The preparation of primary mathematics teachers in Singapore: programs and outcomes from the TEDS-M study

This paper describes five aspects of primary mathematics teacher education in Singapore: (a) the teaching profession in Singapore, (b) the structure of pre-service teacher education programs offered by the National Institute of Education, (c) self-reports of Singapore future primary mathematics teachers about the opportunities to learn mathematics-related contents offered by these programs, based on the Teacher Education and Development Study in Mathematics (TEDS-M) survey, (d) the performance of these future teachers in mathematics content knowledge and mathematics pedagogical content knowledge assessed by the TEDS-M study, and (e) the relationships of opportunities to learn with this performance. The paper concludes with some suggestions about how to improve the quality of initial teacher preparation in the areas of recruitment and training.     

Over-nonlocal gradient enhanced plastic-damage model for concrete

Classical continuum models exhibit strong mesh dependency during softening. One method to regularize the problem is to introduce a length scale parameter via the nonlocal formulation. However, standard nonlocal enhancement (either by integral or gradient formulation) may serve only as a partial localization limiter for many material models. The “over-nonlocal” formulation, where the weight for the nonlocal value is greater than unity and the excesses compensated by assigning a negative weight to the local value, is able to fully regularize certain material models when standard nonlocal enhancement fails to do so. A plastic-damage model for concrete is formulated with this over-nonlocal enhancement via the gradient approach and the full regularizing capabilities demonstrated.     

PIV measurements of the flow field inside an enclosed cubical cavity in natural convection

The natural convective velocity field in an enclosed air-filled cubical cavity with two opposing isothermal faces and the remaining four sides having a well-defined linear temperature rise from the cold to the hot face has been measured at different physical orientations and Rayleigh (Ra) numbers. In particular, two components of the velocity at the mid-plane have been measured by using particle image velocimetry (PIV) at Ra = 10⁶ and 6 × 10⁶ at each of two different physical orientations: heating-from-the-side (HFS), and heating-from-below (HFB). The 95% confidence limit uncertainties in the measured velocity vectors are about 2% for laminar flow. The accuracy and integrity of the experiments were validated by the comparison to some well-established CFD results at the HFS orientation at Ra = 10⁶. It was concluded that the experimental method is sound and so findings at other orientations and at other values of Ra should have an accuracy consistent with the findings of the uncertainty analysis. Therefore, the other results can be confidently used as benchmark data for testing CFD codes. The turbulence intensities at the mid-plane are also presented.     

Processing the capillary viscometry data of fluids with yield stress

The capillary viscometer is used to measure the shear stress-shear rate relationship of a wide range of purely viscous fluids. It is however not considered as an appropriate instrument for obtaining the yield stress and the post-yield behaviour of fluids that have a yield stress. This is partly because conventional methods of processing the capillary viscometry data of purely viscous fluids cannot be applied to similar data of fluids with yield stress. The unavoidable experimental noise in the capillary data, particularly at low shear rates, also makes it difficult to obtain a reliable estimate of the yield stress from capillary data. In this investigation the problem of converting the capillary viscometry data of yield stress fluids into a shear stress-shear rate curve and a yield stress is formulated as a Volterra integral equation of the first kind. This is an ill-posed problem i.e. noise in the data will be amplified by inappropriate methods of data processing. A method, based on Tikhonov regularisation that takes into account the ill-posed nature of the problem, is then developed to solve this problem for fluids with yield stress. The performance of this method is assessed by applying it to a set of “synthetic” capillary viscometry data with added random noise and to a set of experimental data for a concentrated suspension of TiO₂ taken from the literature. In both cases Tikhonov regularisation was able to extract the complete shear properties of these fluids from capillary viscometry data alone. Received: 22 November 1999/Accepted: 17 December 1999     

Structural studies of ammonium nitrate 1. Phases III,IV and V

The laser Raman spectra of NH₄NO₃ and ND₄NO₃ have been measured between 210 and 320 K. It is shown that the phase transition V → IV is probably a λ transition which occurs gradually between 210 and 256 K with an abrupt change at 256 K. The λ transition is due to rotational disorder of ammonium ions as shown by the localised disorder mode at 172 cm^?1. The spectrum of phase IV shows clear evidence of T and L components of the nitrate ion asymmetric stretch. This is inconsistent with the assigned space group Pmmn. An explanation based on a thermally inducted IV → III transition is proposed.     

Simultaneous analysis of all five organic priority pollutant fractions

Acrolein, acrylonitrile, volatile organics, base/neutral extractables, acid extractables, and pesticide fraction organics are analyzed in a single chromatographic run. This is accomplished by injecting the extractable organics, then applying a cryogenic focus to the front of the column, and desorbing the volatile components. The column utilized for this procedure is a fused silica open tubular (FSOT) column coated with the liquid phase SE-54. Minimum detection limits of this procedure by electron impact GC/MS are shown to be? 1 μg/liter in tests conducted on actual water samples.     

Polyelectrolyte complex films derived from polyethyleneoxide-maleic acid copolymer and chitosan: preparation and characterization

Polyelectrolyte complex films were prepared with polyethyleneoxide-maleic acid copolymer and chitosan using a casting/solvent evaporation method. The films were examined in terms of their IR spectra, surface and cross-section morphologies, cytotoxicity, and swelling behavior at different pH levels. To assess the potential of these films as a biomedical device, the profiles of the release of model drug from the CS/PEOMA films were examined at pH 4.8. The surface morphology of the films was quite smooth and uniform, and the cross-sectional morphology was dense and homogeneous. The swelling behaviors of CS/PEOMA films were found to depend on the pH of the solution as well as on the CS/PEOMA composition. Drug release from different CS/PEOMA films at pH 4.8 was found to be dependent on film composition. The results showed the potential applicability of CS/PEOMA film as a drug delivery vehicle.