Investigating Elementary Mathematics Curricula: Focus on Students With Learning Disabilities

The purpose of this study was to investigate three elementary mathematics curricula to examine the accessibility for students with learning disabilities (LD) with regards to challenges associated with working memory. We chose to focus on students' experiences when finding the area of composite shapes due to the multiple steps involved for solving these problems and the potential for these problems to tax working memory. We conducted a qualitative analysis of how each curriculum provided opportunities for students with LD to engage with these problems. During our analysis, we focused on instruction that emphasized visual representations (e.g., manipulatives, drawings, and diagrams), facilitated mathematical conversations, and developed cognitive and metacognitive skills. Our findings indicated a need for practitioners to consider how each curriculum provides instruction for storage and organization of information as well as how each curriculum develops students' thinking processes and conceptual understanding of mathematics. We concluded that all three curricula provide potentially effective strategies for teaching students with LD to solve multi‐step problems, such as area of composite shapes problems, but teachers using any of these curricula will likely need to supplement the curriculum to meet the needs of students with LD.     

Elementary and middle grade students’ constructions of typicality

This study addresses the measures chosen by students when selecting or constructing indices to properties of distributions of data. A series of individual teaching experiments were conducted to provide insight into the development of five 4th to 8th grade students’ conceptualizations of distribution over the course of 8 weeks of instruction. During the course of the teaching experiment (emergent) statistical tasks and analogous teacher activities were created and refined in an effort to support the development of understanding. In the process of development, attempts were made by students to coordinate center and variability when constructing measures to index properties of distributions. The results indicate that consideration of representativeness was a major factor that motivated modification of approaches to constructing indices of distributions, and subsequent coordination of indices of variation and center. In particular, the defining features of student's self-constructed “typical” values and notions of spread were examined, resulting in a model of development constituting eight “categories” ranging from the construction of values that did not reflect properties of the data (Category 1) to measures employing conceptual use of the mean in combination with other indices of center and spread (Category 8).     

Matrix-assisted laser desorption/ionisation mass spectrometric response factors of peptides generated using different proteolytic enzymes

Matrix-assisted laser desorption/ionisation (MALDI) mechanisms and the factors that influence the intensity of the ion signal in the mass spectrum remain imperfectly understood. In proteomics, it is often necessary to maximise the peptide response in the mass spectrum, especially for low abundant proteins or for proteolytic peptides of particular significance. We set out to determine which of the common proteolytic enzymes give rise to peptides with the best response factors under MALDI conditions. Standard proteins were enzymatically digested using four common proteases. We assessed relative response factors by coanalyzing the resulting digests. Thus, when tryptic peptides were added in equimolar quantities to their corresponding Asp-N, chymotrypsin and Glu-C digests, tryptic peptide signals were always predominant in the resulting MALDI mass spectra. Observable peaks attributable to non-tryptic peptides generally contained a terminal basic residue. It was proposed that a terminal basic residue has a disproportionate influence upon gas-phase basicity, and this hypothesis was supported by experiments with model isotopically labelled peptides. Experiments applying Cook's kinetic method showed that the peptide with a C-terminal arginine residue was more basic than the equivalent peptide with an N-terminal arginine, which was more basic than the peptide in which the arginine was mid-chain. Thus, the observation of the higher MALDI mass spectrometry response factors of tryptic peptides in comparison with peptides derived using other proteolytic enzymes corresponds with higher gas-phase basicities and may, along with other factors such as the complexity of the digest, influence the choice of enzyme in "bottom-up" proteomic experiments.     

A flow injection analysis system for monitoring silver (I) ion and iodine residuals in recycled water from recovery systems used for spaceflight

A laboratory-built flow injection analyzer is reported for monitoring the drinking water disinfectants silver (I) ion and iodine in water produced from NASA's water recovery system. This analyzer uses spectrophotometric detection with a custom made 10 cm optical flow cell. Optimization and interference studies are discussed for the silver (I) ion configuration. Subsequent results using the silver (I) configuration with minor modifications and alternative reagents gave promising results for iodine determinations as well. The estimated MDL values for Ag⁺ and I₂ are 52 μg L⁻¹ Ag⁺ and 2 μg L⁻¹ I₂; the mean percent recoveries were 104% and 96.2% for Ag⁺ and I₂ respectfully; and percent relative standard deviations were estimated at 1.4% for Ag⁺ and 5.7% for I₂. The agreement of this potentially multifunctional analyzer to reference methods for each respective water disinfectant is measured using Bland–Altman analysis as well as more traditional estimates.     

Tailoring the trajectory of cell rolling with cytotactic surfaces

Cell separation technology is a key tool for biological studies and medical diagnostics that relies primarily on chemical labeling to identify particular phenotypes. An emergent method of sorting cells based on differential rolling on chemically patterned substrates holds potential benefits over existing technologies, but the underlying mechanisms being exploited are not well characterized. In order to better understand cell rolling on complex surfaces, a microfluidic device with chemically patterned stripes of the cell adhesion molecule P-selectin was designed. The behavior of HL-60 cells rolling under flow was analyzed using a high-resolution visual tracking system. This behavior was then correlated to a number of established predictive models. The combination of computational modeling and widely available fabrication techniques described herein represents a crucial step toward the successful development of continuous, label-free methods of cell separation based on rolling adhesion.     

Synthesis of (2-chlorophenyl)(phenyl)methanones and 2-(2-chlorophenyl)-1-phenylethanones by Friedel-Crafts acylation of 2-chlorobenzoic acids and 2-(2-chlorophenyl)acetic acids using microwave heating

Several 2-(2-chlorophenyl)-1-phenylethanones and (2-chlorophenyl)(phenyl)methanones were prepared by the Friedel-Crafts acylation reaction of 2-(2-chlorophenyl) acetic acids and 2-chlorocarboxylic acids, respectively, in the presence of cyanuric chloride, pyridine, and AlCl₃ or FeCl₃ using microwave heating. The yields of the ketones were significantly higher than those obtained using conventional heating. In addition, similar reactions carried out with the less inexpensive and less toxic FeCl₃ gave titled ketones in comparable yields. Interestingly, the FeCl₃ catalyzed reactions gave pure ketones (no chromatographic purification required), whereas the AlCl₃ catalyzed reaction gave impure product that required chromatographic purification.     

Practical synthetic routes to carbon-substituted nucleosides

Robust practical routes to three different carbon-substituted nucleosides are described. Short synthetic procedures for preparing 1′-homonucleosides, 2′-C-methyl-carbanucleosides and 2′-C-methyl-cyclopropyl/cyclopentyl fused bicyclic ribose analogues are described starting from readily available building blocks.     

Reveal E. coli 2.0 method for detection of Escherichia coli O157:H7 in raw beef

Reveal E. coli 2.0 is a new lateral-flow immunodiagnostic test for detection of E. coli O157:H7 and O157:NM in raw beef trim and ground beef. Compared with the original Reveal E. coli O157:H7 assay, the new test utilizes a unique antibody combination resulting in improved test specificity. The device architecture and test procedure have also been modified, and a single enrichment protocol was developed which allows the test to be performed at any point during an enrichment period of 12 to 20 h. Results of inclusivity and exclusivity testing showed that the test is specific for E. coli serotypes O157:H7 and O157:NM, with the exception of two strains of O157:H38 and one strain of O157:H43 which produced positive reactions. In internal and independent laboratory trials comparing the Reveal 2.0 method to the U.S. Department of Agriculture-Food Safety and Inspection Service reference culture procedure for detection of E. coli O157:H7 in 65 and 375 g raw beef trim and ground beef samples, there were no statistically significant differences in method performance with the exception of a single internal trial with 375 g ground beef samples in which the Reveal method produced significantly more positive results. There were no unconfirmed positive results by the Reveal assay, for specificity of 100%. Results of ruggedness testing showed that the Reveal test produces accurate results even with substantial deviation in sample volume or device incubation time or temperature. However, addition of the promoter reagent to the test sample prior to introducing the test device is essential to proper test performance.     

Screening and determination of polycyclic aromatic hydrocarbons in seafoods using QuEChERS-based extraction and high-performance liquid chromatography with fluorescence detection

A rapid, sensitive, and accurate method for the screening and determination of polycyclic aromatic hydrocarbons (PAHs) in edible seafood is described. The method uses quick, easy, cheap, effective, rugged, and safe (QuEChERS)-based extraction and HPLC with fluorescence detection (FLD). The method was developed and validated in response to the massive Deepwater Horizon oil spill in the Gulf of Mexico. Rapid and highly sensitive PAH screening methods are critical tools needed for oil spill response; they help to assess when seafood is safe for harvesting and consumption. Sample preparation involves SPE of edible seafood portions with acetonitrile, followed by the addition of salts to induce water partitioning. After centrifugation, a portion of the acetonitrile layer is filtered prior to analysis via HPLC-FLD. The chromatographic method uses a polymeric C18 stationary phase designed for PAH analysis with gradient elution, and it resolves 15 U.S. Environmental Protection Agency priority parent PAHs in fewer than 20 min. The procedure was validated in three laboratories for the parent PAHs using spike recovery experiments at PAH fortification levels ranging from 25 to 10 000 microg/kg in oysters, shrimp, crab, and finfish, with recoveries ranging from 78 to 99%. Additional validation was conducted for a series of alkylated homologs of naphthalene, dibenzothiophene, and phenanthrene, with recoveries ranging from 87 to 128%. Method accuracy was further assessed based on analysis of National Institute of Standards and Technology Standard Reference Material 1974b. The method provides method detection limits in the sub to low ppb (microg/kg) range, and practical LOQs in the low ppb (microg/kg) range for most of the PAH compounds studied.     

3He(e,e′pp) and 3He(e,e′pn) reactions at AmPS and MAMI

This paper reports on measurements of the ³He(e,e′pp) reaction measured at AmPS and the ³He(e,e′pn) reaction measured at MAMI. The measurements were performed in similar kinematics to allow a comparison to be made between the cross sections of the two reactions. Results are shown for both reactions together with a comparison for the ³He(e,e′pp) data with continuum Faddeev calculations.