I don't mean to be too critical but "do you understand that?" is not a question to which the answer is ever likely to be useful. It very tempting, but the answer (invariably a sort of glazed "yes") contains no information whatever. When tutoring, your aim should be to elicit evidence of understanding. In other words, ask a question with a definite answer to which a person who did understand what you'd just explained would have no problem responding.
A good ideal to aim for when tutoring something like maths or computer science is never tell them anything - it's amazing what you can manage to teach in a session which consists entirely of you asking them questions and them providing you with answers.
Yes, that sort of Socratic method of teaching works rather better in fairly logical, self-evident areas. Less well in history etc. though you can use a bit of it almost anywhere.
This is only tangentially related, but when I was in school I often wished that the curriculum included an outline of what is known and not known, instead of only teaching what is known with little sense of the big picture of human knowledge.
Actually, maybe it's not so tangential - teachers probably can do a lot to encourage admissions of ignorance if they had a habit of regularly admitting ignorance themselves.
The main cause of this problem seems institutional: the people who instruct us are also the people who evaluate us and assign us grades which determine which schools we get into and such. From an individual perspective, other than some minor missed optimizations (like not admitting ignorance to tutors who don't grade you, out of habit), it looks like a conflict between instrumental and epistemic rationality.
I'm not sure the conflict is exactly between epistemic and instrumental rationality. That would be when believing falsely is instrumentally rational. In this case, one action (concealing ignorance) is both good for one instrumental subgoal (status/positive evaluation) and bad for another (epistemic rationality). The epistemic problem does not lead to benefit; doing something beneficial leads to it.
Here's it phrased another way: In a case of actual conflict, the benefit comes from the absence of true knowledge or the presence of false knowledge, so if one magically learned the truth with nothing else changing, this would negate the instrumental benefit. In the case of concealing ignorance, if one magically learned the information without the tutor knowing of the earlier ignorance this would be even better instrumentally. The ignorance is not necessary for the instrumental benefit, only the tutor's awareness of it.
Here's what I remember of being a confused student:
You don't lie "yeah, I get it" to a tutor because you're afraid of admitting your ignorance. You do it because you don't think the tutor can actually help you with your problem. You realize "Shit, I should have read the book/slept last night/looked at this problem before this minute." Maybe you're so wiped that you're just not thinking about anything but the flash game and the cozy bed waiting for you back at the dorm. Or you're thinking about the shitty grade you just got and how miserable you are. What you positively, definitely, don't have the energy to think about, is math. So you're going to say "Yeah, I get it," and maybe at some point later you'll try to get it.
This problem is compounded when the students feel obliged to stay in the class even if they're not getting anything out of it. The result is a room full of tired, frustrated students terrified of being "found out" or giving the wrong answer. I encourage my undergrad students to leave and work on a problem later if their brains just aren't up to the job, but they never do. It's not clear if this is because of years of authoritarian schooling, or if they just don't trust themselves to do the work outside of a classroom.
I might lose the respect of a tutor, or even a lecturer by admitting my ignorance
That would be a fault in the tutor or lecturer. No-one that I teach will lose my respect for revealing their ignorance or lack of understanding of something (nor for concealing it either). I listen and observe and try to say whatever I think will address their difficulty, and if it doesn't, try something else. And it sounds as if you act similarly in your teaching.
Well thats certainly true, but from the perspective of undergraduate me it didn't seem that way. Admitting ignorance seemed to me like it would come with a loss of respect.
While teachers and lecturers certainly prefer their students to ask questions etc, I think plenty will also be consciously or unconsciously keeping a log of who seems to understand things more quickly and so on. While asking questions is what you're meant to do, and will almost always be of the greatest benefit to you as a student, the fear of losing respect isn't entirely unfounded.
I think it's very hard to be sure that you as a teacher are avoiding all judgement of this sort too, as avoiding all such judgement is both the sort of thing you professionally should be doing, and the sort of thing you'd like to think about yourself. As an academic judging someone's potential for postgrad, or a teacher assessing ability, it's very hard not to be swayed by an air of competence and ability in someone who seems to pick up ideas quickly and without difficulty.
This jives with my experience. Also, the grading I've done for various professors (and specifically the interaction that goes along with the grading) has exposed me to a lot of variations on the attitude of "officially, there are no stupid questions... but there are definitely stupid questions, and I'm tired of them." It's not ubiquitous, but it's common enough to make worrying about the prof's opinion pretty reasonable if you expect them to have any say in your future success beyond the grade you get in their class.
There are also issues around classmates. Even when I don't think I will lose the respect of my classmates for holding up the class until something is explained to my satisfaction, I do expect I will test their patience if it takes me an unusually long time to understand something. Certain concepts I just can't get on a first-pass explanation when put on the spot; it's almost always easier to pretend I understand it and then go home and study it.
I usually prefer to ask questions along the lines of "Does this make sense?" rather than "Do you understand?".
The problem with "does this make sense?" is that one to whom a topic/explanation makes sense cannot necessarily reproduce the principle. You're more likely to get an honest answer asking if it makes sense, but I think that's probably because "making sense" requires a less rigorous facility than "understanding."
Several of my graduate professors have a habit of pulling intuitive leaps into problems that make perfect "sense" when presented, but they aren't the sort of thing that many, if any, of the students are going to be able to make on their own due to lack of such intimate familiarity with the material. It really shows on the problem sets.
While I noticed this tendency in others and myself, I actively resisted it trying not to be afraid of saying "that still doesn't make sense to me". Perhaps it might be a good idea to frequently repeat that you won't think less of someone for admitting your explanation didn't make sense to them, that it probably has more to do with your explanation than with them?
Sometimes I would fake understanding if I gave up hope of understanding at that time (time constraints, poor explanatory skills etc.) and wanted to drop the topic.
There are plenty of pedagological methods here: one of the most obvious is to ask for anonymous questions to be given in on paper between lectures or halfway through etc.
From the point of view of the student, I also sometimes don't ask for explanation because once people start they don't stop. Often if someone keeps on going they'll make it clear, whereas if you stop to ask they spend 20 minutes explaining it even though you realise what they mean after 2.
From the point of view of the student, I also sometimes don't ask for explanation because once people start they don't stop. Often if someone keeps on going they'll make it clear, whereas if you stop to ask they spend 20 minutes explaining it even though you realise what they mean after 2.
Oh man, I hate that. My dad does this all the time - I go far out of my way to ask other people for information because if I let him get started I could be sitting there for an hour and a half, either waiting for him to get to the point by way of going over stuff I already understood, or waiting for him to finish the tangents he goes on after answering the question I asked.
Asking the right questions and estimating the quality of own understanding are nontrivial skills. A person can well understand something about the thing you explain, but won't be able to tell whether the understanding is sufficiently deep, and won't be able to specify what exactly is insufficiently clear.
Having a reliable and constructive (leading to activity that forms required understanding) sense for quality of understanding would, for example, allow one to solve textbook problems with very high degree of reliability (that is, very likely find a solution, which would very likely be correct) even given initially shallow knowledge of background material, given enough time. People rarely demonstrate this skill.
if we want to impress a potential employer we shouldn't admit ignorance (unless the alternative makes us look more ignorant)
Even in a job interview, admitting ignorance of a minor point shows a willingness to admit that one is fallible, which is the first step towards correcting a problem. (This actually happened, and I'm not sure it hurt at all -- certainly not as much as trying to fake not being ignorant would have, in that particular situation.) Maybe this could be included under a very broad umbrella of "making oneself look even more ignorant" -- ignorant of a metacognitive skill?
people create narratives about themselves and sometimes become pigeonholed in that role. social norms reinforce this, start acting different and see how everyone tries to nudge you back into place.
Reading Being a teacher made me think about my experiences tutoring university students. I'm a PhD student, so my teaching currently consists of helping first year undergraduates on problem sheets. I think I'm reasonably good- I try to appreciate what difficulties they are having and anticipate them, by explaining what they are doing means, and approaching the problem in different ways.
One constant frustration I get though is that, having explained a problem to a particular student, the student will give me a blank look, and then mutter "ok". I know what that look means, and will ask "so do you understand that?" "sort of...." "well look at it this way....".
Now some of this may come from me- I'm explaining too fast or in a way they don't understand, and my familiarity with the subject, but I suspect some comes from them. It can be difficult to admit one's ignorance, from my own experience. I, and I suspect others who go on to do university maths, was used to being the best or near the best in school, with "being smart" being part of my core identity, something that made me distinct from my more attractive or more fit peers. Getting to university and realising one is having difficulty with even basic questions can be a knock to ones identity. So I hid my ignorance, and did myself damage. I might lose the respect of a tutor, or even a lecturer by admitting my ignorance, but the alternative is to remain ignorant.
I suspect this is a problem that is common among us all. Its a lot easier to pretend we understand, and sometimes it may help- if we want to impress a potential employer we shouldn't admit ignorance (unless the alternative makes us look more ignorant)- but in general admitting ignorance helps us learn. There is (almost) always someone with more knowledge on a particular subject than you, and a failure to use that resource is a failure of rationality.