A Districtwide Study of Automaticity When Included in Concept‐Based Elementary School Mathematics Instruction

While conceptual understanding of properties, operations, and the base‐ten number system is certainly associated with the ability to access math facts fluently, the role of math fact memorization to promote conceptual understanding remains contested. In order to gain insight into this question, this study looks at the results when one of three elementary schools in a school district implements mandatory automaticity drills for 10 minutes each day while the remaining two elementary schools, with the same curriculum and very similar demographics, do not. This study looks at (a) the impact that schoolwide implementation of automaticity drills has on schoolwide computational math skills as measured by the ITBS and (b) the relationship between automaticity and conceptual understanding as measured by statewide standardized testing. The results suggest that while there may be an association between automaticity and higher performance on standardized tests, caution should be taken before assuming there are benefits to promoting automaticity drills. These results are consistent with those that support a process‐driven approach to automaticity based on familiarity with properties and strategies associated with the base‐ten number system; they are not consistent with those that support an answer‐driven approach to automaticity based on memorization of answers.     

The die swell phenomenon

Summary A polymer melt or solution undergoes an increase in its cross-section when it is forced out of an orifice into air. The normal stress effects and elastic effects shown by these materials are frequently invoked to explain this die swell phenomenon. These explanations are here discussed and criticised. The analogous situation for a Newtonian jet is also discussed and the solution to a related problem of two-dimensional lowReynolds number flow is given.

---

Zusammenfassung Kunststoffschmelzen oder -lösungen zeigen nach dem Austritt aus einer Mündung in Luft eine Aufweitung des Querschnitts. Häufig wird dieses Schwell-Phänomen als Folge von Normalspannungen und Elastizität erklärt. Erklärungen dieser Art werden hier kritisch untersucht.Ebenso wird der entsprechende Fall einer Newtonschen Düsenströmung diskutiert. Für das verwandte Problem einer zweidimensionalen Strömung bei niedrigerReynolds-Zahl wird die Lösung gegeben.

     

1,2-diphosphaacenaphthene 1,2-dications: synthetic, stereochemical and computational study of the stabilising role of naphthalene-1,8-diyl backbone

Syntheses and full characterisation data (including single crystal diffraction) of three 1,2‐diphosphonium dicationic species with the naphthalene‐1,8‐diyl (Nap) backbone are reported. The oxidation of Nap[P(NMe₂)₂]₂ with P₂I₄ to its 1,2‐dication was achieved. meso‐ and rac‐forms of “all carbon” 1,2‐diphosphonium dications were obtained in good yields and purity by double alkylation of the parent diphosphine (1,2‐diphenyl‐1,2‐diphosphaacenaphthene) with methyl triflate or trimethyloxonium tetrafluoroborate. Each methylating reagent produces one of the rac‐ or meso‐forms of the dication diastereospecifically. Structural parameters of the new dications are discussed with respect to other phosphorus 1,2‐dications. DFT (B3LYP) computations revealed the significant role of the naphthalene backbone in stabilisation of the dicationic motif and helped to assess the energy cost of the steric clash of a variety of groups attached to the peri‐positions of naphthalene. The synthesis and single crystal X‐ray data of the extremely crowded Nap[P(?Se)(OiPr)₂]₂ are discussed, and are contrasted with the unsuccessful synthesis of Nap(PtBu₂)₂ from NapLi₂ and ClPtBu₂.     

Self-organization of amphiphilic liquid-crystalline dendrimers in bulk and at the interface

A comparative analysis of the structure and phase behavior of synthesized carbosilane amphiphilic LC dendrimers of the third generation containing mesogenic phenyl and oligo(ethylene glycol) fragments is performed. When phenol groups are replaced with oligo(ethylene glycol) moieties, the temperature interval of the existence of the LC phase in the mesogen-containing dendrimers decreases. The chemical nature of hydrophilic terminal groups is found to control the organization of dendrimers in the smectic mesophase. Structural models for their packing are proposed. Amphiphilic dendrimers are shown to form stable Langmuir films at the water/air interface. Surface-pressure-surface area-isotherms are constructed. The effect of the chemical nature of hydrophilic groups on the formation of a monolayer at the interface and on the packing density of dendrimer molecules in the monolayer is discussed.     

Microproteomic analysis of 10,000 laser captured microdissected breast tumor cells using short-range sodium dodecyl sulfate-polyacrylamide gel electrophoresis and porous layer open tubular liquid chromatography tandem mass spectrometry

Precise proteomic profiling of limited levels of disease tissue represents an extremely challenging task. Here, we present an effective and reproducible microproteomic workflow for sample sizes of only 10,000 cells that integrates selective sample procurement via laser capture microdissection (LCM), sample clean-up and protein level fractionation using short-range SDS-PAGE, followed by ultrasensitive LC-MS/MS analysis using a 10 μm i.d. porous layer open tubular (PLOT) column. With 10,000 LCM captured mouse hepatocytes for method development and performance assessment, only 10% of the in-gel digest, equivalent to ～1000 cells, was needed per LC-MS/MS analysis. The optimized workflow was applied to the differential proteomic analysis of 10,000 LCM collected primary and metastatic breast cancer cells from the same patient. More than 1100 proteins were identified from each injection with >1700 proteins identified from three LCM samples of 10,000 cells from the same patient (1123 with at least two unique peptides). Label free quantitation (spectral counting) was performed to identify differential protein expression between the primary and metastatic cell populations. Informatics analysis of the resulting data indicated that vesicular transport and extracellular remodeling processes were significantly altered between the two cell types. The ability to extract meaningful biological information from limited, but highly informative cell populations demonstrates the significant benefits of the described microproteomic workflow.     

Scalable synthesis of 1-bicyclo[1.1.1]pentylamine via a hydrohydrazination reaction

The reaction of [1.1.1]propellane with di-tert-butyl azodicarboxylate and phenylsilane in the presence of Mn(dpm)(3) to give di-tert-butyl 1-(bicyclo[1.1.1]pentan-1-yl)hydrazine-1,2-dicarboxylate is described. Subsequent deprotection gives 1-bicyclo[1.1.1]pentylhydrazine followed by reduction to give 1-bicyclo[1.1.1]pentylamine. The reported route marks a significant improvement over the previous syntheses of 1-bicyclo[1.1.1]pentylamine in terms of scalability, yield, safety, and cost.     

Selective anion binding by a cofacial binuclear zinc complex of a Schiff-base pyrrole macrocycle

The synthesis of the new cofacial binuclear zinc complex [Zn(2)(L)] of a Schiff-base pyrrole macrocycle is reported. It was discovered that the binuclear microenvironment between the two metals of [Zn(2)(L)] is suited for the encapsulation of anions, leading to the formation of [K(THF)(6)][Zn(2)(μ-Cl)(L)]·2THF and [Bu(n)(4)N][Zn(2)(μ-OH)(L)] which were characterized by X-ray crystallography. Unusually obtuse Zn-X-Zn angles (X = Cl: 150.54(9)° and OH: 157.4(3)°) illustrate the weak character of these interactions and the importance of the cleft preorganization to stabilize the host. In the absence of added anion, aggregation of [Zn(2)(L)] was inferred and investigated by successive dilutions and by the addition of coordinating solvents to [Zn(2)(L)] solutions using NMR spectroscopy as well as isothermal microcalorimetry (ITC). On anion addition, evidence for deaggregation of [Zn(2)(L)], combined with the formation of the 1:1 host-guest complex, was observed by NMR spectroscopy and ITC titrations. Furthermore, [Zn(2)(L)] binds to Cl(-) selectively in THF as deduced from the ITC analyses, while other halides induce only deaggregation. These conclusions were reinforced by density functional theory (DFT) calculations, which indicated that the binding energies of OH(-) and Cl(-) were significantly greater than for the other halides.     

Direct conversion of benzylic and allylic alcohols to phosphonates

Benzyl phosphonate esters often serve as reagents in Horner-Wadsworth-Emmons reactions. In most cases, they can be prepared from benzylic alcohols via formation of the corresponding halide followed by an Arbuzov reaction. To identify a more direct synthesis of phosphonate esters, we have developed a one-flask procedure for conversion of benzylic and allylic alcohols to the corresponding phosphonates through treatment with triethyl phosphite and ZnI(2).     

Selective incorporation of functional dicarboxylates into zinc metal-organic frameworks

Zinc(II) nitrate reacts with different ratios of 1,4-benzenedicarboxylic acid (H(2)bdc) and 2-halo-1,4-benzenedicarboxylic acid (H(2)bdc-X, X = Br or I) to give [Zn(4)O(bdc)(3-x)(bdc-X)(x)], in which preferential incorporation of bdc is observed. The selective incorporation is related to crystal growth rates, and the proportion of incorporated bdc-X rises with increasing reaction time.