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.     

Elution of organic solutes from different polarity sorbents using subcritical water

The intermolecular interactions between organic solutes and sorbent matrices under subcritical water conditions have been investigated at a pressure of 50 bar and temperatures ranging from 50 to 250°C. Both polar and nonpolar organics (chlorophenols, amines, n-alkanes, and polycyclic aromatic hydrocarbons) and five different sorbent matrices (glass beads, alumina, Florisil, silica-bonded C₁₈, and polymeric XAD-4 resins) were used. From the same matrix, the polar solutes always eluted at lower temperatures, while the moderately polar and nonpolar solutes only eluted at higher temperatures. Similar to matrix effects previously observed using supercritical carbon dioxide, the sorbent type greatly influenced the elution efficiency under subcritical water conditions. Lower temperatures are sufficient to elute a particular solute from glass beads, alumina, and Florisil, but higher temperatures (less polar water) are needed to elute the same solute from silica-bonded C₁₈. The highest temperatures were required to elute aromatic organics from XAD-4. These matrix effects demonstrate that, while low temperature water can break inert or dipole interactions between solutes and glass beads, alumina, and Florisil, higher temperature water is required to interrupt the van der Waals attractions between solutes and silica-bonded C₁₈, and even higher temperatures needed to overcome the π-electron interactions between aromatic solutes and XAD-4.     

Luminol Oxidation by Hydrogen Peroxide Catalyzed by Tobacco Anionic Peroxidase: Steady-State Luminescent and Transient Kinetic Studies

The properties of a newly isolated anionic tobacco peroxidase from transgenic tobacco plants overexpressing the enzyme have been studied with respect to the chemiluminescent reaction of luminol oxidation. These were compared to the properties of horseradish peroxidase in the cooxidation of luminol and p -iodophenol, the enhanced chemiluminescence reaction. The pH, luminol and hydrogen peroxide concentrations were optimized for maximum sensitivity using the tobacco enzyme. The detection limit for the latter under the optimal conditions (2.5 m M luminol, 2 m M hydrogen peroxide, 100 m M Naborate buffer, pH 9.3) was about 0.1 p M , which is at least five times lower than that for horseradish peroxidase in enhanced chemiluminescence with p -iodophenol. The rate constants for the elementary steps of the enzyme-catalyzed reaction have been determined: k ₁= 4.9 × 10⁶ M ⁻¹ s¹, k ₂= 7.3 × 10⁶ M ⁻¹ s⁻¹, k ³= 2.1 × 10⁶ M ⁻¹ s⁻¹ (pH 9.3). The similarity of these rate constants is unusual for plant peroxidases. The high catalytic activity of tobacco peroxidase in the luminescent reaction is explained by the high reactivity of its Compound II toward luminol and the high stability of the holoenzyme with respect to heme dissociation. This seems to be a unique property of this particular enzyme among other plant peroxidases.     

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.     

Certain bilateral generating relations for generalized hypergeometric functions

Recently, we introduced a class of generalized hypergeometric functionsI n:(b _q)/α:(a _p) (x, w) by using a difference operator Δ _x,w , where . In this paper an attempt has been made to obtain some bilateral generating relations associated withI _n ^ga (x, w). Each result is followed by its applications to the classical orthogonal polynomials.     

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.     

Thermal analysis and X-ray studies of chiral ferroelectric liquid crystalline materials and their binary mixtures

Summary Thermal properties of a homologous series of ferroelectric liquid crystals S-(-)-[4-(2-n-alkoxy-propionyloxy)]biphenyl-4'-[n-alkoxy-(3,5-dimethyl)]benzoate have been investigated by polarizing optical microscopy and differential scanning calorimetry. The mesophases were identified and confirmed by X-ray too. Three binary mixtures were prepared from the individual homologues. In one of the mixtures (Mix1), the ferroelectric SmC* phase has broadened and became enantiotropic. This mesophase remained monotropic in the other two mixtures (Mix2, Mix3). The chiral nematic N* phase did not appear in Mix1, but remained monotropic for the other two mixtures. Two molecular parameters, the layer spacing and the average intermolecular distance have been calculated from the X-ray results for the homologues and their mixtures. An intercalated tail-to-tail packing of molecules was found both in the single compounds and their mixtures resulting in the layer spacing about half of the molecular length of the single compounds.     

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.