Addressing Prospective Elementary Teachers\u27 Beliefs about the Nature of Mathematics: A Case for Exploring Students\u27 Conceptions of Mathematics in a Math Education Course

Our challenge in preparing Virginia’s K-8 teachers in mathematics is a complex one. Additional requirements, including more challenging math content courses or more innovative pedagogical courses, may provide part of the solution. It is the premise of this paper, however, that additional knowledge and skills are not enough. In order to prepare teachers who will engage in current best practice pedagogy, we must also address teachers’ attitudes and dispositions, their beliefs and conceptions of mathematics itself. This paper will attempt to justify this position. It will also describe strategies used in the Inquiry in Mathematics course in Mary Baldwin’s MAT program intended to elicit and address graduate students’ current, sometimes limited (if not erroneous), notions about what mathematics is really about

The effects of moderate alcohol supplementation on estrone sulfate and DHEAS in postmenopausal women in a controlled feeding study

BACKGROUND: We have demonstrated that moderate alcohol consumption (15 g/d, 30 g/d) for 8 weeks resulted in significantly increased levels of serum estrone sulfate and DHEAS in 51 postmenopausal women in a randomized, placebo-controlled trial. We now report on the relationships between serum estrone sulfate and dehydroepiandrosterone sulfate (DHEAS) levels after 4 weeks of moderate alcohol supplementation, and compare the results to the 8 weeks data to elucidate time-to-effect differences. METHODS: Postmenopausal women (n = 51) consumed 0 (placebo), 15 (1 drink), and 30 (2 drinks) g alcohol (ethanol)/ day for 8 weeks as part of a controlled diet in a randomized crossover design. Blood samples were drawn at baseline, at 4 weeks and at 8 weeks. Changes in estrone sulfate and DHEAS levels from placebo to 15 g and 30 g alcohol per day were estimated using linear mixed models. RESULTS AND DISCUSSION: At week 4, compared to the placebo, estrone sulfate increased an average 6.9% (P = 0.24) when the women consumed 15 g of alcohol per day, and 22.2% (P = 0.0006) when they consumed 30 g alcohol per day. DHEAS concentrations also increased significantly by an average of 8.0% (P < 0.0001) on 15 g of alcohol per day and 9.2% (P < 0.0001) when 30 g alcohol was consumed per day. Trend tests across doses for both estrone sulfate (P = 0.0006) and DHEAS (P < 0.0001) were significant. We found no significant differences between the absolute levels of serum estrone sulfate at week 4 versus week 8 (P = 0.32) across all doses. However, absolute DHEAS levels increased from week 4 to week 8 (P < 0.0001) at all three dose levels. CONCLUSIONS: These data indicate that the hormonal effects due to moderate alcohol consumption are seen early, within 4 weeks of initiation of ingestion

Oil disturbance reduces infaunal family richness but does not affect phylogenetic diversity

Infaunal organisms are susceptible to disturbances such as hypoxia and sediment contamination; changes in infaunal community structure are therefore often used as indicators of anthropogenic disturbance. Susceptibility to disturbance varies across taxa, either due to physiological factors or to behaviors or functional roles that increase exposure. Both sources of variability are likely to be heritable and shared among related taxa. Thus, we would expect oil disturbance to disproportionately affect related taxa and therefore decrease phylogenetic diversity (PD). We test this hypothesis for a shallow water marine infaunal community using a simulation approach that iteratively removes clades with shared vulnerability to oil exposure. Infauna were sampled at two sites in the Chandeleur Islands, LA, that reflect different exposures to crude oil after the Deepwater Horizon event. Seagrass and adjacent bare sediment habitats were sampled in 2015, 5 years after initial oil exposure, and again in 2016 after an acute re-oiling event. We found that strong correlation between PD and family richness masked any detectable PD patterns with oil exposure. For our full community tree, sensitivity analysis indicated that the removal of larger clades did not disproportionately reduce PD, against our prediction. For this pair of sites, PD did not provide a better metric for assessing the impacts of oil exposure than family richness alone. It is possible, however, that finer-scale taxonomic resolution of infaunal communities may better decouple PD from taxonomic richness. More work is needed to fully evaluate the impacts of disturbance on PD

High-resolution computed tomography reconstructions of invertebrate burrow systems

The architecture of biogenic structures can be highly influential in determining species contributions to major soil and sediment processes, but detailed 3-D characterisations are rare and descriptors of form and complexity are lacking. Here we provide replicate high-resolution micro-focus computed tomography (μ-CT) data for the complete burrow systems of three co-occurring, but functionally contrasting, sediment-dwelling inter-tidal invertebrates assembled alone, and in combination, in representative model aquaria. These data (≤2,000 raw image slices aquarium−1, isotropic voxel resolution, 81 μm) provide reference models that can be used for the development of novel structural analysis routines that will be of value within the fields of ecology, pedology, geomorphology, palaeobiology, ichnology and mechanical engineering. We also envisage opportunity for those investigating transport networks, vascular systems, plant rooting systems, neuron connectivity patterns, or those developing image analysis or statistics related to pattern or shape recognition. The dataset will allow investigators to develop or test novel methodology and ideas without the need to generate a complete three-dimensional computation of exemplar architecture

Non-isothermal model for the direct isotropic/smectic-A liquid crystalline transition

An extension to a high-order model for the direct isotropic/smectic-A liquid crystalline phase transition was derived to take into account thermal effects including anisotropic thermal diffusion and latent heat of phase-ordering. Multi-scale multi-transport simulations of the non-isothermal model were compared to isothermal simulation, showing that the presented model extension corrects the standard Landau-de Gennes prediction from constant growth to diffusion-limited growth, under shallow quench/undercooling conditions. Non-isothermal simulations, where meta-stable nematic pre-ordering precedes smectic-A growth, were also conducted and novel non-monotonic phase-transformation kinetics observed.Comment: First revision: 20 pages, 7 figure

Quantum Smoluchowski equation: Escape from a metastable state

We develop a quantum Smoluchowski equation in terms of a true probability distribution function to describe quantum Brownian motion in configuration space in large friction limit at arbitrary temperature and derive the rate of barrier crossing and tunneling within an unified scheme. The present treatment is independent of path integral formalism and is based on canonical quantization procedure.Comment: 10 pages, To appear in the Proceedings of Statphys - Kolkata I

Environmental Constraints on the Mechanics of Crawling and Burrowing Using Hydrostatic Skeletons

Mechanics, kinematics, and energetics of crawling and burrowing by limbless organisms using hydrostatic skeletons depend on the medium and mode in which the organism is moving. Whether the animal is moving over or through a solid has long been considered important enough to distinguish crawling and burrowing as different terms, and in fact the mechanics are very different. Crawlers use mechanisms to increase friction to generate thrust while reducing resistive friction. Burrowers in elastic muds extend their burrows by fracture, whereas sands are fluidized by burrowers much larger than grain sizes and smaller burrowers displace individual grains. Gravitational forces depend on how closely the density of the organism matches that of its fluid surroundings, therefore frictional forces depend on whether the organism is moving through air or water and fluidization on whether sands are saturated or unsaturated