Redesigning geometry assessments to promote advanced geometric thinking: A case study on formal deduction and rigor

Many geometry problems at the university level, particularly in analytic geometry courses, tend to prioritize procedural tasks to foster deeper geometric thinking. This study aims to analyze and redesign existing geometry problems to enhance pre-service mathematics teachers' formal deductive reasoning and rigor in accordance with the Van Hiele model. Employing a case study approach, four geometric problems were analyzed in relation to their alignment with various levels of geometric thinking. The study involved a detailed examination of pre-service mathematics teachers’ responses and the structure of their problems to identify aspects that require improvement to better support higher-order thinking. The methodology included a content analysis of problem design and pre-service mathematics teachers’ answers, focusing on their engagement in formal deduction and generalization. The findings indicate that the current problems insufficiently promote the development of formal deduction and rigor, as they are primarily centered on formula applications without requiring proof or generalization. Specific recommendations are provided in the form of redesigned analytic geometric problems aimed at fostering advanced geometric thinking. These redesigns are expected to help pre-service mathematics teachers tackle more complex mathematical problems by encouraging logical reasoning and argumentation.