arXiv subjects

Stuart Johnson

Publications and source records attributed to Stuart Johnson.

4 recordsLinked to original sources

arXiv2024

Active Learning at Scale: Investigating the Benefits of Peer Instruction in Undergraduate Mathematics

Active learning strategies have been widely recognised for their effectiveness in tertiary education, yet their implementation at scale, particularly in large first-year mathematics courses, presents considerable challenges. A common method for actively engaging students in large classes is through online quizzes, which may include structured peer instruction. In this study, we investigate the effect of having students answer quiz-style questions during class both with and without peer discussion in a first-year large mathematics course (N = 550). We also investigate the short- and long-term effects of each protocol. Our findings indicate that peer instruction enhances student performance in mathematics in the following ways: First, when the responses to questions were measured before and after peer instruction the proportion of questions answered correctly increased by 0.2; second, when correct responses were compared to similar questions the following week the proportion correct increased by 0.34 (compared to 0.07 for the control); finally, when measured at the end of the semester the proportion of questions answered correctly increased by 0.42 (compared to 0.2 for the control). These results align with and build upon previous research on the benefits of peer instruction, indicating a potential long-term association with student knowledge retention of mathematical concepts. This suggests that peer discussion may do more than momentarily improve accuracy -- it could also contribute to more durable learning.

math.HO↗

arXiv2005

Bundle gerbes for Chern-Simons and Wess-Zumino-Witten theories

We develop the theory of Chern-Simons bundle 2-gerbes and multiplicative bundle gerbes associated to any principal $G$-bundle with connection and a class in $H^4(BG, \ZZ)$ for a compact semi-simple Lie group $G$. The Chern-Simons bundle 2-gerbe realises differential geometrically the Cheeger-Simons invariant. We apply these notions to refine the Dijkgraaf-Witten correspondence between three dimensional Chern-Simons functionals and Wess-Zumino-Witten models associated to the group $G$. We do this by introducing a lifting to the level of bundle gerbes of the natural map from $H^4(BG, \ZZ)$ to $H^3(G, \ZZ)$. The notion of a multiplicative bundle gerbe accounts geometrically for the subtleties in this correspondence for non-simply connected Lie groups. The implications for Wess-Zumino-Witten models are also discussed.

math.DG↗

arXiv2004

Holonomy on D-Branes

This paper shows how to construct anomaly free world sheet actions in string theory with $D$-branes. Our method is to use Deligne cohomology and bundle gerbe theory to define geometric objects which are naturally associated to $D$-branes and connections on them. The holonomy of these connections can be used to cancel global anomalies in the world sheet action.

hep-th↗

arXiv2003

Constructions with bundle gerbes

This thesis develops the theory of bundle gerbes and examines a number of useful constructions in this theory. These allow us to gain a greater insight into the structure of bundle gerbes and related objects. Furthermore they naturally lead to some interesting applications in physics.

math.DG↗