Conceptual Limitations in Curricular Presentations of Area Measurement: One Nation’s Challenges

Research has found that elementary students face five main challenges in learning area measurement: (1) conserving area as a quantity, (2) understanding area units, (3) structuring rectangular space into composite units, (4) understanding area formulas, and (5) distinguishing area and perimeter. How well do elementary mathematics curricula address these challenges? A detailed analysis of three U.S. elementary textbook series revealed systematic deficits. Each presented area measurement in strongly procedural terms using a shared sequence of procedures across grades. Key conceptual principles were infrequently expressed and often well after related procedures were introduced. Particularly weak support was given for understanding how the multiplication of lengths produces area measures. The results suggest that the content of written curricula contributes to students’ weak learning of area measurement

Curricular Treatments of Length Measurement in the United States: Do They Address Known Learning Challenges?

Extensive research has shown that elementary students struggle to learn the basic principles of length measurement. However, where patterns of errors have been documented, the origins of students’ difficulties have not been identified. This study investigated the hypothesis that written elementary mathematics curricula contribute to the problem of learning length measurement. We analyzed all instances of length measurement in three mathematics curricula (grades K–3) and found a shared focus on procedures. Attention to conceptual principles was limited overall and particularly for central ideas; conceptual principles were often presented after students were asked to use procedures that depended on them; and students often did not have direct access to conceptual principles. We also report five groupings of procedures that appeared sequentially in all three curricula, the conceptual principles that underlie those procedures, and the conventional knowledge that receives substantial attention by grade 3

Computational design-of-experiment unveils the conformational reaction coordinate of GH125 α-mannosidases

Conformational analysis of enzyme-catalyzed mannoside hydrolysis has revealed two predominant conformational itineraries through B 2,5 or 3H 4 transitionstate (TS) conformations. A prominent unassigned catalytic itinerary is that of exo-1,6-α-mannosidases belonging to CAZy family 125. A published complex of Clostridium perfringens GH125 enzyme with a nonhydrolyzable 1,6-α-thiomannoside substrate mimic bound across the active site revealed an undistorted 4 C 1 conformation and provided no insight into the catalytic pathway of this enzyme. We show through a purely computational approach (QM/MM metadynamics) that sulfur-for-oxygen substitution in the glycosidic linkage fundamentally alters the energetically accessible conformational space of a thiomannoside when bound within the GH12S active site. Modeling of the conformational free energy landscape (FEL) of a thioglycoside strongly favors a mechanistically uninformative 4 C 1 conformation within the GH125 enzyme active site, but the FEL of corresponding O-glycoside substrate reveals a preference for a Michaelis complex in an oS 2 conformation (consistent with catalysis through a B 2,5 TS). This prediction was tested experimentally by determination of the 3D X-ray structure of the pseudo-Michaelis complex of an inactive (D220N) variant of C. perfringens GH125 enzyme in complex with 1,6-α-mannobiose. This complex revealed unambiguous distortion of the -1 subsite mannoside to an oS 2 conformation, matching that predicted by theory and supporting an oS 2 → B 2,5 → 1S 5 conformational itinerary for GH125 α-mannosidases. This work highlights the power of the QM/MM approach and identified shortcomings in the use of nonhydrolyzable substrate analogues for conformational analysis of enzymebound species

Patterns in refractive error and treatment delay in keratoconus-An Australian study.

Keratoconus is the most common primary corneal ectasia and is associated with significant morbidity. In its early stages, keratoconus is often asymptomatic, making the identification of subclinical disease challenging. Refractive error is a parameter that is documented at most routine optometry visits, yet interestingly, changes in refraction of keratoconic patients over time have not yet been studied and compared with the general population. Early diagnosis of keratoconus facilitates timely referral for treatments such as corneal collagen cross-linking, which has been shown to slow disease progression. In this context, documenting delays between initial presentation to the optometrist and referral for collagen-cross-linking as well as comparing the trends in visual acuity and refractive error between keratoconic and non-keratoconic patients over time are particularly relevant

On the Morphology and Chemical Composition of the HR 4796A Debris Disk

[abridged] We present resolved images of the HR 4796A debris disk using the Magellan adaptive optics system paired with Clio-2 and VisAO. We detect the disk at 0.77 \microns, 0.91 \microns, 0.99 \microns, 2.15 \microns, 3.1 \microns, 3.3 \microns, and 3.8 \microns. We find that the deprojected center of the ring is offset from the star by 4.76$\pm$1.6 AU and that the deprojected eccentricity is 0.06$\pm$0.02, in general agreement with previous studies. We find that the average width of the ring is 14$^{+3}_{-2}$, also comparable to previous measurements. Such a narrow ring precludes the existence of shepherding planets more massive than \about 4 \mj, comparable to hot-start planets we could have detected beyond \about 60 AU in projected separation. Combining our new scattered light data with archival HST/STIS and HST/NICMOS data at \about 0.5-2 \microns, along with previously unpublished Spitzer/MIPS thermal emission data and all other literature thermal data, we set out to constrain the chemical composition of the dust grains. After testing 19 individual root compositions and more than 8,400 unique mixtures of these compositions, we find that good fits to the scattered light alone and thermal emission alone are discrepant, suggesting that caution should be exercised if fitting to only one or the other. When we fit to both the scattered light and thermal emission simultaneously, we find mediocre fits (reduced chi-square \about 2). In general, however, we find that silicates and organics are the most favored, and that water ice is usually not favored. These results suggest that the common constituents of both interstellar dust and solar system comets also may reside around HR 4796A, though improved modeling is necessary to place better constraints on the exact chemical composition of the dust.Comment: Accepted to ApJ on October 27, 2014. 21 pages, 12 figures, 4 table

Directly Imaged L-T Transition Exoplanets in the Mid-Infrared

Gas-giant planets emit a large fraction of their light in the mid-infrared ($\gtrsim$3$\mu$m), where photometry and spectroscopy are critical to our understanding of the bulk properties of extrasolar planets. Of particular importance are the L and M-band atmospheric windows (3-5$\mu$m), which are the longest wavelengths currently accessible to ground-based, high-contrast imagers. We present binocular LBT AO images of the HR 8799 planetary system in six narrow-band filters from 3-4$\mu$m, and a Magellan AO image of the 2M1207 planetary system in a broader 3.3$\mu$m band. These systems encompass the five known exoplanets with luminosities consistent with L$\rightarrow$T transition brown dwarfs. Our results show that the exoplanets are brighter and have shallower spectral slopes than equivalent temperature brown dwarfs in a wavelength range that contains the methane fundamental absorption feature (spanned by the narrowband filters and encompassed by the broader 3.3$\mu$m filter). For 2M1207 b, we find that thick clouds and non-equilibrium chemistry caused by vertical mixing can explain the object's appearance. For the HR 8799 planets, we present new models that suggest the atmospheres must have patchy clouds, along with non-equilibrium chemistry. Together, the presence of a heterogeneous surface and vertical mixing presents a picture of dynamic planetary atmospheres in which both horizontal and vertical motions influence the chemical and condensate profiles.Comment: Accepted to Ap

Optimization of DNA Extraction for RAPD and ISSR Analysis of Arbutus unedo L. Leaves

Genetic analysis of plants relies on high yields of pure DNA. For the strawberry tree (Arbutus unedo) this represents a great challenge since leaves can accumulate large amounts of polysaccharides, polyphenols and secondary metabolites, which co-purify with DNA. For this specie, standard protocols do not produce efficient yields of high-quality amplifiable DNA. Here, we present for the first time an improved leaf-tissue protocol, based on the standard cetyl trimethyl ammonium bromide protocol, which yields large amounts of high-quality amplifiable DNA. Key steps in the optimized protocol are the addition of antioxidant compounds—namely polyvinyl pyrrolidone (PVP), 1,4-dithiothreitol (DTT) and 2-mercaptoethanol, in the extraction buffer; the increasing of CTAB (3%, w/v) and sodium chloride (2M) concentration; and an extraction with organic solvents (phenol and chloroform) with the incubation of samples on ice. Increasing the temperature for cell lyses to 70 °C also improved both DNA quality and yield. The yield of DNA extracted was 200.0 ± 78.0 μg/μL and the purity, evaluated by the ratio A260/A280, was 1.80 ± 0.021, indicative of minimal levels of contaminating metabolites. The quality of the DNA isolated was confirmed by random amplification polymorphism DNA and by inter-simple sequence repeat amplification, proving that the DNA can be amplified via PCR

Direct Multipixel Imaging and Spectroscopy of an Exoplanet with a Solar Gravity Lens Mission

We examined the solar gravitational lens (SGL) as the means to produce direct high-resolution, multipixel images of exoplanets. The properties of the SGL are remarkable: it offers maximum light amplification of ~1e11 and angular resolution of ~1e-10 arcsec. A probe with a 1-m telescope in the SGL focal region can image an exoplanet at 30 pc with 10-kilometer resolution on its surface, sufficient to observe seasonal changes, oceans, continents, surface topography. We reached and exceeded all objectives set for our study: We developed a new wave-optical approach to study the imaging of exoplanets while treating them as extended, resolved, faint sources at large but finite distances. We properly accounted for the solar corona brightness. We developed deconvolution algorithms and demonstrated the feasibility of high-quality image reconstruction under realistic conditions. We have proven that multipixel imaging and spectroscopy of exoplanets with the SGL are feasible. We have developed a new mission concept that delivers an array of optical telescopes to the SGL focal region relying on three innovations: i) a new way to enable direct exoplanet imaging, ii) use of smallsats solar sails fast transit through the solar system and beyond, iii) an open architecture to take advantage of swarm technology. This approach enables entirely new missions, providing a great leap in capabilities for NASA and the greater aerospace community. Our results are encouraging as they lead to a realistic design for a mission that will be able to make direct resolved images of exoplanets in our stellar neighborhood. It could allow exploration of exoplanets relying on the SGL capabilities decades, if not centuries, earlier than possible with other extant technologies. The architecture and mission concepts for a mission to the strong interference region of the SGL are promising and should be explored further