Coordinating Theories of Learning to Account for Second-Grade Children's Arithmetical Understandings

This article coordinates social constructivism and socioculturalism orientations to explain 2nd-grade children's reasoning with 2-digit quantities. From a social constructivist position, we illustrate how the classroom teacher and the students constituted what counted as an acceptable mathematical explanation. As children offered informal and conventional ways of interpreting problem situations, they were expected to reason with quantities in sensible ways. From a sociocultural position, we explain how the teacher's and students' contributions were situated within the mathematical ways of knowing constituted by the community at large. Particular children's contributions were clarified in terms of the ways in which they participated in socially organized activities. By coordinating these lenses, we argue the local classroom mathematical practices constrained and enabled the mathematical practices of the wider society.     

Spectroscopic Study of Acid-base Equilibria and Ion Pairing in Supercritical Methanol

Acid-base equilibria between 2,5-dichlorophenol (DCP) and various bases (LiOH, NaOH, and KOH) were studied in ambient to supercritical methanol, by measuring the absorption spectrum of DCP at alkali metal hydroxide molalities ranging up to 10 mmol⋅kg⁻¹, at temperatures up to 250 °C and a pressure of 25.0 MPa. The spectrum was deconvoluted into contributions for the acidic (HA) and basic (A⁻) forms of DCP, taking into account a blue shift of the phenolate (A⁻) spectrum due to the effect of ion pairing with an alkali metal cation. Degrees of dissociation of DCP determined from the spectra suggested that the dissociation constant of DCP has a maximum around 150 °C, whereas that of KOH decreases with temperature. The phenolate-alkali metal ion pairing was examined from the peak shift of the phenolate spectrum in the presence of Li⁺, Na⁺, and K⁺. A smaller cation radius and higher temperature (thus a lower dielectric constant for methanol) give rise to stronger electrostatic interaction in the ion pair. The basicities of the alkali metal hydroxides in supercritical methanol were compared using DCP as an indicator, and were shown to follow the order LiOH < NaOH ≤ KOH. This order is the same as that for the catalytic effect of alkali metal hydroxides on the methylation of phenol in supercritical methanol (Takebayashi et al.: Ind. Eng. Chem. Res. 47:704–709, 2008). Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.     

Stability and Synchronization of a Ring of Identical Cells with Delayed Coupling

We consider a ring of identical elements with time delayed, nearest neighbour coupling. The individual elements are modelled by a scalar delay differential equation which includes linear decay and nonlinear delayed feedback. The linear stability of the trivial solution is completely analyzed and illustrated in the parameter space of the coupling strength and the coupling delay. Conditions for global stability of the trivial solution are also given. The bifurcation and stability of nontrivial synchronous solutions from the trivial solution is analyzed using a centre manifold construction.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday.     

The hydrological response of heavy clay grassland soils to rainfall in south‐west England using δ2H

Stable isotopes of water have been previously used in catchment studies to separate rain‐event water from pre‐event groundwater. However, there are a lack of studies at the smaller scale looking at the separation of event water from pre‐event water. This is particularly relevant for heavy clay soil systems through which the movement of water is uncertain but is thought to be rainwater‐dominated. The data presented here were collected at a rural site in the south‐west of England. The historic rainfall at the site was isotopically varied but similar to the global meteoric water line, with annual weighted means of ?37‰ for δ²H and ?5.7‰ for δ¹⁸O and with no seasonal variation. Drainage was sampled from the inter‐flow (surface runoff + lateral through‐flow) and drain‐flow (55 cm deep mole drains) pathways of two 1 ha lysimeters during two rainfall events, which had δ²H values of ?68‰ and ?92‰, respectively. The δ²H values of the lysimeter drainage water suggest that there was no contribution of event water during the first, small discharge (Q) event; however, the second larger event did show isotopic variation in δ²H values negatively related to Q indicating that rainwater was contributing to Q. A hydrograph separation indicated that only 49–58% of the inter‐flow and 18–25% of the drain‐flow consisted of event water. This was surprising given that these soil types are considered retentive of soil water. More work is needed on heavy clay soils to understand better the nature of water movement from these systems. Copyright © 2010 John Wiley & Sons, Ltd.     

N,N'-Carbonyldiimidazole-mediated functionalization of superparamagnetic nanoparticles as vaccine carrier

Particulates with specific sizes and characteristics can induce potent immune responses by promoting antigen uptake of appropriate immuno-stimulatory cell types. Magnetite (Fe(3)O(4)) nanoparticles have shown many potential bioapplications due to their biocompatibility and special characteristics. Here, superparamagnetic Fe(3)O(4) nanoparticles (SPIONs) with high magnetization value (70emug(-1)) were stabilized with trisodium citrate and successfully conjugated with a model antigen (ovalbumin, OVA) via N,N'-carbonyldiimidazole (CDI) mediated reaction, to achieve a maximum conjugation capacity at approximately 13 microgmicrom(-2). It was shown that different mechanisms governed the interactions between the OVA molecules and magnetite nanoparticles at different pH conditions. We evaluated as-synthesized SPION against commercially available magnetite nanoparticles. The cytotoxicity of these nanoparticles was investigated using mammalian cells. The reported CDI-mediated reaction can be considered as a potential approach in conjugating biomolecules onto magnetite or other biodegradable nanoparticles for vaccine delivery.