In many domains, problem solving involves the application of general domain principles to specific problem representations. In 3 classroom studies with an intelligent tutoring system, we examined the impact of (learner-generated) interactions and (tutor-provided) visual cues designed to facilitate rule-diagram mapping (where students connect domain knowledge to problem diagrams), with the goal of promoting students' understanding of domain principles. Understanding was not supported when students failed to form a visual representation of rule-diagram mappings (Experiment 1); student interactions with diagrams promoted understanding of domain principles, but providing visual representations of rule-diagram mappings negated the benefits of interaction (Experiment 2). However, scaffolding student "generation" of rule-diagram mappings via diagram highlighting supported better understanding of domain rules that manifested at delayed testing, even when students already interacted with problem diagrams (Experiment 3). This work extends the literature on learning technologies, generative processing, and desirable difficulties by demonstrating the potential of visually based interaction techniques implemented during problem solving to have long-term impact on the type of knowledge that students develop during intelligent tutoring.