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This study illustrates how Cognitive Diagnostic Modeling (CDM) can be used to assess fine-grained levels of computational thinking (CT). We analyzed scored responses to the Computational and Spatial Thinking assessment (CaST) from 271 children. We identified four key attributes required to solve tasks: sequencing of codes, fixing a program, spatial orientation of an agent, and rotation on a point. Results indicated that younger children did not master all the attributes, particularly spatial orientation of an agent and rotation on a point. We identified four common mastery profiles of children that were associated with age. Our findings illustrate that mastering spatial orientation is critical to CT ability. Finally, the nuanced information about children’s mastery levels has potential to provide teachers with useful information about what concepts and skills their students are struggling with so that they can adjust instruction to emphasize those concepts.