Learning about diffusion at two levels: Agent-based micro-scale and equation-based macro-scale

Diffusion is a crucial phenomenon in many fields of science and engineering, and it is known to be difficult for students to learn and understand. Ideally, students should understand (1) the macro-level patterns of concentration change including Fick's laws which describe these patterns quantitatively, (2) the micro-level random-walk mechanism of diffusing particles, and (3) how these two levels of description are related, i.e. how the macro emerges from the micro. We describe agent-based models (ABMs) of diffusion designed to help students accomplish these learning goals and report the outcomes of implementing them in a university materials science course. The results indicate that the ABM activities helped students understand the micro-level processes of diffusion compared with students from the previous year, but that gaps remained in their understanding of the macro-level patterns of diffusion and the connection between the levels. We conclude with a brief description of our re-designed learning activities to improve outcomes in future years.