Competencies and behaviors observed when students solve geometry proof problems: an interview study with smartpen technology

Decades of research have established that solving geometry proof problems is a challenging endeavor for many students. Consequently, researchers have called for investigations that explore which aspects of proving in geometry are difficult and why this is the case. Here, results from a set of 20 interviews with students who were taught proof in school geometry are reported. Students who earned A or B course-grades in the proof unit(s) were asked to share their thinking aloud while solving two proof tasks using smartpens. Student thinking was analyzed for two subgroups—students who were successful with both proofs (n = 7) and who were unsuccessful with both proofs (n = 13). Large differences were observed in how often students in the two groups exhibited certain competencies and behaviors. The largest gaps occurred in the ways in which students attended to the proof assumptions, attended to warrants in their proofs, and demonstrated logical reasoning.