Supporting Preservice Teachers' Understanding of Place Value and Multidigit Arithmetic

This article provides an analysis of a teaching experiment conducted in the context of teacher education designed to support preservice teachers' understandings of place value and multidigit addition and subtraction. The experiment addresses the following research question: Can the results from research conducted in elementary mathematics classrooms guide preservice elementary teachers' development of conceptual understanding of the same concepts? In both cases, the students (e.g., elementary students and preservice teachers) participated in activities from an instructional sequence designed to support conceptual understanding of both place value and multidigit addition and subtraction. Analyses of the episodes from the teaching experiment document the learning of the preservice teachers and how that learning was supported by initial conjectures grounded in the research on elementary students' ways of reasoning.     

Magnetism in very thin films of permalloy measured by spin polarized cascade electrons

The spin polarizationP of the low energy cascade electrons excited with a primary unpolarized electron beam is measured with ultrathin films of permalloy (Ni₈₀Fe₂₀) as a function of film thickness, external magnetic field, and temperatureT. Surface adsorbates of small concentrations of less than 10% of a monolayer can change the Curie point and the saturation value ofP ₀(T0) by as much as 30%. The Ta-substrate induces a magnetically dead region in permalloy. Conventional spin wave theory cannot account for the observed smallT-dependence of the magnetizationM. Films on a nonmagnetic substrate are compared to similar films coupled to bulk permalloy over an interface of Ta. TheT-dependence ofM with the coupled films can be explained by spin wave theory. At lowT, the films coupled to the bulk exhibit a faster decrease ofM than the uncoupled films. We propose that this thermal stabilization of the magnetization in very thin ferromagnetic films is due to quenching of the long wavelength spin modes.     

Structural considerations from dielectric measurements on the aliphatic alcohols

Precise static dielectric constants are reported for methanol, ethanol, andn-propanol at 10,25, and 40° C and at pressures up to 3 kbar. The measurements were carried out by a low-frequency bridge method using a threeterminal, all-glass cell. An uncertainty of 0.05% is claimed for the data. The results are compared to data from previous investigations, whith the agreement in the absolute magnitude poor but the agreement in the pressure coefficient reasonable in most cases. The data are analyzed in terms of the Kirkwood correlation factorg _K as obtained from the Fröhlich equation. In all cases, theg _K factor decreases with increased pressure. The problems involved in calculating this factor from the experimental data are discussed, and it is shown that the trends ing _K are very dependent upon the assumptions made in isolating the liquid dipole moment from its gas-phase value. This fact also indicates that an interpretation of theg _K values in terms of stepwise association of correlation dipoles is premature at this time.     

High-resolution four-dimensional 1H-13C NOE spectroscopy using methyl-TROSY, sparse data acquisition, and multidimensional decomposition

An approach for recording four-dimensional (4D) methyl (1)H-(13)C-(13)C-(1)H NOESY spectra with high resolution and sensitivity is presented and applied to Malate Synthase G (723 residues, 82 kDa). Sensitivity and resolution have been optimized using a highly deuterated, methyl-protonated sample in concert with methyl-TROSY, sparse data sampling in the three indirect dimensions, and 4D spectral reconstruction using multidimensional decomposition (MDD). A sparse data acquisition protocol is introduced that ensures that sufficiently long indirect acquisition times can be employed to exploit the decreased relaxation rates associated with methyl-TROSY, without increasing the duration of the 4D experiment beyond acceptable measurement times. In this manner, only a fraction ( approximately 30%) of the experimental data that would normally be needed to achieve a spectrum of high resolution is acquired. The reconstructed 4D spectrum is of similar resolution and sensitivity to three-dimensional (3D) (13)C-edited NOE spectra, is straightforward to analyze, and resolves ambiguities that emerge when 3D data sets only are considered.     

Versatile solid-phase synthesis of secondary amines from alcohols. Development of an N-Boc-(o-nitrobenzene)sulfonamide linker

The development of a versatile amine releasing linker based on the modified o-nitrobenzene sulfonamide protective group is described. This new N-Boc-o-nitrobenzenesulfonamide (Boc-ONBS) linker enables the elaboration on resin of primary and secondary amines by sequential substitution of the sulfonamide moiety using the Mitsunobu reaction. A 16-member array of secondary and Boc protected primary amines was then prepared using this linker.