Simplified toy models can make physics harder to grasp

Idealized models are a natural part of physics research and education. In upper-division physics courses, which tend to be more abstract and sophisticated than the introductory courses, such simplified toy models often serve as pedagogical tools to illustrate concepts and calculations. In the topic of statistical mechanics, we have studied the challenges faced by small problem-solving groups of upper-division students. Our findings indicate that students struggle to recognize the underlying structure of commonly used toy models. Students faced various pitfalls as they tended to rely on surface features of the tasks, in combination with loosely connected ideas about key concepts. Based on our findings, we discuss recommendations for teachers in statistical mechanics and other advanced courses that resort to simplified models to explain complex concepts.