Examining Experts’ Recommendations of Representational Systems for Problem Solving

Pólya and others recognised that an appropriate representation of a problem is key for enabling us to solve it. But choosing the right representation is a problem that novice problem solvers find difficult, so must turn to experts for guidance. In this paper, we present a study that examines how human experts recommend representations. We asked high school mathematics teachers to order representational systems based on their suitability generally, and with respect to a student profile. We found the teachers updated their recommendations based on the problem and student profile, but were inconsistent with each other. This inconsistency highlights a need for more training and support in representational system selection.