Efficiency of Learning from Proof Blocks Versus Writing Proofs

Proof Blocks is a software tool that provides students with a scaffolded proof-writing experience, allowing them to drag and drop prewritten proof lines into the correct order instead of starting from scratch. In this paper we describe a randomized controlled trial designed to measure the learning gains of using Proof Blocks for students learning proof by induction. The study participants were 332 students recruited after completing the first month of their discrete mathematics course. Students in the study completed a pretest on proof writing and a brief (less than 1 hour) learning activity and then returned one week later to complete the posttest. Depending on the experimental condition that each student was assigned to, they either completed only Proof Blocks problems, completed some Proof Blocks problems and some written proofs, or completed only written proofs for their learning activity. We find that students in the early phases of learning about proof by induction are able to learn just as much by using Proof Blocks as by writing proofs from scratch, but in far less time on task. This finding that Proof Blocks are an effective learning tool complements previous findings that Proof Blocks are useful exam questions and are viewed positively by students.