Responsibility is vital in a classroom, not only for students but for teachers too. Responsibility is taking ownership of one's actions. It is to accept your mistake and to help around and work hard. Responsibility is accepting that you are the cause and the solution to the problem. When we take up a responsibility, we should take it with total commitment and honesty. We shouldn't have a responsibility to others but to ourselves too.
At my earlier school, we did an activity, in fact, not an activity but a daily exercise. Every day, after lunch, we had to clean the class. We got duties of dusting, sweeping and mopping. Whoever finished their duty would get to play outside. This taught us responsibility; my favourite task was to mop the floor. If you try it once, you'll realize it's fun to mop the floor, unlike sweeping. Even cleaning the bathroom is a cool duty, well, only if it's a small one!
Cooperation is also an essential aspect of classroom work. Cooperation is the heart of teamwork. As Bob Proctor said, "Cooperation is always more powerful than the competition". Cooperation is working happily in a team and adjusting with others. It is when you help someone not caring about yourself and putting their needs before yours. For example, if you have a friend who needs immediate help and you have to go to a party, you could adjust and go to the party a little late and help your friend instead.
Giving a teamwork duty is perhaps the best way to practice Cooperation in the classroom. In any activity, thoughts often don't match and break into fights and complaints, but with a bit of Cooperation, the work can be done beautifully. A teacher must display an example of responsibility and Cooperation, and students slowly learn.
Responsibility and Cooperation are deeply connected. These are the core values that one needs to work in a team. There is no cooperation if there is no responsibility.