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.     

Parity-locking effect in a strongly-correlated ring

Orbital magnetism in an integrable model of a multichannel ring with long-ranged electron-electron interactions is investigated. In a noninteracting multichannel system, the response to an external magnetic flux is the sum of many diamagnetic and paramagnetic contributions, but we find that for sufficiently strong correlations, the contributions of all channels add constructively, leading to a parity (diamagnetic or paramagnetic) which depends only on the total number of electrons. Numerical results confirm that this parity-locking effect is robust with respect to subband mixing due to disorder.     

Sequential cycloaddition approach to the tricyclic core of vibsanin E. Total synthesis of (+/-)-5-epi-10-epi-vibsanin E

[chemical reaction: see text]. A direct access to (+/-)-5-epi-10-epi-vibsanin E is described, based on three key cycloaddition steps, a rhodium-catalyzed [4 + 3] cycloaddition, a heteronuclear [4 + 2] cycloaddition, and a photochemically induced [4 + 2] cycloaddition.     

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).     

Macroscopic mass and energy balance of a pilot plant anaerobic bioreactor operated under thermophilic conditions

Intensive poultry production generates over 100,000 t of litter annually in West Virginia and 9×10⁶ t nationwide. Current available technological alternatives based on thermophilic anaerobic digestion for residuals treatment are diverse. A modification of the typical continuous stirred tank reactor is a promising process being relatively stable and owing to its capability to manage considerable amounts of residuals at low operational cost. A 40-m³ pilot plant digester was used for performance evaluation considering energy input and methane production. Results suggest some changes to the pilot plant configuration are necessary to reduce power consumption although maximizing biodigester performance.     

PHOTOCHEMISTRY OF DNA CONTAINING IODINATED CYTOSINE*

Abstract— –Irradiation at 313 nm of compounds containing iodinated cytosine moieties results in the photolysis of iodine. Photolysis occurs with a quantum yield of 0·0224·024 for 5-iododeoxycytidine and 5-iododeoxycytidine monophosphate, and 0·004–0·008 for iodinated DNA as well as for iodinated polycytidylate. Photodegradation of the cytosine moiety occurs when air is present during irradiation, presumably due to the reaction of oxygen with the cytosyl radical formed when iodine is lost. This oxygen promoted photodegradation destroys the cytosine chromophore and is complete in the monomers but occurs to only a limited extent in the polymers. In the absence of oxygen or in the presence of ethanol, photodegradation is prevented and the loss of iodine leads exclusively to the formation of the cytosine chromophore. In DNA, the loss of iodine is accompanied by the formation of sugar damage and/or chain breaks. As measured by sedimentation in alkaline sucrose gradients, approximately one break is made for every six iodinqs lost in denatured DNA. The frequency of chain breakage per iodine photolyzed is reduced 2-fold in renatured DNA. Analysis in neutral gradients suggests that half of the breaks observed in alkali are alkali-labile bonds. Both ethanol and cysteamine reduce the number of chain breaks observed in alkali by ˜ 3-fold.     

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.