Dimensions of difficulty in translating natural language into first order logic

In this paper, we present a study of a large corpus of student logic exercises in which we explore the relationship between two distinct measures of difficulty: the proportion of students whose initial attempt at a given natural language to first-order logic translation is incorrect, and the average number of attempts that are required in order to resolve the error once it has been made. We demonstrate that these measures are broadly correlated, but that certain circumstances can make a hard problem easy to fix, or an easy problem hard to fix. The analysis also reveals some unexpected results in terms of what students find difficult. This has consequences for the delivery of feedback in the Grade Grinder, our automated logic assessment tool; in particular, it suggests we should provide different kinds of assistance depending upon the specific 'difficulty profile' of the exercise.