Creative strategies to support student learning through reflection

Reflective practice has become a key attribute of promoting quality teaching and learning. Learning is an active process and include reflective writing, visualising and verbalising to promote critical thinking. In our experience most often than not superficial reflective writing is used. We explored the design of opportunities for students to engage in critical reflection. Theoretical data were obtained through in-depth exploration of the literature to allow contextualisation while arguing a case. A qualitative approach was used. Judgements were not made about the measured quality of reported findings, but on the relevance of reflective strategies to support students, enhance critical reflection and transform practice. Combined with narration and dialogue, reflection can bridge the gap between theoretical ideals and realities of the practice context. Four reflective activities have been identified that could be used to engage students in critical reflection

A comparison of five glucometers in South Africa

Objective: To assess the accuracy and precision of five currently available blood glucose meters in South AfricaBackground: Since the introduction of glucometers, there has been an ongoing, competition-driven development in both meter and strip technology, which has allowed for greater accuracy and reliability of results. Despite the advances in technology, there is significant variation amongst these glucometers necessitating a proper evaluation before use.Methods: Glucose levels in capillary blood samples from 115 patients attending the diabetic clinic at Tygerberg Hospital were measured witheach meter, and compared with the laboratory reference method.Results: The coefficients of variation (CVs) (imprecision) of most meters were acceptable at less than 5%, with a bias ranging from 1.7 to 6.8%. None of the glucometers satisfied the American Diabetes Association (ADA) recommendation of less than 5% bias.Conclusions: The study highlights the need for an objective and independent comparison of all glucometers in South Africa, as the variability observed can impact on patient care.Keywords: glucometer; diabetes; self monitoring (SMBG); analytical error; Clarke error gri

Knotting probabilities after a local strand passage in unknotted self-avoiding polygons

We investigate the knotting probability after a local strand passage is performed in an unknotted self-avoiding polygon on the simple cubic lattice. We assume that two polygon segments have already been brought close together for the purpose of performing a strand passage, and model this using Theta-SAPs, polygons that contain the pattern Theta at a fixed location. It is proved that the number of n-edge Theta-SAPs grows exponentially (with n) at the same rate as the total number of n-edge unknotted self-avoiding polygons, and that the same holds for subsets of n-edge Theta-SAPs that yield a specific after-strand-passage knot-type. Thus the probability of a given after-strand-passage knot-type does not grow (or decay) exponentially with n, and we conjecture that instead it approaches a knot-type dependent amplitude ratio lying strictly between 0 and 1. This is supported by critical exponent estimates obtained from a new maximum likelihood method for Theta-SAPs that are generated by a composite (aka multiple) Markov Chain Monte Carlo BFACF algorithm. We also give strong numerical evidence that the after-strand-passage knotting probability depends on the local structure around the strand passage site. Considering both the local structure and the crossing-sign at the strand passage site, we observe that the more "compact" the local structure, the less likely the after-strand-passage polygon is to be knotted. This trend is consistent with results from other strand-passage models, however, we are the first to note the influence of the crossing-sign information. Two measures of "compactness" are used: the size of a smallest polygon that contains the structure and the structure's "opening" angle. The opening angle definition is consistent with one that is measurable from single molecule DNA experiments.Comment: 31 pages, 12 figures, submitted to Journal of Physics

Crushing damage estimation for pavement with lightly cementitious bases

This paper was transferred from the original CD ROM created for this conference. The material was published using Adobe Acrobat 10.1.0 Technology. The original CD ROM was produced by CE Projects cc. Postal Address: PO Box 560 Irene 0062 South Africa. Tel.: +27 12 667 2074 Fax: +27 12 667 2766 E-mail: [email protected] presented at the 33rd Annual Southern African Transport Conference 7-10 July 2014 "Leading Transport into the Future", CSIR International Convention Centre, Pretoria, South Africa.Crushing (or compression) failure and associated surface deformation of lightly cementitious (stabilised) materials used for base/sub-base course layers in pavements has been well established in the South African pavement design practice since the 1990s. Typically, crushing failure starts at the surface of the cementitious base layer, and could extend to 50 mm deep, depending on tyre load/stress conditions. Recently developed crushing damage relationships for 2, 5, 10, 15 and 20 mm level of deformation (“rut”) were proposed for practical application on these pavements. The aim of this paper is the practical application of these relationships for an un-surfaced and surfaced pavement with a typical stabilised (C3 – quality) base layer. Currently there are up to 15 standard pavement designs with cementitious base layers proposed in TRH 4 (1996). This paper demonstrates the impact of four different tyre models (including overloading) used in the mechanistic-empirical design of these pavements. In particular, the importance of adequate surface protection is demonstrated with reference to the vertical tyre contact stresses expected on these cementitious layers. The impact of the findings extends to the use (or not) of C3 - quality bases and associated surfacings on all categories of pavements carrying up to 10 million E80s. This is considered important towards the upgrading of secondary (or alternative) road pavements using cementitious stabilisers in the base layer, especially in the light of the potential future attraction of heavily loaded vehicles - with or without overloading on the tyres

Modelling tyre-road contact stresses in pavement design and analysis

Paper presented at the 32nd Annual Southern African Transport Conference 8-11 July 2013 "Transport and Sustainable Infrastructure", CSIR International Convention Centre, Pretoria, South Africa.Growing traffic volumes, increasing construction and maintenance costs continually drive for more innovative approaches and methodologies towards sustainable road infrastructure. At the current price levels of around R6000 per metric tonne, bitumen, as a “raw” product, is by far the most costly element in flexible pavements, for example compared to Crushed stone, which is at approximately R170 per metric tonne. Since the asphalt layer or relatively thin bituminous seal acts as the stress barrier between rolling tyres and the road structure it needs to be durable so as to withstand current traffic loading and hence contact stresses, given the environmental forces also acting on it. For road infrastructure to perform as expected, it is important to optimize road pavement design, especially close to the surface of the pavement requiring accurate modelling of tyre-road contact stresses. The aim of this paper is to demonstrate modern ways to idealise tyre-road interaction based on Stress-In-Motion (SIM) results, in particular the way in which numerical analyses are used (and developed) to address non-uniformly distributed tyre contact stresses on the surface of the pavements. A tyre model is demonstrated whereby the SIM measured contact stress distribution is idealised with a multitude of circular and rectangular shapes, mimicking the non-uniform characteristics of the contact stresses inside the tyre contact patch. An example, in terms of pavement layer life and strain energy of distortion, is given highlighting the effects of different tyre-road models on a typical flexible road structure, compared to the traditional circular shape model of a single uniformly distributed contact stress (1D).This paper was transferred from the original CD ROM created for this conference. The material was published using Adobe Acrobat 10.1.0 Technology. The original CD ROM was produced by Document Transformation Technologies Postal Address: PO Box 560 Irene 0062 South Africa. Tel.: +27 12 667 2074 Fax: +27 12 667 2766 E-mail: nigel@doctech URL: http://www.doctech.co.zamv201

Exact Scaling Functions for Self-Avoiding Loops and Branched Polymers

It is shown that a recently conjectured form for the critical scaling function for planar self-avoiding polygons weighted by their perimeter and area also follows from an exact renormalization group flow into the branched polymer problem, combined with the dimensional reduction arguments of Parisi and Sourlas. The result is generalized to higher-order multicritical points, yielding exact values for all their critical exponents and exact forms for the associated scaling functions.Comment: 5 pages; v2: factors of 2 corrected; v.3: relation with existing theta-point results clarified, some references added/update

Asymptotic behaviour of convex and column-convex lattice polygons with fixed area and varying perimeter

We study the inflated phase of two dimensional lattice polygons, both convex and column-convex, with fixed area A and variable perimeter, when a weight \mu^t \exp[- Jb] is associated to a polygon with perimeter t and b bends. The mean perimeter is calculated as a function of the fugacity \mu and the bending rigidity J. In the limit \mu -> 0, the mean perimeter has the asymptotic behaviour \avg{t}/4 \sqrt{A} \simeq 1 - K(J)/(\ln \mu)^2 + O (\mu/ \ln \mu) . The constant K(J) is found to be the same for both types of polygons, suggesting that self-avoiding polygons should also exhibit the same asymptotic behaviour.Comment: 10 pages, 3 figure

Equilibrium size of large ring molecules

The equilibrium properties of isolated ring molecules were investigated using an off-lattice model with no excluded volume but with dynamics that preserve the topological class. Using an efficient set of long range moves, chains of more than 2000 monomers were studied. Despite the lack of any excluded volume interaction, the radius of gyration scaled like that of a self avoiding walk, as had been previously conjectured. However this scaling was only seen for chains greater than 500 monomers.Comment: 11 pages, 3 eps figures, latex, psfi

A numerical adaptation of SAW identities from the honeycomb to other 2D lattices

Recently, Duminil-Copin and Smirnov proved a long-standing conjecture by Nienhuis that the connective constant of self-avoiding walks on the honeycomb lattice is $\sqrt{2+\sqrt{2}}.$ A key identity used in that proof depends on the existence of a parafermionic observable for self-avoiding walks on the honeycomb lattice. Despite the absence of a corresponding observable for SAW on the square and triangular lattices, we show that in the limit of large lattices, some of the consequences observed on the honeycomb lattice persist on other lattices. This permits the accurate estimation, though not an exact evaluation, of certain critical amplitudes, as well as critical points, for these lattices. For the honeycomb lattice an exact amplitude for loops is proved.Comment: 21 pages, 7 figures. Changes in v2: Improved numerical analysis, giving greater precision. Explanation of why we observe what we do. Extra reference

Relaxation of a Single Knotted Ring Polymer

The relaxation of a single knotted ring polymer is studied by Brownian dynamics simulations. The relaxation rate lambda_q for the wave number q is estimated by the least square fit of the equilibrium time-displaced correlation function to a double exponential decay at long times. The relaxation rate distribution of a single ring polymer with the trefoil knot appears to behave as lambda_q=A(1/N^)x for q=1 and lambda_q=A'(q/N)^x' for q=2 and 3, where x=2.61, x'=2.02 and A>A'. The wave number q of the slowest relaxation rate for each N is given by q=2 for small values of N, while it is given by q=1 for large values of N. This crossover corresponds to the change of the structure of the ring polymer caused by the localization of the knotted part to a part of the ring polymer.Comment: 13 pages, 5 figures, uses jpsj2.cl