  Curriculum Analytics (CA) studies curriculum structure and student data to
ensure the quality of educational programs. One desirable property of courses
within curricula is that they are not unexpectedly more difficult for students
of different backgrounds. While prior work points to likely variations in
course difficulty across student groups, robust methodologies for capturing
such variations are scarce, and existing approaches do not adequately decouple
course-specific difficulty from students' general performance levels. The
present study introduces Differential Course Functioning (DCF) as an Item
Response Theory (IRT)-based CA methodology. DCF controls for student
performance levels and examines whether significant differences exist in how
distinct student groups succeed in a given course. Leveraging data from over
20,000 students at a large public university, we demonstrate DCF's ability to
detect inequities in undergraduate course difficulty across student groups
described by grade achievement. We compare major pairs with high co-enrollment
and transfer students to their non-transfer peers. For the former, our findings
suggest a link between DCF effect sizes and the alignment of course content to
student home department motivating interventions targeted towards improving
course preparedness. For the latter, results suggest minor variations in
course-specific difficulty between transfer and non-transfer students. While
this is desirable, it also suggests that interventions targeted toward
mitigating grade achievement gaps in transfer students should encompass
comprehensive support beyond enhancing preparedness for individual courses. By
providing more nuanced and equitable assessments of academic performance and
difficulties experienced by diverse student populations, DCF could support
policymakers, course articulation officers, and student advisors.
