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.

数十年的研究表明，解决几何证明问题对许多学生而言都是一项艰巨的挑战。因此，研究人员呼吁进行调查，以探索几何证明中哪些方面比较困难，以及为什么会这样。在这里，报告了一组20次访谈的结果，这些访谈是通过对学生进行学校几何学证明的授课的。要求在证明单位中获得A或B课程等级的学生大声分享他们的想法，同时使用smartpen解决两个证明任务。对学生的思维进行了两个子组的分析-两种证明都成功的学生（n  = 7）和两种证明都没有成功的学生（n = 13）。观察到两组学生出现某些能力和行为的频率存在很大差异。最大的差距出现在学生参加证明假设，参加证明中的权证以及证明逻辑推理的方式上。