Traditional knowledge-component models describe students' content knowledge (e.g., their ability to carry out problem-solving procedures or their ability to reason about a concept). In many STEM domains, instruction uses multiple visual representations such as graphs, figures, and diagrams. The use of visual representations implies a "representation dilemma": students learn new content from visual representations they may not yet understand at the same time as they learn about visual representations that show content they do not yet understand. Therefore, students' learning of content knowledge and of representational competencies (i.e., knowledge about representations) is invariably intertwined. Consequently, instruction may need to adapt not only to students' acquisition of content knowledge but also to their acquisition of representational competencies. This claim corresponds to the hypothesis that knowledge-component models that describe content knowledge and representational competencies should be more accurate than knowledge-component models that describe only content knowledge. Yet, this hypothesis has not yet been tested. The work in this article tests this hypothesis by comparing knowledge-component models that describe representational competencies and content knowledge to knowledge-component models that describe only content knowledge. Analysis of log data from two experiments on chemistry learning with overall 203 undergraduate students suggests that including representational competencies into knowledge-component models increases model fit if the representational competencies are difficult. This finding suggests that students can learn abstract content knowledge only if they have a prerequisite level of representational competencies, and that educational technologies should use adaptive knowledge-component models that capture representational competencies the student has not yet mastered.