Being a mathematics teacher in times of reform

Within research on mathematics teachers and/or their professional development, the concept of identity emerges as a critique of views of how teaching practice is related to teachers’ ‘internal states’ of knowledge and beliefs. Identity relates teachers’ professional lives to teaching practices and to the contexts in which the teaching and/or professional development occurs. However, what might count as the context still needs in-depth discussion. In order to contribute to the development of a theoretical framework for understanding mathematics teachers’ professional lives, we will draw on one remarkable teacher’s identity as a primary mathematics teacher in relation to one political, sociocultural, and pedagogical context. We use this teacher’s experience to discuss how education policies that create what Ball (2003) called ‘terrors of performativity’ tend to impede the formation of a balanced teacher identity.     

Mononuclear ruthenium complexes containing chiral aminooxazolines: Syntheses, X-ray studies and catalytic activity

The synthesis and characterisation of three novel mononuclear ruthenium(II) complexes containing one of the following chiral auxiliary ligands: 2-amino-(4R)-phenyl-2-oxazoline (amphox), indanyl-2-amino-(4R,5S)-2-oxazoline (aminox) or indanyl-(2′-anilinyl)-(4R,5S)-2-oxazoline (aninox) is described using [Ru₂Cl₄(η⁶-p-cym)₂] (p-cym = 1-isopropyl-4-methylbenzene) as the Ru starting material. The new complexes have been identified as the neutral derivatives [RuCl₂(η⁶-p-cym)(amphox-κ¹N_ox)] (1), [RuCl₂(η⁶-p-cym)(aminox-κ¹N_ox)] (2) and the salt [RuCl(η⁶-p-cym)(aninox-κ²N,N′)]Cl (3). These materials have been fully characterised (elemental analysis, NMR, IR, conductance, MS, etc.) and, in the case of 2 and 3, structurally elucidated in the solid-state using single crystal X-ray diffraction methods. All three complexes show good catalytic activity (max. conversion >99%, TOF = 424 h⁻¹) but only modest enantio-selectivity (max. ee = 40%) for the transfer hydrogenation reaction of acetophenone with isopropyl alcohol. The complexes were also tested in an asymmetric Diels-Alder reaction involving cyclopentadiene and acrolein (max. conversion >99%, TOF = 42 h⁻¹). In this case, the diastereo-selectivity was good to moderate (max. de = 84%), but the ee values were poor (max. ee = 12%).     

Microwave-assisted headspace single-drop microextration of chlorobenzenes from water samples

A one-step and in-situ sample preparation method used for quantifying chlorobenzene compounds in water samples has been developed, coupling microwave and headspace single-drop microextraction (MW-HS-SDME). The chlorobenzenes in water samples were extracted directly onto an ionic liquid single-drop in headspace mode under the aid of microwave radiation. For optimization, a Plackett-Burman screening design was initially used, followed by a mixed-level factorial design. The factors considered were: drop volume, aqueous sample volume, stirring speed, ionic strength, extraction time, ionic liquid type, microwave power and length of the Y-shaped glass-tube. The optimum experimental conditions found from this statistical evaluation were: a 5 μL microdrop of 1-hexyl-3-methylimidazolium hexafluorophosphate exposed for 20 min to the headspace of a 30 mL aqueous sample, irradiated by microwaves at 200 W and placed in a 50 mL spherical flask connected to a 25 cm Y-shaped glass-tube. Under the optimised experimental conditions, the response of a high performance liquid chromatographic system was found to be linear over the range studied and with correlation coefficients ranging between 0.9995 and 0.9999. The method showed a good level of repeatability, with relative standard deviations varying between 2.3 and 8.3% (n = 5). Detection limits were found in the low μg L⁻¹ range varying between 0.016 and 0.039 μg L⁻¹. Overall, the performance of the proposed method demonstrated the favourable effect of microwave sample irradiation upon HS-SDME. Finally, recovery studies from different types of environmental water samples revealed that matrix had little effect upon extraction.     

Strongly hyperbolically convex functions

Let C(w₁,w₂,w₃) denote the circle in through w₁,w₂,w₃ and let denote one of the two arcs between w₁,w₂ belonging to C(w₁,w₂,w₃). We prove that a domain Ω in the Riemann sphere, with no antipodal points, is spherically convex if and only if for any w₁,w₂,w₃∈Ω, with w₁≠w₂, the arc of the circle which does not contain lies in Ω. Based on this characterization we call a domain G in the unit disk D, strongly hyperbolically convex if for any w₁,w₂,w₃∈G, with w₁≠w₂, the arc in D of the circle is also contained in G. A number of results on conformal maps onto strongly hyperbolically convex domains are obtained.     

Early barriers in the matrix photochemical formation of syn-anti randomized FC(O)SeF from the OCSe:F(2) complex

The photochemically induced reaction of OCSe and F(2), isolated together in an Ar matrix at about 15 K, leads to formation of the hitherto-unknown fluorocarbonylselenyl fluoride FC(O)SeF. The reaction occurs via a van der Waals complex O=C=Se...F-F that favors very early formation of the anti conformer. The presence and subsequent decay of a band assigned to the F-F vibration correlated with perturbed OCSe bands seems to confirm this hypothesis. Subsequent irradiation of the matrix leads to randomized FC(O)SeF by a photochemically induced conformational equilibrium between syn and anti forms. Another photochemical reaction channel is the formation of CO and SeF(2) molecules, which are produced in the same matrix cage and then form a loose complex. The changes were monitored and the products characterized experimentally by their IR spectra, and the spectra analyzed in the light of the results of theoretical calculations.     

Direct access to β-oxodiazo compounds by copper(II)-catalyzed oxidative rearrangement of stabilized vinyl diazo derivatives

The copper(II)-catalyzed reaction of alkenyldiazo compounds with iodosylbenzene leading to β-oxodiazo derivatives is reported. This process occurs via an unprecedented 1,2-shift of the diazoacetate function. A selection of the synthetic applications of a representative member of this new class of functionalized diazo derivatives in the regioselective synthesis of substituted 1,4-dicarbonyl compounds is also reported.     

Speciation of the Vanadium (III) Complexes with 6-Methylpicolinic Acid,Salicylic Acid and Phthalic Acid

The complex species formed in aqueous solutions (25 °C, I=3.0 mol⋅dm⁻³ KCl ionic medium) between the V(III) cation and the ligands 6-methylpicolinic acid (MePic, HL), salicylic acid (H₂Sal, H₂L) and phthalic acid (H₂Phtha, H₂L) have been studied by potentiometric and spectrophotometric measurements. Application of the least-squares computer program LETAGROP to the experimental emf(H) data, taking into account the hydrolytic species and hydrolysis constants of V(III), indicates that under the employed experimental conditions the complexes [VL]²⁺, [V(OH)L]⁺, [V(OH)₂L], [V(OH)₃L]⁻, [VL₂]⁺, [VL₃] and [V₂OL₄] form in the vanadium(III)–MePic system. Were observed the complexes [VL]⁺, [VL₂]⁻, [V(OH)L₂]²⁻ and [VL₃]³⁻ in the vanadium(III)–H₂Sal system, and the species [VHL]²⁺, [VL]⁺, [V(OH)L], [VHL₂], [VL₂]⁻, [V(OH)L₂]²⁻, [V(OH)₂L₂]³⁻ and [VL₃]³⁻ in the vanadium(III)–H₂Phtha system. The stability constants of these complexes were determined by potentiometric measurements, and spectrophotometric measurements were made in order to perform a qualitative characterization of the complexes formed in aqueous solution.     

Determination of nitroaromatic explosives in water samples by direct ultrasound-assisted dispersive liquid-liquid microextraction followed by gas chromatography-mass spectrometry

A fast, simple, inexpensive, sensitive, efficient and environmental friendly direct ultrasound-assisted dispersive liquid-liquid microextraction (DUSA-DLLME) procedure has been developed to concentrate five nitroaromatic explosives from water samples prior to quantification by gas chromatography-mass spectrometry (GC-MS). An efficient ultrasonic probe has been used to radiate directly the samples producing very fine emulsions from immiscible liquids. A D-optimal design was used for optimizing the factors and to evaluate their influential upon extraction. The optimum experimental conditions were: sample volume, 10 mL; extraction time, 60 s; cycles, 0.6 s(s⁻¹); power of ultrasound energy, 40% (70 W); and, extractant solvent (chlorobenzene) volume, 20 μL. Under the optimized experimental conditions the method presents good level of repeatability with coefficients of variation under 6% (n = 8; spiking level 10 μg L⁻¹). Calculated calibration curves gave high level of linearity with correlation coefficient values between 0.9949 and 0.9992. Limits of detection were ranged between 0.03 and 0.91 μg L⁻¹. Finally, the proposed method was applied to the analysis of two types of water samples, reservoir and effluent wastewater. The samples were previously analysed and confirmed free of target analytes. At 5 μg L⁻¹ spiking level recovery values ranged between 75 and 96% for reservoir water sample showing that the matrix had a negligible effect upon extraction. However, a noticeable matrix effect (around 50% recovery) was observed for effluent wastewater sample. In order to alleviate this matrix effect, the standard addition calibration method was used for quantitative determination. This calibration method supplied recovery values ranged between 71 and 79%. The same conclusions have been obtained from an uncertainty budget evaluation study.     

Solution Equilibria of Ternary Systems Involving Nickel(II) Ion,Picolinic Acid,and the Amino Acids Histidine,Cysteine, Aspartic and Glutamic Acids

Solution equilibria of the ternary systems Ni(II)–picolinic acid (Hpic) and the amino acids aspartic acid (H₂asp), glutamic acid (H₂glu), cysteine (H₂cys) and histidine (Hhis), where the amino acids are denoted as H _i L, have been studied pH-metrically. The formation constants of the resulting mixed ligand complexes have been determined at 25 °C using a ionic strength 1.0 mol·dm^?3 NaCl. In the Ni(II)–Hpic–H₂asp and Ni(II)–Hpic–H₂glu systems, the complexes [Ni(pic)H₂L]⁺, Ni(pic)HL, [Ni(pic)L]^? and [Ni(pic)L(OH)]^2? were detected. In the Ni(II)–Hpic–H₂cys system the complexes [Ni(pic)H₂L]⁺ and [Ni(pic)L]^? are present. Additionally, in the Ni(II)–Hpic–Hhis system the species [Ni(Hpic)HL]²⁺, Ni(pic)L and [Ni(pic)L(OH)]^? were identified. The species distribution diagrams as functions of pH are briefly discussed.     

Interaction of Molybdenum(VI) Oxyanions with +2 Metal Cations

The association of molybdenum(VI) oxyanions with metal cations was investigated in solutions of low ionic strength, such as those prevailing in most natural waters. Potentiometric titrations were carried out for the systems containing molybdenum(VI) anions and divalent metal cations (M = Mg, Ca, Sr, Ba, Mn, Fe, Co, Ni, Cu, Zn, Cd, Hg and Pb). This selection includes the major cations and some other cations of high environmental relevance. The interaction of iron(III) with Mo(VI) anions was also studied. At neutral and basic pH values and for those systems where the solubility of the molybdate salt is high enough, ionic species pairs such as [M(MoO₄)] predominate. At acidic pH values, [M(HMoO₄)]⁺ and [M(Mo₇O₂₄)]^4– are formed, the latter species are only relevant for total molybdenum concentrations higher than 1 mmol·L^?1. These results provide the basis for molybdenum speciation in natural aquatic systems, on which the environmental fate, bioavailability and toxicity of the element depend.