Teacher interventions and student strategies for circular motion problems: A matrix representation

Students' understanding of forces in circular motion is often incomplete. The problems are not limited to confusions about centripetal acceleration and centrifugal forces. This paper considers possible effects of different interventions by a teacher who has discovered the many types of free-body diagrams drawn by students for circular motion in a vertical plane. Students' free-body diagrams often show a lack of attention to lengths of force arrows and to the direction and size of the sum of forces. The strategies used by students may differ depending on the situation and questioning by the teacher can remind students of critical aspects they have overlooked. The revisions of responses following interventions reveal information that is not available from just a single response. This paper discusses how a matrix can be used to express the probability for revisions of responses for different teacher interventions and also help teachers decide on future interventions.