Training Faculty to Adopt the Ignatian Pedagogical Paradigm, IPP and its Influence on Teaching and Learning: Process and Outcomes

This is the second of two articles describing the action research undertaken by the three trainees and their trainer (author of this article). After formal training, the training team integrated the Ignatian Pedagogical Paradigm (IPP) into their undergraduate courses from fall of 2010 through May 2013 in the College of Professional Studies (CPS) at Marquette University in Milwaukee, Wisconsin. The first article was published in this journal in fall 2012 and provided a narrative describing the faculty development process, predicated on the five constructs of the IPP: Context, Experience, Reflection, Action and Evaluation. This article includes a full description of the training protocol, data collection process, and the qualitative data analysis methods. This training team used an Action Research model put forth by Reil over two years and nine months to determine the influence of the IPP on their teaching. This study seeks to provide others who teach at Jesuit Colleges and Universities a rationale for using the IPP both as pedagogy, a curriculum guide along with specific instructional practices, and learning activities. In addition, a replicable IPP training protocol is provided that is based on best practices derived from analogous research in the fields of contemporary learning, cognitive, and educational research. The study also provides the outcomes related to the impact the infusion of the IPP had on the instructors’ curricula, pedagogies, instructional strategies, learning activities, and assessment practices, as well as the student-teacher learning relationship

On pointless diagonal Fermat curves

We give an improved asymptotic upper bound on the number of diagonal Fermat curves $Ax^{\ell}+By^{\ell}=z^{\ell}$ over $\mathbb{F}_{q}$ with no $\mathbb{F}_{q}$-rational points, where $\ell$ is a prime number dividing $q-1$.Comment: 10 page

Asymmetric evolutionary games

Evolutionary game theory is a powerful framework for studying evolution in populations of interacting individuals. A common assumption in evolutionary game theory is that interactions are symmetric, which means that the players are distinguished by only their strategies. In nature, however, the microscopic interactions between players are nearly always asymmetric due to environmental effects, differing baseline characteristics, and other possible sources of heterogeneity. To model these phenomena, we introduce into evolutionary game theory two broad classes of asymmetric interactions: ecological and genotypic. Ecological asymmetry results from variation in the environments of the players, while genotypic asymmetry is a consequence of the players having differing baseline genotypes. We develop a theory of these forms of asymmetry for games in structured populations and use the classical social dilemmas, the Prisoner's Dilemma and the Snowdrift Game, for illustrations. Interestingly, asymmetric games reveal essential differences between models of genetic evolution based on reproduction and models of cultural evolution based on imitation that are not apparent in symmetric games.Comment: accepted for publication in PLOS Comp. Bio