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.     

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%).     

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.     

Loss of isocyanic acid from the internal oxadiazole ring of protonated molecules of some 2,5-diaryl-1,3,4-oxadiazoles

The fragmentation pattern of some protonated 2,5-diaryl-1,3,4-oxadiazoles is discussed. An unusual decomposition consisting of elimination of the isocyanic acid molecule from the internal oxadiazole ring was found. This fragmentation pathway was deduced on the basis of B/E linked scan mass spectra of metastable ions with liquid secondary ion mass spectrometry as the ionization method and also of low-energy CID mass spectra where electrospray was used as the ionization technique. High resolution measurements were also performed.     

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.     

Azametallacycles from Ag(I)- or Cu(II)-promoted coupling reactions of dialkylcyanamides with oximes at Pt(II)

The dialkylcyanamide complexes cis-[PtCl(NCNR(2))(PPh(3))(2)][BF(4)] 1 and cis-[Pt(NCNR(2))(2)(PPh(3))(2)][BF(4)](2) 2 (R = Me or Et) have been prepared by treatment of a CH(2)Cl(2) solution of cis-[PtCl(2)(PPh(3))(2)] with the appropriate dialkylcyanamide and one or two equivalents of Ag[BF(4)], respectively. Compounds 2 can also be obtained from 1 by a similar procedure. Their reaction with oximes, HON=CR'R' ' (R'R' ' = Me(2) or C(4)H(8)), in CH(2)Cl(2) and in the presence of Ag[BF(4)] or Cu(CH(3)COO)(2), leads to the novel type of azametallacycles cis-[Pt(NH=C(ON=CR'R")-NR2)(PPh3)2][BF4]2 4 upon an unprecedented coupling of the organocyanamides with oximes, in a process that proceeds via the mixed oxime-organocyanamide species cis-[Pt(NCNR(2))(HON=CR'R' ')(PPh(3))(2)][BF(4)](2) 3, and is catalyzed by either Ag(+) or Cu(2+) which activate the ligating organocyanamide by Lewis acid addition to the amide group. In contrast, in the organonitrile complexes cis-[Pt(NCR)(2)(PPh(3))(2)][BF(4)](2) 5 (R = C(6)H(4)OMe-4 or Et), obtained in a similar way as 2 (but by using NCR instead of the cyanamide), the ligating NCR is not activated by the Lewis acid and does not couple with the oximes. The spectroscopic properties of those complexes are reported along with the molecular structures of 2b (R = Et), 4a1 (R = Me, R'R' ' = Me(2)), and 4b1 (R = Et, R'R' ' = Me(2)), as established by X-ray crystallography which indicates that in the former complex the amide-N-atoms are trigonal planar, whereas in the latter (4a1 and 4b1) the five-membered rings are planar with a localized N=C double bond (imine group derived from the cyanamide) and the exocyclic amide and alkylidene groups (in 4b1) are involved in two intramolecular H-bonds to the oxygen atom of the ring.     

A new bicyclic proline-mimetic amino acid

A new constrained bicyclic α-amino acid proline-mimetic was developed. The synthesis was achieved starting from derivatives of the chiral pool, thus allowing to prepare analogues of either l- or d-proline by choosing appropriate stereoisomers of serine and α,β-isopropylidene-glycerol derivatives. The scaffolds were prepared as N-Fmoc-amino acid suitable for solid-phase peptide synthesis.     

Skin Necrosis due to Photodynamic Action of Benzoporphyrin Depends on Circulating Rather than Tissue Drug Levels: Implications for Control of Photodynamic Therapy

In an ideal world, photodynamic therapy (PDT) of abnormal tissue would reliably spare the surrounding normal tissue. Normal tissue responses set the limits for light and drug dosimetry. The threshold fluence for necrosis (TFN) was measured in normal skin following intravenous infusion with a photosensitizer, benzoporphyrin derivative monoacid ring A (BPD-MA) Verteporfin as a function of drug dose (0.25-2.0 mg/kg), wavelength of irradiation (458 and 690 nm) and time interval (0–5h) between drug administration and irradiation. The BPD-MA levels were measured in plasma and skin tissue to elucidate the relationship between TFN, drug kinetics and biodistribution. The PDT response of normal skin was highly reproducible. The TFN for 458 and 690 nm wavelengths was nearly identical and the estimated quantum efficiency for skin response was equal at these two wavelengths. Skin phototoxicity, quantified in terms of 1/ TFN, closely correlated with the plasma pharmacokinetics rather than the tissue pharmacokinetics and was quadratically dependent on the plasma drug concentration regardless of the administered drug dose or time interval between drug and light exposure. This study strongly suggests that noninvasive measurements of the circulating drug level at the time of light treatment will be important for setting optimal light dosimetry for PDT with liposomal BPD-MA, a vascular photosensitizer.