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How to tell professors I am not interested in working with them right now, but might want to, later?
I am PhD student who was (and still am) trying to find an advisor. Over the summer I contacted many professors, and started small 'trial' projects with them. Since people respond at different times and move at different paces, all of these projects started a few weeks apart, towards the end of the summer. I very recently decided I want to focus on one project with the professor I liked best and want to politely let the other professors know that I no longer want to work with them on their projects. I had not met these other people more than thrice (in three weeks), and had only got to the point of finishing reading a couple of their papers. None of these professors was/is paying me for research, either.
Here's the thing, though - the professors who I don't want to work with are the ones who are willing to take me right away, because I have the skill set they want in their groups. The professor who I want to work with wants to 'test' me for a quarter, so there's always the chance that he might eventually reject me. I however do want to give it a fair shot, since I loved his work, working style and personality the most (we've met twice so far, and both were technical meetings).
So coming to the point, I want to have the other professors that like me as back-ups in case this particular professor is not sufficiently impressed with me by the end of the quarter. How do I convey that to them without pissing them off?

You probably know your professors better than anyone on here, as you have interacted with them. Different people respond to rejection in different ways, and this can be a delicate matter.
However, you did note that the professors that you don't want to work with were all responsive to you, which may indicate that they are invested in students. In my experience, faculty who are invested in students want them to do well, and understand that students' research interests will not always perfectly mirror their research interests. Getting a Ph.D. is a long, difficult process, and your professors have gone through it themselves! Thus, they likely know the importance of selecting a research area/advisor that will work best for the student.
My personal advice: Be honest with the professors that you don't want to work with. Tell them that, while you are interested in their research topics/methods, you found a faculty member whose research interests are highly congruent with your personal interests and long-term career goals. You can also tell them that you feel scared that the other faculty member won't take you on, which could open the door for you to directly ask them if they are agreeable to you coming back to work with them, should your relationship with your first choice advisor not work out. Express your appreciation for their responsiveness and for them giving you a chance to work with them.
Some faculty may respond negatively to you, and they may view you as being unreliable or untrustworthy, since you are leaving the projects. I would hope that your faculty will be understanding, if you are able to be open about the situation.
Best of luck!

I want to thank you for your reply. I followed your advice, and I am so happy that I did. I sat in a lecture of one of the professors, so that I could catch her after the lecture; I briefly told her my decision and thanked her for her time - she seemed totally cool with it. The other professor, who I had met with a bit more, I set up an appointment with, and told him of my decision. He was happy for me, wished me luck and said we could collaborate in future. He even gave me some tips on how to plan for my quals. I guess honesty never hurts, even if it's a bit uncomfortable.


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How much should I write about the competing policies?
I'm working on a political science problem that has attracted (by my count) fourteen proposed solutions, ranging from somewhat useful to positively harmful. Some are already law in many countries; others are recent inventions, advanced in papers and amicus briefs by eminent scientists. Several survey papers enumerate these strategies.
My paper recombines three of the methods in a formal relationship. To use this model, the eleven alternatives and all the laws that follow from them must be jettisoned. Some parties (not just authors, but political interests) are sure to defend them.
How much should I write about the competing policies?

I don't think we will be able to help you very much here. On the one hand, if a lot of stuff needs to be jettisoned in favor of your approach, you will need to defend your approach and explain how it is better than the ones you want to throw overboard, so you will certainly need to discuss them to this extent. Then again, how verbose you can be (or are expected to be) will certainly depend on the venue you are aiming for.

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How can I effectively switch fields from physics to math post-undergrad?
I recently graduated with a BA in physics. Towards the tail end of my undergrad career I took the Putnam exam (scored 28 w/o having taken any upper div math), and subsequently took a couple core math courses (one quarter of real analysis, one quarter of proof-based linear algebra). These were the probably the three most enjoyable learning experiences I've had in undergrad, and for the past month or so I've been trying to think about how I could possibly switch to a research career in mathematics but it seems very unfeasible due to the small amount of core classes I took and my inability to do any substantial math research both due to lack of knowledge and lack of faculty connections.
Right now I am taking a gap year working in a physics lab. I am technically able to audit more core math courses at my undergrad institution but wouldn't reasonably be able to do more than two (maximum three) more. I could self-study but am worried about the lack of grades to reflect my learning (although I could take the math GRE and hope for the best). It's my understanding that I'd need a strong foundation in analysis and algebra before being able to do any sort of meaningful research, so my hope is now to get into a master's program where I could fill in my gaps and start working on research, but even these programs require a much more thorough foundation than what I'd be able to build on paper. Is there any way that I could switch to math at this point, with the goal of entering a math PhD program, or is my best bet to try to do theoretical physics and segway that into mathematical physics?
Thanks in advance for your time and answers.

". . . my inability to do any substantial math research both due to lack of knowledge and lack of faculty connections" For pure mathematics and in the U.S., this is essentially a non-issue, as pretty much no one does any real research until dissertation work. For applied mathematics, it might begin playing a small role, but probably not enough for you to be concerned with. What background in math you can demonstrate and what others think your potential is are first order effects. What research you may have done as an undergraduate is a second order effect, maybe even a third order effect.

I suspect you may have to rephrase your question to be less specific to your own specific situation (I'll let those better informed on what's acceptable in this group deal with that issue), but for what it's worth I'm interested in what others might advise you in this situation.

Pick a couple of target departments.  Look carefully at their program of studies, and compare the graduation requirements against your transcript.  This will allow you to identify what gaps there are between the math portion of the degree you did, against a math degree.  Then you'll be in a position to apply now, with more confidence, or to spend a semester or two taking some more classes, and postponing your application.  But really, it's hard to imagine an undergrad field with more affinity with math than physics has.  Congratulations on discovering what you are interested in!

Removing content from your post goes against the spirit of the SE network, and certainly does not remove its history. If you would rather disassociate the question from your account, that is possible, or delete your account entirely.

In the future you can use the contact us link to ask the post to be disassociated from your account. I have done that for you in this case, but it takes a little time.

Sure; apply to a graduate program in math.  Most such applicants have no publications so far, so that will not hold you back.  Take the GRE.  Mention your Putnam score.  If you are in the US and are applying to a US school, you have a good chance of admission... not Harvard or Berkeley, perhaps, but at many good schools.  You may be asked to take some make-up undergraduate course work at the start; but with your Putnam score I am thinking this will easy for you.  And many math programs will let you do that after admitting you as a graduate student.  Write what you wrote here in your application.
Another thought.  Maybe try your own university.  You have met some of the faculty already.  Email the math department, see if there is a recruitment committee for new graduate students; talk to one of them and see what they say.

There are two things you need.

An excellent math GRE score. You have little to no track record, so this is absolutely vital. It's less vital for those with already good track records, although the GRE can certainly kill otherwise good applications if the score is terrible. I can't emphasize enough how important this test is, even though I think it's absolutely moronic. Start studying now. Some searching and sleuthing will reveal quite a bunch of available resources online. Free too!
Three excellent letters of recommendation, at least. Preferably from senior and well-known senior faculty in mathematics, who can attest to your "ability to not just survive, but succeed in graduate school". I think there's a lot of the drivel said in letters of recommendation these days, a la "strongest student I've had in the last X years". The same writer will then proceed to say that next year, and the year after that, etc. But you need this drivel regardless. (How in the world can I know if you'll be the next Grothendieck? I can't.) Don't hate the player, hate the game.
How do I get these letters of recommendation? Great question! I've found that the best letters of recommendation  come from either 1. somebody you've done a reading course with where you've produced an outstanding piece of written work for them, usually an expository paper, 2. someone you've done undergraduate research (or as others might call it, undergraduate "research") with, where you hopefully have solved some minor open problem, or 3. someone's who's (upper-division undergraduate or graduate) course you had the highest or so grade in that had competitive in-class exams (none of this take-home exam nonsense).
(I cannot emphasize enough having at least one letter of recommendation coming from someone who satisfies my third criterion above. Unless you did your undergraduate at Harvard or Princeton and are out of this world amazing, a letter of recommendation that can say this will be vital. Indeed, many of us faculty have observed that there is a strong correlation between strong competitive exam takers and those who have a very strong grasp of the basics.)
How can I get the attention of those elusive senior and not deadwood faculty and get them to love me enough to write me an excellent letter of recommendation, especially for my first and second criterion above? Send an email, show up to their office, catch them somewhere in the math department building, having prepared for such a meeting quite a bit to show you know your stuff. It would be a lie to say they don't bite, some certainly do. But I would say a useful elaboration of "bite" would be "is making sure they're working with someone up to their perhaps quite high standards, and that they're indeed actually learning and coming closer to attaining mastery and not just performing to impress". Sure, mathematics is ultimately about beauty, not jumping through the right hoops, but getting into a good mathematics graduate school is no easy feat these days. Once you get regular meetings going with a faculty member, whether it be for a reading course or to discuss your progress on research, you should prepare for every meeting as if you were expecting an oral examination on the relevant material.

I'll add a bit more later, if I have the time.

Besides applying to a master's program, which as another answer as suggested is a perfectly viable option, you could also consider a post-bac program. I believe both Smith and Brandeis have such programs. They are year-long programs and they are intended for students like you: who have a weak pure math background but are interested in pursuing a graduate degree in math. You would take most of the standard undergraduate math courses, and likely some of the lower master's courses. At Smith, I know they are also focused on bringing in frequent speakers, so you'd form strong connections for apply to a graduate program afterwards.

The thing that worries me about a postbac program is the cost (what I see on the website is that the cost at Brandeis is >$5k per class).  You could get basically the same education by doing the first year of a mid-tier Ph.D. program, and get paid instead.

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My PhD advisor thinks my progress is poor. How should I proceed?
I am a second semester PhD student. I have no publications until now. In the lab I am currently, we use some sort of academic journal to keep track of our progress. Due to classes and TA workload I did not make research progress for two weeks. When I saw my advisor I had not properly structured my journal update. To make things worse when he asked me how much time I did spend on non research activities I was unable to answer as I did not keep track of time.
This discussion ended up with my advisor saying that he might have to convert me to a master's student if I progress like that. He fears I may not be able to make any research progress within the semester with the current rate. He mentioned this warning will be given only once. He said that I should have adapted to the lab's pace until now.
I recognize that my progress was not appropriate, neither was the way to report this through the journal. However, I felt that being converted to a master student is something I really want to avoid.
Therefore I want to try really hard as my goal is the Ph.D.
However, doubts have clouded my head and  I felt I may also have a collaboration issue. I may need to look for another advisor too, although I still believe that if I don't improve something like that may happen again regardless of advisor.
I believe my advisor is a really good and experienced scientist and I respect him, but:

He has converted other PhD students to Master status in the past.
Also, he is very busy and it is not possible for him to discuss research with me for more than 20 minutes per week.
Other students of the lab manage to make appropriate progress but most of them seem stressed.
My advisor encouraged some students to publish survey papers. However afterward he mentioned that they can not yet graduate as the 6 papers he wants us to publish can only be research-related and not surveys.

In this post, I tried to give both my failings and my worries.
What are your suggestions for my situation?
Should I ignore all these and just try harder or should I change my course of action? Or do both?

is the 'academic journal'  you speak of to keep track of your progress an electronic logbook or some method of documenting and logging your work? It sounds as if it is, do you not think it is important to document what you do in the format that is required?

Unless you can make this question more general, ie applicable to people other than yourself, I think it's off-topic, as none of us can know whether your advisor's view is reasonable. Are there any other members of academic staff who know your work and know your advisor who you could turn to for advice?

You have identified both strengths and weaknesses in your advisor, and pros and cons to staying the course.  This is constructive.
One important thing I couldn't find in your assessment, though, was an overview of what the alternatives are.  In other words, are there any other professors that would be a good fit for you?
If not, then I suggest, first, that you find some additional mentors, since 20 minutes per week, on an irregular basis, is not much.  Second, that you get really good at writing those journal entries.  On weeks when you have some extra stuff to report, file it privately, so you have something to pad your entry with on a week that might not look very impressive.
(If yes, then take a class from the other possible advisor, to get to know him or her.  And don't burn your bridges prematurely with your current advisor.)

It is normal this issue makes you upset as it will have a huge impact on your future. Everybody has doubts, and it is good to explore them and not to rush into things wihtout thinking.
First, about your advisor : he seems to be a respectable person (as you say it yourself) so what he is saying needs to be heard.
Maybe you are not meant to do a PhD and it will be better to do a master. You need to ask yourself why a PhD is important for you?, is it mandatory for the professional goals you want to achieve? Are you willing to sacrifice (hobbies for examples) and work more for it?
If you think your advisor doesn't spend enought time with you, you should say it to him and ask him to provide help : by himself or to appoint to you a more senior student.
Final question you should ask yourself and maybe the most important one: besides your advisor, the puplications and other things, do you enjoy studying/working on the content of the PhD?

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What challenges will an international joint PhD program pose to applicant?
To elaborate, “international” means you have to work at institute A for a minimum of X certain years, and work at institute B for a minimum of Y certain years. They are supposed to be far away from each other geographically (like Europe and U.S.)
And “challenges” are the ones during such kind of PhD life.
NOTE: I also posted this question on Quora.
EDIT: To narrow down the question, I particularly want to learn about the challenges in frequent travelling and working with multiple advisors in different locations.

I should preface this by saying I am an Australian living in Germany.
There are many many factors that will define the challenges you as an individual will face, and of course it really depends WHICH countries you are going to spend time in, and where you are from originally. A US/UK joint program for an Australian will not be nearly as tough as a French/Russian program for a Korean.
This is due to what I call "Ausländer tax", which is to say foreigner tax, or put better "outsider tax".
Ausländer tax is an financial, physical and emotional debt that you pay by simply living in a country that you are not native too.
For example, I was paying a moderate Ausländer tax for the first two years of my PhD where every month I would buy a monthly tram ticket to get too and from work. This cost me around $60 a month. After two years I found out there was a special semester tram ticket for students enrolled at the university, which is $90 for the whole semester. After paying this for a year, I then found out that student's don't have to pay for the trams at all if it's before 8am or after 9pm - which pretty much covers 99.9% of my travel times. In essence, I'd paid around $1700 in Ausländer tax for just the trams. Financial Ausländer tax is generally easy to spot. I know i'm paying it by not being able to put in a contribution of my salary towards my pension, for example. I know i'm paying it by being unable to renegotiate my energy bill, because no one at Eon will talk to me in English. I know I pay it every time I get a taxi and speak in English, even though I know very well what the rates should be or the route we should take. Financial Ausländer tax is a bummer but can at least be overcome by being rich.
But Ausländer tax also includes things that are a bit harder to measure, and in cases impossible to overcome. For example, as I cannot speak German to a high standard, walking around town I hear essentially white noise 24/7. People in the street will ask me questions and I won't even know they are talking to me. Sometimes they will be quite offended by this, which makes me feel like shit, and then I have to spend the day at work feeling sorry for myself. Elevator trips are particularly awkward, simply because I have nothing to say. This is 90% a language barrier issue, but 10% a cultural issue, because certain rituals differ from country to country. This constant, unrelenting confusion creates stress and can really wear you down. It is like putting a whale in a zoo. Sure it can survive, and it will generate productive outcomes, but for the whale it is a burden. Worst of all, it's not obvious how to improve the situation for the whale.
There are PLENTY of positives to living abroad however, which I believe outweigh the Ausländer tax certainly for the first few years. You learn the culture, you learn new ways of doing things, and this has a real and practical benefit to you. But after a while, perhaps 2-3 years, these benefits diminish, and the cons of the Ausländer tax accumulate.
The only solution to Ausländer tax is to stop being an Ausländer. To totally integrate with the new culture. This doesn't mean you just learn the new culture - that is what we did in year 1 and 2. It means to adopt the new culture. Redefine yourself and drop the overhead of translating in-and-out of a foreign language/culture by making it your primary language/culture. For some people this is much easier than others, and of course it depends on the cultural delta, but many people never accept this as they are either unable or unwilling to give up their original culture.

Thanks first for your genuine answer :) i feel the same way too because I also lived in Germany for a short time without any German knowledge. However, maybe what you want to emphasize is that enrolling in a joint program will double or triple this kind of unpleasant experience?

Yes, as your cultural delta (difference between cultures) increases, you'll be paying more Aùslander Tax over the years. However you also benefit more from the multiculturalism. So how it pans out and at what point the multiculturalism benefits start to be outweighed by the Aüslander Tax will depend on you and your circumstances.


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Is dishonesty sufficient to terminate a grad student?
I am a professor who runs a research lab at a university. I have a grad student who works with me, and who also has a history of lying. Most recently, he took information home with him that should have been kept in the lab (which was a breach of our IRB/research ethics). I believe that it was an honest mistake, but the problem was how he dealt with it. He told three different stories about what happened with this information, each of which contradicted the others. So, he either has a poor memory for how he handles important study information or he is flat-out lying to me (I believe the latter). I need to trust that my students follow lab procedures when I am not around and that they will be accountable for their actions. I am liable for my students' actions and mistakes.
Would it be reasonable to "terminate" the student based on this and similar incidents? (Each incident individually is below the threshold for "actionable offense," but they are starting to add up). By "terminate," I mean at a minimum that I withdraw as his advisor, though honestly I believe that it is time for him to leave the university altogether.

@AnoninNY How did it turn out?

Termination of the advising/mentoring relationship
You should check with your department or university policies, but at most places you can unilaterally terminate your advisory / mentoring role by emailing the department chair or graduate coordinator. This is, after all, a voluntary role for you. And given that you no longer trust the student, I don't think you can operate as their advisor in good faith yourself (you couldn't write the letters of recc that they'd need for funding or jobs, for example).
If you don't feel the relationship can be repaired, then you should drop them.
If the student has no other advisor, they may be at risk to be an orphan. Since most stages of graduate school (orals, candidacy, continuing enrollment, funding, research) require an advisor, a student who has no advisor is at risk of not being able to continue in the program. There is often a short period of time that is given to the student to find a new advisor. At some places students are formally terminated if they can't advance; at others not being allowed to advance puts them in a limbo state where they cannot enroll but are not terminated.
Departments tend to not like the creation of orphans and there may be informal sanctions for an advisor who orphans students for no good reason. However, you do seem to have a good reason and if true, your colleagues should back you.
The real result is however that the student may have to leave the program.
University Expulsion
Not being able to continue for lack of an advisor is much more common than actual expulsion, given that expulsion procedures usually require a hearing and the presentation of proof of malfeasance.

Thank you, @RoboKaren. Very helpful. This answer agrees with (and clarifies) what my chair has been telling me.

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How to deal with procrastination issues
As a graduate student I switch between many tasks during each week. My activities consist of attending classes, doing homework, grading, working on my research and studying for exams. However I notice that from time to time I tend to procrastinate and this happens mostly when I have to switch from one task to another or when I feel that a task is difficult and I am not yet sure of how to handle it. It also may occur when I work at home in Sundays or when unexpected lab meetings interrupt me from my schedule.
My situation is not that I do not feel productive, but some hours per week can be lost due to this issue (which is an important thing).
In general the main idea of my problem is: I tend to procrastinate when switching tasks.
To protect me from distractions I have installed browser plug-ins that do not allow me viewing distracting websites more than 5 minutes per day.
I also try to keep track of how much time I spend on each task and have established a relatively stable weekly program.
However I believe I could benefit from better time management advices to handle procrastination...
What are your suggestions ?
p.s. Sometimes what also takes time, is communicating with family and friends. I am an international student and I dont want to lose touch with my people. Although I have a relatively steady pattern of communication with them (usually within weekends) nostalgia beats me wanting more discussion.
----EDIT----
Most answers seem to suggest micromanagement time approaches.
However I believe that micromanagement tends to take a lot of time too.
How can you reduce effectively the time it takes to make a schedule for a specific day ?

@obelix Exactly! Switching tasks is hard, and the best opportunity to procrastinate. If this question is really a duplicate, I find it much better than the "original"

See also [Productivity.SE] Stack Exchange

Instead of editing the closed question, please start a new post with only the new question that you added below.

Suggestions (overlapping rather than mutually exclusive; different techniques may work to different extents for different people):
• Keep really detailed to-do lists. Break tasks into small pieces ahead of time in as much detail as you can envision them. Cross things off one by one so that you don't either a) get lost between tasks, or b) run into a vague item, e.g. 'do report', and drift off to the Internet because you don't have enough to go on in order to get started. Optional: buying an oversized permanent marker so that crossing things off the list strikes you as decisive and worth celebrating.
• Build some rest-time into your schedule. If you know you'll need 30 minutes to decompress after teaching that class, put that on your schedule. Otherwise you'll be trying to force yourself to work and it will probably not go well.
• Carrot and stick. This is one of the two things that helps me out a lot. I bought a delicious cookie but it has a Post-It Note on it saying that I'm not giving it to myself until I've updated my CV, finished that abstract, and gotten caught up on responding to my undergrads' emails to me. I earn a day off every week unless I'm feeling extremely behind.
• Compile  distracting ideas into a 'later list'. This is the other. I'm not a major procrastinator, but when I'm being creative and productive, I'm often hit by unhelpful urges from elsewhere in my brain. If I pursue these instantly, then they sidetrack me and I lose a lot of time to YouTube/Wikipedia/Google Images/etc. But I don't want to forget about them, either. So I write them down on a sheet of paper, and then put it aside for later. Example might look like:
Reread hilarious email that [friend] sent me about his cat.
Search for [TV show from childhood] on YouTube.
Friends having baby. Look up that pattern for a knitted DNA model.
Check email.
Redesign personal letterhead.
Check email.
Look for [long-lost magazine issue] on eBay.
Did they ever find [missing kid from the 1990s]? Ask Google.
Browse Academia SE.
Check email.
Track down [friend]'s blog and see if his wife has given birth yet.
Get caught up on [webcomic I forgot about for a while].
Check email.
Text goofy note about silly dream to [friend].
Can't remember what the word 'palimpsest' means - look it up.
Add a bunch of books to GoodReads.
Check email.
Check email.
Okay, really, what are tangerines, botanically speaking? Ask Wikipedia.
Track down email address for [friend of friend].
Check email.
Look up video instructions on how to replace a zipper.
See if I can get [Windows 98 strategy game] to run on my laptop.
Order book by [colleague] to poke through.
Check email.
Revive dead LiveJournal account and see if anyone's still around.

Voted up because this is the first time I have seen the idea of making a list of distracting ideas to come back to later. Great idea!

To add to your final suggestion, I've also found it useful to install a browser extension such as Pocket, Evernote etc. which saves articles etc. to read later. The best are those which allow you to right-click an intriguing-looking link and save it for later without actually having to open it. Some of them also download it to your phone so you can read it on the bus home.

@Quizzical Creature: Thanks! I'm probably not the only person to have thought of this approach, but it saved my rear-end through an intense undergrad degree. To say nothing of grad school. Though I haven't yet figured out whether I think idly about tangerines only while I have many more relevant things to do.

@Luna: Ooh, Pocket looks super useful and this is the first I've heard of it, as far as I can recall. Thanks for pointing it out!

To offer an implementation of several of TrikeProfs points: I use a Bullet Journal for organization, which helped me a lot with a set of similar problems.
What is a Bullet Jounal?
A Bullet Journal is a combination of ToDo-list and a calender that you write from scratch. For each day you create a list that contains bullets, which can be task you want to finish, appointments/events to attend and can also serve as a notebook foe stuff you learned during that day.
[✓] Read paper x                        completed task
[>] Write summary of paper x            moved task
[ ] Feed the cat                        unfinished task
( ) 12:30 Lunch with co-workers         appointment
( ) 14:00 Lab meeting                   appointment
 •  A Bullet Journal might help         note
    me to organize my workload.

There are rules for handling bullets: If you finished a task, you tick it off and are done with it. If you did not finish a task on that day, you have to move it to another day. If the task is no longer relevant, you have to strike it out. If you adhere to this rules, at least in theory, no task can be forgotten. Once it hits the journal, you are stuck with it.
On the other hand, these rules are more of a proposition and it is quite common for everyone to change them to fit theirs style of work. I added weekly overviews to keep a closer look on my appointments and a monthly wrap-up of everything I have learned and want to keep in mind.
A more detailed explanation can be found on the website. They have a really nice video.
Why this works for me
Most of these points translate to the suggestions TrikeProf made:

Writing down what I want achieve forces me to have a goal.
Ticking off a bullet (1) gives me a warm fuzzy feeling and (2) means I can forget about it and focus on the next task.
I can take notes that I will find again.
If I really do not want to forget something, I add it to the journal.

Make it work for you
As said, for me this works quite well, but that is due to a period of learning. It takes work, but in my opinion it is worth it.
Some things to keep in mind for successful journaling:

Write down what you want get done today: I think this is crucial for your specific problem.
Do not overload your days: If you put too much stuff into one day you might get frustrated. This works for me because finishing tasks is fun. Carrying then with you is not.
Create the right bullets: Break down big task into several bullets. This is especially helpful for overwhelmingly big tasks, as it allows you to handle them bit by bit. [ ] Read paper x is more intimidating and offer less reward than:
[ ] Read introduction of paper x
[ ] Read methods chapter of paper x
[ ] Read conclusion of paper x
[ ] Write a short summary of paper x

Which you can handle one by.
Another aspect of this is to write bullets which have a fixed and easy to identify end point. While
[ ] Improve runtime of program

can never truly be finished
[ ] Fix runtime problem in function foobar

can either be finished or marked as "unsolvable".
Rephrase bullets: If you can not get a task done, rephrase it or split it up (see above).
[ ] Research topic y
vs.
[ ] Look for papers on topic y
[ ] Skim and categorize papers on topic y
... add more as you go along

Disclaimer
You might want to be cautious to take advice from me on procrastination. I should really prepare the talk I am giving tomorrow instead of writing stuff on stackexchange. But it helps me to not forget so many tasks. I promise :)
I am not sure if this is necessary here, but: I am in no way associated with the creator of Bullet Journal whatsoever.


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How do deal with low self-confidence after a failed research rotation?
In short, my third rotation research supervisor withdrew support on a Friday afternoon before my scheduled qualifying exam the following Wednesday. I had been rotating in the lab for about three months. He said that I did not have the cognitive ("critical thinking") or emotional abilities to be a PhD student. Apparently I was getting too much input from my postdoc mentor and the other graduate students, so he did not feel comfortable having me take the exam to possibly join the lab. (Even I were to pass, he would still "fail" me.) Because the lab is large, I was mainly supervised and received feedback from the postdoc. He maintained that I did good work throughout the rotation and was asking questions at an appropriate level for my experience. A staff scientist enjoyed working me as well and felt I was making appropriate progress.
When it came time to present the written report to the PI before the qualifying exam (which already had been approved by the postdoc) he was not pleased and could not believe that my postdoc mentor had approved it. He maintained that I would be absolutely picked apart by the committee for various errors. I needed to apologize and say how stupid it was to appease him. I asked other graduate students about his behavior, and they agreed he can be very condescending. I still felt uneasy though about the discrepancy in expectations between the PI and my postdoc mentor.
While the PI was not supervising my daily activities, he knew of my personal struggles during my rotation. My medication for anxiety had been changed at the beginning of the rotation, and I was experiencing enough symptoms that he caught me crying during a meeting. I explained my diagnosis, and he was very kind and supportive and told me to let him know how I was doing. I kept him updated throughout the rotation, and maybe shared more details than I should have, but I felt I was safe because his wife is a mental health professional. I never shared to get sympathy. I just wanted to make sure he knew that I was trying my best, and I could sense my work was not up to my usual standards. I felt it was the responsible thing to do. Because I was not up to par for a few weeks, he asked for my rotational time to extend beyond the qualifying exam to make sure that we could work together. The uncertainty was hard to deal with, but older students in the lab assured me that he had never let someone go who had rotated that long.
In the week before the qualifying exam, I moved and got diagnosed with an infection. The move provoked my anxiety, and the infection of course did not help, so I let him know what was going on because my draft edits were going to be late. That Friday afternoon, all of my problems that week, along with my mental health history in general, were used to substantiate that I was not emotionally ready for a PhD.
Because my first rotation mentor was a poor fit, and my second rotation mentor lacked funding, the department gave me a fourth rotation. The lab I am in now aligns well with my goals. However, I cannot escape the feeling that I am not catching on soon enough and I'm making mistakes on topics I "should" know. I am very worried that this PI will kick me out as well when he finds out what I actually know. The negative thought is always creeping in that I am not good enough, and maybe the third rotation PI was right. Realistically, my previous two mentors did not sense any problems, and my undergrad mentor maintains I will be a good grad student.
I'd appreciate any thoughts or advice. Thanks.

Related question: “I've somehow convinced everyone that I'm actually good at this” - how to effectively deal with Imposter Syndrome

You are also discussing this with your mental health professional(s), right?  They'll probably do a better job at helping you distinguish which concerns are supported by facts and which are not, better than random people on the internet anyway.

But it sounds to me like the upshot is simply that you've identified a lab you don't want to work in.  That's presumably partly the point of rotations.  Three months is extremely short on the time scale of research, and you'll certainly have up and down cycles of productivity and success much longer than that.

It sounds like your present rotation could be a good match. Rather than speculate on what it is that you "should" know, it may be a good idea to specifically ask your present PI for guidance. You could point out that you're very interested in this field, but are worried about your preparation for it, and that both you and the group would benefit from sketching out more explicitly what it is that you should master. (As a PI, I would be happy to get this request.) It is, of course, possible that these skills will be beyond your grasp, but don't assume prematurely that that will be the case!

Perhaps the PI in your 3rd rotation was right, perhaps not. He made a statement, you can record it, but do not act on it. See how the 4th goes, without prejudice. Perhaps your personalities didn't fit, perhaps he is an aggressive PI, perhaps he had a bad day; many factors play a role. Superviser/supervisees personalities need to match, too, not just skill sets.

@MadJack in fact, while the title does refer to "impostor syndrome" nothing in the body of this question indicate such a "syndrome". This might be of interest though: http://academia.stackexchange.com/q/47783/10643

You will increase the chances of getting useful replies by summarizing your long post and indicating what your most pressing and concrete question is.

@CapeCode Good point; perhaps OP should edit their question.

The last paragraph is probably your anxiety speaking. Everyone makes mistakes, you have backing from most other people but this one person who unfortunately had the power to set you back. You should be fine.

I'm editing your question to replace "imposter syndrome" with a more objective term.  Please roll back if you don't like the edit.

As suggested in a comment, ask your present PI to sketch out explicitly the goals for this rotation.  Take the initiative by writing a first draft, but ask the PI to help you refine your list.
Send the PI regular progress reports.
Try to find a support group.
It's fine to let a PI know of your diagnosis, but unless this person has personally demonstrated his or her trustworthiness, over a significant period of time, I suggest you draw some clear boundaries in your own mind, between what personal information you will share with a PI, vs. what personal information you will share with a support group or a therapist.
Read what I wrote about figuring out which educational accommodations would be helpful for you in this other answer.
Consider having a few sessions of EMDR about the specific trauma of the recent failed rotation.  Here is a link to get you started reading about EMDR: https://www.emdr.com/what-is-emdr/


text:
Open data and copyrights for a thesis
In  my thesis, I am using other people's open data, and I cut and paste the description of it and reference its source and its copyright (if it is identifiable in the source).
My question is if that's the correct way to handle open data. Is cutting and pasting the description of the data (from its source) OK as long as I reference it, or should I interpret it myself?

Look at the licensing of the data you're using, and it will explain what you need to do.  Usually open-source things require attribution, and may restrict its use for profit, but it's based entirely on what license it's on.  For example, fred.saitlouisfed.org has instructions for citing its data series in the FAQ.

@JeffL.Thank you for your answer, moreover, as I am not experienced in the Academia about my second question, is it tolerable to copy paste the description (I am not lazy is just I have many sources and it does not make sense to me alternating each description). Many thanks, you could provide perhaps an answer below.

The citations should come directly from the source, and the details will depend on how they've licensed it.  There's a lot more to open-source licensing, but when you're just doing the citing proper attribution is the main thing you need to concern yourself with.
Here's one example from the St. Louis Fed database, on their data series for GDP:

Suggested Citation:
US. Bureau of Economic Analysis, Real Gross Domestic Product
  [A191RL1Q225SBEA], retrieved from FRED, Federal Reserve Bank of St.
  Louis; https://fred.stlouisfed.org/series/A191RL1Q225SBEA, October 24,
  2016.

Here's another from ICPSR (https://www.icpsr.umich.edu/icpsrweb/ICPSR/studies/32241?classification=ICPSR.I.A.3.):

Citation
United States Department of Commerce. Bureau of the Census,
  United States Department of Labor. Bureau of Labor Statistics, and
  United States Department of Agriculture. Economic Research Service.
  Current Population Survey, December 2010: Food Security Supplement.
  ICPSR32241-v1. Ann Arbor, MI: Inter-university Consortium for
  Political and Social Research [distributor], 2011-12-16.
  http://doi.org/10.3886/ICPSR32241.v1

In my experience most data series have a citation right on the page now days.  If it doesn't, try looking in the site's FAQ, or elsewhere on their site for how they wish to be cited.

If you have a DOI for the dataset, http://citation.crosscite.org/ will format the citation for you.


text:
Should non-native speakers get extra time to compose exam answers?
Today I met with a student who had plagiarized answers on an exam from online sources. She explained to me with apparent honesty that she had spent too long answering the first two questions and then run out of time. In her telling, being a non-native speaker makes grammatical writing in English very slow going. On this exam, I expected the students to write approximately ten to twenty sentences in an hour.
Sometimes our academic counseling department requests disability-related accommodations which allow certain students 1.5x or 2x time for an exam. However, I've never seen one related specifically to speech and language.
Does non-native speech warrant extra time when writing exam answers?

The first part (academic dishonesty/cheating/plagiarism) might make it hard for people to offer a fair analysis of the question and it's answer, as that's obviously bogus excuse for cheating - yet the real question you have is an otherwise interesting one.

I'll not post this as an answer since it is my opinion: I don't think non-native students should get extra time. Part of studying abroad is being able to deal with the language barrier and learning to overcome it. If non-native speakers get extra time, they might not feel the need to improve as much.  And where do you draw the line at which someone does not get extra time any more?

Comments are not for extended discussion; this conversation has been moved to chat.

I know several English-only speakers which should be allotted 5x-6x time for an exam based on the logic you're proposing... If the non-native speaker becomes a professor in an English university then it would be astonishingly painful and unfair for the students taking that course; I speak on behalf of students based on my own experience.

@MonkeyZeus time limits are for practicality not to set difficulty.  It shouldn't matter to other students who comfortably had enough time to answer.  This only becomes a problem when the time limits are set badly and normal ability students must rush to finish.

@JamesRyan: Again you take a broad swipe at teachers without justification from your own teaching practices and experiences.   There is a wide range of tasks such that taking 1.5 to 2 times as long to complete them as the standard amount of time taken by those who have mastered the task is rightly viewed as not having mastered the task.  Needing 10 minutes to write a sentence is a degree of slowness that would be disqualifying in a wide array of academic (and other) circumstances.  Attributing these realities to bad teaching seems a bit irresponsible; certainly it helps no actual students.

What are the TOEFL and SAT score requirements for this course/dept? How many semesters has this student been there and how did they get through those? Does the dept do anything special for incoming students with low scores, to preempt this?

@PeteL.Clark when you are doing a course on a particular subject you should be tested on that particular subject not non-native literacy. Who is to say that they won't go on to become an academic in their native language? Literacy for any future job is a seperate qualification, it absolutely is bad teaching to conflate the two. If an institution takes on non-native speakers to a course then it has a responsibility to make allowances to enable them to complete the course.

"Who is to say that they won't go on to become an academic in their native language?" That's not how curricula work in higher education at all.  I am about to teach students in my course about uniform convergence of functions.  In deciding whether to test them on this topic, I don't try to figure out whether they will make use of it in their eventual careers (which will probably not be in academia but probably will be in the US): rather I decide how important it is to the course and major they have chosen to study...

...At virtually all American universities, an integral goal is for students to be highly proficient at reading / writing / intellectual discourse in the English language.  These goals result in formalized language/writing requirements in many subject area courses, e.g. including mathematics.  If you think that this "conflation" is "bad teaching," then you are really not buying into the ethos of the American university.  Which is fine -- most university students are not American and most Americans are not university students.  But just saying "Bad!" to a whole academic culture is not helpful.

Disability conditions are applicable when there is an uncontrollable disadvantage that prevents the person fairly demonstrating their knowledge, skill and ability in the same timeframe.
This is not the case for a person who has and takes the option of moving to a country or region where their language proficiency is not sufficient to demonstrate knowledge or skill.
Such a person has the choice of developing their language skills to sufficiency or of simply studying at a university where the common language is one they are fluent in. They control the situation and therefore, it is their obligation to resolve it, not the assessor's duty.
Where these two groups intersect is a case rare enough that it should be handled on its own merits according to any applicable policy and law (which most likely will mean the extra time is given to account for the disability).

Indeed, the fundamental distinction is that of "control". A person with dyslexia has no control over the circumstances. A non-native speaker does: they could enroll in a program in their native language. They actively chose to be in this position of hardship. (One could make a distinction here, if the conditions in their home country are such that this choice does, in fact, not exist, e.g. because there simply is no system of higher education or there is danger to life and health, but there is no indication of that in the OP's description of the circumstances.)

By this logic, would we give different rights to refugees (displaced from their home country by circumstance) than to immigrants (left by choice)?

Refugees tend to receive additional support for integration, like language classes (anecdotal confirmation here). Immigrants don't just show up without planning and having some capability already. I think both are covered already outside of what the university might do.

"Disability conditions are applicable because there is an uncontrollable disadvantage" I would suggest changing that "because" to a "when." As written, your first sentence reads like you're about to answer the question, "Yes," and then you answer, "No."

-1. Setting aside whether or not an office of disability services would give these considerations their official stamp, I totally 100% disagree with the philosophy behind this answer. As educators, we shouldn't avoid making reasonable accommodations for students just because it's in response to something that's technically under their control. It seems awfully petty and cruel to tell a student they shouldn't study at a university due to language issues when the only language issue is the design of the exam.

@MikeHaskel Playing devil's advocate here: You say '...in response to something that's technically under their control.'  If a student writes really slowly but has no disability are you implying they should get extra time?

It's not a reasonable accommodation to give extra time for someone who simply isn't up to the literacy requirements of the course, the same as there is no accommodation for someone who hasn't the prior knowledge requirements.

@JörgWMittag: "if the conditions in their home country are such that this choice does, in fact, not exist, e.g. because there simply is no system of higher education or there is danger to life and health" - I'm not at all a fan of university rankings, but ... if "no system of higher education" is a valid reason, it could also be argued that from the point of view of universities that put much emphasis on university rankings for graduate admission, students from countries/language areas without sufficiently highly ranked universities did not actively "choose the hardship" of going abroad.

@jmite "different rights for refugees (forced displacement) vs. immigrants (choice)?" I can only speak for the country I live in: the Netherlands is, as far as I know, more or less open to anyone who is here because their life would be in mortal danger in their own country. People who arrives here because of financial advantages is much more often shown the door. I am not sure I agree with the answer we are commenting on, but differentiating between something you can help (skill) and something you can't help (disability) is not necessarily wrong in my opinion.

@jmite Yes, refugees and regular immigrants are treated differently, as they should be. For example, see this page from the UN: www.unhcr.org/news/latest/2016/7/55df0e556/unhcr-viewpoint-refugee-migrant-right.html

@MikeHaskel, no. Everyone who can study at university and doesn't have a disability can learn a language, especially english. It's the student's responsibility to do so in time for the exam.

This probably seems like a reasonable answer to someone who's used to running exams, but has lost sight of the actual objective of those exams. Put yourself in the shoes of someone outside academia who's (for example) accessing a job applicant. The costs/rewards of and incorrect/correct assessment are much higher for the assessor than they are in education. Admittedly that person has less "students" to deal with, but accommodations are typically made.

I disagree with the basic philosophy behind this answer. In the modern world it is not uncommon for a person to be born in one country, attend university in another and continue their career in a third (then a fourth, fifth, etc.) It seems wrong to prejudice that later career on the basis of fluency in a language that may soon be irrelevant to them. There are more appropriate ways to assess and certify ability in a language - this should not be rolled into an exam score in Whateverology. As for extra time or not: does it make for a fairer assessment of the "skill under test"? Maybe, maybe not.

In a perfect world I think this is a good answer; in the real world, I think that universities owe the foreign students they are using as cash cows a little more than this answer implies although what exactly that should entail I am not sure on.

If you disagree with the answer, please utilize the downvote; if you agree, upvote. Please take extended discussion to [chat].

If the test isn't about language skills, design it such that people with weaker language skills still can complete it. In most but not all cases tests should test knowledge and understanding, not speed.  So if you're worried that people with weaker language skills can't complete in time, just allow more time for all students and allow students who finish early to leave early. If you want to ask more questions in less time, you can always use more multiple choice or similar types of questions.
Giving a short time limit mostly tests who's performing better under stress and who's better at learning answers by heart - which is perfectly fine if that's what you want to test.

While I agree with the general "having lessons in non-native language is a choice" sentiment, I think this also raises a good point. There must be a spread of students with different language skills (and varying writing speeds, for example). Ideally the test would ignore those unless it's actually testing them.

I disagree with your bolded assertion. Tests should test understanding, not knowledge. Speed matters in tests because it is a proxy for your ability to effectively deploy your understanding. Someone who understands the material well should be expected to be able to answer questions faster than someone who doesn't. Unfortunately, of course, there are other factors at play in the speed at which students can answer questions so it's not a great proxy.

I agree about your bold-face assertion, but the simplicity of language on a test is dependent on the material being tested. STEM fields would likely be heavy in numbers and have more basic situational language (CH2=CH2 reacts with Pt in what process to...), but more technical names (dimethoxymethane, hydrogenation) that should be known or are specifically being tested. Arts and other fields would likely be more heavy in conceptual language (what is the main thematic argument Dickens...). In both cases, however, this language/concept is what's being tested, regardless of native language.

@JackAidley I agree with the understanding part, and disagree with your conclusion. Testing speed tests so many things (how a student performs under stress, learning answers by heart, etc) that I find it very hard to support your claim that giving less time rewards students who understand better.

@Daevin I'm pretty sure any test which contains the question "what is the main thematic argument Dickens..." is supposed to test language skills, among other things.

@Peter Yes, and is the point of the test (and likely rest of the course). On that basis, since it is an expectation of the course, the student should have studied more to understand the language, and should not be granted extra time.

@Jack Ailey "who understands the material well should be expected to be able to answer questions faster" what kind of science it is where you are able to answer correctly without understanding, just takes a while?

+1 to the answer "knowledge/understanding/application", delete as appropriate. The other answers concentrate on who we should make exceptions for and whether they're deserving or not. Instead, we should step back and think about what we're actually trying to achieve.

I agree that evaluation methods should test factors you want to guarantee, and as directly as reasonable at that. However, "knowledge" and "understanding" are pretty vague terms and that would come into play when designing tests. I'd say that "performance at solving tasks from relevant domain" is more practical, since it's less ambiguous. Ideally, you just translate "what student who passed the course must" part to tests and that part, in turn, is derived from course's selling points. You get what you pay for - or, in this case, what you test.

@h22 I don't know what do you mean by "understanding" but for math-heavy stuff methods that take time are pretty common. Simplest example - a pupil may know formula for cos(a - b) and all other similar formulas (sin/cos, +/-) - or a pupil may know only one and be able to derive others in no time. Remembering a gist of some method and reliably deriving all details on spot is just as valid as a strategy as memorizing the whole method, however these methods have different tradeoffs.

In short: no, not speaking the language a course is taught in is not enough in its own right to warrant extra time.
As @Nij pointed out, it is the student's choice to have attended this particular academic institution, and they chose to attend an institution where the spoken language is not their native language. An exception would be if it is in the academic institution's policy (i.e. for some institutions where a significant portion of the student body are international students, it may be the case) to grant this student and others extra time based on language.
Another issue here, it seems, is that the student is using this as an excuse (or at the very least, as justification) for committing plagiarism and academic dishonesty. Every student has the choice to cheat or not, and this student decided to cheat. There should be absolutely no excuse for academic dishonesty, and there is absolutely no justification for it.
It should have been apparent to the student before taking the exam that the language the exam was presented in would cause them problems, and the student should have sought help by either the professor (you?)/T.A./academic department with authority to grant extra time. In the event that the student may have been overconfident in their abilities to read/write/speak the language, the student should have approached you immediately afterwards to explain the situation and request extra time.
I would also like to point out that the university I attended had a policy to translate an exam into a student's native language upon request, and I've heard of several other institutions with this policy. These policies were presented in the acceptance materials for my university, and I was not registered as an international student. My point being the student should have been aware of their options before the exam, and it is the students' responsibility to seek these options.

Presumably the student also chose not to take sufficient English as a Second Language (ESL) prior to attending the class. Often, that's a whole extra year of full-time study.

@AlexR Very true. At the university I attended, there was an English proficiency exam that a student could not graduate without passing (perhaps restricting progress beyond first-year, even). If a student failed, there were classes that had to be taken before attempting again. So the institution did its best to ensure students were capable of sufficient English, and also provided means for students that were more comfortable in their native language. There is no excuse, at that point.

Sometimes, access to a dictionary (instead of more time) might be more valuable to a non-native speaker (if the exam cannot be provided in a more comfortable language). Still, that's a point better addressed before taking the exam, and no excuse for cheating. Also, IMHO English has a rather simple grammar (at least compared to German, my native language), so I feel that language difficulties are more likely to arise from the intrinsic meaning of certain phrases (e.g. "he stopped smoking" vs. "he stopped to smoke"), which can be eased by access to a dictionary.

@Daevin, FWIW, she had never taken one of my exams before. yes, she was sanctioned for violating the student code of conduct.

+1 for "the student is using this as an excuse ... for committing plagiarism and academic dishonesty"

@AaronBrick You may be lenient towards her for that (if you are you're one of the nicest professors I've ever heard of), and that's your prerogative, but neither have any of the students who haven't taken one of your examinations before. Really, the point of my answer is that students are accountable for their own actions and knowing their responsibilities.

Most schools I researched when choosing a uni, required non-native English speakers to prove their proficiency at English via a certified exam (IELTS, TOEFL, or schools' own exam). Required level of English was never lower than C1 on CEFR scale, which implies that the student

Can understand a wide range of demanding, longer clauses, and recognize implicit meaning.
Can express ideas fluently and spontaneously without much obvious searching for expressions.
Can use language flexibly and effectively for social, academic and professional purposes.
Can produce clear, well-structured, detailed text on complex subjects, showing controlled use of organizational patterns, connectors and cohesive devices.

I.e. if a student does not satisfy those, he/she should not be at school in the first place.
In my personal experience as a non-native freshman, ENG 101 essay was not very hard to write in dedicated time (150 minutes for 800-1000 words). Most complications rose from structuring the essay, not picking the right words - the latter is fairly easy acquired, even by watching TV or playing video games.
If your course requires extensive writing with complicated vocabulary, then it would be nice of you to warn your students of possible complications.
One other thing from my experience (I'm studying in a non-English speaking country, but medium of instruction is English in my uni) - there are a lot of people who can barely conjure a sentence, even despite the facts I mentioned on the top, and the fact that my school has a prep school to get people up to B2-C1. Somehow those people just get through - but it's their responsibility from then on. After all, C1 (in my case it's not even C1, it's 6.5 IELTS) is actually a threshold at which you are eligible to study in a uni, the most basic level at which you should be comfortable.

+1. The rest is an interesting anecdote, but that paragraph in the middle is an important thing: students should know the expectations before they start, or as soon as possible after they start along with the option to withdraw or drop a level if it is apparently beyond their current ability.

Unless the quality of the language is part of the exam, tell students you do not care about the small mistakes in the grammar. As long as these mistakes do not make the sentence difficult to understand, or even change the meaning so that the answer qualifies as incorrect. "A transformer", "the transformer", "a transformers" - why a physicist should care much.
This will eliminate the possibility of the foreign student to complain that lots of time has been spent perfecting the grammar.

Yeah, I agree with this. I have never really been in a non-writing class where anything has specifically said "use perfectly formatted sentences". I know I sometimes even go so far as to forget words when writing, and I've never got something wrong because of that unless it legitimately changed the meaning and made it indecipherable.I'm not sure why any foreign student would be concerned.Just put the words on the paper.If a professor were that picky about grammar and took points off purely for "bad english" I would think that people would've already tried complaining to a department by then.

@TheGreatDuck: That must be the explanation why so many user manuals for technical devices and software are written in abysmal language.

@O.R.Mapper I'm not saying that there is an excuse for poor language skills. I'm merely making a point that no professor is going to expect perfect articulated wording on an exam unless it is a writing exam. Sure, paper's and things should be to the best of one's ability at a decent standard. However, there's no need to be nitpicky on a test. If someone happens to say "an equations" in a math exam I doubt the professors going to take away points, especially if they know or suspect the person is a foreign exchange student. Granted, they might point out the error for future reference.

Does the student even know it's acceptable to make grammar mistakes in the interest of efficiently explaining their ideas? Literally if the instructor has never taught this then the student has no chance of knowing this. It may be worth observing that both in "the real world" of industry and later on in academia the majority of communication is naturally done hastily and under time pressure, in the form of a stack of email that must be resolved before one can get on with work. And email, of course, is influenced by the speaker's own conversation style, and it is usually clear enough.
ESL speakers can become fluent while making more or less systematic categories of grammatical deviations that are more or less within the bounds of business English. But the entire culture of written examination in school emphasizes the wrongness of the deviations and not the fact that the communication itself is clear and fluent, and this may be the main issue with your student's struggles.
A certain amount of grammar mistakes only modestly impacts readability. Even if it moderately impacts readability, not penalizing these mistakes in a time-pressure quiz or test format is a good idea. This applies to all students. ESL and all students deserve time offline to polish.
Work with your student to find compromises between what they can express fluently and efficiently, and what they can express grammatically in the allocated time. The student may understand this as a bargain: they focus on clarity, and you forgive mistakes. I would suggest being collaborative with the student. Perhaps you will have a need to penalize some mistakes that compromise clarity, but the student deserves the chance to work through which mistakes are better to make.
I want to emphasize an important point about this answer: I advocate no special treatment in grading for the ESL student here. Education should be specialized to the students in need, and changes to evaluation is a last resort. (Of course reflecting on this situation may lead to new perspective in grading, but that's the point of asking questions like this in the first place.)
Now, the OP's question can be answered independent of the act of plagiarism, but I do have something to say about that regarding the circumstance: I would emphasize that inasmuch as justice is about punishment, it is also about when punishment ends so that the perpetrator may get on with their time in society. In this case, it means not depriving the student of their right to quality education assuming the punishment is anything less than expulsion. At the risk of being political, I might suggest that part of what turned the student to this crime was lacking any other way to succeed. That is within your ability to impact as an educator, and relating this empathy to a path forward in this student's education has nothing to do with lessening or excusing the offense.

Unless the exam is about the English language itself, non-native speaking students should have an extra time because they take more time to read, understand and write in English.
An example to this question.
Cisco CCNA exams are only available in English in most countries. The exams in English speaking countries must be solved in 90 minutes, while in non-native countries must be solved in 120 minutes (they have more 30 minutes).
One might think it is unfair that non-English speakers have more time to solve the exam and have a better grade. But they spend more time reading, understanding and writing, which is less time on thinking, the main objective of the exam. Hence the extra half-hour.

Your answer is not convincing, because (i) CCNA is an industry certification, not an academic exam and more importantly (ii) you are talking about an exam which is not in the language of the nation it is given in.  This question is about exams given at English-speaking universities in English-speaking countries.

@PeteL.Clark You are correct, but my answer was focused on explaining WHY non-native speaking students need the extra time.

But it doesn't explain why non-native speakers need more time in this context.  Yes, under a large set of exam conditions they will do worse than if the exam was given in their native language.  Students who are bad at mental arithmetic will do worse under a large set of exam conditions than they would with a calculator.  That does not mean that they need to be provided with calculators.

@PeteL.Clark You have to analyze what you want to evaluate. If arithmetic is what you want to evaluate, don't provide calculators in order to better evaluate the students skills. If it is another area of maths where you think arithmetic would consume too much time, then provide calculators.
If you want to evaluate english skills, give them all the same time. If not, and you want to evaluate thinking, then give some extra time to non-native speakers. (This comment here is my opinion and not facts)

Cisco CCNA exams are not truly time limited anyone that had learned what is required can complete them in half of the allowed time.   The additional time for none-natives allows most words in the questions and on the multi choose answers to be looked up in a dictionary!

There are great answers already, but I hope my personal perspective may also be helpful.
I have team member who is deaf, which is considered a disability by most.  But he will not accept that he is disabled and has held himself to the same standard as everyone else, which makes him a great asset to our team.  He doesn't communicate verbally, but performs his responsibilities as well as anyone else on the team.  He isn't afraid of difficult tasks and rises to whatever challenge we throw at him.
I teach a class with a "hearing-impaired" student who also insists that she does not have a disability.  She is very bright, capable and a good learner, in part because she has had to work a little harder.  From each of these individuals, I have learned that while some accommodations should be made for special circumstances, if we go too far, we do more to handicap the student/employee/friend/family member than their actual condition.
For the student mentioned in the question, if she is allowed to use the language barrier as an excuse for cheating and to receive special accommodations for future tests, she will be further handicapped, not helped.  If you care about her personal and academic development, you need to hold her to a higher standard and convince her to believe in herself and put forth the effort required to succeed despite the obstacles and challenges.  In the long run, she'll be miles ahead if she breaks this shell on her own.

I think this depends on whether you give other people who might write their answers slowly additional time. For example, people with dyslexia also write and read more slowly.
I think that in general, if people with dyslexia also get extra time (which is, in my country, usually only 20% (at most) of the allotted time extra), then you can consider giving the same extra time to that person. I know this is done for high school exchange students.
However, I would only do this for a limited period of time. After, say, a year (or maybe even earlier) of university, it can and should be expected that the student knows the language well enough that he or she is not slowed down by it extremely, especially if the test requires only ten to twenty sentences an hour, which is not a lot. If they still don't know the language they're expected to know after a year, they are going to have a hard time when studying anyway.
I tried to write this answer primarily for students who didn't cheat, by the way. I think that is currently irrelevant to the question. However, in such cases, you might of course decide that the student has wasted their right on extra time.

There are two separate issues here, but both come to the same answer.
If the student is studying maths, physics or engineering, then using fully grammatically-correct sentences should not be part of the marking scheme.  So long as the maths/physics/engineering is clear and correct, supporting text is secondary.  Any exam should not generally be asking for long essay-form questions because it is not an appropriate way of assessing the course.  Since there shouldn't be a need for large amounts of writing in English, there should be no need for extra time to be allowed.
If the student is studying some subject which requires discussion, conversation and writing in English, their standard of written and spoken English has to be good enough to allow this.  This applies just as much for native English speakers as non-native English speakers.  Native English speakers are often not taught English grammar at school to academic-level standards, so a native English speaker may well have the same problem as a non-native English speaker with written assessments.  Regardless, the ability to communicate in written English is a core requirement for the course.  If the student cannot meet that core requirement, a foundation year to get all their skills up to scratch may be more appropriate for them, but you can't allow them extra time to cover their lack of core skills.
For a further problem, your student has clearly cheated in the exam, been caught cheating, and admitted cheating.  Your organisation should have a standard policy for dealing with cheating, and saying "I couldn't finish the exam in time" is not a justification.  Students who approach their teachers/tutors/lecturers with their academic problems ahead of time are likely to get some kind of help, whether that's extra mentoring in English or whatever.  Students who cheat and then say "I couldn't do it" as justification can only get what the disciplinary process says they deserve though.

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TA struggling with how much time grading takes
This semester I was assigned as a TA to a Class that I am not very familiar with.
As a result, grading takes me too much time.
For example, for a class of 74 people, it took me 24 hours to grade their assignments (7 exercises per person). One of the reasons it takes me that much time is that I have to study in order to refresh the content in my head before grading.
What should I do in order to make the procedure more time-efficient?
Should I tell my concerns to the professor I am TA for and as well as my PhD supervisor ? I fear I might seem lazy or unproductive.
To cope with workload whenever I have grading to do I make sure I finish it within one day so that I can focus on the other stuff I have to do in the next days of the week.
-----------------------Edit with answers to questions-----------------------
Since people asked more questions about my situation here are answers:
I keep office hours for 2 hours per week.
I have to grade 3 packages of these assignments for the whole semester.
The first package was for 91 people the second was for 74.
The was provided with indicative solutions but the answers are open-ended

Is this for a whole semester, or one thing you were grading that had 7 items? For a whole semester you are doing fine, but if this is supposed to be done weekly then you have a big problem

Has your professor provided a grading rubric, or just said, "Here... grade these!"

How many of these problem sets will you be grading over the course of the semester?  How many hours per week are you working for your TA contract?  If you're on a 20 hour per week contract, and its taking you 24 hours to do your week's work, then you're putting somewhat more time into this than you should, but not a lot more.

The fact that you're only grading three "packages" for the whole semester makes a big difference.  It's the difference between spending very roughly 3 times as much time grading as you probably should and spending very roughly the amount of time grading you probably should!

Possible duplicate of What are some ways to increase grading speed?. Also see http://academia.stackexchange.com/questions/19112/

As mentioned above, this question is likely a duplicate. I would suggest to rephrase the answer so that the issue whether or not or how to approach your prof is in the focus. Some answers have also addressed this issue.

One thing I might do in your shoes is to grade all the answers to the problems one at a time.
That is grade problem 1 on the assignment for all 74 students, then grade problem 2, and then add up the scores for the seven problems at the end.
That way, you can "prepare" for one problem, grade it on an "assembly line," and then forget about it after you go on to the next problem.

Right. This also improves the uniformity of the grading process.

Given the details you have provided 2 hours of office hour a week plus 3 24-hour grading tasks comes out to around 8 hours a week (assuming a 12 week semester). Adding in another 3-5 hours a week attending the lectures and a couple of hours of prep time, puts you at maybe 15 hours. Often TA contracts are for 20 hours a week. If that is the case, 24 hours to grade these problem sets is not unreasonable. If your contract is only 10 hours a week, then it might be too long and they might need to hire additional TAs.
Another way to look at it is you are grading 518 (7*74) problems. That is under 3 minutes a problem. If you are expected to provide feedback beyond a score, it is going to be hard to grade much faster than that. If you are expected to spend less time grading, then you should discuss alternative marking schemes with whoever is in charge of the class.

This answer assumes the TA has no deadline for grading. This is not often the case in my experience. Professors usually expect me to have the grades up within 7-10 days of the hw being assigned. If that is also the case for the OP, it would lead to working over 20 hours per week when grading.

@Hadi maybe 24 hours over 10 days, which could span 3 weeks, wouldn't even be over working. Most faculty are not going to be sympathetic to a complaint that you had to work more some weeks and less others. Contractually, I am not sure it matters either. Would need to read the TA contract carefully to male sure the time commitment is not nominal.

I understand it probably wouldn't be too bad only going over a few hours every few weeks. In my university that would be a violation of the contract. Faculty should not be able to "save" TA working hours for later.

@Hadi consistently going over is clearly unfair. I am not sure to the extent that the hours can be saved. Legally, I think that it probably depends on the specifics of the contract. Practically speaking, I would be a little disappointed if a TA didn't have the flexibility to work 15 hours one week and 25 hours the next.

agreed. I think there should be some flexibility. I actually just looked up the contract at our university and I was wrong. It permits some flexibility and this case would not be a violation. The topic is a bit touchy for me because the faculty I TA for this term tends to drop 40 hours of work on me without notice after several weeks of 2-3 hours a week and it's really disrupting my research (I'm on a 10 hr/week contract).

Definitely, you should discuss this with the professor teaching the class, since 24 hours to grade a problem set is almost certainly more time than they want you to spend on it.
What makes sense depends on how the timing works out.  For example, you say you have to study the material yourself before grading.  If you are spending an hour doing that, then that aspect sounds reasonable, and the issue is just whether the overall workload is too high.  If you need to spend five or ten hours a week on that, then you probably aren't the right person to grade for this class, although it could be a worthwhile experience if you want to put in that much time.
Aside from time spent studying, the big question is how much time it should take to grade a single problem.  Anything takes a long time when you multiply it by 74, so it could be that the class is just too large and they need to hire a second grader to help.  24 hours for 518 problems averages out to about 2.8 minutes per problem (including study time).  For some problems, such as lengthy proofs where the students try diverse approaches and need personalized feedback, 2.8 minutes per problem would be quite efficient.  For routine calculus exercises, it would be painfully slow.  It could be that you are putting more effort into this than the professor actually has in mind, so it's important to have a conversation about expectations.
Don't worry about disappointing the professor.  It's much better to find out about these issues early on, and nobody puts that much weight on grading anyway.  (Nobody thinks it's the most important thing you should be doing as a grad student, or a true test of your abilities, so nobody will judge you too harshly.)  I'd bet the most likely outcome is that you'll be told you are too conscientious and just need to do what you can in a reasonable amount of time, rather than doing a perfect job.  But the only way to find out is to have the conversation.


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Suitability of top UK graduate programs, compared to US ones
As I check forums to compare top UK schools (specifically: Oxbridge and Imperial College) v.s. top US schools (MIT, Stanford, Caltech, etc.), most of people have mentioned the subjects, just like stuffs below, to consider higher priority for electing US schools:

The UK academic system is archaic, as the yearly system of examination has a very important role in the students' studies.
Students must choose their major, at first, and continue to the end.
...

But, all of these cases are about the undergraduate studies.
In the case of graduate studies, one often consider all top ten schools in the same level, roughly, where the most important factor could be the coherency between the graduate student and her supervisor.
If we confirm above argument, there is no real difference for an international student, in view of the academic system. Actually, the remained factors would be the whether, funding and stuffs like that?
Is there any important factor (except supervisor) for an international graduate student, to opt between potential offers the top universities in US and GB?

I don't get what having annual exams has to do with being archaic. The US system has so many exams there's no time for learning in between them. Annual exams allow for assessing whole areas rather than just small subtopics.

@DavidRicherby: I suspect the OP is just repeating what they’ve been told — I’ve heard lots of people in the US who do believe that about the UK system.  (Just as lots of people in the UK have equally dismissive prejudices about the US system.)

I'm working on a PhD in electrical engineering at a high ranked school in the US engineering and there are qualifying exams for the first two years.

I'm not sure about master's degrees, but there are a few important differences between US and UK doctorates.
Duration. UK doctorates can be (and most often are) as short as 3 years. There are now 4-year degrees (the so-called 1+3 degrees), which combine master's degree and doctorates much like the US programmes, but normal 3-year doctorates are still the norm. US doctorates take at least 5 years to complete, and you can often exit with a master's degree. One of the downsides of the shorter doctorates in the UK is that the number of papers you publish during your doctorate will be typically less than the number of publications of someone who had 5 to 8 years to complete their doctorate.
Funding: Unlike undergraduate and master's degrees, which have been turned into a business, where universities are all too happy to accept international applicants who pay exorbitant amounts of money (at least 2 times the fees of UK/EU students), the situation in the UK with doctorates is quite different. Since doctoral candidates are getting paid, the funding is typically reserved for UK/EU students because the funding body is British/European. There are, of course, funding opportunities for international students, but they are much rarer and competitive. This answer may be of interest to you. I think the US funding bodies are more generous with their funding.
Application: The application process is also very different. In the US, as far as I know, you apply to a department and you don't have to decide on a topic or supervisor for some time. And even then, it's easier to switch topics/supervisors. However, in the UK, when applying for doctorates, you need to write a research proposal and preferably to have already identified a supervisor who can supervise you. Some places even require you to have a supervisor who has agreed to supervise you to support your application. And if your funding is tied up to a supervisor, good luck trying to switch supervisors.
Content: UK doctorates are very focused. There is no coursework, no TAing if you are properly funded (unless you want to), or any of that. Just full-time research on a topic you've already chosen.

The 'fewer papers' point makes no sense. PhDs in the UK are shorter because the people coming in are already more specialised. In the UK you begin research immediately, whereas the extra years in the US are usually a result of taking taught courses first, so don't lead to significantly more time on research.

Depending on the subject, I would say that four years is much more normal than three for a PhD in the UK.

@JessicaB I suppose it depends on the field. In my experience, it simply takes some time to get into things, and people typically become most productive towards the end of their 2nd year. Many of my peers didn't submit any papers before the second half of their second year. Many people graduate with just 2 papers. In the same field, people who have completed their PhD in the US have at least 5 publications.

I agree with 101010111100. The courses at a master level are no substitution for the start of the research.

Plenty of people in life sciences will leave even quite successful PhDs without any papers, because 3 years is simply not long enough for a new starter to learn the ropes and complete a publication level study.

A year and a half ago I found myself applying to top Ph.D programs in the US and in the UK in Mathematics. Having been accepted in one of each, I considered the following factors carefully:
The most important factor, in my opinion, is the availability of funding for international students: In top US programs, funding is virtually guaranteed as a teaching assistantship or research fellowship; the amount of the funding is enough for one to cover all basic living expenses, and then even save some, hopefully. But even in top UK programs, such funding is not guaranteed, and even in the case when there is some funding available, the amount of the funding will not be enough to cover everything.
Unless your family is rich or you are comfortable taking some huge loan, it would be necessary to search for external scholarships, but these, in turn, may demand your time after graduation (for example, if sponsored by a foreign government, sometimes you will need to go back to the foreign country and work there).
If funding is not an issue, then another important factor is the time it takes to complete the degree: in UK, 4 years appears to be very common, since the program is far more focused on research from the very start. In top US programs, however, it can take anywhere from 4 to 6 years, because one has to pass written qualifiers, pass certain core courses, etc..
Finally, another factor to consider is that, depending on the career you're studying, one country or the other may provide better opportunities in practice to get your desired job later. If, for example, you want to work as an academic in the US, studying in the US will make networking, visa issues, etc. much easier. An analogous observation holds if you want to work in Europe instead (although, with the UK exiting the EU, this may change in the relatively near future).
Best of luck in your decision-making!

I don't whether your assertion about the inappropriate funding in top UK schools is a personal experience or not, but as I heard from the accepted people to Oxbridge, all of them are considerably happy and satisfied with their funding packages. Don't you believe that the availability of funding issue would not be so harsh, at least for top-10 UK universities?

Well, seeing as my personal experience deals with a program at Oxford, then I think it is important to carefully consider the availability of funding for UK schools. Keep in mind that the situation is different depending on the program, your citizenship status, and your residence status (for example, EU citizens who live abroad the EU are not eligible for all of the offers available to EU citizens residing in the EU).

This is heavily discipline dependent. In life sciences, almost all UK and EU students will have applied to a particlar funded position, and they are likely to have pretty much everything covered for the length of the PhD (as longs are you are happy on approx minimum wage). But international students this is not the case, and the student will either need a scholarship (most unis give out one or two of these a year, foreign governments/charitys give more) or be prepared to pay £20k/year tution fees + £10k/year bench fees + £14k/year living expenses.