Whenever you’re explaining a complex idea to someone, it makes sense to check their understanding. There’s no sense in continuing to explore the idea if the listener is stuck. They’re not going to be able to follow you. However, there are two problems with asking someone if they understand.

The first problem is ego. Everyone wants to learn. Nobody believes they know everything. And yet, in the moment, people often don’t want to admit a lack of understanding. Sometimes they don’t want to admit it to you, but quite often they don’t even want to admit it to themselves. Saying they understand allows them to continue believing the story they want to tell about themselves. That’s a difficult habit to break.

The second problem is confusion. It’s possible to be simultaneously confused about an idea and also be confused about your confusion. In other words, your misunderstanding of the idea is compounded by a lack of awareness that you understand. This is related to the Dunning–Kruger effect. In the words of the great George Bernard Shaw: “The single biggest problem in communication is the illusion that it has taken place.” They think they understand, they tell you they understand, and so you think they understand. You can’t rely on answers. You need a proof.

That means you have to check understanding in different ways, ones that don’t have the same level of ego threat and also don’t rely on the judgment of an unreliable judge. There are at least two ways to do that. One is to ask them to explain the idea back to you in their own words. Assuming they’re not just using a thesaurus to replace your words with theirs, that will get you some of the way there.

Of course, purely abstract understanding, even if sound, does not mean practical understanding. Thus the second test is to have them apply the idea. It could be to a hypothetical situation or a real problem, but have them apply the idea to some specific situation. That will demonstrate the understanding. What’s especially good about this is, if they don’t fully understand the idea, they’ll be more likely to realize it, because they’ll get stuck or come up with a nonsensical result. Better they figure it out themselves than have you tell them.