Shutler, Paul

Teachers’ judgements of the cognitive demand of mathematical assessment items have implications for the nature of students’ learning experiences. However, existing taxonomies for classifying cognitive demand are often not customised for pre-university or A-level mathematics teachers to use. This paper reports on the development and field-testing of a cognitive demand instrument specifically for helping A-level mathematics teachers to sharpen their judgements of the cognitive demand of A-level mathematical assessment items. Fourteen A-level Mathematics teachers from a junior college and an Integrated Programme school in Singapore participated in this study, where they rated the cognitive demand of assessment items on selected Pure Mathematics topics from the national A-level examinations using the cognitive demand instrument. The instrument was found to be useful to the teachers in providing them with an awareness of how the cognitive demand of A-level mathematical assessment items could be understood through the dimensions of complexity, abstractness, and strategy.

The coded aperture imaging (CAI) technique has been used to investigate the spatial distribution of DD fusion in a 1.6 kJ plasma focus (PF) device operated in, alternatively, pure deuterium or deuterium-krypton admixture. The coded mask pattern is based on a singer cyclic difference set with 25% open fraction and positioned close to 90° to the plasma focus axis, with CR-39 detectors used to register tracks of protons from the D(d, p)T reaction. Comparing the coded aperture imagingprotonimages for pure D2 and D2-Kr admixture operation reveals clear differences in size, density, and shape between the fusion sources for these two cases.

The Coded Aperture Imaging (CAI) technique has been applied with CR-39 nuclear track detectors to image alpha particle source spatial distributions. The experimental setup comprised: a 226Ra source of alpha particles, a laser-machined CAI mask, and CR-39 detectors, arranged inside a vacuum enclosure. Three different alpha particle source shapes were synthesized by using a linear translator to move the 226Ra source within the vacuum enclosure. The coded mask pattern used is based on a Singer Cyclic Difference Set, with 400 pixels and 57 open square holes (representing ρ = 1/7 = 14.3% open fraction). After etching of the CR-39 detectors, the area, circularity, mean optical density and positions of all candidate tracks were measured by an automated scanning system. Appropriate criteria were used to select alpha particle tracks, and a decoding algorithm applied to the (x, y) data produced the de-coded image of the source. Signal to Noise Ratio (SNR) values obtained for alpha particle CAI images were found to be substantially better than those for corresponding pinhole images, although the CAI-SNR values were below the predictions of theoretical formulae. Monte Carlo simulations of CAI and pinhole imaging were performed in order to validate the theoretical SNR formulae and also our CAI decoding algorithm. There was found to be good agreement between the theoretical formulae and SNR values obtained from simulations. Possible reasons for the lower SNR obtained for the experimental CAI study are discussed.

In this work, we report the emergence of the Hands, Head and Heart framework that arose within the curriculum review for subject knowledge courses for primary school pre-service teachers in the National Institute of Education, Singapore. Through an initial grounded analysis of a survey of pre-service teachers and faculty focus group meeting data, the responses were broadly categorised into hands, head and heart domains and these formed an initial framework for discussions in the review committee meetings. By revisiting the data from the survey, an analysis through a complexity lens revealed the emergence of a characteristic nested self-similarity of the framework. Over the course of several committee meetings, further self-similarity was discovered. We conjecture that the Hands, Head and Heart framework and its self-similarity property provide a potential basis for a holistic approach to curriculum review. We used this framework to revise the learning objectives of the subject knowledge curriculum by resolving perspectives which previously seemed contradictory.

We present the first experimental results obtained using Singer product apertures. We image X-rays scattered from spherical aluminium targets, using a Crypix detector. Despite the relatively low resolution of the apertures, 13 × 13 and 21 × 21 pixels drilled into a tungsten sheet, much higher resolutions are achieved in practice using Fenimore and Cannon’s fine sampling and delta decoding techniques.

Total Quality Management (TQM) is a management philosophy developed by W.E. Deming, based on his experiences in US industry before and during the Second World War. The subsequent adoption of TQM by Japanese industry, but not by the US, is widely credited for the former's miraculous post-war reconstruction and the current massive trade imbalance between the two countries. In 1986, Deming published a book entitled Out of the Crisis, in which he summarised his ideas and exhorted US industry to adopt them as the Japanese had done. Although intended for an industrial audience, his book was also read by educationalists, who attempted to apply his ideas in their own situation. Since then, a number of researchers, including Byrnes(1992), Bonstingl(1992) and Fields (1 994), have explored the concept of Total Quality Management in education. A recently founded journal, Quality Assurance in Education, is also devoted to this topic. The aim of this article is to explain the TQM philosophy to the unfamiliar reader in as few words as possible. The explanation is based on Deming's famous "Fourteen Points," as discussed in his book Out of the Crisis. The following sections describe how TQM operates in the manufacturing industry, elaborate on how TQM may be applied analogously in education, and deal with a few of the usual objections to the application of TQM in education.

A 3 kJ plasma focus was operated with a 3He-D2 gas mixture, with partial pressures in the ratio of 2:1, corresponding to an atomic number ratio of 1:1 for 3He and D atoms. The fusion reactions D(3He,p)4He and D(d,p)3H were measured simultaneously using CR-39 polymer nuclear track detectors placed inside a pinhole camera positioned on the forward plasma focus axis. A sandwich arrangement of two 1000 μm thick CR-39 detectors enabled the simultaneous registration of two groups of protons with approximate energies of 16 MeV and 3 MeV arising from the D(3He,p)4He and D(d,p)3H reactions, respectively. Radial track density distributions were obtained from each CR-39 detector and per-shot average distributions were calculated for the two groups of protons. It is found that the D(3He,p)4He and D(d,p)3H proton yields are of similar magnitude. Comparing the experimental distributions with results from a Monte Carlo simulation, it was deduced that the D(3He,p)4He fusion is concentrated close to the plasma focus pinch column, while the D(d,p)3H fusion occurs relatively far from the pinch. The relative absence of D(d,p)3H fusion in the pinch is one significant reason for concluding that the D(3He,p)4He fusion occurring in the plasma focus pinch is not thermonuclear in origin. It is argued that the bulk of the D(3He,p)4He fusion is due to energetic 3He2+ ions incident on a deuterium target. Possible explanations for differing spatial distributions of D(3He,p)4He and D(d,p)3H fusion in the plasma focus are discussed.