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.     

The collection and determination of atmospheric gaseous bromine and iodine

A procedure has been developed which allows for the isolation, collection and analysis of atmospheric gaseous iodine and bromine. Particulate matter is removed from the airstream to be sampled by electrostatic precipitation. The gaseous halogen species are adsorbed onto specially cleaned activated charcoal. After irradiation of the charcoal sample with thermal neutrons, the iodine and bromine are removed from the charcoal, isolated, and purified as the AgX precipitate. The amounts of gaseous iodine and bromine are then determined by β-counting. The system works well for air sheds with low particulate iodine and bromine concentrations relative to that in the gaseous phase. In air sheds where the particulate halogen predominates, the gas phase measurements are more uncertain.     

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 and properties of new glucocationic surfactants: model structures for marking cationic surfactants with carbohydrates

[reaction: see text] In this work, we report the synthesis of a new series of glucocationic surfactants, a class of surfactants we introduced very recently. The preparation of the surfactants is based on the synthesis of the 2-bromoethyl-2,3,4,6-tetra-O-acetyl-beta-D-glucopyranoside, whose preparation was studied in order to improve yields and stereoselectivity of this key intermediate. These glucocationic amphiphiles were prepared and studied as a model of cationic surfactants marked with a carbohydrate moiety. The use of carbohydrates as markers on cationic lipids was recently introduced to induce recognition by specific receptors, present on the surface of cell membranes. The chemicophysical characterization of these model structures can give more insight on the aggregation behavior. Conductivity and surface tension measurements were performed in order to characterize the compounds from the amphiphilic point of view. The results showed a different effect of the glucosidic moiety on the cmc value with respect to the glucopyridinium cationic surfactants. The surfactants also showed the tendency to form premicellar aggregates in solution when the hydrophobicity is raised.     

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.     

A novel synthesis of enantiopure octahydropyrrolo[3,4-b]pyrroles by intramolecular [3 + 2] dipolar cycloaddition on chiral perhydro-1,3-benzoxazines

[reaction: see text] Condensation of N-substituted glycines with chiral 3-allyl-2-formyl perhydro-1,3-benzoxazines forms an azomethine ylide that cyclizes to give octahydropyrrolo[3,4-b]pyrrole derivatives. The [3 + 2] dipolar cycloadditions are stereoespecific leading to a single diastereoisomer. The chemical yields are dependent on the reaction temperature and the presence or absence of a base.     

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.     

The vibrational spectrum of dibutadieneiron carbonyl

A vibrational assignment has been proposed for (C₄H₆)₂Fe(CO). The internal butadiene modes show that there is very little interaction between the two C₄H₆ molecules, and that electronically it is very similar to C₄H₆ in (C₄H₆)Fe(CO)₃.