Crutch or Catalyst: Teachers' Beliefs and Practices Regarding Calculator use in Mathematics Instruction

This study investigated K‐12 teachers' beliefs and reported teaching practices regarding calculator use in their mathematics instruction. A survey was administered to more than 800 elementary, middle and high school teachers in a large metropolitan area to address the following questions: (a) what are the beliefs and practices of mathematics teachers regarding calculator use? and (b) how do these beliefs and practices differ among teachers in three grade bands? Factor analysis of 20 Likert scale items revealed four factors that accounted for 54% of the variance in the ratings. These factors were named Catalyst Beliefs, Teacher Knowledge, Crutch Beliefs, and Teacher Practices. Compared to elementary teachers, high school teachers were significantly higher in their perception of calculator use as a catalyst in mathematics instruction. However, the higher the grade level of the teacher, the higher the mean score on the perception that calculator use may be a way of getting answers without understanding mathematical processes. The mean scores for teachers in all three grade bands indicated agreement that students can learn mathematics through calculator use and using calculators in instruction will lead to better student understanding and make mathematics more interesting. The survey results shed light on teachers' self reported beliefs, knowledge, and practices in regard to consistency with elements of the National Council of Teachers of Mathematics Principles and Standards for School Mathematics (2000) technology principle and the NCTM use of technology position paper (2003). This study extended previous research on teachers' beliefs regarding calculator use in classrooms by examining and comparing the results of teacher surveys across three grade bands.     

Synthesis of novel 1,3,4‐oxadiazinane‐2‐thiones derived from (1R,2S‐ephedrine, (1S,2S)‐pseudoephedrine and (1R,2S)‐norephedrine

A several novel 1,3,4‐oxadiazinan‐2‐thiones have been synthesized by the cyclization of β‐hydrazino‐alcohols with either carbon disulfide or 1,1′‐thiocarbonyldiimidazole (TCDI).     

Effect of amine ligand bulk on the interaction of methionine with platinum(II) diamine complexes

Molecular mechanics and dynamics calculations have been used in conjunction with experimental data to study the effects of amine ligand bulk on the formation of both guanine and methionine complexes with platinum diamine compounds. The AMBER force field has been supplemented with previous modifications [Yao; et al. Inorg. Chem. 1994, 33, 6061-6077. Cerasino; et al. Inorg. Chem. 1997, 36, 6070-6079] and has been further modified to include parameters for platinum bound to the sulfur atom of methionine. Molecular mechanics calculations with this modified AMBER force field have suggested that a platinum complex with two sulfur-bound methionine ligands and a bulky diamine ligand (N,N,N',N'-tetramethylethylenediamine, Me(4)en) would have severe interligand clashes; such interligand clashes are less pronounced in bis(9-ethylguanine) complexes. Consistent with these observations, NMR studies with [Pt(Me(4)en)(D(2)O)(2)](2+) have indicated that guanine 5'-monophosphate reacts in a 2:1 guanine:platinum ratio while both methionine and N-acetylmethionine react with only a 1:1 stoichiometry. Methionine forms a chelate via the sulfur and nitrogen atoms whereas N-acetylmethionine forms a chelate via the sulfur and oxygen atoms. The oxygen of the latter chelate can be displaced by the addition of guanosine 5'-monophosphate, although complete displacement of the N-acetylmethionine was not observed.     

Synthesis of crystalline skutterudite superlattices using the modulated elemental reactant method

A series of samples ((AB)(x)(CD)(y))(z) were prepared containing both short repeat units (AB and CD) and long repeat units ((AB)(x)(CD)(y)), where the short repeat units were designed to have the composition appropriate to form square M(4)Sb(12) skutterudites (M = Fe, Co, or Ir; square = vacancy, La, or Y). X-ray diffraction and reflectivity were used to follow the evolution of the films from amorphous, layered materials to crystalline skutterudite superlattices as a function of annealing temperature and time. In all cases, the short repeat units interdiffused and crystallized the expected skutterudite, while the long repeat period persisted after annealing. The skutterudites crystallize with random crystallographic orientation with respect to the substrate. The observed splitting of the peaks in the high-angle diffraction data from the IrSb(3)/CoSb(3) sample indicates the formation of a novel superlattice structure with each grain having a random crystallographic orientation of the skutterudite lattice with respect to the superlattice direction.     

Synthesis of l,l-puromycin

l,l-Puromycin, a diastereomer of the natural peptidyl nucleoside antibiotic puromycin, has been synthesized from l-xylose in 13 steps.     

Mechanistic study of enantiomeric recognition with native gamma-cyclodextrin by capillary electrophoresis,reversed-phase liquid chromatography,nuclear magnetic resonance spectroscopy,electrospray mass spectrometry and circular dichroism techniques

The possible mechanisms for the chiral recognition of 2(S)-(3,5-bis-trifluoromethyl-phenyl)-2-[3(S)-(4-fluorophenyl)-4-(1H-[1,2,4]triazol-3-ylmethyl)-morpholin-2(R)-yloxy]-ethanol (compound A) and its enantiomer with native gamma-cyclodextrin (gamma-CD) were investigated using capillary electrophoresis (CE), reversed-phase liquid chromatography (RPLC), proton (1H), fluorine (19F) and carbon (13C) nuclear magnetic resonance spectroscopy (NMR), electrospray mass spectrometry (ESI-MS) and circular dichroism (CD). All experiments provided clear evidence of the formation of diastereomeric complexes between the enantiomers and gamma-CD. Proton, fluorine and carbon NMR spectra suggested that both aromatic rings, with mono-fluoro and bis-tri-fluoro functional groups, on the guest molecule were partially included into the cavity of the gamma-CD. ESI-MS spectra indicated that the diastereomeric complexes have a 1:1 stoichiometric ratio. The binding constants of the diastereomeric complexes obtained by CE, RPLC and CD were compared. The effects of the gamma-CD concentration, organic modifiers and temperature on the CE-chiral separation were also investigated.     

A Convenient One-Step Gingerol Synthesis

Racemic 6-gingerol can be obtained in a one-pot reaction by hexanal addition to the dianion of zingerone at low temperature. Similarly, addition of octanal or decanal to the dianion provides 8-gingerol or 10-gingerol, respectively. Acid treatment of the gingerols allows for formation of the corresponding shogaols.     

Reconstitution of Nucleosome Demethylation and Catalytic Properties of a Jumonji Histone Demethylase

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Highlights? Catalytic domain of JMJD2A (cJMJD2A) removes methyl marks in a distributive manner ? Homogeneously methylated nucleosomes were used as substrates ? Quantitative assay for nucleosome demethylation has been developed     

Absolute potassium cation affinities (PCAs) in the gas phase

The potassium cation affinities (PCAs) of 136 ligands (20 classes) in the gas phase were established by hybrid density functional theory calculations (B3-LYP with the 6-311+G(3df,2p) basis set). For these 136 ligands, 70 experimental values are available for comparison. Except for five specific PCA values-those of phenylalanine, cytosine, guanine, adenine (kinetic-method measurement), and Me(2)SO (by high-pressure mass spectrometric equilibrium measurement)-our theoretical estimates and the experimental affinities are in excellent agreement (mean absolute deviation (MAD) of 4.5 kJ mol(-1)). Comparisons with previously reported theoretical PCAs are also made. The effect of substituents on the modes of binding and the PCAs of unsubstituted parent ligands are discussed. Linear relations between Li+/Na+ and K+ affinities suggest that for the wide range of ligands studied here, the nature of binding between the cations and a given ligand is similar, and this allows the estimation of PCAs from known Li+ and/or Na+ affinities. Furthermore, empirical equations relating the PCAs of ligands with their dipole moments, polarizabilities (or molecular weights), and the number of binding sites were established. Such equations offer a simple method for estimating the PCAs of ligands not included in the present study.