Understanding “understanding”


This past Saturday, I was grading a batch of tests that weren’t looking so great at the time, and I tweeted:

I do ask these two questions a lot in my classes, and despite what I tweeted, I will probably continue to do so. Sometimes when I do this, I get questions, and sometimes only silence. When it’s silence, I am often skeptical, but I am willing to let students have their end of the responsibility of seeking help when they need it and handling the consequences if they don’t.

But in many cases, such as with this particular test, the absence of questions leads to unresolved issues with learning, which compound themselves when a new topic is connected to the old one, compounded further when the next topic is reached, and so on. Unresolved questions are like an invasive species entering an ecosystem. Pretty soon, it becomes impossible even to ask or answer questions about the material in any meaningful way because the entire “ecosystem” of a student’s conceptual framework for a subject is infected with unresolved questions.

Asking if students understand something or if they have questions is, I am realizing, a poor way to combat this invasion. It’s not the students’ fault — though persistence in asking questions is a virtue more students could benefit from. The problem is that students, and teachers too, don’t really know what it means to “understand” something. We tend to base it on emotions — “I understand the Chain Rule” comes to mean “I have a feeling of understanding when I look at the Chain Rule” — rather than on objective measures. This explains the common student refrain of “It made sense when you did it in class, but when I tried it I didn’t know where to start“. Of course not! When you see an expert do a calculation, it feels good, but that feeling does not impart any kind of neural pathway towards your being able to do the same thing.

So what I mean by my tweet is that instead of asking “Do you understand?” or “Do you have any questions?” I am going to try in the future to give students something to do that will let me gauge their real understanding of a topic in an objective way. This could be a clicker question that hits at a main concept, or a quick and simple problem asking them to perform a calculation (or both). If a student can do the task correctly, they’re good for now on the material. If not, then they aren’t, and there is a question. Don’t leave it up to students to self-identify, and don’t leave it up to me to read students’ minds. Let the students do something simple, something appropriate for the moment, and see what the data say instead.

This may have the wonderful side effect of teaching some metacognition as well — to train students how to tell when they do or do not know something.

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4 Comments

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4 responses to “Understanding “understanding”

  1. Nice post, Robert. I particularly like this sentence: “When you see an expert do a calculation, it feels good, but that feeling does not impart any kind of neural pathway towards your being able to do the same thing.” It’s the same logic I use in not posting solutions to old exams for my students (or at least waiting until very near the exam date to do so). Students tend to decide they’ll “study” by reading the solutions to the old exams. Everything makes perfect sense there, where I’ve carefully laid out the solution for them. They think they understand, but in the end, they couldn’t reproduce it, let alone solve a problem that is new to them but requires the same skills.

    Now if only we could come up with a good way to get students to understand that these approaches are not taken out of instructor “laziness,” but out of wanting to help the students truly understand.

  2. I often follow up “Do you understand?” with “Tell me what you understand about it.” A literacy teacher taught me that.

  3. I think you are going a little bit in the wrong direction there. In my opinion, learning to gauge your own level of understanding and asking/researching until you got in your comfort zone is a, maybe the key skill any student should learn during his undergrad studies. Take this responsibility away from them and they might not learn the lesson. Then, they pass you courses but fail later when their environment expects them to take care of themselves.

    Of course, while a lecturer or TA presents something, everything appears to be clear to most students. Only few will be able to follow your thoughts so well that they can actually spot errors, let alone understand. Ironically, the better the presentation the worse this effect hits! I have always felt that (weekly) exercises are a very good tool to make students confront the material on their own. (Worked for me, and I am a terrible slacker when it comes to reworking stuff.)

  4. Philly

    To follow up on Raphael’s comment, I too give weekly assignments because I don’t think you can learn how to do something solely by watching someone else. You need to do it at least once yourself. As far as the better the presentation the worse the effect, I purposely try to make mistakes, especially common mistakes, during demonstrations and then ask, “now why didn’t that work?”