This Work In Progress focuses on student perceptions of the effectiveness of three content delivery modes; a) traditional, residential in-class b) class capture for asynchronous online delivery, and c) modularized targeted content videos for online and blended or flipped classroom mode. Despite the growth of MOOCs and the concomitant shift from long lecture videos to learning modules, many online courses still rely on a class capture method. A recent study on video use by students in online courses recommends the use of short videos, six to nine minutes in length, based on student viewing habits. [1] The student behavior was inferred from click-stream data captured within the LMS but there was no direct interaction with students to gauge impressions of the content delivery or impact on learning. To improve both the residential and online experience requires a deeper understanding of those features which promote learning in each approach. Some of this understanding can be gleaned from traditional academic course evaluations, but student perceptions yield an additional level of understanding. For this study we analyzed data from multiple offerings of a 7-week graduate level numerical analysis course; Application of Finite Element Analysis. Over three years this course was offered residentially and online using multiple delivery modes. We categorize the delivery modes as Traditional, Class-Capture, and Modularized/Blended. Each student studied the material using one delivery mode and was then asked to review the material using another delivery mode. The students were asked to evaluate the perceived learning attained based on their original content delivery mode and the alternate mode. The feedback from this analysis, combined with traditional course evaluations will be used to develop a more comprehensive and objective survey to be used in the next round of courses.

We propose a new algorithm for constructing finite-element meshes suitable for spacetime discontinuous Galerkin solutions of linear hyperbolic PDEs. Given a triangular mesh of some planar domain# and a target time value T , our method constructs a tetrahedral mesh of the spacetime domain [0, T] in constant running time per tetrahedron in IR using an advancing front method. Elements are added to the evolving mesh in small patches by moving a vertex of the front forward in time. Spacetime discontinuous Galerkin methods allow the numerical solution within each patch to be computed as soon as the patch is created. Our algorithm employs new mechanisms for adaptively coarsening and refining the front in response to a posteriori error estimates returned by the numerical code. A change in the front induces a corresponding refinement or coarsening of future elements in the spacetime mesh. Our algorithm adapts the duration of each element to the local quality, feature size, and degree of refinement of the underlying space mesh. We directly exploit the ability of discontinuous Galerkin methods to accommodate discontinuities in the solution fields across element boundaries.

The mathematical process of everting a sphere (turning it inside-out allowing self-intersections) is a grand challenge for visualization because of the complicated, ever-changing internal structure. We have computed an optimal minimax eversion, requiring the least bending energy. Here, we discuss techniques we used to help visualize this eversion for visitors to virtual environments and viewers of our video The Optiverse.