The ability to identify the important takeaways from a previously-seen solution and apply them in different contexts is an important problem-solving skill. However, this skill, known as analogical reasoning, is traditionally left implicit in algorithms courses. Students are expected to develop the skill naturally as they progress through the course. In this study, we aim to conduct a more thorough investigation of analogical reasoning in algorithms. We integrate explicit metacognitive scaffolds for reflection and schema development into an undergraduate algorithms course. Then, on course exams, we insert an additional task alongside select algorithm design questions, in which students are asked to describe how a previously-seen problem influenced their design. We analyzed both the previously-seen problem selected by the student and the stated similarity. Within the 142 comparisons analyzed, we find that 37% provide insight about the underlying solution structure, and these comparisons were significantly associated with higher scores on the problem. Furthermore, about one-third of the comparisons were with a problem that course staff also selected, and these comparisons were not only much more likely to be structural but were also correlated with higher performance on the question. Our results indicate that the analogical reasoning skills are closely tied to success in the algorithms course, and encourage instructors to integrate explicit demonstrations into their curriculum.