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Days ago a professor told me to ask in class when I don't understand something and that he could keep explaining until it's clear for me. Being honest I'm a little slow to understand mathematics in general.

The thing is I really need to understand what he teach otherwise I'm going to fail the course.

As I said before, I'm not very smart so if I do what my professor suggest I might end up upsetting him because I'm going to keep telling him 'again please I still don't get it' at least 4 or more times..

My question to you, as experienced mathematics educators, is

  1. Should I ask only one or two times (to not upset him) if I don't understand something and to search by myself?

  2. Should I keep asking (many ... many times) until I understand something?

If I do 2. Does that can have negative consequences to me as student?

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    $\begingroup$ I think if your questions derail the class for a long time (more than a couple minutes) and you are the only one with the issue, versus class in general, than it is not fair or efficient for teacher to remediate you. However, I would just let the teacher draw the line. He needs to say, see me after class...and then give you one on one attention. But you should also, put forth best effort in the one on one. In addition, you should pre-read lessons, do practice problems ahead of time, etc. so that you are better prepared for lecture. $\endgroup$ – guest Jun 13 '18 at 0:37
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    $\begingroup$ Ask 2 questions the first class. If you have more questions, go to the prof's office hours. Ask the prof whether it would have been ok to ask in class the question you are posing in the office. If he says yes, ask a few more the next time. Ask another student if your questions are helpful or a distraction. I like students to ask questions. When I (rarely) get a student who asks too many questions, I just ask if we can address those in my office hour. $\endgroup$ – Sue VanHattum Jun 13 '18 at 22:42
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How many times one can ask a given professor a question depends on the professor. There are professors who do not like questions ("this is not a good question"). There are professors who will forget about the rest of the class to attend to a question, however, misguided, spending five minutes answering whatever nonsensical question, boring the rest of the class in the process.

The size of the class matters. It can be difficult and even problematic to handle numerous questions in large lecture halls. Once there are more than 80-100 students in the room the dynamic of answering questions changes. The student can be physically far away from the professor. Attending to individual needs does not always help in maintaining the concentration of a large group of people.

Nonetheless, my sentiment, I think shared by many professors, is that most students do not ask enough questions.

Questions can be valuable for the professor because sometimes they signal or highlight particular misunderstandings and confusions, and generally what is asked by one student could/should be asked by many. The professor is gleefully talking about computing the flux of an electric field across some surface and the student asks what that $\Omega$ thing below the integral sign is ...

On the other hand, there are occasional students who really do ask too many questions. Most semesters I don't have one of these students in class, but last semester I did, and it requires some work to handle it well. The potential problem is that the constant questions interrupt the flow of class and distract other students. These problematic students tend to act like class is a private tutoring session, and what characterizes them is the indiscriminate nature of the questions they ask - they ask about notation, about the meaning of the logarithm, about philosophically why we need to parameterize surfaces, about famous French engineers, etc. Usually this is a sign of immaturity, of someone who has not yet learned to censor himself or lives in a mental bubble, blissfully unaware of those around him. Also it can indicate a poorly developed ability to distinguish between the trivial (the professor's handwritten $u$ and $v$ look too similar, but from context it is obvious, upon reflection, which is which) and the meaningful (the problem turns on whether that $u$ is really a $v$). Some very strong students ask a lot of questions too, but these are usually distinguishable from the problematic ones because of the quality of the questions they ask. I don't mean that they ask sophisticated high level questions - I mean that they ask questions that address a basic and key issue, even if elementary.

As a student, how to tell if you are asking too many questions? If you are asking yourself that question, it is highly likely that you are not asking too many questions in class. The self-awareness to pose the question suggests a sense of limits that suggests it is unlikely that who asks it is passing those limits.

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I think this depends a lot on the type of questions (or rather prompts);

If you keep asking the professor "again, please", you shouldn't do it perhaps more than once. Most likely, (s)he will repeat what was just said, but that's useful only if you had problems understanding it due to noise or being distracted.

If you could understand the words clearly but not the meaning, you should think hard about the exact point where the professor lost you and ask about this point in the most specific way possible, showing your thought process and your current obstacle.

The latter kind of question is way more difficult than a simple "again, please", but also generally useful, also for other students.

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As a math professor myself, I want to point out one of the biggest things students in your position tend to forget: you are not alone. If you're confused about something, odds are that lots of other students are just as confused. I can't tell you how many times I've taught a class how to do a problem, and then discovered when they turned in the next assignment that eighty percent of the class had missed something crucial. If any one of them had asked for clarification, they would have all gotten the question right. So ask. Many professors, myself included, will redirect you ("that's a great question; how about we talk about it in my office hours?") if you start to ask too many questions or questions that the professor judges the other students don't need to hear about.

If you're concerned, though, here's a good rule of thumb: try not to ask the same question more than twice. "Can you repeat that?" is fine, and "Sorry, I still didn't get it, could you go through it one more time?" is okay, but after that you should probably make a note to yourself about what lost you and then go see the professor in office hours. This is partly because at a certain point class time needs to be spent on the next thing, but there's a more important concern: generally, if a student needs repetition of something more than twice, it's because there's an earlier thing they aren't understanding. One-on-one, the professor can help you figure out what that was.

Try to be as specific as you can. "Can you repeat that?" is okay if you think you just missed something, but "Can you explain how you got from step 5 to step 6?" or even "where did that $x^2$ in step 6 come from?" is much better. The more specific you can be, the better the professor can address the issue.

Of course, your instructor might have his or her own opinions about what is and is not a "good question". But the professor has specifically told you that you should ask questions if you're confused; that means they think, based on their interactions with you outside of class, that your questions are good ones. So go ahead and ask. The worst thing that's likely to happen is that you ask a few annoying questions one day and the professor asks you to back off a little!

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