Cognitive Demands and Second-Language Learners: A Framework for Analyzing Mathematics Instructional Contexts

The issues involved in teaching English language learners mathematics while they are learning English pose many challenges for mathematics teachers and highlight the need to focus on language-processing issues related to teaching mathematical content. Two realistic-type problems from high-stakes tests are used to illustrate the complex interactions between culture, language, and mathematical learning. The analyses focus on aspects of the problems that potentially increase cognitive demands for second-language learners. An analytical framework is presented that is designed to enable mathematics teachers to identify critical elements in problems and the learning environment that contribute to increased cognitive demands for students of English as a second language. The framework is proposed as a cycle of teacher reflection that would extend a constructivist model of teaching to include broader linguistic, cultural, and cognitive processing issues of mathematics teaching, as well as enable teachers to develop more accurate mental models of student learning.     

One-dimensional fluid and circuit simulation of an AC plasmadisplay cell

A one-dimensional multispecies model of a helium filled AC plasma display cell is described. The model includes a continuity equation for each species. Poisson's equation and a circuit equation. The fill gas is helium for which the cross sections for ionization and excitation for the various atomic states are well known. The reaction rates for the different species were parametrized as functions of E/N using a zero-dimensional spatial and two velocity multispecies Boltzmann kinetic code. Calculations are performed using address and sustain voltages operating at a frequency of 50 kHz to model the pulse behavior of a dielectric barrier discharge which occurs over a time scale on the order of 200 ns or less. The code simulates multipulse behavior and shows reasonably good agreement with experimental data. The simulations show that the circuit filters out the discharge dynamics and that the pulse width of the discharge current depends on the circuit RC time constant. Using a 123 V sustain voltage, the calculated discharge current is 0.4 A with a full width at half maximum (FWHM) of 28 ns. Experimental values using a 120 V sustain voltage are 0.32 A discharge current and 42 ns FWHM     

Magnetic behaviour and site occupation of YFe12-x V x (x=2,3,4)

The effects of vanadium substitution on the iron magnetism in YFe_12-x V _x compounds (x～2–4) have been studied by⁵⁷Fe Mössbauer spectroscopy. The preference of vanadium atoms for the 8i site of these ThMn₁₂-structure type compounds is confirmed. The rapid collapse of the iron sublattice magnetization with increasing vanadium concentration is analysed in terms of the ‘magnetic valence’ model.     

Samuelson maps—recent results

Samuelson maps are maps whose Jacobian matrix has nowhere vanishing leading principal minors. This paper surveys some recent results on invertibility of Samuelson maps and their decomposition into maps that fix all but one coordinate. The most noteworthy result is that real, rational, everywhere defined Samuelson maps are invertible. Proofs are sketched or omitted entirely.     

Preparation and characterization of a set of IAEA reference air filters for quality control in air-pollution studies

Several sets of reference air filters were prepared as part of an IAEA evaluation of the performance of laboratories involved in air-pollution studies. Each set comprised three polycarbonate membrane filters, two of which were loaded with urban air particulate matter (APM) obtained in Vienna or Prague, and one unloaded filter. The filters were loaded by filtration of a suspension of the APM materials in water. The homogeneity both of bulk APM materials and of the loaded filters was evaluated and found suitable by determining several elements by instrumental neutron-activation analysis (INAA), proton-induced X-ray emission (PIXE), and micro-X-ray energy-dispersive fluorescence analysis (micro-EDXRF). After evaluation of the homogeneity, INAA, PIXE, EDXRF, atomic absorption spectrometry (AAS), inductively coupled plasma optical emission spectrometry (ICP-OES), and ICP mass spectrometry (ICP-MS) were used to characterize the filter materials and establish "target values" and their associated standard deviations for 15 elements. Problems encountered during the preparation of these unique, simulated air filters and the criteria for setting both the target values and standard deviations are presented.