An Exploration of Pre-service Mathematics Teachers’ Routine thinking in Solving Problems in Geometry: A Case Study of a University in Ghana

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Concerns have been raised that many mathematics classrooms follow a set of distinctive rules in solving mathematical tasks. Despite the impact of teachers’ knowledge on instructional design, and the critical role geometry plays in school mathematics curricula, research shows that pre-service mathematics teachers demonstrate more ritualised (procedural) knowledge in solving geometric problems than explorative (conceptual) knowledge. This study, therefore, explored the nature of eight Ghanaian pre-service mathematics teachers’ routine thinking in solving questions in geometry. A test consisting of 16 questions was administered to them. Those who solved 12 or more questions correctly were deemed to have performed well and were assigned to Group A, whilst those who solved fewer than 12 questions were deemed not to have performed so well and were assigned to Group B. The study used the interpretivist paradigm following the qualitative approach. The data was gathered through tests and semi-structured interviews. The results showed that the solution strategies of the three pre-service teachers in Group B were more ritualised, as they solved most of the tasks using a set of procedures. This ritualised thinking was evident in the solutions of those in Group B compared to those in Group A, whose routine strategies were more objectified and property-guided. Following these solution approaches, the study concluded that the Group B pre-service teachers demonstrated more ritualised thinking in solving geometric tasks than explorative thinking, which was more evident in the discourses of those in Group A. It was recommended that mathematics pre-service teachers should be equipped with an explorative sense or reasoning in addition to their ritualised or procedural reasoning. Findings will help develop pre-service mathematics teachers’ geometric reasoning by designing targeted instructional activities for learning geomet

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