Ways to teach modelling—a 50 year study

This article describes a sequence of design research projects, some exploratory others more formal, on the teaching of modelling and the analysis of modelling skills. The initial motivation was the author’s observation that the teaching of applied mathematics in UK high schools and universities involved no active modelling by students, but was entirely focused on their learning standards models of a restricted range of phenomena, largely from Newtonian mechanics. This did not develop the numeracy/mathematical literacy that was so clearly important for future citizens. Early explorations started with modelling workshops with high school teachers and mathematics undergraduates, observed and analysed—in some case using video. The theoretical basis of this work has been essentially heuristic, though the Shell Centre studies included, for example, a detailed analysis of formulation processes that has not, as so often, been directly replicated. Recent work has focused on developing a formative assessment approach to teaching modelling that has proved both successful and popular. Finally, the system-level challenges in trying to establish modelling as an integral part of mathematics curricula are briefly discussed

Reduction in Natural Death and Renal Failure From a Systematic Screening and Treatment Program in an Australian Aboriginal Community

BACKGROUND: Australian Aborigines in remote areas are experiencing an epidemic of renal and cardiovascular disease. In November 1995, we introduced a renal and cardiovascular treatment program into the Tiwi community, which has a three- to fivefold increase in death rates and a recent annual incidence of treated end-stage renal disease (ESRD) of 2760 per million. Our previous study described an estimated 50% reduction in renal failure and all-cause natural deaths in the treatment group through December 31, 1998. We now describe a reduction in these events through mid 2000. METHODS: People eligible for treatment were those with confirmed hypertension, diabetics with microalbuminuria or overt albuminuria, and people with overt albuminuria, regardless of blood pressure and diabetes. Treatment centered around the use of perindopril (Coversyl, Servier), with additional agents as needed to reach defined blood pressure goals, attempts at control of glucose and lipid levels, and health education. Two hundred and sixty-seven people, or 30% of the adult population, have been enrolled, with mean follow up of 3.39 years. Rates of terminal endpoints were compared on an intention-to-treat basis with those of 327 historical controls matched for baseline disease severity, who were followed for a mean of 3.18 years in the pre-treatment program era, against a background of no treatment or inconsistent changing treatment. RESULTS: Terminal events occurred in 38 controls and 23 people in the treatment group. The estimated rate of natural deaths in the treatment group was 50% that of the controls, (P=0.012); the rate of renal deaths was 47% (P=0.038) and the rate of non-renal deaths was 54% that of controls (P=0.085). Survival benefit in the treatment group was observed at all levels of overt albuminuria, in non-diabetics and diabetics, in normotensive as well as hypertensive people, and in people who had been taking angiotensin converting enzyme-inhibitors (ACEi) in the pre-program era, as well as those who had not. Benefit was absent among the low death rates of people without overt albuminuria, and questionable among people with glomerular filtration rates (GFRs

Comparison of mannitol and methacholine to predict exercise-induced bronchoconstriction and a clinical diagnosis of asthma

<p>Abstract</p> <p>Background</p> <p>Asthma can be difficult to diagnose, but bronchial provocation with methacholine, exercise or mannitol is helpful when used to identify bronchial hyperresponsiveness (BHR), a key feature of the disease. The utility of these tests in subjects with signs and symptoms of asthma but without a clear diagnosis has not been investigated. We investigated the sensitivity and specificity of mannitol to identify exercise-induced bronchoconstriction (EIB) as a manifestation of BHR; compared this with methacholine; and compared the sensitivity and specificity of mannitol and methacholine for a clinician diagnosis of asthma.</p> <p>Methods</p> <p>509 people (6–50 yr) were enrolled, 78% were atopic, median FEV₁92.5% predicted, and a low NAEPPII asthma score of 1.2. Subjects with symptoms of seasonal allergy were excluded. BHR to exercise was defined as a ≥ 10% fall in FEV₁on at least one of two tests, to methacholine a PC₂₀≤ 16 mg/ml and to mannitol a 15% fall in FEV₁at ≤ 635 mg or a 10% fall between doses. The clinician diagnosis of asthma was made on examination, history, skin tests, questionnaire and response to exercise but they were blind to the mannitol and methacholine results.</p> <p>Results</p> <p>Mannitol and methacholine were therapeutically equivalent to identify EIB, a clinician diagnosis of asthma, and prevalence of BHR. The sensitivity/specificity of mannitol to identify EIB was 59%/65% and for methacholine it was 56%/69%. The BHR was mild. Mean EIB % fall in FEV₁in subjects positive to exercise was 19%, (SD 9.2), mannitol PD₁₅158 (CI:129,193) mg, and methacholine PC₂₀2.1(CI:1.7, 2.6)mg/ml. The prevalence of BHR was the same: for exercise (43.5%), mannitol (44.8%), and methacholine (41.6%) with a test agreement between 62 & 69%. The sensitivity and specificity for a clinician diagnosis of asthma was 56%/73% for mannitol and 51%/75% for methacholine. The sensitivity increased to 73% and 72% for mannitol and methacholine when two exercise tests were positive.</p> <p>Conclusion</p> <p>In this group with normal FEV₁, mild symptoms, and mild BHR, the sensitivity and specificity for both mannitol and methacholine to identify EIB and a clinician diagnosis of asthma were equivalent, but lower than previously documented in well-defined populations.</p> <p>Trial registration</p> <p>This was a multi-center trial comprising 25 sites across the United States of America. (NCT0025229).</p

Police Culture and Police Leadership

Police leadership is a key focus for police practitioners and academics. However, little attention has been paid to the relationship between police leadership and police culture. In a policing field where, in rhetorical terms, leadership is presented as a means of limiting the damage caused by occupational culture, it is important for commentary to provide a critical focus upon the relationship between these two complex concepts. This chapter provides, by drawing on international policing literature and contexts, a conceptual and critical account of three main issues. First, whether or not police leaders can be conceptualized as having a particular cultural orientation. Second, by explaining the inherent conceptual tensions in the relationship. Finally, it explores the assumption that police culture represents a barrier to police leadership

Chronic cough and sputum production are associated with worse clinical outcomes in stable asthma

SummaryBackgroundChronic cough and sputum production (chronic mucus hypersecretion) is a poorly described clinical feature of asthma. Our objective was to identify clinical, immunological and computed tomography (CT) measures of airway wall dimensions associated with these symptoms in smokers and never smokers with asthma.MethodsCross-sectional data was analysed from 120 smokers and never smokers with asthma. Participants with and without a history of chronic mucus hypersecretion were compared for clinical outcomes, sputum differential cell counts and CT measures of airway dimensions (wall thickness, luminal area and percent wall area).ResultsChronic mucus hypersecretion occurred in a higher proportion of smokers with asthma (56%) than never smokers with asthma (20%), (p < 0.001) and the proportion of patients with these symptoms increased with asthma severity (p = 0.003). Smokers with asthma and chronic mucus hypersecretion had worse current clinical control than smokers without those symptoms [ACQ score 2.3 versus 1.6, p = 0.002]. A greater proportion of never smokers with chronic mucus hypersecretion required short courses of oral corticosteroids in the last year (58% versus 19%, p = 0.011). Sputum neutrophil and eosinophil counts were similar in asthma patients with or without chronic mucus hypersecretion. Of those with severe asthma and chronic mucus hypersecretion, a CT measure of airway lumen area was reduced in smokers compared to never smokers (11.4 mm2 versus 18.4 mm2; p = 0.017).ConclusionsChronic mucus hypersecretion occurs frequently in adults with stable asthma, particularly in smokers with severe disease and is associated with worse current clinical control in smokers and more exacerbations in never smokers

Prevalence of chronic kidney disease in population-based studies: Systematic review

which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Background: Chronic kidney disease (CKD) is becoming a major public health problem worldwide. This article reviews the published evidence of prevalence of CKD in population-based study samples that used the standardized definition from the Kidney Disease Outcomes Quality Initiative of the National Kidney Foundation (K/DOQI) practice guideline, and particularly focus on performance of serum-creatinine based equations for GFR estimation. We provide a summary of available data about the burden of CKD in various populations. Methods: We performed a systematic review of available published data in MEDLINE. A combination of various keywords relevant to CKD was used in this research. Related data of included studies were extracted in a systematic way. Results: A total of 26 studies were included in this review. The studies were conducted in different populations, and the number of study participants ranged from 237 to 65181. The median prevalence of CKD was 7.2 % in persons aged 30 years or older. In persons aged 64 years or older prevalence of CKD varied from 23.4 % to 35.8%. Importantly, the prevalence of CKD strongl

Longitudinal study of ‘retraining’ non-maths specialist teachers to become capable, confident teachers of mathematics

One of the key problems to be solved in mathematics education in England is that the demand for mathematics teachers is far in excess of the supply. Acknowledging that there are simply too few mathematics teachers, the UK government has invested significantly in retraining programmes. These programmes ‘retrain’ out-of-field teachers, that is, teachers of other subjects or from other phases, to teach secondary mathematics. The increased mathematical demand of the reformed GCSE courses coupled with the expectation that most post-16 students will engage with some mathematics (studying for A and AS levels, a Core Maths qualification or re-sitting GCSE) means many more teachers of mathematics will be needed. We consider the viability of a retraining course as an effective way of alleviating the problem of the lack of well qualified teachers for mathematics. In this four-year longitudinal study, we followed teachers during their year of ‘retraining’ and in the succeeding years. Once a participant completes their part-time one-year course, the teacher is considered ‘retrained’. However, we conclude that without ongoing professional development involving collaborative support retraining courses alone can have little impact on the problem of the lack of competent and confident teachers of mathematics in the secondary sector