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I am a first year math phd student. I could get a scholarship from my government and notified the director of graduate studies of my department (which is now my provisional advisor) that I wish to decline my TAship position for the next term. He advised me to think more about it and told me to think about it 2 more weeks. He told me that I should keep being a TA.

Well, my TA duties are a burden and I do not learn nothing of math from it. Besides that, it drives me crazy. I do really detest having to deal with those undergrad students. I prefer to devote myself to learn and then do my research. But my advisor wants me to think more about it, Why? If I am not a TA, I could have more time to work on my advisor's projects. Besides that, I do not think my department would have any trouble to find another TA. My school is not Harvard but it is ranked among the 30 best of USA, so there is a lot of people that want to be a TA there.

Why does my advisor want me to keep being a TA?

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14  
Have you asked the director why you should continue as a TA? One possibility is that future career paths may require at least some teaching, and so you should be learning to teach mathematics.. – Patricia Shanahan Mar 4 at 21:49
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I speculate that possibly the DGS is being a little bit selfish, and is worrying more about staffing courses than with your professional development. I would consider getting a second opinion from another professor in your department. That said, if you detest undergraduates, I would strongly urge you to eventually look for a career path which will not require you to teach them. – Anonymous Mar 4 at 22:35
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What kind of career are you planning on? If you want to go into industry, or work for the NSA, it might be fine to skip TA duties. If there is some possibility that you may want to become a professor, you should how to teach, and how to tolerate teaching. If this is your attitude, though, I really hope you do not become a professor... – Steven Gubkin Mar 4 at 22:58
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Why are you asking us what he thinks, instead of asking him? – David Richerby Mar 5 at 0:35
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@StevenGubkin: “If this is your attitude, though, I really hope you do not become a professor” seems a bit harsh — lots of students have a pretty immature professional outlook, but it can change completely as they go through grad school. I’d rather wish the OP success in their career, and a change of attitude about teaching. – PLL Mar 5 at 13:56

You need to ask your advisor, since nobody else can say for sure what his reasoning might be, but here are some possible explanations:

  1. You do a great job as a TA, much better than whoever might replace you, and the department would be unhappy to lose your services.

  2. You do a poor job as a TA and need to take this opportunity to improve your teaching skills before they interfere with your career.

  3. Having more teaching experience on your CV or better teaching evaluations may help when you apply for jobs, even aside from whatever you might learn in the process.

  4. If you "detest having to deal with those undergrad students", you may be miserable working in academia. It's much better for you to figure out now whether/how you can handle teaching successfully without having it feel like a huge burden. Delaying confronting this issue isn't necessarily in your best interests.

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Why not just just ask your advisor? They said something and you don't understand it - asking them for clarification is the obvious next step, whether it's about mathematics or anything else.

With that said, your program might have a requirement that all grad students serve as a TA for some number of courses, and your advisor wants you to get the requirement out of the way now; if nothing else, they are probably trying to help your career by ensuring your teaching record is not empty when the time comes to apply for jobs.

P.S. While your temperament about teaching seems to have improved since (what I assume is) your previous post, I strongly recommend you reconsider using the word "detest". If I were your student and were on the receiving end of such an attitude, I'd feel quite bad and certainly not motivated to learn anything more about mathematics. On a more selfish note, if it becomes known in your department that you have such a negative attitude about teaching, it can affect the teaching letter that will be sent as a part of your future job applications.

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+1. I find the open hostility towards teaching "those undergrad students" worrisome. Few people enjoy grading Calculus I, but it's not as if, when a professor, you can just focus on research: you still have to deal with kids who at least contribute to your salary. – gnometorule Mar 5 at 0:04
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I think the OP should be honest above anything else. It is OK to detest teaching. That said, perhaps he is not in an appropriate place and he might be happier elsewhere. – emory Mar 5 at 1:07

Another potential reason is that you said you could get a scholarship next year, but could is different from will. Is this scholarship guaranteed? If not, your DGS might be advising you to wait until you are 100% sure you have funding before you decline the TA position.

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The other answers so far are good, but there is another possibility.

"so there is a lot of people that want to be a TA there."

Elite universities still get TA shortages. They compete for the best qualified graduate students. Sometimes enrollment falls below projections, and sometimes alternative funding for graduate students exceeds projections, resulting in a TA shortage. University rules may limit the power of the director of graduate studies to acquire additional graduate students in this case, so the director might ask students to TA when they do not have to.

If you agree to TA when you are not obligated to do so, try to get something in return. Beware that your government scholarship may run out at a time when your department has a TA surplus, leaving you without funding. I was threatened with this situation once (I resolved it by winning some outside funding).

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