Impacts of professional development focused on teaching engineering applications of mathematics and science

With the recent national emphasis on preparing children for future careers in science, technology, engineering, and mathematics, K-12 teachers are being called upon to include engineering in their instruction. This study explores the impacts of a summer professional development (PD) program focused on the engineering applications of mathematics and science on in-service K-12 teachers' (a) personal engineering efficacy, (b) engineering teaching efficacy, and (c) perceived barriers to teaching engineering. This quantitative study revealed that a single engineering-focused PD could increase teachers' personal engineering efficacy and engineering teaching efficacy and reduce particular perceived barriers to teaching engineering. No differences existed in pre- to post workshop assessment scores based on grade level taught, gender, or years of teaching experiences. However, pre- to post workshop assessment differences existed between participants depending on the discipline they taught and wether or not they had previously used engineering activities in their classrooms. These findings suggest that a single engineering PD can have significant impacts on in-service teachers' personal engineering efficacy, engineering teaching efficacy, and perceived barriers to teaching engineering, but a one-size-fits-all approach to such PD is not equally effective for all participants.     

A quasicancellation property for the direct product of graphs

We are motivated by the following question concerning the direct product of graphs. If A×C≅B×C, what can be said about the relationship between A and B? If cancellation fails, what properties must A and B share? We define a structural equivalence relation ∼ (called similarity) on graphs, weaker than isomorphism, for which A×C≅B×C implies A∼B. Thus cancellation holds, up to similarity. Moreover, if C is bipartite, then A×C≅B×C if and only if A∼B. We conjecture that the prime factorization of connected bipartite graphs is unique up to similarity of factors, and we offer some results supporting this conjecture.     

Phoenix mars mission—The thermal evolved gas analyzer

The Phoenix spacecraft that was launched to Mars in August 2007 landed safely on the Martian northern arctic region on May 25, 2008. It carried six experiments to study the history of water on the planet and search for organic molecules in the icy subsurface Martian soil. The spacecraft is a lander with an arm and scoop designed to dig a trench though the top soil to reach an expected ice layer near the surface. One of the instruments on board is the thermal evolved gas analyzer (TEGA), which consists of two components, a set of eight very small ovens that will heat samples of the ice soil mixtures from the trench to release imbedded gases and mineral decomposition products, and a mass spectrometer that serves as the analysis tool for the evolved gases, and also for measurements of the composition and isotopic ratios of the gases that comprise the atmosphere of Mars. The mass spectrometer is a miniature magnetic sector instrument controlled by microprocessor-driven power supplies. One feature is the gas enrichment cell that will increase the partial pressures of the noble gases in an atmosphere sample by removing all the active gases, carbon dioxide, and nitrogen, to improve the accuracy of their isotopic ratio measurements.     

Simultaneous high speed PIV and CH PLIF using R-branch excitation in the C2Σ+-X2Π (0,0) band

Simultaneous particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) utilizing R-branch transitions in the C-X (0,0) band were performed at a 10-kHz repetition-rate in a turbulent premixed flame. The CH lines at 310.690?nm (from the R-branch of the C-X band) used here have greater efficiency than A-X and B-X transitions, which allows for high-framerate imaging with low laser pulse energy. Most importantly, the simultaneous imaging of both CH PLIF and PIV is enabled by the use of a custom edge filter, which blocks scattering at the laser wavelength (below ～311?nm) while efficiently transmitting fluorescence at longer wavelengths. The Hi-Pilot Bunsen burner operated with a turbulent Reynolds number of 7900 was used to demonstrate simultaneous PIV and CH PLIF utilizing this filtered detection scheme. Instances where pockets of products were observed well upstream of the mean flame brush are found to be the result of out-of-plane motion of the flame sheet. Such instances can lead to ambiguous results when interpreting the thickness of reaction layers. However, the temporally resolved nature of the present diagnostics facilitate the identification and proper treatment of such situations. The strategy demonstrated here can yield important information in the study of turbulent flames by providing temporally resolved flame dynamics in terms of flame sheet visualization and velocity fields.     

Effectiveness of universal pre-enrichment broth for recovery of Salmonella from selected dairy foods

The relative efficiencies of 2 Bacteriological Analytical Manual (BAM) pre-enrichments, lactose broth (LAC) and brilliant green water (BGW), were compared with Universal Pre-enrichment (UP) broth for the recovery of individual Salmonella serovars from instant nonfat dry milk (NFDM), dry whole milk (DWM), lactic casein (LC), and liquid whole milk (LWM). BGW was compared with UP broth for the analysis of NFDM and DWM but not with the other 2 matrixes. LAC was compared with UP broth for the analysis of LC and LWM. UP broth was made both from a commercial dehydrated preparation (UPC) and from individual ingredients (UPI). Bulk quantities of the selected dairy foods were inoculated with Salmonella serovars at levels intended to produce fractionally positive results, where at least half of the test portions analyzed, with one of the methods being evaluated, would be shown to be Salmonella-positive. For NFDM, in 6 of 9 experiments, with 2 different Salmonella serovars, BGW was significantly more productive than either UPI or UPC broth (p < 0.05). Salmonella was recovered from 118 of 180 test portions with BGW, from 25 of 180 test portions with UPC, and from 14 of 180 test portions with UPI. For DWM, in 2 of 4 experiments, with 2 different Salmonella serovars, BGW was significantly more productive than either UPI or UPC broth (p < 0.05). Salmonella was recovered from 67 of 80 test portions with BGW, from 36 of 80 test portions with UPC, and from 37 of 80 test portions with UPI. For LWM, in 9 of 9 experiments, with 3 different Salmonella serovars, there were no significant differences among the broths. Salmonella was recovered from 120 of 180 test portions with LAC, from 135 of 180 test portions with UPC, and from 129 of 180 test portions with UPI. For LC, in 5 of 7 experiments, with 2 different Salmonella serovars, both UPI and UPC broth were significantly more productive than LAC (p < 0.05). Salmonella was recovered from 42 of 140 test portions with LAC, from 114 of 140 test portions with UPC, and from 114 of 140 test portions with UPI. In addition, overall results showed that UPC and UPI broths were equivalent for the recovery of Salmonella from the foods tested, without regard to their performance in comparison with either LAC or BGW.