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.     

Azidoethoxyphenylalanine as a Vibrational Reporter and Click Chemistry Partner in Proteins

An unnatural amino acid, 4‐(2‐azidoethoxy)‐L ‐phenylalanine (AePhe, 1 ), was designed and synthesized in three steps from known compounds in 54 % overall yield. The sensitivity of the IR absorption of the azide of AePhe was established by comparison of the frequency of the azide asymmetric stretch vibration in water and dimethyl sulfoxide. AePhe was successfully incorporated into superfolder green fluorescent protein (sfGFP) at the 133 and 149 sites by using the amber codon suppression method. The IR spectra of these sfGFP constructs indicated that the azide group at the 149 site was not fully solvated despite the location in sfGFP and the three‐atom linker between the azido group and the aromatic ring of AePhe. An X‐ray crystal structure of sfGFP‐149‐AePhe was solved at 1.45 Å resolution and provides an explanation for the IR data as the flexible linker adopts a conformation which partially buries the azide on the protein surface. Both sfGFP‐AePhe constructs efficiently undergo a bioorthogonal strain‐promoted click cycloaddition with a dibenzocyclooctyne derivative.     

Increased Water Reduction Efficiency of Polyelectrolyte‐Bound Trimetallic [Ru,Rh,Ru] Photocatalysts in Air‐Saturated Aqueous Solutions

The groundbreaking use of polyelectrolytes to increase the efficiency of supramolecular photocatalysts in solar H₂ production schemes under aqueous aerobic conditions is reported. Supramolecular photocatalysts of the architecture [{(TL)₂Ru(BL)}₂RhX₂]⁵⁺ (BL=bridging ligand, TL=terminal ligand, X=halide) demonstrate high efficiencies in deoxygenated organic solvents but do not function in air‐saturated aqueous solution because of the quenching of the metal‐to‐ligand charge‐transfer (MLCT) excited state under these conditions. The new photocatalytic system incorporates poly(4‐styrenesulfonate) (PSS) into aqueous solutions containing [{(bpy)₂Ru(dpp)}₂RhCl₂]⁵⁺ (bpy=2,2′‐bipyridine, dpp=2,3‐bis(2‐pyridyl)pyrazine). PSS has a profound impact on the photocatalyst efficiency, increasing H₂ production over three times that of deoxygenated aqueous solutions alone. H₂ photocatalysis proceeds even under aerobic conditions for PSS‐containing solutions, an exciting consequence for solar hydrogen‐production research.     

Operating stresses on S. S. “Michigan” propeller

The failure at sea of a number of merchantship propeller blodes initiated a research program supported by the Maritime Administration, the American Bureau of Shipping, the American President Lines and the States Steamship Company. Although extensive theoretical work has been carried out in the past (predicting propeller operating stresses), very little full-scale experimental stress measurements have been obtained. Brewer Engineering Laboratories, Inc. was retained by the sponsors to attach and protect fifty strain gages on the test propeller at the locations chosen by Littleton Research and Engineering Corporation. The propeller strain gages were protected from the severe environment by means of synthetic rubber and metallic overlays. The gage wiring was led down each blade and into a specially machined, hollow tailshaft through a waterproof bulkhead. The S.S. “Michigan”, with the test group aboard, sailed from Long Beach, Calif., in April 1970. The ship called at the ports of San Francisco, Yokohama, Naha, Manila, Bogo and Hong Kong during the test period. Throughout the trip across the Pacific, the gaging and instrumentation functioned without degradation or evidence of distress after onemillion propeller shaft turns. At the end of five weeks at sea and two-million turns, all but eight gages exhibited low ground resistance. The S.S. “Michigan” went into dry dock at the Bethlehem Steel Shipyard at Terminal Island, Calif., on June 15, 1970. The propeller was removed and all strain gages checked for continuity and ground resistance. Forty-two of the original 50 strain gages were found to be intact. No sign of deterioration due to cavitation or electrolysis attack existed on the metallic overlays or spot welding. Wire chafing within the fairwater adapter cap accounted for the low ground resistance values observed at the end of the voyage to Hong Kong.     

Measurement of thermal stresses within an experimental nuclear-reactor vessel head

This paper describes certain tests and techniques employed in measuring stresses within an experimental nuclear-reactor head of unusual design. The incorporation of certain desired design features necessitated that the head be extremely thick. Due to the thickness and its complex geometry, it was considered desirable to determine stress distribution within the head under conditions of steady-state pressure combined with rapid heating and cooling transients within the reactor, in order to determine safe limits for the operation of the head. A photoelastic study of a three-dimensional model of the reactor head was completed in 1956; this study permitted prediction of the stress distribution throughout the head as a function of internal pressure, but it was not possible to assimilate the head thermal stresses by photoelastic means. It is the purpose of this paper to describe the technique employed in measuring thermal stresses in the interior of the head, under simulated operating conditions of steady-state pressure and temperature transients.     

A Conjugate Addition Approach to Diazo-Containing Scaffolds with β Quaternary Centers

Structurally complex diazo-containing scaffolds are formed by conjugate addition to vinyl diazonium salts. The electrophile, a little studied α-diazonium-α,β-unsaturated carbonyl compound, is formed at low temperature under mild conditions by treating β-hydroxy-α-diazo carbonyls with Sc(OTf)₃. Conjugate addition occurs selectively at the 3-position of indole to give α-diazo-β-indole carbonyls, and enoxy silanes react to give 2-diazo-1,4-dicarbonyl products. These reactions result in the formation of tertiary and quaternary centers, and give products that would be otherwise difficult to form. Importantly, the diazo functional group is retained within the molecule for future manipulation. Treating an α-diazo ester indole addition product with Rh₂(OAc)₄ caused a rearrangement to occur to give a 2-(1H-indol-3-yl)-2-enoate. In the case of diazo ketone compounds, this shift occurred spontaneously on prolonged exposure to the Lewis acidic reaction conditions.     

Formal and total synthesis of (±)-cycloclavine

A ring fragmentation and intramolecular azomethine ylide 1,3-dipolar cycloaddition sequence of reactions was successfully used in the preparation of a known (±)-cycloclavine precursor in good overall yield. Results of efforts to incorporate the tetrasubstituted cyclopropane ring present in cycloclavine are also discussed.