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.     

Diastereoselective carbonyl phosphonylation using chiral N,N′-bis-[(S)-α-phenylethyl]-bicyclic phosphorous acid diamides

Addition of aldehydes to the P-anion derivatives of chiral phosphorous acid diamides (1S,2S,1′S,1″S)-2 and (1R, 2R,1′S,1″S)-2 in THF gave α-hydroxyphosphonamides in good yield (64-100%) and moderate diastereoselectivities.     

Biological Activity of Flavonoids Copper Complexes

Three flavonoid copper(II) complexes Cu₂(quercetin)(CH₃COO)₃(CH₃OH) ( 1 ), Cu(anthrarufin)(CH₃COO)·1/2H₂O ( 2 ) and Cu(naringin)(OCH₃)(CH₃OH)₂ ( 3 ) have been synthesized and characterized by elemental analysis, IR, electronic absorption and EPR (X‐band) spectroscopy. The complexes have a strong protective action over the Δsod1 mutant of S. cerevisiae against reactive oxygen radicals generated by an external source of free radicals (H₂O₂ or the superoxide‐generating, menadione). On the other hand, the complexes cleave DNA efficiently even in the absence of reducing agents. The main reactive oxygen species responsible for the DNA strand cleavage have been determined using radical scavengers. A probably mechanism of the DNA damage is proposed.     

Asymmetric synthesis by chiral ruthenium complexes : VI. Enantiomer-discrimination in the hydrogen transfer from racemic alcohols to prochiral ketones in the presence of H4Ru4(CO)8[(−)-diop]2

Hydrogen transfer from racemic alcohols to prochiral ketones in the presence of H₄Ru₄(CO)₈[(?)-DIOP]₂ has been examined. The enantiomer-discrimination is influenced by the structure of the reactants, temperature and the excess of phosphine present.     

Determination of fluoride in complex liquid matrices by electrothermal atomic absorption spectrometry with in-furnace oxygen-assisted ashing

A new chemical method is reported for the determination of total fluoride in complex liquids and suspensions, such as fruit juices, urine, serum and blood. It is based on the formation of the A1F radical in a graphite furnace afterin situ oxygen-assisted ashing of the untreated sample. The absorbance of this radical is measured at 227.45 nm. The method is relatively easy to use and provides a low detection limit (14 ng/ml) and reasonable reproducibility (5–10%).     

Synthesis of beta-lactams by Ag+-induced ring expansion of 1-hydroxycyclopropylamines: a theoretical analysis

A theoretical analysis of the silver-induced ring expansion of N-chloro-N-methyl-1-hydroxycyclopropylamine to form N-methyl-2-azetidinone, and of the Cl(-) elimination from this substrate without Ag(+) assistance, was performed using the B3LYP method and the 6-31+G(d) basis set for C, N, O, H, and Cl atoms and the relativistic effective core pseudopotential LANL2DZ complemented with one set of f polarization functions (zeta(f) = 0.473) for the Ag atom. The partial Ag(+)-assisted extrusion of Cl(-) at the rate-determining transition state provokes an important change in the nodal properties of the frontier molecular orbitals of the H(3)CClNCOHAg(+) fragment, thus making very stabilizing HOMO-LUMO interactions between this fragment and the C(2)H(4) moiety possible. This interaction leads to the ring opening and release of most of the strain energy, giving rise to a low energy barrier for the process. Also, by assisting the Cl(-) extrusion, Ag(+) avoids the elimination of the hydroxyl hydrogen atom, which would provoke the fragmentation of the system instead of the formation of the beta-lactam.     

Arcs in the Hall Planes

Using a transformation tecnique for designs introduced in [1], I construct a class of arcs embeddeable in the Hall plane and in the dual of the Hall plane of order q proving also their completeness in the unital of Grüning. Math. Subj. Class.: 51A35 Non Desarguesian affine and projective planes. 51E22 Blocking sets, ovals, k-arcs.     

Cycloaddition reaction of 2-azadienes derived from beta-amino acids with electron-rich and electron-deficient alkenes and carbonyl compounds. Synthesis of pyridine and 1,3-oxazine derivatives

Functionalized keto-enamines 6 were obtained by nucleophilic addition of enol ethers to the imine moiety of 2-azadienes derived from dehydroaspartic esters 4. Reactions of 2-azadiene 4c containing three electron-withdrawing substituents (CO(2)R) with enol ethers 5 in the presence of lithium perchlorate led to the formation of tetrahydropyridine derivatives 7 in a regio- and stereoselective fashion. 2H-[1,3]-oxazines 10 and pyridine derivatives 12 and 13 were obtained by heterocycloaddition reactions of electron-poor azadienes 4d-g containing two electron-withdrawing substituents (4-O(2)N-C(6)H(4), CO(2)R) in positions 1 and 4 with carbonyl derivatives (ethyl glyoxalate 9a and diethyl ketomalonate 9b) and the electron-deficient olefin tetracyanoethylene 11.     

Ion pair charge-transfer complexes between anionic and cationic metal-dithiolenes [M(II) = Pd,Pt

New [M(R(2)pipdt)(2)](BF(4))(2) salts [R(2)pipdt = N,N'-dialkyl-piperazine-2,3-dithione; M = Pd(II), R = Me and M = Pt(II), R = Me, Et, Pr(i)] bearing redox-active cationic dithiolene complexes have been prepared and characterized. These cations react with the redox-active [M(mnt)(2)](2-) [M = Pd(II), Pt(II); mnt = maleonitrile-2,3-dithiolate] anionic dithiolenes to form salts describable as ion pair charge-transfer complexes. X-ray crystallographic studies have shown that [M(Me(2)pipdt)(2)][M(mnt)(2)] complexes, with M = Pd(II) and Pt(II), are isomorphous. Crystal data of the Pt salt (3a): triclinic, Ponemacr; (No. 2); Z = 1; T = 293(2) K; a = 6.784(7) A, b = 8.460(6) A, c = 13.510(5) A, alpha = 100.63(2) degrees, beta = 104.04(2) degrees, gamma = 96.90(2) degrees; R1 = 0.0691 [wR2 = 0.2187 (all data)]. Structural data show that approximately square-planar [Pt(Me(2)pipdt)(2)] dications and regular square-planar [Pt(mnt)(2)] dianions form an infinite anion-cation one-dimensional stack along axis a with a Pt...Pt a/2 distance of 3.392 A and a Pt...Pt...Pt angle of 180 degrees. Anions and cations arrange themselves face-to-face so as to take on a staggered arrangement. These salts exhibit strong absorptions in the visible-near-infrared region assigned to ion pair charge-transfer transitions. A relation between the optical and thermal electron transfer in the solid state is obtained using a "Marcus-Hush model", and a solid-state electrical conductivity in agreement with expectations is observed. Vibrational spectroscopy is in agreement with the existence of charge-transfer interactions between the cationic and anionic components of the salts.