Pre-service mathematics teachers’ handling of a pupil’s incorrect reasoning with a correct answer

This study, using a scriptwriting task, examines how 52 Czech pre-service mathematics teachers (PMTs) handled a situation in which a fictional pupil’s incorrect reasoning resulted in a correct answer. The participants were asked to imagine and provide a script that reflects how the situation could evolve in response to the pupil’s incorrect reasoning with a correct answer (IRCA). We found some PMTs allowed the teacher in the scripts to take an active role in directing pupils to realize the IRCA and refute it through counter-examples. After orienting pupils, the teacher moved pupils’ thinking forward by foregrounding new strategies towards a more preferred strategy. However, some PMTs allowed pupils in the scripts to take more responsibility in recommending alternative strategies in response to the IRCA and justify the strategies. PMTs suggested teacher involvement or intervention in creating counter-examples considerably more frequently than letting pupils in the scripts provide alternative strategies and justifications. The results of the study highlight the important role of PMTs in harmonizing teaching strategies in their scripts with the curricular necessities and cognitive developments of pupils.