How Preservice Teachers Interpret and Respond to Student Geometric Errors

Recognizing and responding to students' thinking is essential in teaching mathematics, especially when students provide incorrect solutions. This study examined, through a teaching scenario task, elementary preservice teachers' interpretations of and responses to a student's work on a task involving reflective symmetry. Findings revealed that a majority of preservice teachers identified the student's errors from conceptual aspects of reflection rather than from procedural aspects. However, when they responded to the student's errors, preservice teachers tried to cope with them by invoking procedural knowledge. This study also revealed the three types of responses and two different forms of address by preservice teachers to student errors; these categories might provide insight into the difficulties arising in communication between students and teachers.     

Straightforward preparation of polymers based on oligodimethylsiloxane and alkylamine

Novel oligodimethylsiloxane‐based polymers with alkyl side chain were synthesized in bulk by step‐growth polymerization between α,ω‐glycidyl ether oligodimethylsiloxanes and a monoalkylamine in the absence of catalyst and at temperatures ranging between 80 and 180 °C. Matrix assisted laser desorption ionization time of flight results attested for the high reactivity of the amine functions with the glycidyl groups and revealed that the main polymer structure was (A₂B₂)_n type with alkyl moieties as dangling chains. No etherification was observed during the reaction even at high temperatures and the nature of the end groups strongly depended on the molar ratio between glycidyl and amine functions. Polymerization reactions were followed by ¹H NMR and the kinetics of the glycidyl‐amine reaction pointed out the dependence of temperature, molar ratio, and the molar mass of the oligodimethylsiloxane. High conversion rates were obtained, especially with the lowest molecular weight oligodimethylsiloxane. An optimized kinetic model derived from the Horie's model was discussed and permitted to correctly fit the experimental data. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Mössbauer quadrupole splittings and electronic structure in heme proteins and model systems: a density functional theory investigation

We report the results of a series of density functional theory (DFT) calculations aimed at predicting the (57)Fe M?ssbauer electric field gradient (EFG) tensors (quadrupole splittings and asymmetry parameters) and their orientations in S = 0, (1)/(2), 1, (3)/(2), 2, and (5)/(2) metalloproteins and/or model systems. Excellent results were found by using a Wachter's all electron basis set for iron, 6-311G for other heavy atoms, and 6-31G for hydrogen atoms, BPW91 and B3LYP exchange-correlation functionals, and spin-unrestricted methods for the paramagnetic systems. For the theory versus experiment correlation, we found R(2) = 0.975, slope = 0.99, intercept = -0.08 mm sec(-)(1), rmsd = 0.30 mm sec(-)(1) (N = 23 points) covering a DeltaE(Q) range of 5.63 mm s(-)(1) when using the BPW91 functional and R(2) = 0.978, slope = 1.12, intercept = -0.26 mm sec(-)(1), rmsd = 0.31 mm sec(-)(1) when using the B3LYP functional. DeltaE(Q) values in the following systems were successfully predicted: (1) ferric low-spin (S = (1)/(2)) systems, including one iron porphyrin with the usual (d(xy))(2)(d(xz)d(yz))(3) electronic configuration and two iron porphyrins with the more unusual (d(xz)d(yz))(4)(d(xy))(1) electronic configuration; (2) ferrous NO-heme model compounds (S = (1)/(2)); (3) ferrous intermediate spin (S = 1) tetraphenylporphinato iron(II); (4) a ferric intermediate spin (S = (3)/(2)) iron porphyrin; (5) ferrous high-spin (S = 2) deoxymyoglobin and deoxyhemoglobin; and (6) ferric high spin (S = (5)/(2)) metmyoglobin plus two five-coordinate and one six-coordinate iron porphyrins. In addition, seven diamagnetic (S = 0, d(6) and d(8)) systems studied previously were reinvestigated using the same functionals and basis set scheme as used for the paramagnetic systems. All computed asymmetry parameters were found to be in good agreement with the available experimental data as were the electric field gradient tensor orientations. In addition, we investigated the electronic structures of several systems, including the (d(xy))(2)(d(xz),d(yz))(3) and (d(xz),d(yz))(4)(d(xy))(1) [Fe(III)/porphyrinate](+) cations as well as the NO adduct of Fe(II)(octaethylporphinate), where interesting information on the spin density distributions can be readily obtained from the computed wave functions.     

Encapsulation of palladium in polyurea microcapsules

An interfacial polymerisation approach is adopted to encapsulate palladium(II) acetate and palladium nanoparticles in polyurea microcapsules for use in catalysis.     

Stable (amino)(phosphino)carbenes: difunctional molecules

(Amino)(phosphino)carbenes are stable due to the donation of the nitrogen lone pair, the phosphino group remains strongly pyramidalized. Reactions can be performed selectively at the carbene center, but also at the phosphorus center leading to new stable carbenes. These difunctional molecules can be considered as hybrid ligands.     

Numerous potentially functional but non-genic conserved sequences on human chromosome 21

The use of comparative genomics to infer genome function relies on the understanding of how different components of the genome change over evolutionary time. The aim of such comparative analysis is to identify conserved, functionally transcribed sequences such as protein-coding genes and non-coding RNA genes, and other functional sequences such as regulatory regions, as well as other genomic features. Here, we have compared the entire human chromosome 21 with syntenic regions of the mouse genome, and have identified a large number of conserved blocks of unknown function. Although previous studies have made similar observations, it is unknown whether these conserved sequences are genes or not. Here we present an extensive experimental and computational analysis of human chromosome 21 in an effort to assign function to sequences conserved between human chromosome 21 (ref. 8) and the syntenic mouse regions. Our data support the presence of a large number of potentially functional non-genic sequences, probably regulatory and structural. The integration of the properties of the conserved components of human chromosome 21 to the rapidly accumulating functional data for this chromosome will improve considerably our understanding of the role of sequence conservation in mammalian genomes.     

Materials chemistry: macroporous crystalline vanadium oxide foam

Porous inorganic solids can be synthesized in complex forms, and here we describe a simple method to create an ultralight, macroporous, crystalline vanadium oxide foam by bubbling oxygen gas produced in situ through a viscous vanadium oxide gel. This foaming process could be extended to other metal oxides.     

Ab Initio calculations of the anisotropic dielectric tensor of GaAs/AlAs superlattices

The static dielectric properties of (001)(GaAs)(p)/(AlAs)(p) superlattices have been calculated as a function of their period p for 1< or = p < or =12, starting from density-functional theory. The interplay between quantum confinement and local field effects is shown to be crucial. For light polarized in the growth direction it leads to the otherwise surprising justification of the use of a classical effective medium theory, even for the smallest periods. Only the inclusion of both contributions allows in ab initio and in semiempirical calculations to reproduce the experimentally observed birefringence.     

Description of pulse propagation in a dispersive medium by use of a pulse quality factor

We investigated how the duration of short laser pulses evolves in a dispersive material, using rms widths and a propagation law based on a pulse quality factor. Experiments were carried out with femtosecond pulses (10 to 25fs at the temporal waist) propagating in bulk fused silica. Excellent agreement was found between theory and experiment. This approach does not require complete characterization of laser pulses and eliminates the need for any assumption regarding the interpretation of autocorrelation traces. The method is of general validity, and it can be applied to pulses of arbitrary shape.