Despite that fact that proof is considered a central mathematical process, and policy documents have consistently recommended that proof be taught in school mathematics, success with proof remains elusive. A preponderance of evidence suggests that proof is challenging for teachers to teach (e.g., Cirillo, 2011; Knuth, 2002) and for students to learn (e.g., Chazan, 1993; Senk, 1985). Factors identified as contributing to these challenges include: impoverished curricula (Otten et al., 2014); teachers’ content and pedagogical knowledge (Knuth, 2002); and the lack of recommendations about how to scaffold proof so that students can be successful (Cirillo et al, 2017).
PISC draws on pilot study data and findings that suggest a promising approach to scaffolding the introduction to proof in geometry. Based on these findings, we developed the Geometry Proof Scaffold (GPS)—a pedagogical framework that outlines eight sub-goals and corresponding competencies that can be taught one at a time. For example, prior to being asked to work on a proof, students learn to draw valid conclusions from given information or assumptions. The eight sub-goals in the GPS are: Understanding Geometric Concepts, Defining, Coordinating Geometric Modalities, Conjecturing, Drawing Conclusions, Using Common Sub-Arguments, Understanding Theorems, and Understanding the Nature of Proof.