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Instruction in many STEM domains heavily relies on visual representations, such as graphs, figures, and diagrams. However, students who lack representational competencies do not benefit from these visual representations. Therefore, students must learn not only content knowledge but also representational competencies. Further, as learning progresses, knowledge likely becomes more abstract, so that content knowledge may no longer be tied to a specific representation. This raises the question of whether students integrate representational competencies with content knowledge as learning progresses. The present study addresses this question by building knowledge-component models using log data collect-ed from two studies in an introductory electrical engineering course. We compared knowledge-component models that separate representational competencies from content knowledge to knowledge-component models that integrate representational competencies with content knowledge. Our results show that as learning progressed, integrated knowledge-component mod-els had better model fit. This finding indicates that over time, students' representational competencies become gradually integrated into content knowledge. Further, this suggests that different knowledge-component models might be needed at different times during a learning progression.
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