• Evan Fuller
  • Keith Weber
  • Juan Pablo Mejia-Ramos
  • Kathryn Rhoads
  • Aron Samkoff


In a widely cited paper, Leron (1983) proposed presenting proofs in a novel format that he called “structured proofs” and suggested that presenting proofs in this format improved students’ comprehension. Our research investigates how structured proofs might aid or hinder students’ comprehension. In a qualitative study, we presented structured proofs to students to examine how they read and perceived this type of proof presentation. Although some students valued the summaries contained in structured proofs, many complained that structured proofs “jumped around” and required them to scan different parts of the proof to coordinate information. In a larger quantitative study, we found that students who had read a structured proof were better at identifying a good summary of the proof than students who had read a linear proof, but performed somewhat (although usually not statistically significantly) worse on questions concerning justifications within the proof, transferring the ideas from the proof to another setting, and illustrating the ideas of the proof using examples.