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.     

Atomic resolution three-dimensional electron diffraction microscopy

We report the development of a novel form of diffraction-based 3D microscopy to overcome resolution barriers inherent in high-resolution electron microscopy and tomography. By combining coherent electron diffraction with the oversampling phasing method, we show that the 3D structure of a nanocrystal can be determined ab initio at a resolution of 1 A from 29 simulated noisy diffraction patterns. This new form of microscopy can be used to image the 3D structures of nanocrystals and noncrystalline samples, with resolution limited only by the quality of sample diffraction.     

Magnetic resonance imaging in a model of atherosclerosis: use of a collar around the rabbit carotid artery

Transverse cardiac-cycle gated high resolution magnetic resonance images have been obtained from the neck of the New Zealand white rabbit both in normal animals and from those in which a collar had been earlier positioned around one carotid artery. The study included animals fed on normal and on high cholesterol diets with the surgical modification having been demonstrated previously to cause a rapid and reproducible lesion resembling early atherosclerosis. The aim of the work was to investigate the attainable spatial resolution and sensitivity at a field strength of 2 T using a large radiofrequency transmitter system and a surface coil receiver with which spin-echo images have been obtained. Visualization was enhanced using a three-dimensional interpolation technique. An image resolution of 200 microns was readily obtained but was shown to be insufficient for delineating pathological features within the artery wall such as intimal layer thickening. The results have been compared with histopathological findings which confirmed that any morphological changes were within the pixel resolution of the image. Extensions to the methodology are proposed which should be able to detect atherosclerotic changes with a resolution of 50 microns within a feasible imaging time. In addition, the MRI study of how the surgical intervention alters the artery shape and curvature was carried out and the MRI demonstrated that collar implantation in general does not occlude the artery and causes only a slight and gradual degree of curvature to the vessel.     

The systematics of nuclear single-particle states (II). the region A < 35

The energies of single-particle states in nuclei with A < 35 are obtained as eigenvalues of a local Saxon-Woods potential with depth depending linearly on A and on the nuclear symmetry parameter.     

Substituted aziridines by lithiation-electrophile trapping of terminal aziridines

[reaction: see text] Regio- and stereoselective deprotonation of N-Bus (Bus = tert-butylsulfonyl)-protected terminal aziridines with lithium 2,2,6,6-tetramethylpiperidide generates a nonstabilized (H-substituted) aziridinyl anion that undergoes in situ or external electrophile trapping under experimentally straightforward conditions to give trans-disubstituted aziridines in good to excellent yields.     

Unsaturated 1,2-amino alcohols and ethers from aziridines and organolithiums

Organolithium-induced ring-opening of aziridines of 2,5-dihydrofuran (5 and 8) and 1,4-dimethoxybut-2-ene (16, 17 and 23) gives 3-substituted 2-aminobut-3-en-1-ols 9-15 and amino ethers 18-20 and 24-26.     

Sulfur K-edge XAS and DFT calculations on [Fe4S4]2+ clusters: effects of H-bonding and structural distortion on covalency and spin topology

Sulfur K-edge X-ray absorption spectroscopy of a hydrogen-bonded elongated [Fe4S4]2+ cube is reported. The data show that this synthetic cube is less covalent than a normal compressed cube with no hydrogen bonding. DFT calculations reveal that the observed difference in electronic structure has significant contributions from both the cluster distortion and from hydrogen bonding. The elongated and compressed Fe4S4 structures are found to have different spin topologies (i.e., orientation of the delocalized Fe2S2 subclusters which are antiferromagnetically coupled to each other). It is suggested that the H-bonding interaction with the counterion does not contribute to the cluster elongation. A magneto-structural correlation is developed for the Fe4S4 cube that is used to identify the redox-active Fe2S2 subclusters in active sites of HiPIP and ferredoxin proteins involving these clusters.