies is to reach a deep understanding of writing in school mathematics. Such an understanding is dependent on examining different aspects of writing. The four studies together examine how the concept of communication is described in authoritative texts, how students’ writing is viewed by teachers and how students make use of different communicational resources in their writing. The results of the four studies indicate that students’ writing is more complex than is acknowledged by teachers and authoritative texts in mathematics education. Results point to a sophistication in students’ approach to the merging of the two functions of writing, writing for oneself and writing for others. Results also suggest that students attend, to various extents, to questions regarding how, what and for whom they are writing in school mathematics. The relationship between writing and achievement is dependent on students’ ability to have their writing reflect their knowledge and on teachers’ thorough knowledge of the different features of writing and their awareness of its complexity. From a communicational perspective the ability to communicate [in writing] in mathematics can and should be distinguished from other mathematical abilities. By acknowledging that mathematical communication integrates mathematical language and natural language, teachers have an opportunity to turn writing in mathematics into an object of learning. This offers teachers the potential to add to their assessment literacy and offers students the potential to develop their communicational ability in order to write in a way that better reflects their mathematical knowledge.

Tear film surface quality with soft contact lenses using dynamic-area high-speed videokeratoscopy

Objectives. To evaluate the performance of the dynamic-area high-speed videokeratoscopy technique in the assessment of tear film surface quality with and without the presence of soft contact lenses on eye. Methods. Retrospective data from a tear film study using basic high-speed videokeratoscopy, captured at 25 frames per second, (Kopf et al., 2008, J Optom) were used. Eleven subjects had tear film analysis conducted in the morning, midday and evening on the first and seventh day of one week of no lens wear. Five of the eleven subjects then completed an extra week of hydrogel lens wear followed by a week of silicone hydrogel lens wear. Analysis was performed on a 6 second period of the inter-blink recording. The dynamic-area high-speed videokeratoscopy technique uses the maximum available area of Placido ring pattern reflected from the tear interface and eliminates regions of disturbance due to shadows from the eyelashes. A value of tear film surface quality was derived using image rocessing techniques, based on the quality of the reflected ring pattern orientation. Results. The group mean tear film surface quality and the standard deviations for each of the conditions (bare eye, hydrogel lens, and silicone hydrogel lens) showed a much lower coefficient of variation than previous methods (average reduction of about 92%). Bare eye measurements from the right and left eyes of eleven individuals showed high correlation values (Pearson’s correlation r = 0.73, p < 0.05). Repeated measures ANOVA across the 6 second period of measurement in the normal inter-blink period for the bare eye condition showed no statistically significant changes. However, across the 6 second inter-blink period with both contact lenses, statistically significant changes were observed (p < 0.001) for both types of contact lens material. Overall, wearing hydrogel and silicone hydrogel lenses caused the tear film surface quality to worsen compared with the bare eye condition (repeated measures ANOVA, p < 0.0001 for both hydrogel and silicone hydrogel). Conclusions. The results suggest that the dynamic-area method of high-speed videokeratoscopy was able to distinguish and quantify the subtle, but systematic worsening of tear film surface quality in the inter-blink interval in contact lens wear. It was also able to clearly show a difference between bare eye and contact lens wearing conditions.

Measuring performance of municipal real estate : softening the impact of financial crisis to local governments

Asset management in local government is an emerging discipline and over a decade has become a crucial aspect towards a more efficient and effective organisation. One crucial feature in the public asset management is performance measurement toward the public real estates. This measurement critically at the important component of public wealth and seeks to apply a standard of economic efficiency and effective organisational management especially in such global financial crisis condition. This paper aims to identify global economic crisis effect and proposes alternative solution for local governments to softening the impact of the crisis to the local governments organisation. This study found that the most suitable solution for local government to solve the global economic crisis in Indonesia is application of performance measurement in its asset management. Thus, it is important to develop performance measurement system in local government asset management process. This study provides suggestions from published documents and literatures. The paper also discusses the elements of public real estate performance measurement. The measurement of performance has become an essential component of the strategic thinking of assets owners and managers. Without having a formal measurement system for performance, it is difficult to plan, control and improve local government real estate management system. A close look at best practices in public sectors reveals that in most cases these practices were transferred from private sector reals estate management under the direction of real estate experts retained by government. One of the most significant advances in government property performance measurement resulted from recognition that the methodology used by private sector, non real estate corporations for managing their real property offered a valuable prototype for local governments. In general, there are two approaches most frequently used to measure performance of public organisations. Those are subjective and objective measures. Finally, findings from this study provides useful input for the local government policy makers, scholars and asset management practitioners to establish a public real estate performance measurement system toward more efficient and effective local governments in managing their assets as well as increasing public services quality in order to soften the impact of global financial crisis.

Osteoarthritis Index delivered by mobile phone (m-WOMAC) is valid, reliable, and responsive

Objectives: To evaluate the validity, reliability and responsiveness of EDC using the WOMAC® NRS 3.1 Index on Motorola V3 mobile phones. ---------- Methods: Patients with osteoarthritis (OA) undergoing primary unilateral hip or knee joint replacement surgery were assessed pre-operatively and 3-4 months post-operatively. Patients completed the WOMAC® Index in paper (p-WOMAC®) and electronic (m-WOMAC®) format in random order. ---------- Results: 24 men and 38 women with hip and knee OA participated and successfully completed the m-WOMAC® questionnaire. Pearson correlations between the summated total index scores for the p-WOMAC® and m-WOMAC® pre- and post-surgery were 0.98 and 0.99 (p<0.0001). There was no clinically important or statistically significant between-method difference in the adjusted total summated scores, pre- and post-surgery (adjusted mean difference = 4.44, p = 0.474 and 1.73, p = 0.781). Internal consistency estimates of m-WOMAC® reliability were 0.87 – 0.98. The m-WOMAC® detected clinically important, statistically significant (p<0.0001) improvements in pain, stiffness, function and total index score. ---------- Conclusions: Sixty-two patients with hip and knee OA successfully completed EDC by Motorola V3 mobile phone using the m-WOMAC® NRS3.1 Index; completion times averaging only 1-1.5 minutes longer than the p-WOMAC® Index. Data were successfully and securely transmitted from patients in Australia to a server in the USA. There was close agreement and no significant differences between m-WOMAC® and p-WOMAC® scores. This study confirms the validity, reliability and responsiveness of the Exco InTouch engineered, Java-based m-WOMAC® Index application. EDC with the m-WOMAC® Index provides unique opportunities for using quantitative measurement in clinical research and practice.

Australian construction industry KPIs

The Australian Construction Industry Forum (which is a peak industry association) and the Australian Procurement and Construction Council (which is a peak government organisation) have jointly agreed on a set of KPIs for the Australian Construction Industry. The goal of such a process is to work collaboratively in order to lift industry performance overall, and thereby bring about economic and social benefits to the industry and broader community. This paper seeks to underpin the process of KPI measurement by providing: an overview of international approaches to KPI measurement, summary of difficulties identified in performance measurement together with possible responses to these problems, and finally a discussion on the various methods for reporting KPIs. A number of findings throughout the paper, based on the review, made in order to advance the goal of performance measurement in the construction industry in Australia. Such findings would be relevant to other countries considering a KPI measurement process as well.

Exploring health behaviour determinants of ageing Australians with chronic diseases

Background: Chronic disease presents overwhelming challenges to elderly patients, their families, health care providers and the health care system. The aim of this study was to explore a theoretical model for effective management of chronic diseases, especially type 2 diabetes mellitus and/or cardiovascular disease. The assumed theoretical model considered the connections between physical function, mental health, social support and health behaviours. The study effort was to improve the quality of life for people with chronic diseases, especially type 2 diabetes and/or cardiovascular disease and to reduce health costs. Methods: A cross-sectional post questionnaire survey was conducted in early 2009 from a randomised sample of Australians aged 50 to 80 years. A total of 732 subjects were eligible for analysis. Firstly, factors influencing respondents‘ quality of life were investigated through bivariate and multivariate regression analysis. Secondly, the Theory of Planned Behaviour (TPB) model for regular physical activity, healthy eating and medication adherence behaviours was tested for all relevant respondents using regression analysis. Thirdly, TPB variable differences between respondents who have diabetes and/or cardiovascular disease and those without these diseases were compared. Finally, the TPB model for three behaviours including regular physical activity, healthy eating and medication adherence were tested in respondents with diabetes and/or cardiovascular diseases using Structure Equation Modelling (SEM). Results: This was the first study combining the three behaviours using a TPB model, while testing the influence of extra variables on the TPB model in one study. The results of this study provided evidence that the ageing process was a cumulative effect of biological change, socio-economic environment and lifelong behaviours. Health behaviours, especially physical activity and healthy eating were important modifiable factors influencing respondents‘ quality of life. Since over 80% of the respondents had at least one chronic disease, it was important to consider supporting older people‘s chronic disease self-management skills such as healthy diet, regular physical activity and medication adherence to improve their quality of life. Direct measurement of the TPB model was helpful in understanding respondents‘ intention and behaviour toward physical activity, healthy eating and medication adherence. In respondents with diabetes and/or cardiovascular disease, the TPB model predicted different proportions of intention toward three different health behaviours with 39% intending to engage in physical activity, 49% intending to engage in healthy eating and 47% intending to comply with medication adherence. Perceived behavioural control, which was proven to be the same as self-efficacy in measurement in this study, played an important role in predicting intention towards the three health behaviours. Also social norms played a slightly more important role than attitude for physical activity and medication adherence, while attitude and social norms had similar effects on healthy eating in respondents with diabetes and/or cardiovascular disease. Both perceived behavioural control and intention directly predicted recent actual behaviours. Physical activity was more a volitional control behaviour than healthy eating and medication adherence. Step by step goal setting and motivation was more important for physical activity, while accessibility, resources and other social environmental factors were necessary for improving healthy eating and medication adherence. The extra variables of age, waist circumference, health related quality of life and depression indirectly influenced intention towards the three behaviours mainly mediated through attitude and perceived behavioural control. Depression was a serious health problem that reduced the three health behaviours‘ motivation, mediated through decreased self-efficacy and negative attitude. This research provided evidence that self-efficacy is similar to perceived behavioural control in the TPB model and intention is a proximal goal toward a particular behaviour. Combining four sources of information in the self-efficacy model with the TPB model would improve chronic disease patients‘ self management behaviour and reach an improved long-term treatment outcome. Conclusion: Health intervention programs that target chronic disease management should focus on patients‘ self-efficacy. A holistic approach which is patient-centred and involves a multidisciplinary collaboration strategy would be effective. Supporting the socio-economic environment and the mental/ emotional environment for older people needs to be considered within an integrated health care system.

Travel context : development of a model to measure destination brand performance across different travel situations

Purpose: There is a lack of theory relating to destination brand performance measurement in the destination branding literature, which emerged in the late 1990s (see for example Dosen, Vransevic, & Prebezac, 1998). Additionally, there is a lack of research about the importance of travel context in consumers’ destination decision making (Hu & Ritchie, 1993). This study develops a structural model to measure destination brand performance across different travel situations. The theory of planned behaviour (TpB) was utilised as a framework to underpin the consumer-based brand equity (CBBE) hierarchy to develop a model of destination brand performance. Research approach: A proposed model of destination brand performance was developed through a review of the literature. The first study was used to identify destination image attributes (the core construct) using an analysis of the literature, a document analysis, and personal interviews using the Repertory Test qualitative technique. Underpinned by Personal Construct Theory (PCT), the Repertory Test enables the elicitation of attributes consumers use to evaluate destinations when considering travel. Data was examined in the first study to i) identify any attribute differences in travel contexts and ii) create a scale for use in a questionnaire. A second study was conducted to test the proposed model using a questionnaire with eight groups of participants to assess four destinations across two travel contexts. The model was tested utilising structural equation modelling. Findings: The first study resulted in a list of 29 destination image attributes for use in a scale index. Attributes were assessed across travel contexts and few differences were identified. The second study assessed the congruence of destination brand identity (the destination marketing organisation’s desired image) and destination brand image (the actual perceptions held by consumers) using importance-performance analyses. Finally, the proposed model of destination brand performance was tested. Overall the data supported the model of destination brand performance across travel contexts and destinations. Additionally, this was compared to consumers’ decision sets, further supporting the model. Value: This research provides a contribution to the destination marketing literature through the development of a measurement of destination brand performance underpinned by TpB. Practically; it will provide destination marketing organisations with a tool to track destination brand performance, relative to key competing places, over time. This is important given the development of a destination brand is a long term endeavour.

A fiber Bragg grating temperature sensor with adjustable sensitivity [一种灵敏度系数可调的光纤光栅温度传感器]

As a novel sensing element, fiber Bragg grating (FBG) is sensitive to both temperature and strain. Basing on this character, high sensitivity FBG temperature sensor can be made. However, as a result of the strain limit of the fiber, the temperature range it can endure is quite narrow. This drawback limits its application and complicates its storage and transport. We design and manufacture a FBG temperature sensor with tunable sensitivity. By tuning its sensitivity, its temperature range is changed, which enlarges its application field, solves the problem of storage and transport, and brighten the future of FBG in temperature measurement. In experiment, by changing the fixing position of the bimetal we tuned the sensitivity of the high sensitivity FBG sensor to different values (-47 pm/℃，-97.7 pm/℃，-153.3 pm/℃).

A method for predicting rain-induced instability of an individual slope

Awareness to avoid losses and casualties due to rain-induced landslide is increasing in regions that routinely experience heavy rainfall. Improvements in early warning systems against rain-induced landslide such as prediction modelling using rainfall records, is urgently needed in vulnerable regions. The existing warning systems have been applied using stability chart development and real-time displacement measurement on slope surfaces. However, there are still some drawbacks such as: ignorance of rain-induced instability mechanism, mislead prediction due to the probabilistic prediction and short time for evacuation. In this research, a real-time predictive method was proposed to alleviate the drawbacks mentioned above. A case-study soil slope in Indonesia that failed in 2010 during rainfall was used to verify the proposed predictive method. Using the results from the field and laboratory characterizations, numerical analyses can be applied to develop a model of unsaturated residual soils slope with deep cracks and subject to rainwater infiltration. Real-time rainfall measurement in the slope and the prediction of future rainfall are needed. By coupling transient seepage and stability analysis, the variation of safety factor of the slope with time were provided as a basis to develop method for the real-time prediction of the rain-induced instability of slopes. This study shows the proposed prediction method has the potential to be used in an early warning system against landslide hazard, since the FOS value and the timing of the end-result of the prediction can be provided before the actual failure of the case study slope.

Food and Brisbane households : dietary, social and health consequences of food insecurity

Background & Aims: Access to sufficient amounts of safe and culturally-acceptable foods is a fundamental human right. Food security exists when all people, at all times, have physical, social, and economic access to sufficient, safe and nutritious food to meet their dietary needs and food preferences for an active and healthy life. Food insecurity therefore occurs when the availability or access to sufficient amounts of nutritionally-adequate, culturally-appropriate and safe foods, or, the ability to acquire such foods in socially-acceptable ways, is limited. Food insecurity may result in significant adverse effects for the individual and these outcomes may vary between adults and children. Among adults, food insecurity may be associated with overweight or obesity, poorer self-rated general health, depression, increased health-care utilisation and dietary intakes less consistent with national recommendations. Among children, food insecurity may result in poorer self or parent-reported general health, behavioural problems, lower levels of academic achievement and poor social outcomes. The majority of research investigating the potential correlates of food insecurity has been undertaken in the United States (US), where regular national screening for food insecurity is undertaken using a comprehensive multi-item measurement. In Australia, screening for food insecurity takes place on a three yearly basis via the use of a crude, single-item included in the National Health Survey (NHS). This measure has been shown to underestimate the prevalence of food insecurity by 5%. From 1995 – 2004, the prevalence of food insecurity among the Australian population remained stable at 5%. Due to the perceived low prevalence of this issue, screening for food insecurity was not undertaken in the most recent NHS. Furthermore, there are few Australian studies investigating the potential determinants of food insecurity and none investigating potential outcomes among adults and children. This study aimed to examine these issues by a) investigating the prevalence of food insecurity among households residing in disadvantaged urban areas and comparing prevalence rates estimated by the more comprehensive 18-item and 6-item United States Department of Agriculture (USDA) Food Security Survey Module (FSSM) to those estimated by the current single-item measure used for surveillance in Australia and b) investigating the potential determinants and outcomes of food insecurity, Methods: A comprehensive literature review was undertaken to investigate the potential determinants and consequences of food insecurity among developed countries. This was followed by a cross-sectional study in which 1000 households from the most disadvantaged 5% of Brisbane areas were sampled and data collected via mail-based survey (final response rate = 53%, n = 505). Data were collected for food security status, sociodemographic characteristics (household income, education, age, gender, employment status, housing tenure and living arrangements), fruit and vegetable intakes, meat and take-away consumption, presence of depressive symptoms, presence of chronic disease and body mass index (BMI) among adults. Among children, data pertaining to BMI, parent-reported general health, days away from school and activities and behavioural problems were collected. Rasch analysis was used to investigate the psychometric properties of the 18-, 10- and 6-item adaptations of the USDA-FSSM, and McNemar's test was used to investigate the difference in the prevalence of food insecurity as measured by these three adaptations compared to the current single-item measure used in Australia. Chi square and logistic regression were used to investigate the differences in dietary and health outcomes among adults and health and behavioural outcomes among children. Results were adjusted for equivalised household income and, where necessary, for indigenous status, education and family type. Results: Overall, 25% of households in these urbanised-disadvantaged areas reported experiencing food insecurity; this increased to 34% when only households with children were analysed. The current reliance on a single-item measure to screen for food insecurity may underestimate the true burden among the Australian population, as this measure was shown to significantly underestimate the prevalence of food insecurity by five percentage points. Internationally, major potential determinants of food insecurity included poverty and indicators of poverty, such as low-income, unemployment and lower levels of education. Ethnicity, age, transportation and cooking and financial skills were also found to be potential determinants of food insecurity. Among Australian adults in disadvantaged urban areas, food insecurity was associated with a three-fold increase in experiencing poorer self-rated general health and a two-to-five-fold increase in the risk of depression. Furthermore, adults from food insecure households were twoto- three times more likely to have seen a general practitioner and/or been admitted to hospital within the previous six months, compared to their food secure counterparts. Weight status and intakes of fruits, vegetables and meat were not associated with food insecurity. Among Australian households with children, those in the lowest tertile were over 16 times more likely to experience food insecurity compared to those in the highest tertile for income. After adjustment for equivalised household income, children from food insecure households were three times more likely to have missed days away from school or other activities. Furthermore, children from food insecure households displayed a two-fold increase in atypical emotions and behavioural difficulties. Conclusions: Food insecurity is an important public health issue and may contribute to the burden on the health care system through its associations with depression and increased health care utilisation among adults and behavioural and emotional problems among children. Current efforts to monitor food insecurity in Australia do not occur frequently and use a tool that may underestimate the prevalence of food insecurity. Efforts should be made to improve the regularity of screening for food insecurity via the use of a more accurate screening measure. Most of the current strategies that aim to alleviate food insecurity do not sufficiently address the issue of insufficient financial resources for acquiring food; a factor which is an important determinant of food insecurity. Programs to address this issue should be developed in collaboration with groups at higher risk of developing food insecurity and should incorporate strategies to address the issue of low income as a barrier to food acquisition.

Dynamics of reverse salience as technological performance gap: An empirical study of the personal computer technology system

The evolution of technological systems is hindered by systemic components, referred to as reverse salients, which fail to deliver the necessary level of technological performance thereby inhibiting the performance delivery of the system as a whole. This paper develops a performance gap measure of reverse salience and applies this measurement in the study of the PC (personal computer) technological system, focusing on the evolutions of firstly the CPU (central processing unit) and PC game sub-systems, and secondly the GPU (graphics processing unit) and PC game sub-systems. The measurement of the temporal behavior of reverse salience indicates that the PC game sub-system is the reverse salient, continuously trailing behind the technological performance of the CPU and GPU sub-systems from 1996 through 2006. The technological performance of the PC game sub-system as a reverse salient trails that of the CPU sub-system by up to 2300 MHz with a gradually decreasing performance disparity in recent years. In contrast, the dynamics of the PC game sub-system as a reverse salient trails the GPU sub-system with an ever increasing performance gap throughout the timeframe of analysis. In addition, we further discuss the research and managerial implications of our findings.

Comparison of visual status of Iranian military and commercial drivers

Background There is no legal requirement for Iranian military truck drivers to undergo regular visual checkups as compared to commercial truck drivers. Objectives This study aimed to evaluate the impact of drivers’ visual checkups by comparing the visual function of Iranian military and commercial truck drivers. Patients and Methods In this comparative cross-sectional study, two hundred military and 200 commercial truck drivers were recruited and their Visual Acuity (VA), Visual Field (VF), color vision and Contrast Sensitivity (CS) were assessed and compared using the Snellen chart, confrontation screening method, D15 test and Pelli-Robson letter chart, respectively. A questionnaire regarding driving exposure and history of motor-vehicle crashes (MVCs) was also filled by drivers. Results were analyzed using an independent samples t-test, one-way ANOVA (assessing difference in number of MVCs across different age groups), chi-square test and Pearson correlation at statistical significance level of P < 0.05. Results Mean age was 41.6 ± 9.2 for the military truck drivers and 43.4 ± 10.9 for commercial truck drivers (P > 0.05). No significant difference between military and commercial drivers was found in terms of driving experience, number of MVCs, binocular VA, frequency of color vision defects and CS scores. In contrast, the last ocular examination was significantly earlier in military drivers than commercial drivers (P < 0.001). In addition, 4% of military drivers did not meet the national standards to drive as opposed to 2% of commercial drivers. There was a significant but weak correlation between binocular VA and age (r = 0.175, P < 0.001). However, CS showed a significantly moderate correlation with age (r = -0.488, P < 0.001). Conclusions The absence of legal requirement for regular eye examination in military drivers caused the incompetent drivers to be missed in contrast to commercial drivers. The need for scientific revision of VA standard for Iranian drivers is also discussed. The CS measurement in visual checkups of older drivers deserves to be investigated more thoroughly.

Communicating consequences with costs: A commentary on Corso et al's cost of injury

Estimating the economic burden of injuries is important for setting priorities, allocating scarce health resources and planning cost-effective prevention activities. As a metric of burden, costs account for multiple injury consequences—death, severity, disability, body region, nature of injury—in a single unit of measurement. In a 1989 landmark report to the US Congress, Rice et al1 estimated the lifetime costs of injuries in the USA in 1985. By 2000, the epidemiology and burden of injuries had changed enough that the US Congress mandated an update, resulting in a book on the incidence and economic burden of injury in the USA.2 To make these findings more accessible to the larger realm of scientists and practitioners and to provide a template for conducting the same economic burden analyses in other countries and settings, a summary3 was published in Injury Prevention. Corso et al reported that, between 1985 and 2000, injury rates declined roughly 15%. The estimated lifetime cost of these injuries declined 20%, totalling US$406 billion, including US$80 billion in medical costs and US$326 billion in lost productivity. While incidence reflects problem size, the relative burden of injury is better expressed using costs.

Crystal growth and characterization of two-leg spin ladder compounds: Sr14Cu24O41 and Sr2Ca12Cu24O41

Single crystals of Sr14−xCaxCu24O41 (x=0 and 12) are grown by the travelling solvent floating zone technique using an image furnace. The grown crystals are characterized for their single crystallinity by the X-ray and Neutron Laue method. The magnetic susceptibility measurements in Sr14Cu24O41 show considerable anisotropy along the main crystallographic axes. Low-temperature specific heat measurement and DC susceptibility measurement in Ca-doped crystal showed antiferromagnetic ordering at 2.8 K at ambient pressure. High-pressure AC susceptibility measurement on Ca-doped crystal showed a sharp superconducting transition at 2 K under 40 kbars. Tc onset reached a maximum value of 9.9 K at 54 kbars. The bulk superconductivity of the sample is confirmed by the high-pressure AC calorimetry with Tc max=9.4 K and TN=5 K at 56 kbars.

On the design of quadratic weirs

This paper considers the problem of the design of the quadratic weir notch, which finds application in the proportionate method of flow measurement in a by-pass, such that the discharge through it is proportional to the square root of the head measured above a certain datum. The weir notch consists of a bottom in the form of a rectangular weir of width 2W and depth a over which a designed curve is fitted. A theorem concerning the flow through compound weirs called the “slope discharge continuity theorem” is discussed and proved. Using this, the problem is reduced to the determination of an exact solution to Volterra's integral equation in Abel's form. It is shown that in the case of a quadratic weir notch, the discharge is proportional to the square root of the head measured above a datum Image a above the crest of the weir. Further, it is observed that the function defining the shape of the weir is rapidly convergent and its value almost approximates to zero at distances of 3a and above from the crest of the weir. This interesting and significant behaviour of the function incidentally provides a very good approximate solution to a particular Fredholm integral equation of the first kind, transforming the notch into a device called a “proportional-orifice”. A new concept of a “notch-orifice” capable of passing a discharge proportional to the square root of the head (above a particular datum) while acting both as a notch, and as an orifice, is given. A typical experiment with one such notch-orifice, having A = 4 in., and W = 6 in., shows a remarkable agreement with the theory and is found to have a constant coefficient of discharge of 0.61 in the ranges of both notch and orifice.