Context: Students often misunderstand programming problem descriptions. This can lead them to solve the wrong problem, which creates frustration, obstructs learning, and imperils grades. Researchers have found that students can be made to better understand the problem by writing examples before they start programming. These examples are checked against correct and wrong implementations -- analogous to mutation testing -- provided by course staff. Doing so results in better student understanding of the problem as well as better test suites to accompany the program, both of which are desirable educational outcomes. Inquiry: Producing mutant implementations requires care. If there are too many, or they are too obscure, students will end up spending a lot of time on an unproductive task and also become frustrated. Instead, we want a small number of mutants that each correspond to common problem misconceptions. This paper presents a workflow with partial automation to produce mutants of this form which, notably, are not those produced by mutation-testing tools. Approach: We comb through student tests that fail a correct implementation. The student misconceptions are embedded in these failures. We then use methods to semantically cluster these failures. These clusters are then translated into conceptual mutants. These can then be run against student data to determine whether we they are better than prior methods. Some of these processes also enjoy automation. Knowledge: We find that student misconceptions illustrated by failing tests can be operationalized by the above process. The resulting mutants do much better at identifying student misconceptions. Grounding: Our findings are grounded in a manual analysis of student examples and a quantitative evaluation of both our clustering techniques and our process for making conceptual mutants. The clustering evaluation compares against a ground truth using standard cluster-correspondence measures, while the mutant evaluation examines how conceptual mutants perform against student data. Importance: Our work contributes a workflow, with some automation, to reduce the cost and increase the effectiveness of generating conceptually interesting mutants. Such mutants can both improve learning outcomes and reduce student frustration, leading to better educational outcomes. In the process, we also identify a variation of mutation testing not commonly discussed in the software literature.