Let's understand punishment vs reinforcement to answer this question.
Reinforcement in behavioral psychology is described as increasing a behavior while punishment is described as decreasing the behavior. The idea was greatly explored by B.F. Skinner, who tested on rats in the lab.
Positive and negative reinforcement refers to the addition or removal of a consequence, in order to increase the behavior of someone.
So say I want my child to keep doing the dishes, and in doing so, I tell him that I would give him an allowance for every week he does the dishes. The allowance would count as a added consequence for the behavior (the act of doing the dishes). This is positive reinforcement. Negative reinforcement would just mean removing something to increase the behavior.
Positive and negative punishment refer to again, the addition or removal of a stimulus but this time, to decrease the behavior.
So say I wanted my child to not skip class, and in asking him to do so, I tell him I will take away his phone for every day he does miss class. This is negative punishment. Negative meaning the taking away of the phone and the punishment meaning decreasing the behavior of skipping class.
If a teacher wanted to introduce behavioral learning, like operant conditioning described above, the teacher would likely want to use positive reinforcement as a means to achieve his/her goals. Positive reinforcement has been shown to show long term affects more than punishment.
Depending on who the students are and their age level, different things will work for different classroom settings. If the students are young, candy or including games might work if you wanted the students to work quickly and quietly so that the extra time would be used as 'free time'. If students are in a high school level education, extra credit or the such could be incorporated to attain the same type of behavior from them.