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.     

Resonances in the electronic quenching of O(1D) by N2. A numerical quantum mechanical study for the collinear collision

The close coupled equations for the collinear collision O(¹D) + N₂ (¹Σ⁺_g) → O(³P) + N₂(¹Σ⁺_g) have been solved numerically for a model of two crossing potential curves assuming a constant spin-orbit coupling. Comparison between the results of an atom-atom like model and the converging results reveals a substantial (factor of ≈ 40) enhancement of the electronic quenching at room temperature together with high vibrational excitation of N₂. These results, and the study of the peaks appearing in the quenching probabilities as a function of the incident energy, clearly confirm that the high efficiency of this reaction is mainly due to resonances (quasibound states), as has been lately suggested.     

Fractional revivals in the rovibrational motion of I2

Motivated by pump-probe experiments of I(2) in a room-temperature sample, the detection of fractional revivals is investigated using full-dimensional quantum wave packet calculations. It is shown that the structures observed in the pump-probe signal depend sensitively on the probe parameters employed and that the observed signal reflects a particular phase effect between fractional revivals.     

Electronic nonadiabatic transitions in the reactive (Ar+ + H2, Ar + H+2, ArH+ + H) system. Numerical results for the collinear configuration

In this communication are presented exact quantum mechanical nonadiabatic electronic transition probabilities for the collinear reaction Ar⁺ + H₂(v_i = 0) → ArH⁺(v_f) + H. The calculations were performed using a potential surface calculated by the DIM method. It is established that large probabilities (≈ 1.0) can be obtained only if there is enough translational energy to overcome a potential barrier formed due to the crossing between v_i = 0 of the Ar⁺ + H₂ system and v_i = 2 of the Ar + H⁺₂ system. The threshold for the reaction is found to be 0.06 eV.     

9,9-diphenyl-1,9,10,10a-tetrahydro-2H-phenaleno[1,9-bc]pyrans

Reaction between some naphtho[2,1-b]pyrans and 1,1-diphenylethene affords 9,9-diphenyl-1,9,10,10a-tetrahydro-2H-phenaleno[1,9-bc]pyrans.     

Monodentate sigma-N and Bidentate sigma-N,sigma-N' Coordination of 1,1-Bis((N-p-tolylimino)diphenylphosphoranyl)ethane, CHCH(3)(PPh(2)=NC(6)H(4)-4-CH(3))(2), to Platinum(II)

The new ligand, 1,1-bis((N-p-tolylimino)diphenylphosphoranyl)ethane (1,1-BIPE), 1, has been synthesized by means of a Staudinger reaction of 1,1-bis(diphenylphosphino)ethane (1,1-dppe) with 2 equiv of p-tolylazide. Bridge-splitting reactions of Pt(2)Cl(4)(PR(3))(2) with 1 readily afforded sigma-N monodentate complexes, [PtCl(2)(PR(3)){1,1-BIPE-sigmaN}] (2a, PR(3) = PEt(3); 2b, PR(3) = PMe(2)Ph). Conversion of 2 into the six-membered platinacycle [PtCl(PR(3)){1,1-BIPE-sigmaN,sigmaN'}](+)[X](-) (3) (X = Cl, PtCl(3)(PR(3)), BF(4)) took place after prolonged stirring, its reaction rate being strongly dependent on the type of phosphine (>5 days for 2ain the presence of NaBF(4), 1 h for 2b) and the metal-to-ligand ratio. The compounds 1, 2, and 3 have been fully characterized by (1)H, (31)P{(1)H}, and (13)C{(1)H} NMR and IR spectroscopy, elemental analysis, or FAB mass spectroscopy. The molecular structures of CHCH(3)(PPh(2)=NC(6)H(4)-4-CH(3))(2) (1) and [PtCl(PMe(2)Ph){(N(pTol)=PPh(2))(2)CHCH(3)}](+)[Cl](-) (3b) have been determined by X-ray crystallography. Crystal data for 1: space group P2(1)/c with a = 8.9591(5) ?, b = 19.1961(12) ?, c = 21.9740(9) ?, beta = 105.069(4) degrees, V = 3649.1(3) ?(3), and Z = 4. The structure refinement converged to R = 0.080 and R(w) = 0.109. Crystal data for 3b: monoclinic, space group P2(1)/c with a = 12.4021(7) ?, b = 16.9705(11) ?, c = 23.760(2) ?, beta = 109.544(5) degrees, V = 4712.7(5) ?(3), and Z = 4. The structure refinement converged to R1 = 0.057, wR2 = 0.122. Variable temperature NMR spectroscopy has revealed that complexes 3 exclusively adopt a twisted boat conformation with the methyl group in equatorial position at low temperature, in agreement with the solid state structure of 3b as determined by X-ray crystallography. Boat-to-boat inversion is assumed to take place at temperatures above 293 K. Furthermore, for 3, hindered rotation of one of the p-tolyl substituents on nitrogen has been established at low temperatures.     

Combining fixed- and moving-grid methods to study direct dissociation processes involving nonadiabatic transitions

We present a novel quantum-dynamics approach suitable for computing direct dissociation processes, including electronic transitions. This approach combines quantum trajectories in the Lagrangian reference frame with standard fixed-grid wave packets in order to overcome the limitations and difficulties of both techniques. As a model application, we consider the ultrafast photodissociation of H2 excited by a femtosecond extreme UV laser pulse.     

PdS2C2(COOMe)2](6n) (n = 0, -1, -2, -3, -4): hexanuclear homoleptic palladium dithiolene complexes

Reaction of a stoichiometric equivalent of the zinc-dithiolene complex, (tmeda)ZnS2C2(COOMe)2 (tmeda = tetramethylethylenediamine), with (MeCN)2PdCl2 results in a 1:1 homoleptic dithiolene that forms the hexanuclear cluster [PdS2C2(COOMe)2]6 (1). X-ray structure analysis of 1 indicates a Pd6S12 core comprised of six face-centered palladium atoms and 12 edge-centered sulfur atoms situated on an imaginary approximate cube. Complex 1 undergoes four distinct and reversible one-electron redox steps in dichloromethane at -186, -484, -1174, and -1524 mV versus a standard calomel electrode (ferrocenium+/ferrocene redox couple 409 mV). The two-electron reduction product of 1, [Bu4N]2[(PdS2C2(COOMe)2)6] (2), has been chemically isolated and characterized.     

Evaluation of a commercial enzymatic test kit regarding the quantitative analysis of different free fatty acids

The quantitative determination of the total free fatty acids (FFAs) is an important analytical task because FFAs exhibit important physiological effects and are also relevant in many other fields, for instance, in food research. Our aim was to investigate whether a commercially available enzymatic test kit developed for the determination of FFAs in human serum is also suitable to determine different physiological and nonphysiological FFAs and to which extent the impact on the sensitivities (i.e., the accuracy by which a given FFA can be determined) differ. It will be shown that the chain length as well as the double bond content has a significant impact on the sensitivity by which a given FFA can be determined. For instance, palmitic acid (16:0) is determined with an approximately 20 times higher sensitivity in comparison to docosahexaenoic acid (22:6n-3). All data were obtained by measuring the concentrations of the FFAs by gas chromatography, and selected FFAs were also determined in a complex matrix of human serum. It is concluded that this kit is not useful if major alterations of the FFA composition of a complex mixture are expected because the individual FFAs are not detected with the same sensitivities: the concentrations of polyunsaturated FFA determined by this kit are wrong. Figure

The used enzymatic kit detects different free fatty acids with significantly different sensitivities: the number of carbon atoms and the number of double bonds massively contribute to these differences     

An Inexpensive Laser Raman Spectrometer Based on CCD Detection

We describe an inexpensive modular Raman spectrometer system that can be assembled from commercial components for under $5000. Three typical applications are presented: a demonstration of a vibrational isotope effect, a Raman polarization experiment, and a resonance Raman experiment. This spectrometer system should make it easier to include the important topic of Raman spectroscopy in the undergraduate physical and analytical chemistry laboratory curricula.