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

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