Opportunity to learn in the preparation of mathematics teachers: its structure and how it varies across six countries

Cross-national research studies such as the Program for International Student Assessment and the Third International Mathematics and Science Study (TIMSS) have contributed much to our understandings regarding country differences in student achievement in mathematics, especially at the primary (elementary) and lower secondary (middle school) levels. TIMSS, especially, has demonstrated the central role that the concept of opportunity to learn plays in understanding cross-national differences in achievement Schmidt et al., (Why schools matter: A cross-national comparison of curriculum and learning  2001). The curricular expectations of a nation and the actual content exposure that is delivered to students by teachers were found to be among the most salient features of schooling related to academic performance. The other feature that emerges in these studies is the importance of the teacher. The professional competence of the teacher which includes substantive knowledge regarding formal mathematics, mathematics pedagogy and general pedagogy is suggested as being significant—not just in understanding cross-national differences but also in other studies as well (Hill et al. in Am Educ Res J 42(2):371–406, 2005). Mathematics Teaching in the 21st Century (MT21) is a small, six-country study that collected data on future lower secondary teachers in their last year of preparation. One of the findings noted in the first report of that study was that the opportunities future teachers experienced as part of their formal education varied across the six countries (Schmidt et al. in The preparation gap: Teacher education for middle school mathematics in six countries, 2007). This variation in opportunity to learn (OTL) existed in course work related to formal mathematics, mathematics pedagogy and general pedagogy. It appears from these initial results that OTL not only is important in understanding K-12 student learning but it is also likely important in understanding the knowledge base of the teachers who teach them which then has the potential to influence student learning as well. This study using the same MT21 data examines in greater detail the configuration of the educational opportunities future teachers had during their teacher education in some 34 institutions across the six countries.     

A two-scale model for one-dimensional arrays of cantilevers and its verification

We present a simplified model of the mechanical behavior of large arrays of cantilevers in the dynamic operating regime. The supporting base is assumed to be elastic thus cross-talk effect between the cantilevers is taken into account. Beforehand, the model has been mathematically justified starting from a thin plate model, using the two-scale approximation theory issued from homogenization theory and taking into account the strong heterogeneities of the system. The resulting model is not standard, so in this paper dedicated to its verification, we focus on some of its features in particular those related to the structure of its eigenmodes by both a qualitative and a quantitative analysis.     

The electronic origin of the dual fluorescence in donor-acceptor substituted benzene derivatives

The origin of the dual fluorescence of DMABN (dimethylaminobenzonitrile) and other benzene derivatives is explained by a charge transfer model based on the properties of the benzene anion radical. It is shown that, in general, three low-lying electronically excited states are expected for these molecules, two of which are of charge transfer (CT) character, whereas the third is a locally excited (LE) state. Dual fluorescence may arise from any two of these states, as each has a different geometry at which it attains a minimum. The Jahn-Teller induced distortion of the benzene anion radical ground state helps to classify the CT states as having quinoid (Q) and antiquinoid (AQ) forms. The intramolecular charge transfer (ICT) state is formed by the transfer of an electron from a covalently linked donor group to an anti-bonding orbital of the pi-electron system of benzene. The change in charge distribution of the molecule in the CT states leads to the most significant geometry change undergone by the molecule which is the distortion of the benzene ring to a Q or AQ structure. As the dipole moment is larger in the perpendicular geometry than in the planar one, this geometry is preferred in polar solvents, supporting the twisted intramolecular charge transfer (TICT) model. However, in many cases the planar conformation of CT excited states is lower in energy than that of the LE state, and dual fluorescence can be observed also from planar structures.     

Mixed micellization between natural and synthetic block copolymers: β-casein and Lutrol F-127

Amphiphilic block copolymers and mixtures of amphiphiles find broad applications in numerous technologies, including pharma, food, cosmetic and detergency. Here we report on the interactions between a biological charged diblock copolymer, β-casein, and a synthetic uncharged triblock copolymer, Lutrol F-127 (EO(101)PO(56)EO(101)), on their mixed micellization characteristics and the micelles' structure and morphology. Isothermal titration calorimetry (ITC) experiments indicate that mixed micelles form when Lutrol is added to monomeric as well as to assembled β-casein. The main driving force for the mixed micellization is the hydrophobic interactions. Above β-casein CMC, strong perturbations caused by penetration of the hydrophobic oxypropylene sections of Lutrol into the protein micellar core lead to disintegration of the micelles and reformation of mixed Lutrol/β-casein micelles. The negative enthalpy of micelle formation (ΔH) and cooperativity increase with raising β-casein concentration in solution. ζ-potential measurements show that Lutrol interacts with the protein micelles to form mixed micelles even below its critical micellization temperature (CMT). They further indicate that Lutrol effectively masks the protein charges, probably by forming a coating layer of the ethyleneoxide rich chains. Small-angle X-ray scattering (SAXS) and cryogenic-transmission electron microscopy (cryo-TEM) indicate relatively small changes in the oblate micellar shape, but do show swelling along the small axis of β-casein micelles in the presence of Lutrol, thereby confirming the formation of mixed micelles.     

High performance two-color one megapixel CMOS ROIC for QWIP detectors

FLIR Systems, Inc. has designed and fabricated the ISC0501 CMOS readout integrated circuit (ROIC) for quantum well infrared photodetectors (QWIPs). The ISC0501 is a two-color 1024 × 1024 format array with a 30 μm pixel pitch. The ROIC contains a separate analog signal path for each wavelength band. Separate signal paths allow the two-colors to have optimized detector biases, integration times, offsets and gains. This architecture also allows both colors to simultaneously sample a scene and readout the pixel data. This paper will describe the interface, design and features of the ROIC as well as a summary of the characterization test results. A sample image is included from a focal plane array (FPA) built by the Jet Propulsion Laboratory (JPL) using the ISC0501 ROIC with QWIP detectors designed by JPL.     

The temperature stability of punch-through diodes

There is a single value of current, where the temperature dependence of voltage across a punch-through diode is close to zero over a wide temperature range. The sign of the dependence is negative below this value and positive above. A model which accounts for this behaviour in terms of the injection mechanism gives excellent agreement with experiment.     

Non-minimal and non-universal supersymmetry

I motivate and discuss non-minimal and non-universal models of supersymmetry and supergravity consistent with string unification at 10¹⁰ GeV.     

The effects of vortex breakdown bubbles on the mixing environment inside a base driven bioreactor

The bubble-type vortex breakdown inside a cylinder with flow driven by rotation of the base, has applications in mixing. We investigate this phenomena and its effect on the environment inside an open cylinder, with potential application as a tissue-engineering bioreactor, with tissue-scaffolds of two different geometries immersed in the fluid. Addition of scaffolds induces a blockage effect, hindering the flow in the central vortex core returning to the rotating base. This promotes early onset of vortex breakdown and alters the final shape of vortex breakdown bubbles. Placement of the scaffolds centrally on the cylinder axis yields almost identical levels and distributions of shear stress between the upper and lower surfaces of scaffolds. A change from a disk shaped to an ellipsoidal scaffold, of the same size, reduces the intensity of the maximum shear stresses at the scaffold surface by up to 50%. There is a range of Reynolds numbers where increasing Reynolds number, and hence possibly increasing mixing efficiency, leads to a decrease in the maximum levels of fluid forces at the scaffold surfaces. This is an important conclusion for scaffold based tissue engineering where improved mixing is sought, but often sacrificed in favor of minimizing fluid forces.