Problem types used in math lessons: the relationship between student achievement and teacher preferences

The purpose of this study was to determine the relationship between the problems teachers preferred in mathematics lessons and student achievement in different types of problems. In accordance with this purpose, nine mathematics teachers were interviewed, and corresponding problems were prepared and administered to 225 eighth-grade students. The findings indicate that problem types are dependent on teacher preferences. It was found that curriculum-dependent and routine problems were dominant for teacher preferences. Students are more successful at with missing data, problems that are visual and do not require the use of different strategies. They have lower success at long problems, those that contain irrelevant data, problems that require the use of different strategies and difficult problem types. It was found that problem types at which students were successful and which teachers preferred were related. These results relay information about problems used in the learning environment and effect of problem-solving experiences on students' success.     

Polarimetric interferometer for measuring nonlinearity error of heterodyne interferometric displacement system

This letter presents a polarimetric interferometer(PI) that can measure the ellipsometric parameter θ with an accuracy of 0.01 leading to a potential accuracy of 17 pm.The PI is constructed and compared with a commercial heterodyne interferometer(HI).Given its low nonlinearity,the PI is used to measure the residual nonlinearity of a heterodyne interferometric displacement system.A rotating half-wave plate is used to compensate for a part of the nonlinearity error caused by the misalignment of the axis between input polarizing states and beamsplitter.     

Simulations of nanowire bend tests for extracting mechanical properties

Mechanical properties of nickel nanowires are characterized based on the numerical simulations of bend tests performed with a customized atomic force microscope (AFM) and scanning electron microscope (SEM). Nickel nanowire specimens are subjected to bending loads by the tip of the AFM cantilever. The experimental force versus bending displacement curves are compared against simulations from finite element analysis and peridynamic theory, and the mechanical properties are extracted based on their best correlations. Similarly, SEM images of fractured nanowires are compared against peridynamic failure simulations. The results of this study reveal that nickel nanowires have significantly higher strengths than their bulk counterparts, although their elastic modulus values are comparable to bulk nickel modulus values.     

A novel method for quantification of ethanol and methanol in distilled alcoholic beverages using Raman spectroscopy

In this study, direct quantification of ethanol and methanol in distilled alcoholic beverages using Raman spectroscopy was performed. Raman spectra of varying ethanol–methanol mixtures were obtained, baseline corrections were made, and the data were normalized using Raman scattering intensity of an internal standard (acetonitrile, 921 cm^–1). Then, calibration graphs were produced for ethanol and methanol concentrations in the ranges of 0–7 M and 0–10 M, respectively. Accurate R² values of the calibration graphs proved the notable linear correlations (0.998 for ethanol and 0.998 for methanol). The method was validated based on linearity, sensitivity, intraday and interday repeatability, and recovery tests. The limit of detection and limit of quantification values of the validated method were determined for ethanol concentration as 1.2 and 3.7 mM, and for methanol concentration as 3.4 and 10.3 mM, respectively. The ability of the developed method to detect ethanol and methanol concentrations in real samples was also investigated. The results of the developed method were compared with the experimental results from traditional method and high correlation value (R² = 0.926) was obtained. Besides being sensitive and cheap, the developed method is rapid with the analysis time of less than 30 s. Furthermore, it eliminates labor‐consuming operations, chromatographic separation, and measurement error due to the high number of experiment steps in the standard method. Copyright © 2012 John Wiley & Sons, Ltd.     

Detection of melamine in milk by surface-enhanced Raman spectroscopy coupled with magnetic and Raman-labeled nanoparticles

A new method based on surface-enhanced Raman spectroscopy (SERS) has been developed for sensitive and rapid detection of melamine. Spherical magnetic-core gold-shell nanoparticles (AuNPs) and rod-shaped gold nanoparticles (nanorods) labeled with a Raman-active compound were used to form a complex with the melamine molecules. 5,5'-Dithiobis(2-nitrobenzoic acid) was used as Raman-active compound because it is readily adsorbed by a gold nanoparticle surface forming a self-assembled monolayer (SAM) and has strong Raman scattering at 1330 cm(-1), because of the symmetric NO(2) stretch. The calibration curve was obtained by plotting Raman band area at 1330 cm(-1) against melamine concentration. A linear relationship was obtained with a high determination coefficient (R(2)=0.997). The method was validated for linearity, sensitivity, precision (intra-day and inter-day repeatability), and recovery. In the model system, the limits of detection (LOD) and quantification (LOQ) were 0.38 and 1.27 mg L(-1), respectively. For melamine-spiked milk samples, LOD and LOQ values were 0.39 mg L(-1) and 1.30 mg L(-1), respectively. Intra and inter-day precision were 3.73 and 4.94 %, respectively. This method was applied to samples of skimmed milk that had been spiked with melamine at different concentrations. The recovery of the method was 95-109 % in the concentration range 2-15 mg L(-1), and average RSD was 1.71 %. Total analysis time was less than 15 min.     

A Sodium Supported Borate Ester: Synthesis,Spectral Characterization and Crystal Structure of dimeric Sodium Organoborate Complex [Na(py)][B(hyncaH<Subscript>−2</Subscript>)<Subscript>2</Subscript>]<Subscript>2</Subscript>

Abstract  A dimeric sodium supported borate complex, [Na(py)][B(hyncaH₋₂)₂]₂ (1) (py = pyridine, hynca = 1-hydroxynaphthalene-2-carboxylic acid), has been synthesised by the reaction of NaBH₄ with two equivalents of hynca in anhydrous THF and following crystallization from py/H₂O solution afforded borate ester derivative. The complex has been fully characterized by FT-IR in the solid state and by NMR (¹H and ¹³C) spectroscopy and electrospray ionization mass spectrometry in solution. The molecular structure of the title compound was determined by single crystal X-ray diffraction. Structure analysis of complex 1 confirmed the presence of an anionic complex [B(hyncaH₋₂)₂]⁻ in which boron atom is coordinated simultaneously by two hynca ligands utilising both alkoxide and carboxylate groups for bonding. The Na atom is six- coordinate to five O atoms of hydroxy carboxylic acid and one pyridine N atom. Crystal data: crystal system, monoclinic, a = 10.971(3) Å, b = 6.839(3) Å, c = 30.545(5) Å, β = 92.20(2)°, space group P2₁/c (#14), V = 2,290(1) Å³, Z = 4. Index Abstract  There are limited examples of alkali metal supported borate ester complexes.      

Aminated styrene polymers as dehydrohalogenating agents

Copolymers of styrene and methyl methacrylate, cross-linked with divinylbenzene, can be chloromethylated and then aminated to almost the theoretical extent. The aminated polymers can utilise approx 50% of the amine residues to dehydrobrominate n-bromoalkanes.     

Bis(pyridine‐2,6‐dimethanol‐N,O,O′)cobalt(II) and ‐copper(II) disacchar­inate dihydrate: three‐dimensional structures with extensive hydrogen bonds and aromatic π–π‐stacking interactions

Bis­(pyridine‐2,6‐di­methanol‐N,O,O′)­cobalt(II) disaccharinate dihydrate, [Co(C₇H₉NO₂)₂](C₇H₄NO₃S)₂·2H₂O, (I), and bis­(pyridine‐2,6‐di­methanol‐N,O,O′)copper(II) disaccharinate dihydrate, [Cu(C₇H₉NO₂)₂](C₇H₄NO₃S)₂·2H₂O, (II), collectively [M(dmpy)₂](sac)₂·2H₂O (where M is Co^II or Cu^II, sac is the saccharinate anion and dmpy is pyridine‐2,6‐di­methanol), are isostructural. The [M(dmpy)₂]²⁺ cations exhibit distorted octahedral geometry in which the two neutral dmpy species act as tripodal N,O,O′‐tridentate ligands. The crystal packing is determined by hydrogen bonding, as well as by weak pyridine–saccharinate π–π‐stacking interactions.