Interpreting Middle School Students' Proportional Reasoning Strategies: Observations From Preservice Teachers

This paper reports the findings of an investigation of 11 preservice secondary school teachers' interpretations of the development of proportional reasoning strategies used by middle school students. The preservice teachers examined samples of solution strategies generated by middle school students in proportional reasoning situations and prepared written responses of their views concerning the developmental levels indicated in the students' work. Each preservice teacher also participated in an hour‐long interview, in which the researchers asked for elaboration and clarification of the written responses and, in some cases, challenged the preservice teachers to consider alternative interpretations for the middle school students' work. The interviews were audiotaped for later analysis by the investigators, and key aspects of both the written and audiotaped responses were entered into a spreadsheet and later tabulated into categories indicating trends in the preservice teachers' interpretations. Some implications for the preparation of preservice middle school science and mathematics teachers are included.     

Elastic beams of greatest lateral extent

Numerical solutions are presented for the deflections of slender, uniform elastic beams, self-loaded and built into a supporting wall. The beams are alike in every property but length. There exists a critical length which maximizes the lateral reach; longer beams droop so much under their own weight that their tips actually move closer to the supporting wall. The critical length depends only on the angle at which the beam leaves the supporting wall.     

Synthesis of novel migrastatin and dorrigocin A analogues from D-glucal

The synthesis of a range of analogues of the migrastatin macrolide core has been achieved from tri-O-acetyl-D-glucal in order to facilitate structure-activity studies. Efficient macrolactone formation was achieved in the presence of a reactive olefin, by increasing steric hindrance in the olefin environment. Acyclic analogues of migrastatin, structurally related to dorrigocin A, have also been prepared from D-glucal. The dorrigocin A analogues were prepared using the combination of the cross metathesis of ethyl 6-heptenoate with a glycal derivative and a subsequent allylic rearrangement-alkene isomerisation reaction (Perlin reaction). A synthetic route is thus provided that will enable dorrigocin A analogues to be prepared in parallel to migrastatin analogues in the search for novel anti-cancer and anti-arthritic therapeutics. Biological evaluation of one migrastatin and one dorrigocin A sugar derived analogue show that they inhibit proliferation and serum-induced migration of tumour and synovial cells at higher concentrations than evodiamine. Dorrigocin A analogues displayed similar potency to analogues of the migrastatin core.     

Crystal structure and silica condensing activities of silicatein alpha-cathepsin L chimeras

Cathepsin L mutants with the ability to condense silica from solution have been generated and a 1.5 A crystal structure of one of these chimeras allows us to rationalise the catalytic mechanism of silicic acid condensation.     

A structural systematic study of three isomers of difluoro‐N‐(4‐pyridyl)benzamide

The isomers 2,3‐, (I), 2,4‐, (II), and 2,5‐difluoro‐N‐(4‐pyridyl)benzamide, (III), all with formula C₁₂H₈F₂N₂O, all exhibit intramolecular C—H...O=C and N—H...F contacts [both with S(6) motifs]. In (I), intermolecular N—H...O=C interactions form one‐dimensional chains along [010] [N...O = 3.0181 (16) Å], with weaker C—H...N interactions linking the chains into sheets parallel to the [001] plane, further linked into pairs via C—H...F contacts about inversion centres; a three‐dimensional herring‐bone network forms via C—H...π(py) (py is pyridyl) interactions. In (II), weak aromatic C—H...N(py) interactions form one‐dimensional zigzag chains along [001]; no other interactions with H...N/O/F < 2.50 Å are present, apart from long N/C—H...O=C and C—H...F contacts. In (III), N—H...N(py) interactions form one‐dimensional zigzag chains [as C(6) chains] along [010] augmented by a myriad of weak C—H...π(arene) and O=C...O=C interactions and C—H...O/N/F contacts. Compound (III) is isomorphous with the parent N‐(4‐pyridyl)benzamide [Noveron, Lah, Del Sesto, Arif, Miller & Stang (2002). J. Am. Chem. Soc. 124 , 6613–6625] and the three 2/3/4‐fluoro‐N‐(4‐pyridyl)benzamides [Donnelly, Gallagher & Lough (2008). Acta Cryst. C 64 , o335–o340]. The study expands our series of fluoro(pyridyl)benzamides and augments our understanding of the competition between strong hydrogen‐bond formation and weaker influences on crystal packing.     

Parametric harmonic-to-fundamental ratio contrast echocardiography: a novel approach to identification and accurate measurement of left ventricular area under variable levels of ultrasound signal attenuation

Objectives

We introduced a harmonic-to-fundamental ratio (HFR) of the radiofrequency (RF) signals that reduces confounding effects of attenuation. We studied whether HFR analysis of RF signals received from contrast microbubbles allows accurate measurement of the left ventricular (LV) cavity area under varying levels of attenuation.

Background

Attenuation is a fundamental problem in ultrasound imaging and limits the use of clinical echocardiography.

Methods

RF data from short axis systolic and diastolic scans were obtained from 14 open-chest dogs following left-atrial bolus of Optison. Attenuation was induced by interposed silicone pads calibrated to induce 7 dB or 14 dB reductions of the backscattered RF signal. RF images were reconstructed from the RF signals, HFR values calculated for each image pixel for 0 dB, 7 dB and 14 dB attenuation conditions, and LV area obtained by summation of “LV cavity pixels”. A reference LV cavity area was obtained from endocardial border tracings in enhanced scans by experts.

Results

Correlation of the HFR-defined and reference areas at systole was R = 0.95, R = 0.94, and R = 0.91 for 0 dB, 7 dB and 14 dB levels of attenuation, respectively, and at diastole was R = 0.95 for 0 dB, 7 dB and 14 dB levels of attenuation. The mean difference from both systolic and diastolic values was <1.45 cm² (i.e. negligible) in all attenuation settings.

Conclusion

Our novel HFR method supports precise measurement of the LV cavity area in contrast images with simulated high attenuation of ultrasound signals.     

Competition of charge-density waves and superconductivity in sulfur

A one-dimensional charge-density wave (CDW) instability is shown to be responsible for the formation of the incommensurate modulation of the atomic lattice in the high-pressure phase of sulfur. The coexistence of, and competition between, the CDW and the superconducting state leads to the previously observed increase of T{c} up to 17 K, which we attribute to the suppression of the CDW instability, the same phenomenology found in doped layered dichalcogenides.     

Persistence time of charge carriers in defect states of molecular semiconductors

Charge carriers in organic crystals are often trapped in point defects. The persistence time of the charge in these defect states is evaluated by computing the escape rate from this state using non-adiabatic rate theory. Two cases are considered (i) the hopping between separate identical defect states and (ii) the hopping between a defect state and the bulk (delocalized) states. We show that only the second process is likely to happen with realistic defect concentrations and highlight that the inclusion of an effective quantum mode of vibration is essential for accurate computation of the rate. The computed persistence time as a function of the trap energy indicates that trap states shallower than ～0.3 eV cannot be effectively investigated with some slow spectroscopic techniques such as THz spectroscopy or EPR commonly used to study the nature of excess charge in semiconductors.     

An investigation of paint from a mural in the church of Sainte Madeleine, Manas, France

The pigment in brown paint samples taken from a church in the Drôme region of France has been shown to be almost pure 6‐bromoindigo and 6,6′‐dibromoindigo. The composition of the pigment was established by comparison with 6‐bromoindigo and 6,6′‐dibromoindigo standards using atmospheric pressure photoionization combined with liquid chromatography and tandem mass spectrometry. The brown paint samples were taken from a frieze of ca 20 brown images having symmetric tree‐like forms composed of five overlapping filled circles representing foliage. The tree‐like images, simple rather than artistic, had a metallic luster. The molar ratio of 6‐bromoindigo and 6,6′‐dibromoindigo in the brown paint pigment (98:2) is remarkably similar to that of shellfish purple from the Mediterranean Murex brandaris (96.5:3.5) thus, it is possible that the origin of the indigoid compounds in the brown paint pigment is the eastern coast of the Mediterranean Sea. As the production of Tyrian purple ended with the fall of Byzantium in 1453, purple pigment had to have been produced prior to this time. We have conjectured about the circumstances that may account for the use of ‘purple’ in this manner in the Drôme region and how the pigment was transported there from the eastern coast of the Mediterranean Sea during the time of the Crusades. Copyright © 2011 John Wiley & Sons, Ltd.     

Fast ethylamine gas sensing based on intermolecular charge-transfer complexation

We have investigated the fast ethylamine gas sensing of 2-chloro-3,5-dinitrobenzotrifluoride(CDBF) loaded poly(acrylonitrile) nanofiber based on an intermolecular charge-transfer complexation.Reversible response and recovery were achieved using alternating gas exposure.This system shows a fast ethylamine gas sensing within 0.4 s.