When you’ve understood a subject, there’s a tendency to take parts of the subject for granted. You make more assumptions about how things will work, and why one thing is used versus another. After all, you have spent so much time thinking about the subject that you know it inside and out. This familiarity implies potential sources of confusion don’t even cross your mind because you know how wrong they are. In other words, you start to figure that everyone else probably knows the same amount as you do, so certain things aren’t stated.
This happens quite often in teaching. I’ve been on both sides of the equation. The teaching side of the situation is like I wrote above. It’s not that a teacher is ignoring sources of confusion on purpose. It’s that they are so far past that state of confusion that it doesn’t even register. Of course that equation works in this way, how else would it go?
As a student, this can be frustrating. Often, the questions I have as a student are ill-posed, and not quite thought out. This is to be expected, since I’m learning the subject! However, it then becomes a challenge when asking a teacher, because I have to try and formulate it in a way that they can understand, though I barely understand it myself. This leads to teachers answering questions that weren’t being asked. What’s interesting though is that, as a student, I can understand what one of my classmates is asking, even though the teacher may interpret the question in a different manner. This suggests that there is something to be gained by being in the space between an expert and a beginner. Here, you are able to understand what the beginners are saying, because you are aware of how you had those same difficulties not long in the past. This means that you are in a unique position to help those who are struggling right below your level.
This is part of the reason I am a tutor. I know that it makes for good practice in the art of explanation, because it requires me to relate to the difficulties a student is having. When they have a question, not only is the answer itself important, but the source of the question is as well. What kind of perspective did they have on the concept that caused them to ask this kind of question? Does this perspective suggest that they lack some understanding in another related concept, or was it only with this specific concept? These are questions that you need to reflect on when teaching. Remember, you can’t just go and ask them! If you could do that, then you wouldn’t need to be helping them.
If they’re having difficulty, it’s up to me to find a way to relate the new concept with something they have already seen. I shouldn’t necessarily seek to convert them to my way of thinking, at least not right off. If a student is having difficulty in some area, what they don’t need is to be converted from their way of thinking to my way of thinking. Sometimes, this might be an option if their mental model is off from what the concept, but often only smaller nudges in the right direction are needed. Therefore, the better approach would be to understand their way of viewing things, and try to bridge the gap from what they understand to what I understand.
To get a feeling for why trying to completely switch a student’s viewpoint about a concept doesn’t work well, think about any subject that you have difficulty in. Then, while working with one particular resource in that subject (say, within a textbook), try and get your question answered by looking at another textbook. I bet you will be more confused with the notation and the manner of presentation, which will end with you not getting your question answered. The better way to understand a topic you are stuck on is to ask someone who is both familiar with the topic and your specific textbook. Then, that person will be able to help you, since they can speak the same language as you.
I’m not saying that students should always stick to one textbook or one resource. Getting information from multiple viewpoints can be helpful. However, trying to use multiple resources while stuck may lead to more problems. At minimum, a student will have to “re-learn” the concepts from the new resource, which takes time.
This is similar to the situation in which a student does not understand a topic and a teacher is trying to parse through that misunderstanding. The teacher has to be aware of the way the student is thinking about the subject, and they have to figure this out indirectly. It’s not an easy job, but it’s the challenge of good teaching (or good tutoring).
Remember, if you’ve taught a subject for a long time, chances are that you’ve acquired blind spots that students can be trapped in. It’s up to you to look around and make sure that you’re understanding the student’s difficulty from their point of view. Otherwise, you’re setting yourself up for a conversation in which both student and teacher are speaking past each other.