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I have just started master's in math. There is a class with a very "powerful" (great researcher) professor and I'm taking it. However, there is a classmate of mine who, every time the professor asks a question, she answers it. I find this a little bit anoyying because sometimes I want also to participate in class because sometimes I also have an idea and also because it seems that in academia there is a big component on "reputation" and I'm afraid that if I don't talk in class, I'm not going to get a letter of recomendation of that professor (and I make a big effort in class!). At the same time, I don't want to start a war about who answers questions more quickly.

As in masters program, teachers don't grade exams, the only way to get a good reputation, letter of recommendation and so on, is by participating in class.

How can I deal with that situation? What is the best strategy to get noticed in class with such an anoyying student?

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    You say they don't grade their own papers, but does the professor hold office hours? – Jeff Feb 3 '18 at 20:38
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    Yes. But he prefers to be asked questions about the class by email. – HeMan Feb 3 '18 at 20:48
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To answer your first question, there's nothing stopping you from answering or asking questions in class. If the other student answers questions by raising her hand, you could do so too; if she speaks out to answer questions, you could do so too.

There is also no way you can ask someone else to change the way they behave in class as long as it is not disruptive to others. Just as you have your own reasons for wanting to answer questions, so may your classmate - maybe she wants a letter of recommendation too; maybe she just is the kind of student who naturally tends to voice out her thoughts while learning; maybe she just doesn't like keeping silent when she knows or thinks she knows the answers. Do you really expect to ask someone to not answer something so that you could get a letter of recommendation?

To answer your broader question, trying to impress a professor by answering questions in class isn't probably the most efficient way to go about it. Make sure you get high scores in their homework/exams. If you get a good enough grade, you might even request doing a research project with them (if that's where you are interested in going). Professors understand that several bright students may stay silent in class for various reasons - maybe they are shy, maybe they aren't comfortable speaking publicly in English, or whatever other reason.

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    I would say there might be a problem here, but not with the frequent answerer - profs should try (and generally do) diversify the people they take questions from, because just getting answers from one exceptionally bright student might skew the Prof's perception of "where everyone is" in terms of understanding. – CSSTUDENT Feb 4 '18 at 4:35
  • @CSSTUDENT just because she answers first is no guarantee that she is the brightest... – Solar Mike Feb 4 '18 at 9:18
  • @CSSTUDENT I agree with your comment - the onus is on the professor to ensure everyone gets a chance - for instance when I'm TA-ing, and see only one student answering questions all the time, I specifically say I want other people to answer the next time I ask a question. However, the student answering questions is definitely not obliged to stop doing so for someone else's "benefit". – convexityftw Feb 4 '18 at 17:52
  • If I ask the students questions in class and get multiple hands i never go with the “always answering” person - more than half the time (s)he is the only one to raise a hand anyway. In most classes the solution to OP’s question is really just to raise hand more often. – daniello Feb 4 '18 at 18:45

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