The missing link in teachers’ knowledge about common fractions division

The current study explored the difficulties teachers encounter when teaching common fractions division, focusing on teachers’ knowledge concerning this issue. Nine teachers who study towards a M.Ed. degree in mathematics education demonstrated the algorithms they apply in order to solve fractions division problems, described how they teach the subject, and attempted to explain a student's mistake, in understanding a word problem involving dividing by fraction. The findings indicate there is a missing link in the teachers’ pedagogical capability, stemming from insufficient content knowledge. They presented different solution algorithms and reported using constructivist teaching methods, yet the methods they described couldn't lead a student to understand the logic behind the algorithm they teach (invert-and-multiply – multiplication by an inverse number, in accordance with the requirements of the curriculum). Furthermore, the participating teachers did not possess specialized mathematics content knowledge (SCK) and knowledge of content and students (KCS), enabling them to identify the source of a student's misconception.     

Iron chemistry of an asymmetrically substituted,triazole-functionalised calixarene ligand

The synthesis and characterisation of an asymmetrically substituted calix-triazole ligand are reported. The ligand reacts with the Fe(II) precursor Fe₂Mes₄ to yield an iron(II) calixarene complex that is oxidised by dioxygen to provide a dinuclear Fe(III) compound featuring an oxido bridge.     

Characterization and Optimization of Polymeric Bispicolamine Chelating Resin: Performance Evaluation via RSM Using Copper in Acid Liquors as a Model Substrate through Ion Exchange Method

Advanced technologies of electronics industries have led to environmental contamination concerns, especially waste print circuit boards containing a very high concentration of copper (II) ions, which can be discharged in wastewater containing many contaminated metals. A low pH is a necessity for treating industrial wastewater containing heavy metals to meet engineering process design. A novel polymeric bispicolamine chelating resin, Dowex-M4195, was applied as an alternative for investigating the behavior of copper (II) in acidic solution via an ion exchange method in a batch experiment system. Characterization of physical and chemical properties before and after ion exchange were also explored through BET, SEM-EDX, FTIR and XRD. Response surface methodology was also applied for optimization of copper (II) removal capacity using design of experiment for selective chelating resin at a low pH. The results indicate that H⁺ Dowex-M4195 chelating resin had a high-carbon content and specific surface area of >64% and 26.5060 m²/g, respectively. It was predominantly macropore porous in nature due to the N₂ gas adsorption isotherm and exhibited type IV with insignificant desorption hysteresis loop of H1-type. It was spherical and cylindrical. After the ion exchange process of copper (II)-loaded H⁺ Dowex-M4195, the specific surface area and total pore volume decreased by about 17.82% and 5.39%, respectively, as compared to H⁺ Dowex-M4195. Hysteresis loop, isotherm and pore size distribution were also similar. Regarding the functional group, the surface morphology and crystalline structures of H⁺ Dowex-M4195 showed copper (II) compound based on the structure of chelating resin that confirmed effective ion exchange behavior. The design of optimization indicated that copper (II) removal capacity of about 31.33 mg/g was achieved, which could be obtained at 6.96 h, pH of 2 (a desirable low pH), dose of 124.13 mg and concentration of 525.15 mg/L. The study indicated that the H⁺ Dowex-M4195 (which is commercially available on the market) can successfully be applied as an alternative precursor through the ion exchange method for further reuse and regeneration of the copper (II) in the electronic waste industries and other wastewater applications needed to respond the policy of biocircular green economy in Thailand.     

The different behavior of rutile and anatase nanoparticles in forming oxy radicals upon illumination with visible light: an EPR study

Photoexcited TiO(2) has been found to generate reactive oxygen species, yet the precise mechanism and chemical nature of the generated oxy species especially regarding the different crystal phases remain to be elucidated. Visible light-induced reactions of a suspension of titanium dioxide (TiO(2)) in water were investigated using electron paramagnetic resonance (EPR) coupled with the spin-trapping technique. Increased levels of both hydroxyl (˙OH) and superoxide anion (˙O(2)(-)) radicals were detected in TiO(2) rutile and anatase nanoparticles (50 nm). The intensity of signals assigned to the ˙OH and ˙O(2)(-) radicals was larger for the anatase phase than that originating from rutile. Moreover, illumination with visible (nonUV) light enhanced ˙O(2)(-) formation in the rutile phase. Singlet oxygen was not detected in water suspension of TiO(2) neither in rutile nor in anatase nanoparticles, but irradiation of the rutile phase with visible light revealed a signal, which could be attributed to singlet oxygen formation. The blue part of visible spectrum (400-500 nm) was found to be responsible for the light-induced ROS in TiO(2) nanoparticles. The characterization of the mechanism of visible light-induced oxy radicals formation by TiO(2) nanoparticles could contribute to its use as a sterilization agent.     

Solvent tuning of a conical intersection: direct experimental verification of a theoretical prediction

We report an ultrafast study of a merocyanine molecule, whose fluorescence lifetime was tuned by changing the solvent's polarity. A recent theoretical prediction that the fluorescence lifetime is considerably shortened upon lowering the polarity of the solvent, due to tuning of the conical intersection properties, is fully confirmed (Xu et al. J. Phys. Chem. A 2009, 113, 9779-9791). This constitutes a direct measurement of a previously predicted tunable property of a conical intersection.     

Cyclopropenyllithiums as a new source of 1,1-bismetalated cyclopropyl derivatives

The allylmetalation of functionalised cyclopropenyllithium derivatives leads to the unique formation of 1,1-bismetalated cyclopropyl species that react selectively with different electrophiles.     

Initiation and inhibition of protein biosynthesis studies at high resolution

Analysis of the high resolution structure of the small subunit from Thermus thermophilus shed light on its inherent conformational variability and indicated an interconnected network of features allowing concerted movements during translocation. It also showed that conformational rearrangements may be involved in subunit association and that a latch-like movement guarantees processivity and ensures maximized fidelity. Conformational mobility is associated with the binding and the anti association function of initiation factor 3, and antibiotics interfering with prevent the initiation of the biosynthetic process. Proteins stabilize the structure mainly by their long basic extensions that penetrate into the ribosomal RNA. When pointing into the solution, these extensions may have functional roles in binding of non-ribosomal factors participating in the process of protein biosynthesis. In addition, although the decoding center is formed of RNA, proteins seem to serve ancillary functions such as stabilizing ist required conformation and assisting the directionality of the translocation.     

Synthesis and bioactivity of labelled germination stimulants for the isolation and identification of the strigolactone receptor

Strigolactones are highly potent germination stimulants for seeds of the parasitic weeds Striga and Orobanche spp. The induction of seed germination is thought to proceed via a receptor-mediated mechanism. Isolation and purification of the strigolactone receptor by affinity chromatography using immobilized avidin or streptavidin requires a biotin labelled strigolactone analogue. For this purpose biotin has been attached, directly as well as indirectly, via a hydrophilic linker to the amino function of optically active amino-GR24. Using the same amino substituted synthetic stimulant GR24, labelled stimulants have been prepared which may be suitable for the identification of the receptor by means of fluorescence correlation spectroscopy, scanning force microscopy or photoaffinity techniques. Bioassays of the labelled stimulants reveal that the germination activity on seeds of Striga hermonthica is retained. Crystal data for the diastereoisomer (+)-8 are reported.