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

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

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

Cardiac disease in young adult patients with end-stage renal disease since childhood: A Dutch cohort study

Cardiac disease in young adult patients with end-stage renal disease since childhood: A Dutch cohort study.BackgroundCardiovascular disease is the most important cause of death in patients with pediatric end-stage renal disease (ESRD). Yet, few data exist on cardiac function in these patients. We assessed the extent of cardiac abnormality and analyzed its association with potential determinants in young adult patients with pediatric ESRD in a long-term follow-up study.MethodsAll Dutch living adult patients with ESRD onset at age of 0 to 14 years between 1972 and 1992 were invited for echocardiography and blood pressure assessment. Special attention was paid to evidence of left ventricular hypertrophy (LVH), diastolic dysfunction, and aortic valve calcification. We collected data on determinants by review of all medical charts.ResultsOf all the 187 living patients, 140 participated in the study. Of those, 110 patients had received a transplant and 30 patients were on dialysis. Mean age was 29.2 (20.7 to 41.8) years. Left ventricular mass index (LVMI) exceeded 150 g/m2 in 47% of all male patients and 120 g/m2 in 39% of all female patients, both consistent with LVH. Diastolic dysfunction, defined as an early over atrial transmitral blood flow velocity (E/A ratio) <1, was found in 18 (13%) patients; 27 (19%) had aortic valve calcification. Multiple regression analysis revealed the following: a high LVMI was associated with a current high blood pressure (β = 0.46, P < 0.001) and male gender (β = 0.21, P = 0.009), a low E/A ratio with aging (β = -0.28, P < 0.001) and a glomerular filtration rate (GFR) <25 mL/min/1.73 m2 (β = -0.29, P < 0.001), and aortic valve calcification with prolonged peritoneal dialysis (β = 0.36, P < 0.001).ConclusionYoung adult patients with pediatric ESRD are at risk for LVH caused by hypertension and for aortic valve calcification. Diastolic function decreases with age and is enhanced by a current low GFR. Prolonged peritoneal dialysis may enhance aortic valve calcification