Keep in mind that in South Korea people generally don't worry about asbestos. There is no government regulation really to speak of, no licensing or training available to people removing asbestos and thus little / no safety precautions taken in most cases. You can find many sources to support my claims. Here is just one: http://worldasbestosreport.org/articles/killing_future/Korea_experience.php
It is very likely that if this is ACM, there were zero precautions taken in it's removal. Which means, there is likely asbestos covering many objects over the room and being stirred up by normal day to day activities and thus, breathed in by people in that class room.
Maybe your pictures are of ACM, maybe they are not. I agree with the previous poster, they do look like ACM which I've handled previously. I do NOT agree with other posters that it necessarily takes time and repeated/prolonged exposure to put you at greater risk of mesothelioma than someone who is not exposed at all. While studies prove that prolonged exposure increases the risks, you are not devoid of risk from shorter exposures by any means. There are many cases of people who worked around asbestos for only periods of weeks developing mesothelioma 15 - 20 years later. My point being, you should avoid all exposure to asbestos whenever possible.
There are risks to traveling to other countries which are not as concerned with everyday health hazards as we are. Consider yourself fortunate you are traveling to these places and experiencing wonderful things. Weigh that with the fact that there are always risks. What action you choose to take when there is an apparent risk is up to you. Do you simply leave / not participate in anything where there is a seemingly obvious risk like what you've just described? Do you take the sample and test it to put your mind at ease? Do you clean the area and abate assuming it was asbestos and then forget about it? No one can tell you exactly what to do. All we can tell you is this:
Trial and error has proven that Asbestos can be pretty dangerous stuff. It's not like you're just breathing in second hand cigarette smoke for a few weeks, it's most definitely a little worse than that. On the grand scale of people who get mesothelioma, I think most would agree it's pretty minimal risk based on what you described but there are many factors I don't know. How long are you at this school? Is there additional construction going on or is it all over? How well did they clean up (appears not well).