What Is a Fraction? Developing Fraction Understanding in Prospective Elementary Teachers

Classroom teachers need a well‐developed deep understanding of fractions and pedagogic practices so they can provide meaningful experiences for students to explore and construct ideas about fractions. This study sought to examine prospective elementary teachers' understandings of fraction by focusing specifically on their use of fractions meanings and interpretations. Results indicated that prospective elementary teachers bring with them to their final methods course a limited understanding of fractions and that experiences in methods courses resulted only in minor improvement of those limited understandings. The limited part‐whole understanding of fractions that prospective elementary teachers entered the course with was resilient. The implications of this study suggest a need for prospective elementary teachers to continue to develop their conceptual understanding of fractions and for changes to the content and instructional strategies of mathematics content courses designed for prospective elementary teachers.     

Order of Reactivity of OH/NH Groups of Glucosamine Hydrochloride and N-Acetyl Glucosamine Toward Benzylation Using NaH/BnBr in DMF

The order of reactivity of OH and NH groups of glucosamine hydrochloride (GlcNH₂^.HCl) and N-acetyl glucosamine (GlcNAc) toward benzylation with NaH/BnBr in DMF was investigated. For GlcNH₂^.HCl, benzyl groups were introduced in the order of N-Bn > N-Bn₂ > 1-O-Bn > 6-O-Bn > 4-O-Bn > 3-O-Bn; for GlcNAc, benzyl groups were introduced in the order of 1-O-Bn > 6-O-Bn > 4-O-Bn > 3-O-Bn > N-Bn. A range of partially benzylated 2-N,N′-dibenzyl glucopyranosides and GlcNAc derivatives were obtained in a single step.     

Liquid chromatography–mass spectrometry applications for quantification of endogenous sex hormones

Liquid chromatography, coupled with tandem mass spectrometry, presents a powerful tool for the quantification of the sex steroid hormones 17‐β estradiol, progesterone and testosterone from biological matrices. The importance of accurate quantification with these hormones, even at endogenous levels, has evolved with our understanding of the role these regulators play in human development, fertility and disease risk and manifestation. Routine monitoring of these analytes can be accomplished by immunoassay techniques, which face limitations on specificity and sensitivity, or using gas chromatography–mass spectrometry. LC–MS/MS is growing in capability and acceptance for clinically relevant quantification of sex steroid hormones in biological matrices and is able to overcome many of the limitations of immunoassays. Analyte specificity has improved through the use of novel derivatizing agents, and sensitivity has been refined through the use of high‐resolution chromatography and mass spectrometric technology. This review highlights these innovations, among others, in LC–MS/MS steroid hormone analysis captured in the literature over the last decade.     

Synthesis of glycopolymers via click reactions

This mini-review describes recent work in the field of glycopolymer synthesis, with a focus on methods that have employed “click chemistry” and controlled polymerization methodology. A variety of carbohydrates with clickable groups such as azide, alkyne, and thiol moieties provide new routes to glycopolymers. Several studies use copper catalyzed azide-alkyne cycloaddition (CuAAC) reactions to synthesize glycomonomers or to incorporate carbohydrates into a clickable polymeric backbone. Alternatively, there are many thiol based click reactions which provide metal-free synthesis, which are discussed in details.     

Determination of 131mXe and 133mXe in the presence of 133gXe via combined beta-spectroscopy and delayed coincidence

The International Monitoring System for the Comprehensive Nuclear-Test-Ban Treaty will include measurements of Xe fission products. Pacific Northwest National Laboratory has developed an automated system for separating Xe from air which detects Xe fission products using a beta-gamma counting system for ^131mXe, ^133mXe, ^133gXe, and ^135gXe. Betas and conversion electrons are detected in a plastic scintillation cell containing the Xe sample. Gamma and X-rays are detected in a NaI(Tl) scintillation detector which surrounds the plastic scintillator sample cell. Two-dimensional pulse-height spectra of gamma-energy versus beta-energy are obtained. The plastic scintillator spectrum in coincidence with the 31-keV X-rays from ^131mXe. ^133mXe, and ^133gXe is a complex mixture of conversion electrons and betas. A new technique to simultaneously measure the delayed coincidence (T _1/2 = 6.27 ns) between beta-particles from ^133gXe and conversion electrons depopulating the 81-keV state in 133 Cs is being developed. This technique allows separation of the ^133gXe beta spectrum from the conversion electrons due to ^131mXe and ^133mXe and uniquely quantifies all three nuclides.     

Excited-State Properties of Thymidine and Their Relevance to Its Heterogeneous Emission in Double-Stranded DNA

Published results on synthetic polynucleotides point to T as the major emitting fluorophore in DNA. We have reported also that the bases of the nonalternating polynucleotide poly(dA).poly(dT), in which T was selectively excited, undergo large-amplitude motions on the picosecond-nanosecond time scales (S. Georghiou et al., Biophys. J. 70, 1909-1922, 1996). In that study, the fluorescence decay profile of the T bases of this polynucleotide was found to contain a number of components; these may be considered to be the result of the motions of the bases that give rise to a distribution of stacked geometries of varying rigidity as well as dispersion and polar interactions. Here, we report the results of a study that we have undertaken in order to test this hypothesis. To this effect, we have studied the photophysical properties of thymidine (1) in aqueous buffer and in a number of organic solvents and (2) in aqueous sucrose solutions of viscosity extending to 149 cP. The results suggest that the fluorescence quantum yield decreases with an increase in the polarizability of the solvent, whereas it increases with an increase in the solvent polarity (on the basis of the empirical parameter of solvent polarity ETN) or viscosity. These findings suggest the following for the photophysical properties of the T bases in DNA: (1) Base stacking results in two antagonistic effects, namely it causes a reduction in fluorescence as a result of dispersion interactions and an enhancement as a result of a reduction in the motions of the bases and (2) exposure of the bases to the aqueous environment results in fluorescence enhancement.     

Dendrimers in thiol‐ene crosslinked networks and the effect of subsequent generations on thermoset properties

A series of well‐defined allyl‐ether functionalized polyester dendrimers has been synthesized via the divergent approach using traditional esterification reactions. Two commercially available trifunctional thiols, trimethylolpropane tri(3‐mercaptopropanoate) (TRIS) and ethoxylated trimethylolpropane tri(3‐mercaptopropanoate) (ETTMP), were incorporated with the dendrimers into the thiol‐ene polymer networks. The thiol‐ene reactions were conducted at room temperature and cured by UV light without the addition of photoinitiatior. Highly crosslinked films were obtained and characterized with respect to mechanical (DMA) and thermal (DSC and TGA) properties. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 589–601, 2009     

Macroscopic and spectroscopic characterization of selenate, selenite, and chromate adsorption at the solid–water interface of γ-Al2O3

The interaction of selenate, selenite, and chromate with the hydrated surface of γ-Al₂O₃ was studied using a combination of macroscopic pH edge data, electrophoretic mobility measurements, and X-ray absorption spectroscopic analyses. The pH edge data show generally increased oxyanion adsorption with decreasing pH, and indicate ionic strength-(in)dependent adsorption of chromate and selenate across the pH range 4–9, and ionic strength-(in)dependent adsorption of selenite in this pH range. The adsorption of chromate peaks at pH 5.0, whereas for selenate and selenite no pH adsorption maxima are observed. Electrophoretic mobility measurements show that all three oxyanions decrease the zeta potential of γ-Al₂O₃ upon adsorption; however, only selenite decreased the pH_PZC of the γ-Al₂O₃ sorbent. EXAFS data indicate that selenite ions are coordinated in a bridging bidentate fashion to surface AlO₆ octahedra, whereas no second-neighbor Al scattering was observed for adsorbed selenate ions. Combined, the results presented here show that pH is a major factor in determining the extent of adsorption of selenate, selenite, and chromate on hydrated γ-Al₂O₃. The results point to substantial differences between these anions as to the mode of adsorption at the hydrated γ-Al₂O₃ surface, with selenate adsorbing as nonprotonated outer-sphere complexes, chromate forming a mixture of monoprotonated and nonprotonated outer-sphere adsorption complexes, and selenite coordinating as inner-sphere surface complexes in bridging configuration.