Crowd-scale interactive formal reasoning and analytics

Large online courses often assign problems that are easy to grade because they have a fixed set of solutions (such as multiple choice), but grading and guiding students is more difficult in problem domains that have an unbounded number of correct answers. One such domain is derivations: sequences of logical steps commonly used in assignments for technical, mathematical and scientific subjects. We present DeduceIt, a system for creating, grading, and analyzing derivation assignments in any formal domain. DeduceIt supports assignments in any logical formalism, provides students with incremental feedback, and aggregates student paths through each proof to produce instructor analytics. DeduceIt benefits from checking thousands of derivations on the web: it introduces a proof cache, a novel data structure which leverages a crowd of students to decrease the cost of checking derivations and providing real-time, constructive feedback. We evaluate DeduceIt with 990 students in an online compilers course, finding students take advantage of its incremental feedback and instructors benefit from its structured insights into course topics. Our work suggests that automated reasoning can extend online assignments and large-scale education to many new domains.