Knowing and Teaching Middle School Mathematics: A Professional Development Course for In‐Service Teachers

This article describes a professional development course intended to improve the content understanding of middle school mathematics teachers. The design of the course included three professional learning strategies: problem solving, examination of student thinking, and discussion of research. The concepts studied in the course included multi‐digit subtraction, multi‐digit multiplication, operations with fractions, and concepts of area and perimeter. Results from pre‐ and post‐tests administered to the nineteen participants indicate a significant increase in the mean score for each concept and document growth in the teachers' content understanding. In particular, their solutions moved from primarily procedural to more conceptual. Responses to an open‐ended survey indicate other important aspects of the professional development. Examples of teachers' work and comments are included.     

Selective cleavage of acetals with ZnBr2 in dichloromethane

A selective cleavage of acetals of 1,2- and 1,3-diols has been achieved under mild conditions using ZnBr₂ in dichloromethane at room temperature. Acetal types cleavable by this procedure include benzylidene, isopropylidene and cyclohexylidene acetals. This method is compatible with several other types of hydroxyl protecting groups such as Bn, Bz, TBDPS, TIPS and TBDMS.     

Synthesis of Enantiopure Primary Amines by Stereoselective Ring Opening of Chiral Octahydro-1,3-benzoxazines by Grignard and Organoaluminum Reagents

Chiral 1,3-perhydrobenzoxazines 1, 2, and 9-14, prepared by condensation of 8-(benzylamino)menthol with different aldehydes, react with alkylmagnesium bromides and trimethylaluminum leading to the open amino alcohols 3a-d, 4a-d, and 15-20 in excellent chemical yields and good to excellent diastereomeric excess. The sequential elimination of the menthol appendage by heating with P(2)O(5) and the benzyl group by hydrogenolysis lead to primary amines 7a-d, 8a-d, and 27-30 in excellent chemical yields and ee. The addition of the alkyl group from the Grignard derivatives and the methyl group from the trimethylaluminum occurs from opposite sides of the heterocycle, yielding the final primary amines with the same stereochemistry.     

The reaction of β-aminoenones with substituted acetonitriles. Regiospecific synthesis of 2(1H)-pyridones

Unsymmetrically substituted β-aminoenones react with malononitrile, cyanomethylphenylsulfone, benzoyl-acetonitrile and ethyl cyanoacetate, in very mild conditions, to yield regiospecifically 3-functionalized 2(1H)-pyridones in high yields.     

Volumetric Properties of Binary Mixtures of Isomeric Butanols and C8 Solvents at 298.15 K

Excess molar volumes, V _m ^E, over the whole composition range for binary mixtures of 1-butanol, 2-butanol, and 2-methyl-2-propanol + 1-octanol, or 2-octanol, or di-n-butyl ether, or n-hexylacetate were determined at 298.15 K from density measurements carried out with a vibrating-tube densimeter. Small V _m ^E values, both positive and negative, are displayed by mixtures containing 1- or 2-octanol, whereas positive and larger values are always found for mixtures containing dibutyl ether and hexylacetate. These results can be justified in terms of H-bonding interactions and/or steric hindrance due to the branched alkyl chains. Partial molar volumes at infinite dilution of the isomeric butanols in the C8 compounds were also calculated from the apparent molar volumes in dilute solution. The solute-solvent interactions and the effects of the local organisation of the solvent around the butanol molecules were discussed using the void and cavity volumes as different estimates of the intrinsic volume of the molecules. The volumetric behavior of butanols seems to be determined by the solute-solvent interactions rather than packaging effects.     

On the [2,3] sigmatropic rearrangement of allylic nitro compounds

Allylic nitro compounds undergo relatively clean [2,3] sigmatropic rearrangement upon heating in refluxing 1,2-dichlorobenzene in the presence of DABCO to give the corresponding allylic alcohols via the intermediate allylic nitrite. [reaction: see text]     

Solid-phase extraction clean-up procedure for the analysis of PAHs in lichens

A clean-up procedure based on a solid-phase extraction column was optimized for determination of polycyclic aromatic hydrocarbons (PAHs) in lichen extracts to remove co-extracted compounds from the matrix in the final extract. Several kinds of solid phases were evaluated: normal phase (-NH₂ and alumina), strong anion exchange and reversed phase. The -NH₂ columns were the most effective by using a packed solid bed of 500?mg. The lichen raw extract was loaded on the column previously conditioned with dichloromethane and hexane. Hexane (0.5?mL) was used as rinsing solvent, and PAHs were quantitatively eluted (80–97%) using 2?mL of hexane–dichloromethane (65–35) as eluting solvent. In these conditions, even the heaviest PAHs were quantitatively eluted. The optimized SPE method provides a short time and low-solvent-consumption sample clean-up compared with other conventional methods based on column chromatography. The analytical procedure, dynamic sonication-assisted extraction, followed by the optimized solid-phase extraction clean-up, was used to determine the 16 EPA priority PAHs from native lichens collected from the Aragon valley in central Pyrenees. The PAH concentrations in lichen samples ranged from 352 to 1654?ng?g^?1, and the minimum concentration value was established as the regional reference PAH levels in the area.     

Experimental and Theoretical Studies on Arene‐Bridged Metal–Metal‐Bonded Dimolybdenum Complexes

The bis(hydride) dimolybdenum complex, [Mo₂(H)₂{HC(N‐2,6‐iPr₂C₆H₃)₂}₂(thf)₂], 2 , which possesses a quadruply bonded Mo₂^II core, undergoes light‐induced (365 nm) reductive elimination of H₂ and arene coordination in benzene and toluene solutions, with formation of the Mo^I₂ complexes [Mo₂{HC(N‐2,6‐iPr₂C₆H₃)₂}₂(arene)], 3?C₆H₆ and 3?C₆H₅Me , respectively. The analogous C₆H₅OMe, p‐C₆H₄Me₂, C₆H₅F, and p‐C₆H₄F₂ derivatives have also been prepared by thermal or photochemical methods, which nevertheless employ different Mo₂ complex precursors. X‐ray crystallography and solution NMR studies demonstrate that the molecule of the arene bridges the molybdenum atoms of the Mo^I₂ core, coordinating to each in an η² fashion. In solution, the arene rotates fast on the NMR timescale around the Mo₂‐arene axis. For the substituted aromatic hydrocarbons, the NMR data are consistent with the existence of a major rotamer in which the metal atoms are coordinated to the more electron‐rich C?C bonds.     

New method for determination of trihalomethanes in exhaled breath: Applications to swimming pool and bath environments

A method for the estimation of the human intake of trihalomethanes (THMs), namely chloroform, bromodichloromethane, dibromochloromethane and bromoform, during showering and bathing is reported. The method is based on the determination of these compounds in exhaled breath that is collected by solid adsorption on Tenax using a device specifically designed for this purpose. Instrumental measurements were performed by automatic thermal desorption coupled to gas chromatography with electron capture detection. THMs in exhaled breath samples were determined during showering and swimming pool attendance. The levels of these compounds in indoor air and water were also determined as reference for interpretation of the exhaled breath results. The THM concentrations in exhaled breath of the volunteers measured before the exposure experiments showed a close correspondence with the THMs levels in indoor air where the sampler was located. Limits of detection in exhaled breath were dependent on THM analytes and experimental sites. They ranged between 170 and 710 ng m⁻³ in the swimming pool studies and between 97 and 460 ng m⁻³ in the showering studies. Application of this method to THMs determination during showering and swimming pool activities revealed statistically significant increases in THMs concentrations when comparing exhaled breath before and after exposure.