Problem posing on vectors in space: preservice teachers’ perspectives

This study examines preservice elementary mathematics teachers’ problem-posing processes related to vectors in space. Adopting a qualitative case study design, the problem-posing process was analyzed by treating the phases of orientation, connection, generation, and reflection as analytic units, focusing on the cognitive, linguistic, and reasoning-based actions exhibited at each phase. The findings reveal that preservice teachers experience considerable difficulties in establishing meaningful connections between mathematical structures and real-life contexts, particularly when posing vector problems in three-dimensional environments. In addition, causal attribution processes became salient during the reflection phase, with participants frequently explaining their successes and difficulties by referring to their conceptual understanding, prior experiences, and perceived competence. The results offer implications for the design of theory-based learning environments that support problem-posing processes in mathematics teacher education, particularly for advanced mathematical topics.