There are three basic types of error correction:
1. Teacher correction: The teacher corrects the student.
2. Self correction: The teacher indicates the student has made a mistake or error (usually by repeating in a quizzical tone) and gives the student an opportunity to self-correct.
3. Peer correction: The teacher asks other students to correct the mistake or error.
A decision to correct or not is based on many factors: the most important criteria is whether the activity you are doing is for accuracy or fluency.