Connect the Dots to Prove It
Mark McCartin-Lim, Beverly Park Woolf, Andrew McGregor · 2018
This paper describes a new method for helping students improve their ability to develop proofs, a skill necessary for comprehending and appreciating the foundational topics of computer science. Our method transforms ordinary pen-and-paper homework problems into a puzzle-like game, where students connect dots to justify assertions, in a quest to reach a desired goal. We have implemented a software tutoring system using this method, for students to use at home as an optional study aid. Potentially, our system could one day become a full replacement for traditional hand-written homework, which has the additional benefit for course instructors of automating the grading of student work. Our system is also easy to adapt to any class that requires students to write proofs, and it is easy for instructors to create new problems to use with this system. This stands in contrast to many other educational tools for teaching proofs, which are limited to specific topic domains. We have demonstrated the versatility of our system by testing it in two computer science classes at a large public university. One was a Sophomore-level discrete mathematics course where the students were learning first-order prepositional logic, and the other was a Junior-level algorithms course where students were being first exposed to the concept of NP-completeness. Students from our experiments reported that they would like our system to be used in more of their classes.