Enabling the Practice of Mathematics Teachers in Context: Toward a New Equity Research Agenda

In this article, I address the need for a more clearly articulated research agenda around equity issues by proposing a working definition of equity and a focal point for research. More specifically, I assert that rather than pitting them against each other, we must coordinate (a) efforts to get marginalized students to master what currently counts as “dominant” mathematics with (b) efforts to develop a critical perspective among all students about knowledge and society in ways that ultimately facilitate (c) a positive relationship between mathematics, people, and equity on the planet. I make this argument partly by reviewing the literature on (school) contexts that engage marginalized students in mathematics. Then, I argue that the place that holds the most promise for addressing equity is a research agenda that emphasizes enabling the practice of teachers and that draws more heavily on design-based and action research, thereby redefining what the practice of mathematics means along the way. Specific research questions are offered.     

Mössbauer studies of spin wave excitations in Fe/Ag multilayers

The magnetic properties of molecular beam epitaxially (MBE) grown FE(110)/Ag(111) heterostructures were investigated with Mössbauer spectroscopy. The Fe bilayers were fixed at 3 ML (monolayer) thickness and the Ag bilayer thickness varied from 4 ML to 20 ML. We found that as the Ag layer became thick enough (>17 ML) to magnetically isolate the Fe layers, a quasi-linear temperature dependence of the hyperfine field results due to the 2-D spin wave excitations. As the Ag layer is reduced, a dimensional crossover in the excitations is induced by the magnetic interaction between Fe layers which makesM(T) change from a two-dimensionalT relation to a three-dimensionalT ^3/2 dependence. We constructed a simple theoretical model to motivate the explanation for the experimental results and obtained approximate values for the interlayer coupling strength for various Ag bilayer thicknesses.     

Cyclometallation. Palladium 2-arylpyridine complexes

A number of new cyclometallated compounds of palladium with 2-arylpyridines have been synthesized and characterized. Palladium acetate has been proven to be a more useful starting material than Li₂PdCl₄, since the resulting acetato-bridged dimers, [Pd(OAc)(2-arylpyridine)]₂, unlike the chloro-bridged dimers, are conveniently soluble in common organic solvents. The effect of varying substituents on the aryl nucleus supports the concept that after initial N-complexation, the 2-position of the aryl nucleus undergoes electrophilic attack by the palladium atom. Detailed NMR studies of the soluble acetato compounds showed that the 6-heteroaryl and “ortho” to the Pd-C bond protons in the complexes are shifted (≈0.75 and 0.5 ppm, respectively) upfield from the ligand position. These shielding effects are believed to be due primarily to through-space interactions of overlying aromatic rings and secondarily to through-bond (Pd-to-ligand) effects. Both acetato- and chloro-bridged dimers will react with certain ligands to give mononuclear species containing the intact cyclometallated ligand.     

Quantum chemistry-based interpretations on the lowest triplet state of luminescent lanthanides complexes. Part 1. Relation between the triplet state energy of hydroxamate complexes and their luminescence properties

In this paper, we evaluate the potential use of theoretical calculations to obtain an energy scale of the lowest ligand-centred triplet excited state in luminescent terbium(III) complexes. In these complexes, non-radiative deactivation of the terbium emitting state via a back-energy transfer process (T1<--Tb(5D4)) is a common quenching process. Consequently the prediction of the energy gap between these two excited states should be useful for programming highly luminescent Tb(III) systems. We report on a strategy based upon experimental and theoretical investigations of the excited state properties of a series of four simple aromatic hydroxamate ligands coordinated to Tb(III) and Gd(III) ions. By using previously reported crystallographic data, the structural and energies properties of these systems were investigated in the ground and first excited triplet states at the density functional theory (DFT) level of calculations. Our theoretical results are consistent with a triplet excited state T1 which is localised on one ligand only and whose the energy level is independent of the lanthanide ion nature (Tb(III), Gd(III)). A good agreement between the calculated adiabatic transition energies and experimental data derived from emission spectra is obtained when a corrective term is considered. These satisfactory results are an indication that this type of modelling can lead to discriminate in terms of the position of the lowest ligand triplet energy level the best antenna among a family of chromophoric compounds. In addition this theoretical approach has provided indications that the difference between the adiabatic transition energies of all the investigated complexes can be mainly explained by metal-ligand electrostatic interactions. The influence of the number of antennae on the quantum yield and the luminescence lifetime is discussed.     

High-performance liquid chromatographic determination of major organic acids in apple juices and ciders

Summary A reversed-phase high-pressure liquid chromatographic method is presented for the simultaneous separation and determination of malic, citric, lactic, succinic and ascorbic acids in apple juices and ciders. After filtration and/or degasification, the organic acids in the sample are separated on a LiChrosorb/C₁₈ column and quantified by using a rapid diode array detector. The method is considered to be a suitable choice for the accurate and precise determination (C.V. 5%) of these compounds.     

Thermodynamic study of the complexation processes between 6,7-dihydro-3(H)-6-methyl-5-methoxy-7-oxo-vic-triazolo (4,5-d) pyrimidine and Cu(II), Zn(II), Cd(II) and Hg(II)

The compound 6,7-dihydro-3(H)-6-methyl-5-methoxy-7-oxo-vic-triazolo (4,5-d) pyrimidine (LH) has been characterized by IR, ¹H-NMR and UV-visible spectroscopy. Furthermore, its acid behaviour in aqueous solutions at variable temperatures and ionic strengths have been studied.The stability constants of the complexes formed by LH with Cu(II), Zn(II), Cd(II) and Hg(II) metal ions at different ionic strengths and temperatures have been calculated by the method of Chabereck and Martell. From these data, the thermodynamic functions for the corresponding complexation processes have been obtained.     

In silico studies toward the discovery of new anti-HIV nucleoside compounds through the use of TOPS-MODE and 2D/3D connectivity indices. 2. Purine derivatives

The TOPological Substructural MOlecular DEsign (TOPS-MODE) approach has been used to predict the anti-HIV activity in MT-4 assays (Estrada et al., 2002) of a diverse range of purine-based nucleosides. A database of 206 nucleosides has been selected from the literature and a theoretical virtual screening model has been developed. The model is able of discriminating between compounds that have anti-HIV activity and those that do not, with a good classification level of 85% in the training and 82.8% in the cross-validation series. On the basis of the information generated by the model, the correct classification of practically 80% of compounds from an external prediction set has been achieved using the theoretical model. Furthermore, the contribution of a range of molecular fragments to the pharmacological action has been calculated and this could provide a powerful tool in the design of nucleoside analogues that show activity against the HIV. Finally, a QSAR model has been developed that allows quantitative data to be obtained regarding the pharmacological potency shown by this type of compound.     

Citrate complexes of tin(IV) studied by liquid-liquid extraction with 5,7-dichloro-8-quinolinol

The tin(IV)/5,7-dichloro-8-quinolinol/chloroform extraction system is used to determine the composition and the stability constants of the aqueous complexes of tin(IV) with citric acid, in the pH range 2.0–3.5. The tin(IV):citric acid ratios found are 1:1 and 1:2, depending on the concentration of the acid. The conditional stability constants are (5.5 ± 0.4) × 10³ and (1.3 ± 0.3) × 10³ for the 1:1 and 1:2 complexes, respectively. This extraction system is convenient in studies of aqueous tin(IV) complexes that cannot be extracted into chloroform.     

Calorimetric study of the proximity effect in aliphatic diesters

Excess molar enthalpies,H ^E , at atmospheric pressure and 303.15 K are reported for binary mixtures of 1-chlorohexane with diethyl oxalate, diethyl malonate, diethyl succinate, diethyl glutarate, diethyl adipate, diethyl pimelate and diethyl sebacate. These experimental results, together with those obtained previously on the excess enthalpies of aliphatic diester+n-hexane mixtures, are interpreted in terms of molecular surface interactions between aliphatic, chlorinated and carboxylate groups. Comparison of the enthalpy interchange parameters reveals a decrease of the intermolecular interactions with decreasing intramolecular COO-COO distance in the diester molecule.

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Zusammenfassung Bei Atmosphärendruck und 303,15 K gemessene molare Überschußenthalpien (H ^E werden für binäre Gemische von 1-Chlorhexan mit Diäthyloxalat, Diäthylmalonat, Diäthylsuccinat, Diäthylglutarat, Diäthyladipat, Diäthylpimelat bzw. Diäthylsebacat angegeben. Diese experimentellen Ergebnisse werden zusammen mit den früher für Gemische von aliphatischen Diestern und n-Hexan erhaltenen Resultaten als molekulare Oberflächenwechselwirkungen zwischen aliphatischen, chlorierten und Carboxylatgruppen interpretiert. Ein Vergleich der Enthalpieaustauschparameter läßt eine Verminderung der intermolekularen Wechselwirkungen mit abnehmendem intramolekularem Abstand zwischen den COO-Gruppen erkennen.

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(H ^E ) 303,15 K 1- , , , , , . , + -, , . COO-COO .