On the geometry of the smallest circle enclosing a finite set of points

A number of numerical codes have been written for the problem of finding the circle of smallest radius in the Euclidean plane that encloses a finite set P of points, but these do not give much insight into the geometry of this circle. We investigate geometric properties of the minimal circle that may be useful in the theoretical analysis of applications. We show that a circle C enclosing P is minimal if and only if it is rigid in the sense that it cannot be translated while still enclosing P. We show that the center of the minimal circle is in the convex hull of P. We use this rigidity result and an analysis of the case of three points to find sharp estimates on the diameter of the minimal circle in terms of the diameter of P.     

School Reform in a Vacuum: Demographic Change,Social Policy,and the Future of Children

In their search for magic bullets to fix failing schools, policymakers seldom directly address powerful ecological factors impacting schooling. This article identifies several major demographic, societal, economic, and educational changes and trends in U.S. society over the past several years; analyzes their impact on schoolchildren; and offers a series of policy recommendations for public sector reform initiatives that show promise in ameliorating these conditions, which in turn would improve the educational prospects for all children, particularly those most at risk.     

Examining preservice teacher content and pedagogical content knowledge needed to teach reading in elementary school

Recently, increased attention has been placed on the importance of having knowledgeable and skilled teachers in order to influence reading achievement. Yet many international reports suggest that large numbers of children are not learning to read. How can we better prepare teachers with the necessary knowledge to teach reading? The current study examined the reading instructional knowledge of elementary education preservice teachers (N = 87) from two teacher education programmes. Programme A required five reading methods courses and Programme B required two methods courses. Findings indicate that the preservice teachers presented fairly robust levels of knowledge in the areas of phonological awareness, phonics, comprehension and vocabulary. However, we found statistically significant differences in knowledge based on the programme attended and the number of courses completed. Suggestions for improving reading teacher education are provided.     

Teacher job satisfaction: lessons from the TSW Pathfinder Project

Government policy assumes that modernization and remodelling will be effective as external intervention mechanisms to improve job satisfaction. Based on data collected as part of the evaluation of the ‘Transforming the School Workforce Pathfinder Project’, an argument is presented here which suggests that internal management models may be more effective in improving teacher job satisfaction. By comparing the responses of teachers within primary and special schools with those from secondary schools, internal factors are identified which may be more relevant than externally imposed measures.     

‘Quicksand of Hate’: Experiences of Islamophobia and Poetic Resistance

How might English classrooms be spaces where Muslim students are empowered to recognise and resist Islamophobia? This qualitative study draws on theories of critical consciousness and Islamophobia to show how Bassim, a Muslim student, makes sense of Islamophobic encounters through the poetic and analytic writing he creates in his public high school English classroom. When examined intertextually, Bassim’s words offer a glimpse of what Islamophobic experiences are like for some contemporary Muslim students. The findings suggest that through his English class, Bassim is able to use poetic and analytic writing as the means by which he recognises and resists Islamophobia. Further, this study indicates that more work should take up the implications of students’ religious beliefs and the ways those beliefs shape their writing – particularly when they are members of a marginalised religion.     

Effect of a randomised 12-week resistance training programme on muscular strength,cross-sectional area and muscle quality in women having undergone Roux-en-Y gastric bypass

The purpose of this study was to examine the effect of a 12-week resistance training programme on fat-free mass (FFM), muscle cross-sectional area, muscular strength and muscle quality in women who underwent Roux-en-Y gastric bypass surgery. Participants were 16 women (mean age = 44.9 ± 10.2 years) from bariatric surgical groups who were randomly assigned into either a control or an intervention group. Air displacement plethysmography measured FFM and magnetic resonance imaging measured quadriceps muscle cross-sectional area and whole thigh muscle cross-sectional area. Muscular strength and quality was assessed using an estimated 1-Repetition Maximum assessment. All measurements were collected twice, at baseline and at a 12-week follow-up. There were significantly greater improvements in leg press strength (mean differences = 55.4%, P < 0.001, Cohen’s d = 2.4), leg extension strength (mean differences = 18.0%, P = 0.014, Cohen’s d = 0.86) and leg press muscle quality (mean differences = 54.5%, P < 0.001, Cohen’s d = 1.9) in the intervention group compared to the control group following the resistance training programme. The resistance training intervention significantly improved muscular strength and quality; however, it did not illicit changes in FFM or muscle cross-sectional area in women who underwent Roux-en-Y gastric bypass surgery.