Visual programming as an instrument for prospective teachers’ reasoning in geometric pattern generalization

We investigated how prospective elementary teachers collaboratively use visual programming to generalize geometric patterns. Using a block-based programming platform, three pairs engaged in tasks requiring coding and rule generation. Data sources included a demographic survey, screen and video recordings, process entries, and semi-structured post-interviews. Guided by instrumental sociogenesis and constructionism, this study explored reasoning processes during collaborative programming of geometric patterns and solving geometric pattern problems. Findings revealed that visual programming facilitated engagement with rule generation by using dynamic objects and visual cues, which mediated mathematical reasoning. Pairs demonstrated varying reasoning approaches, from associative chaining to hierarchical reasoning, while navigating instrumental integration processes. Collaborative problem-solving and programming encouraged higher-level reasoning, yet the level of instrumental integration varied among pairs. These results showed the potential of integrating visual programming in teacher education to support algebraic thinking and collaborative learning. Implications include extending generalization studies to areas such as statistics and exploring visualization’s role in rule generation through programming. Findings are further discussed.