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.     

The effect of solvent upon molecularly thin rotaxane film formation

We have investigated variations in molecularly thin rotaxane films deposited by solvent evaporation, using atomic force microscopy (AFM). Small changes in rotaxane structure result in significant differences in film morphology. The addition of exo-pyridyl moietes to the rotaxane macrocycle results in uniform domains having orientations corresponding to the underlying substrate lattice, while a larger, less symmetric molecule results in a greater lattice mismatch and smaller domain sizes. We have measured differences in film heights both as a function of the solvent of deposition and as a function of surface coverage of rotaxanes. Based on these observations we describe how the use of solvents with higher hydrogen-bond basicity results in films which are more likely to favour sub-molecular motion.     

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.     

XPS investigations of ink‐jet printed paper

Different ink‐jet printed paper materials were investigated using X‐ray photoelectron spectroscopy (XPS) yielding the elemental composition of the near‐surface region of the papers. We found significant differences with respect to the detected elements and their atomic concentrations in the different inks studied here. Two different groups of inks could be identified by means of a lower ratio of the O and C atomic concentrations and lower concentrations in specific trace elements like Mg, Na and Si. High‐resolution spectra of C 1s and O 1s core levels allowed a detailed determination of the chemical state of the respective elements. On the basis of a detailed deconvolution of these XPS signals, significant differences between all the investigated ink‐jet printed papers were found, thereby allowing their discrimination. The applicability of the measurements and, more generally, the XPS technique for forensic investigations of paper are discussed. Copyright © 2007 John Wiley & Sons, Ltd.