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]     

Reactivity Studies of Iridium Pyridylidenes [TpMe2Ir(C6H5)2(C(CH)3C(R)NH] (R=H,Me, Ph)

The reactivity of a series of iridium? pyridylidene complexes with the formula [Tp^Me2Ir(C₆H₅)₂(C(CH)₃C(R)N H] ( 1 a – 1 c ) towards a variety of substrates, from small molecules, such as H₂, O₂, carbon oxides, and formaldehyde, to alkenes and alkynes, is described. Most of the observed reactivity is best explained by invoking 16 e^? unsaturated [Tp^Me2Ir(phenyl)(pyridyl)] intermediates, which behave as internal frustrated Lewis pairs (FLPs). H₂ is heterolytically split to give hydride? pyridylidene complexes, whilst CO, CO₂, and H₂C?O provide carbonyl, carbonate, and alkoxide species, respectively. Ethylene and propene form five‐membered metallacycles with an IrCH₂CH(R)N (R=H, Me) motif, whereas, in contrast, acetylene affords four‐membered iridacycles with the IrC(?CH₂)N moiety. C₆H₅(C?O)H and C₆H₅C?CH react with formation of Ir? C₆H₅ and Ir? C?CPh bonds and the concomitant elimination of a molecule of pyridine and benzene, respectively. Finally the reactivity of compounds 1 a – 1 c against O₂ is described. Density functional theory calculations that provide theoretical support for these experimental observations are also reported.     

Prospects of anionic nanolipoplexes in nanotherapy: transmission electron microscopy and light scattering studies

Currently nanosystems composed of polynucleotides and lipid vesicles (nanolipoplexes) are considered to be promising tools for gene therapeutics. Successful in vivo application of these vectors depends on their physicochemical, technological and biological characteristics including morphology, size distribution, molecular interactions and stability. Anionic nanoliposomes (DPPC:DCP:CHOL) were prepared by two different techniques, namely the conventional thin-film hydration method followed by extrusion, and the heating method (HM), in which no volatile solvent or detergent is used. A non-viral and non-cationic gene transfer vector was constructed by incorporating plasmid DNA (pcDNA3.1/His B/lacZ) to the HM-nanoliposomes by the electrostatic mediation of Ca²⁺ ions. Transfection efficiency of the nanolipoplexes was evaluated using a human bronchial epithelial cell line (16HBE14o-) in the presence of serum. Particle characterisation, stability of the formulations and lipid–DNA interaction studies were performed using transmission electron microscopy (TEM) and light scattering. TEM pictures of nanolipoplexes showed presence of two to four closely packed vesicles with signs of fusion. Efficient delivery of plasmid DNA and subsequent β-galactosidase expression was achieved using the anionic nanolipoplexes. Transfection efficiency increased with lipid:DNA ratio up to 7:1 (w/w), where transfection efficiency was 12-fold higher than in untreated cells. Further increase in lipid ratio decreased transfection. These nanolipoplexes appear to be safe, stable and efficient in the protection and delivery of DNA to different cells and tissues.