Failing to Capitalise on Contingent Events: An Investigation into a Secondary Mathematics Teacher’s Responses to Triggers of Contingency During the Teaching of Algebra

Abstract Responding constructively to unexpected events during a lesson is a particularly challenging facet of teaching. This study aimed to investigate how a secondary school mathematics teacher responded to learners’ unexpected or unplanned offers in the teaching of algebra. A total of three sequential lessons were video recorded and the quality of the teacher’s responses to unexpected learner questions was analysed. The first author then conducted a video-stimulated recall (VSR) interview with the teacher to understand her rationale and decision making in response to the contingent incidents identified within her lessons. The results indicate that the teacher did acknowledge unexpected learners’ offers but failed to probe or interrogate the learners’ thinking “in the moment.” Another key finding was that the reflection-oriented questions during the VSR interview proved fruitful in assisting the teacher to reflect on how she responded to unexpected learners’ offers. We note that the teacher was able to articulate a justification for her actions associated with “deliberate reflection” and that she was able to envisage alternatives to how she responded to unplanned moments related to “critical reflection.” The teacher acknowledged the lesson’s potential limitations after responding to reflection-orientated questions during the VSR interview.