The Effect of Student Learning Styles on the Learning Gains Achieved When Interactive Simulations Are Coupled with Real-Time Formative Assessment via Pen-Enabled Mobile Technology

This paper describes results from a project in an undergraduate engineering physics course that coupled classroom use of interactive computer simulations with the collection of real-time formative assessment using pen-enabled mobile technology. Interactive simulations (free or textbook-based) are widely used across the undergraduate science and engineering curriculia to help actively engaged students increase their understanding of abstract concepts or phenomena which are not directly or easily observable. However, there are indications in the literature that we do not yet know the pedagogical best practices associated with their use to maximize learning. This project couples student use of interactive simulations with the gathering of real-time formative assessment via pen-enabled mobile technology (in this case, Tablet PCs). The research question addressed in this paper is: are learning gains achieved with this coupled model greater for certain types of learners in undergraduate STEM classrooms? To answer this, we correlate learning gains with various learning styles, as identified using the Index of Learning Styles (ILS) developed by Felder and Soloman. These insights will be useful for others who use interactive computer simulations in their instruction and other adopters of this pedagogical model; the insights may have broader implications about modification of instruction to address various learning styles.Comment: 6 pages 2 tables and 1 figur

Bagchi's Theorem for families of automorphic forms

We prove a version of Bagchi's Theorem and of Voronin's Universality Theorem for family of primitive cusp forms of weight $2$ and prime level, and discuss under which conditions the argument will apply to general reasonable family of automorphic $L$-functions.Comment: 15 page

Mod-discrete expansions

In this paper, we consider approximating expansions for the distribution of integer valued random variables, in circumstances in which convergence in law cannot be expected. The setting is one in which the simplest approximation to the $n$'th random variable $X_n$ is by a particular member $R_n$ of a given family of distributions, whose variance increases with $n$. The basic assumption is that the ratio of the characteristic function of $X_n$ and that of R_n$ converges to a limit in a prescribed fashion. Our results cover a number of classical examples in probability theory, combinatorics and number theory