Charting the microworld territory over time: design and construction in mathematics education

The study discusses the development of theoretical ideas and constructs related to digital microworlds within the mathematics education community and their implications for interpretations of mathematics learning. Starting from Papert’s introduction of the concept during ICME 2 in 1972, we trace the evolution of theoretical approaches concerning the essence of the idea in an attempt to situate the notion of constructionism in the light of contemporary frameworks. We argue that microworlds, and the search for a learnable mathematics, have a continued relevance to mathematics education, but that the lens research attention has shifted over time, with the current foci on communal design, situated and embodied approaches and artefacts whose use crosses boundaries between different practices. To illustrate these shifts and the challenges that still remain, we present examples from our current work involving the use of microworlds for learning and teaching through communication, design and construction.     

A review of oxyhalide disinfection by-products determination in water by ion chromatography and ion chromatography-mass spectrometry

This paper is a review of ion chromatographic (IC) separations of inorganic oxyhalide disinfection by-products (DBPs) in water and beverages. The review outlines the chemical mechanisms of formation, regulation of maximum allowable levels, chromatographic column selection and speciation. In addition, this review highlights the application of IC coupled to mass spectrometry (MS) for trace and elemental composition analysis of oxyhalides, along with the analytical considerations associated to enable sensitive analysis. Furthermore, a review of literature concerning IC determination of inorganic oxyhalide DBPs in environmental matrices, including water, published since 2005 is presented, with a focus on MS detection, and a discussion on the relative performance of the methods. Finally some prospective areas for future research, including fast, selective, multi-analyte analysis, for this application are highlighted and discussed.     

Infrared Spectroscopy During Electrocatalytic Turnover Reveals the Ni‐L Active Site State During H2 Oxidation by a NiFe Hydrogenase

A novel in situ IR spectroscopic approach is demonstrated for the characterization of hydrogenase during catalytic turnover. E. coli hydrogenase 1 (Hyd‐1) is adsorbed on a high surface‐area carbon electrode and subjected to the same electrochemical control and efficient supply of substrate as in protein film electrochemistry during spectral acquisition. The spectra reveal that the active site state known as Ni‐L, observed in other NiFe hydrogenases only under illumination or at cryogenic temperatures, can be generated reversibly in the dark at ambient temperature under both turnover and non‐turnover conditions. The observation that Ni‐L is present at all potentials during turnover under H₂ suggests that the final steps in the catalytic cycle of H₂ oxidation by Hyd‐1 involve sequential proton and electron transfer via Ni‐L. A broadly applicable IR spectroscopic technique is presented for addressing electrode‐adsorbed redox enzymes under fast catalytic turnover.     

Arylation of [6,6]-spiroacetal enol ethers: reactivity and rearrangement

Attempts to selectively arylate [6,6]-spiroacetal enol ethers at the 2-position delivered unexpected results. Palladium-mediated arylation conditions afforded the double-Heck product, whereas reaction with benzenesulfinic acid resulted in a facile rearrangement into the corresponding 5-phenylsulfonyl-3,4,5,6-tetrahydrochromans, providing access to 5-aryl-3,4,5,6-tetrahydrochroman and hexahydrochroman derivatives.     

AGSE: A Novel Grape Seed Extract Enriched for PP2A Activating Flavonoids That Combats Oxidative Stress and Promotes Skin Health

Environmental stimuli attack the skin daily resulting in the generation of reactive oxygen species (ROS) and inflammation. One pathway that regulates oxidative stress in skin involves Protein Phosphatase 2A (PP2A), a phosphatase which has been previously linked to Alzheimer’s Disease and aging. Oxidative stress decreases PP2A methylation in normal human dermal fibroblasts (NHDFs). Thus, we hypothesize agents that increase PP2A methylation and activity will promote skin health and combat aging. To discover novel inhibitors of PP2A demethylation activity, we screened a library of 32 natural botanical extracts. We discovered Grape Seed Extract (GSE), which has previously been reported to have several benefits for skin, to be the most potent PP2A demethylating extract. Via several fractionation and extraction steps we developed a novel grape seed extract called Activated Grape Seed Extract (AGSE), which is enriched for PP2A activating flavonoids that increase potency in preventing PP2A demethylation when compared to commercial GSE. We then determined that 1% AGSE and 1% commercial GSE exhibit distinct gene expression profiles when topically applied to a 3D human skin model. To begin to characterize AGSE’s activity, we investigated its antioxidant potential and demonstrate it reduces ROS levels in NHDFs and cell-free assays equal to or better than Vitamin C and E. Moreover, AGSE shows anti-inflammatory properties, dose-dependently inhibiting UVA, UVB and chemical-induced inflammation. These results demonstrate AGSE is a novel, multi-functional extract that modulates methylation levels of PP2A and supports the hypothesis of PP2A as a master regulator for oxidative stress signaling and aging in skin.     

A characterization of level planar graphs

We present a characterization of level planar graphs in terms of minimal forbidden subgraphs called minimal level non-planar (MLNP) subgraph patterns. We show that an MLNP subgraph pattern is completely characterized by either a tree, a level non-planar cycle or a level planar cycle with certain path augmentations.     

A traceless linker for aliphatic amines that rapidly and quantitatively fragments after reduction

Reduction sensitive linkers (RSLs) have the potential to transform the field of drug delivery due to their ease of use and selective cleavage in intracellular environments. However, despite their compelling attributes, developing reduction sensitive self-immolative linkers for aliphatic amines has been challenging due to their poor leaving group ability and high pK_a values. Here a traceless self-immolative linker composed of a dithiol-ethyl carbonate connected to a benzyl carbamate (DEC) is presented, which can modify aliphatic amines and release them rapidly and quantitatively after disulfide reduction. DEC was able to reversibly modify the lysine residues on CRISPR–Cas9 with either PEG, the cell penetrating peptide Arg₁₀, or donor DNA, and generated Cas9 conjugates with significantly improved biological properties. In particular, Cas9–DEC–PEG was able to diffuse through brain tissue significantly better than unmodified Cas9, making it a more suitable candidate for genome editing in animals. Furthermore, conjugation of Arg₁₀ to Cas9 with DEC was able to generate a self-delivering Cas9 RNP that could edit cells without transfection reagents. Finally, conjugation of donor DNA to Cas9 with DEC increased the homology directed DNA repair (HDR) rate of the Cas9 RNP by 50% in HEK 293T cell line. We anticipate that DEC will have numerous applications in biotechnology, given the ubiquitous presence of aliphatic amines on small molecule and protein therapeutics.

Reduction sensitive linkers (RSLs) have the potential to transform the field of drug delivery due to their ease of use and selective cleavage in intracellular environments.     

Analysis of silica hydride and surface hydrosilation reactions by solid-state NMR in the preparation of<Emphasis Type="Italic"> p</Emphasis>-chlorobenzamide bonded silica phase

²⁹Si and ¹³C CP-MAS NMR spectroscopy was used to follow the conversion of native silica to a p-chlorobenzamide bonded silica material. The benzamide bonded phase was prepared via a hydrosilation reaction of a hydride silica intermediate with p-chloro-N-allylbenzamide. Solid-state NMR was used to show the disappearance of reactive surface hydride species (M_H) and to identify newly formed bonded chemical species on the silica surface. DRIFT spectroscopy, elemental analysis, and specific surface-area determinations (BET) of the prepared phases are also reported.