An investigation of assessment and feedback practices in fully asynchronous online undergraduate mathematics courses

Research suggests it is difficult to learn mathematics in the fully asynchronous online (FAO) instructional modality, yet little is known about associated teaching and assessment practices. In this study, we investigate FAO mathematics assessment and feedback practices in particular consideration of both claims and findings that these practices have a powerful influence on learning.

A survey questionnaire was constructed and completed by 70 FAO undergraduate mathematics instructors, mostly from the USA, who were each asked to detail their assessment and feedback practices in a single FAO mathematics course. Alongside these questions, participants also answered the 16-item version of the Approaches to Teaching Inventory. In addition, a novel feedback framework was also created and used to examine how feedback practices may be related to participants' approaches to teaching.

Results show that assessment and feedback practices are varied and complex: in particular, we found there was not a simple emphasis on summative assessment instruments, nor a concomitant expectation these would always be invigilated. Though richer assessment feedback appears to be emphasized, evidence suggests this feedback may not be primarily directed at advancing student learning. Moreover, we found evidence of a reliance on computer--human interactions (e.g. via computer-assisted assessment systems) and further evidence of a decline in human interactions, suggesting a dynamic that is both consistent with current online learning theory and claims FAO mathematics courses are becoming commodified. Several avenues for further research are suggested.     

Estimation of the conformal factor under bounded Willmore energy

We prove for closed, orientable surfaces in $\ \mathbb{R }^3\ $ with Willmore energy less that $\ 8 \pi - \delta \ $ and whose conformal structures are compactly contained in moduli space that after applying appropriate Möbius transformations the conformal factors between the induced metrics and conformal metrics of constant curvature are uniformly bounded by constants depending only on $\ \delta > 0,$ the genus of the surfaces and the compact subset of the moduli space. Secondly, for a given sequence of closed, orientable surfaces as above, we prove that the conformal factor remains bounded without applying Möbius transformations if and only if no topology is lost. Similar estimates hold in higher codimension.     

Spectral approximation for compact integral operators by degenerate kernel methods

We establish a new improved error estimate for the solution of the integral equation eigenvalue problem by degenerate kernel methods. In [6] these estimates were proved under the assumption of normality of the original kernel as well as of the approximating degenerate kernel. Now we consider any compact integral operator and a general Banach space situation, in contrast to the Hilbert space setting in [6], This will be done by combining the techniques in [6] with the suitably transformed estimates of [5]. Our results show that degenerate kernel methods have, besides their overall property of furnishing easy approximations to eigenfunctions, for eigenvalues an order of convergence comparable to quadrature methods.     

A Discrete Element Approach for Wave Propagation in Thin Rods

Wave propagation and evoked side effects, such as material failure, are important parts of analysis of dynamically exposed structures like buildings or machinery. One of the numerical analysis tools for wave propagation is the well-known Finite Element Method (FEM) with its impressive performance but also with the drawback of not being able to model easily material failure, discontinuities and contacts. In contrast, the Discrete Element Method (DEM) is capable to describe these effects on a meso-scale more easily. The here selected concept is based on a DEM particle which is considered as deformable, and can establish and remove lasting bonds with other particles. The simulation example used is a thin rod that has been an extensive numerical and experimental research subject since the last century. A longitudinal wave is excited within the thin rod by simulating an impact on one end of the rod in a free-free configuration. It is found, that the simulation data, the velocity profile and the resulting displacement at the end of the rod, are in good agreement with experimental obtained data. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Transient calorimetric diagnostics for plasma processing

We present a detailed study of the Gaussian laser propagation through a dielectric system composed by two right angle prisms. We investigate the transition between the spatial coherence limit, which exhibits wave-like properties and for which the resonance phenomenon can be seen, and the decoherence limit, which exhibits particle-like properties and for which the multiple diffusion occurs. We also analyze the tunneling at critical angles. In our numerical analysis, we shall use BK7 and Fused Silica prisms and a Gaussian He-Ne laser with a wavelength of 632.8 nm and beam waists of 2 mm and 200 μm.     

Two-loop SUSY QCD corrections to the chargino masses in the MSSM

We have calculated the two-loop strong interaction corrections to the chargino pole masses in the scheme in the minimal supersymmetric standard model with complex parameters. We have performed a detailed numerical analysis for a particular point in the parameter space and found corrections of a few tenths of a percent. We provide a computer program that calculates chargino and neutralino masses with complex parameters up to .     

Syntheses and Crystal Structures of Two Cadmium Methanetetrabenzoates Featured by Open Framework and Infinite Layers

Colorless single crystals of Cd₂[μ₈‐MTB] · 3H₂O · DMF ( 1 ) were prepared in DMF/H₂O solution [ 1 : space group C2/c (no. 15) with a = 1821.30(6), b = 2175.08(6), c = 1269.87(4) pm, β = 129.684(1)°]. The connection between the methane‐p‐benzoate tetraanions (MTB^4–) and the Cd²⁺ cations leads to a three‐dimensional framework with channels extending along [1 10] and [110] with openings of 670 pm × 360 pm. The channel‐like voids accommodate water molecules and N,N‐dimethylformamide (DMF) molecules not bound to Cd²⁺. Colorless single crystals of [Cd₄(2,2′‐bipy)₄(μ₇‐MTB)₂] · 7DMF ( 2 ) were prepared in DMF in the presence of 2,2′‐bipyridine [ 2 : space group P1 (no. 2) with a = 1224.84(4), b = 1418.85(5), c = 2033.49(4) pm, α = 85.831(2)°, β = 88.351(2)°, γ = 68.261(1)°]. The coordination of MTB^4– to Cd²⁺ results in infinite layers parallel to (001). The layers, not connected by any hydrogen bonds, contain small openings of about 320 pm × 340 pm.     

Transformation of a [4+6] Salicylbisimine Cage to Chemically Robust Amide Cages

In recent years, interest in shape‐persistent organic cage compounds has steadily increased, not least because dynamic covalent bond formation enables such structures to be made in high to excellent yields. One often used type of dynamic bond formation is the generation of an imine bond from an aldehyde and an amine. Although the reversibility of the imine bond formation is advantageous for high yields, it is disadvantageous for the chemical stability of the compounds. Amide bonds are, in contrast to imine bonds much more robust. Shape‐persistent amide cages have so far been made by irreversible amide bond formations in multiple steps, very often accompanied by low yields. Here, we present an approach to shape‐persistent amide cages by exploiting a high‐yielding reversible cage formation in the first step, and a Pinnick oxidation as a key step to access the amide cages in just three steps. These chemically robust amide cages can be further transformed by bromination or nitration to allow post‐functionalization in high yields. The impact of the substituents on the gas sorption behavior was also investigated.