Application of Graph Theory to Analysing Student Success Through Development of Progression Maps

Abstract

Student progression is influenced by a number of factors including the pre- and co-requisite structures. Simply viewing pass/fail rates of individual courses is not sufficient to understand an academic programmes progression profile. In this study, the emphasis was on identifying the major obstacles to progression towards graduation.

The approach involved generating progression tree structures that revealed the routes by which students pass through the curriculum. Identifying these routes allows for their support to be implemented in practical ways, e.g. by alternative timetabling so that frequently occurring progression routes would experience fewer scheduling clashes.

It was discovered that an large number of progression paths exist even in a structured degree programmes. Further tree analysis was therefore required. The primary approach was to observe the students on the minimum-time-to-graduate route and to determine which events (which courses) caused students to fail out of the minimum time route. The approach was therefore to determine which courses caused the (remaining) minimum time students fail onto longer graduation routes. This result was further distilled to the top five areas obstructing graduation.

The methods were applied to an undergraduate Chemical Engineering programme. The system identified three courses in the second year second semester of the programme, with one course in particular, ENCH2TD, causing 45% of all minimum time students in that semester to fail out onto a route requiring an extra year of study. The method therefore consistently identified major obstacles to progression in an academic programme.