Whenever one of my students struggles on a question that I think is important (i.e. one that is similar to an exam question), I encourage them to master the question. Most students, when they hear me say so, think they know what I mean. However, they are often mistaken.

In my mind, there are several levels to understanding a question.

The first level is simply being able to do the question without looking at notes. This can be accomplished through memorization of the process. It’s not a high bar to clear, but it’s surprising how many students will simply glance at their notes and reassure themselves that they remember them. The test for this level is simple: on a blank sheet of paper, is the student able to do redo the process?

The second level is being able to explain why the correct answer is correct, and the original process was incorrect. Once a student knows the process, it’s important for them to be able to articulate why their original process was incorrect. That’s the first step in being able to generalize the approach to other similar problems, and to recognize the limitations of the approach. Again, the test is simple: where did the original process go wrong?

The third level is mastery. This is when the student is able to teach the question. I often encourage students to literally imagine someone sitting next to them, and explain step-by-step how to go through the problem, answering any questions that might arise. This includes explicitly stating why the process is correct for that question, and what similar questions would also be appropriate for the same process. The test is whether the student can actually teach the question to someone else.

In order to reach the third level, a student must work hard, but also be reflective. In order to encourage both the memorization of the correct process as well as the achievement of mastery, I ask my students to both use an error log and employ spaced repetition. I also ask leading questions to make sure my students reach the second and third levels of understanding an important question. This is a key part of the learning process.