Characterizing the complexity of curricular patterns in engineering programs

Abstract

Engineering programs tend to follow common patterns for educating undergraduate students through the sophomore year. For instance, a portion of a common curricular pattern for electrical engineering involves the sequence: Calculus I → Calculus II → Differential Equations → Circuits I. In mechanical engineering programs the common curricular pattern includes the sequence: Calculus I → Calculus II → Differential Equations → Mechanics. The curricular patterns themselves are more complicated than these sequences, often involving additional pre- and co-requisite courses that must be passed in order for a student to progress through the curriculum. These patterns may be modeled as directed graphs, and the complexity of the pattern can then be characterized according to the delay and blocking factors present in the graphs. The key point is that failure to pass a course that occurs earlier in a curricular pattern, or the inability to start the pattern on schedule (e.g., due to math placement issues) will often necessitate a delay in graduation. Because these engineering curricular patterns are complex, they tend to produce a longer time-to-degree than other disciplines. A number of schools have implemented engineering curricular reforms that are aimed at improving on-time graduation rates. These generally involve modifying the patterns described above in some way that is meant to improve student success. We can think of curricular design patterns as being constructed so as to yield a particular set of student learning outcomes. In this paper we apply curricular analytics techniques to these patterns in order to quantify the extent to which particular reforms should improve graduation rates. Our work involves breaking curricular complexity into two components: (1) the structural complexity, which is determined by the manner in which the courses in a curriculum are organized, e.g., prerequisites, number of courses, etc., and (2) the instructional complexity, which is determined by the inherent difficulty of the courses in the curriculum, the quality of the faculty and academic support, etc. We then demonstrate how these measures can be used within a simulation environment to estimate the impact that particular curricular improvements will have on student outcomes. This will reveal that many engineering curricula have highly "sensitive" course patterns (and in some cases individual courses) that will yield large increases in graduation rates for small improvements in course success rates. Finally, we demonstrate how curricular analytics can be used to compare the complexities of similar programs at different institutions, as well as how these tools can be used to guide faculty discussions around curricular reform.