A geometry teacher's use of a metaphor in relation to a prototypical image to help students remember a set of theorems

• The study examines a geometry teacher's use of a metaphor and a prototypical image.
• The teacher organized students’ knowledge for retrieving that knowledge later.
• The metaphor reminded students of heuristics for working with diagrams.
• The metaphor mediated the work on a problem and the introduction of a theorem.
• The metaphor helped to consolidate the collective memory of the mathematics class.

This article asks the following: How does a teacher use a metaphor in relation to a prototypical image to help students remember a set of theorems? This question is analyzed through the case of a geometry teacher. The analysis uses Duval's work on the apprehension of diagrams to investigate how the teacher used a metaphor to remind students about the heuristics involved when applying a set of theorems during a problem-based lesson. The findings show that the teacher used the metaphor to help students recall the apprehensions of diagrams when applying several theorems. The metaphor was instrumental for mediating students’ work on a problem and the proof of a new theorem. The findings suggest that teachers’ use of metaphors in relation to prototypical images may facilitate how they organize students’ knowledge for later retrieval.