Much of the work that students do in high school classrooms does not call for students to seek a full understanding of what they are learning. This lack of depth often leaves students unprepared for the difficult work they will encounter in college. Research suggests that involving students in topics that interest them, as well as providing them with an authentic audience increases their motivation, and also helps students think more deeply about their work. The Looking for Patterns of Injustice in the Everyday (LPI) curriculum asks students to decide on and research an inequality in their community, then to share their findings with those who can make change. LPI was implemented in a large Southern California high school classroom with students from mainly Hispanic, and low-income backgrounds. Students who participated in LPI completed regular reflections and compiled reports of their findings, as well as a presentation to share with an adult audience. To evaluate students' growth, the teacher/ researcher observed and recorded their conversations, as well as looked closely at the work they were producing. The data collected showed that students began to use evidence more as well as engage in higher level thinking about their classwork. They also became more motivated as they shared their findings with others. Students became more active in their community as they began to seek ways to correct the injustices they discovered. The results of the implementation indicates that by giving students an authentic audience and topic, teachers have the potential to promote student understanding, as well as increase their engagement on and off campus

Computational modeling of tissue-scale cardiac electrophysiology requires numerically converged solutions to avoid spurious artifacts. The steep gradients inherent to cardiac action potential propagation necessitate fine spatial scales and therefore a substantial computational burden. The use of high-order interpolation methods has previously been proposed for these simulations due to their theoretical convergence advantage. In this study, we compare the convergence behavior of linear Lagrange, cubic Hermite, and the newly proposed cubic Hermite-style serendipity interpolation methods for finite element simulations of the cardiac monodomain equation. The high-order methods reach converged solutions with fewer degrees of freedom and longer element edge lengths than traditional linear elements. Additionally, we propose a dimensionless number, the cell Thiele modulus, as a more useful metric for determining solution convergence than element size alone. Finally, we use the cell Thiele modulus to examine convergence criteria for obtaining clinically useful activation patterns for applications such as patient-specific modeling where the total activation time is known a priori.