Educational systems often claim to teach similar problem-solving skills, yet learners may develop fundamentally different cognitive schemas depending on the system design. This discrepancy highlights the need to examine schema equivalence and transferability across educational contexts. However, the lack of formal definitions and computational models for cognitive schemas has hindered direct comparisons of what learners actually acquire in different systems. This study proposes computational cognitive schemas (CCS) as a formal framework to address these challenges. CCS models problem-solving as state transitions guided by discrete cognitive devices, enabling explicit representation and comparison of schemas across educational systems. The framework establishes a hierarchical structure from individual solution processes to generalized schemas, supported by device ontology theory. Our approach enables systematic comparison between educational systems by identifying common and distinct cognitive operations, facilitating schema-centered design that makes learning goals explicit and comparable. These findings contribute to improving interoperability between educational systems and advancing evidence-based educational system design.