I encourage teaching contractions at all levels because this is how Americans actually speak and newcomers struggle at all levels with contractions. I purposely model typical speech by using contractions in class, rather than proper English.
Beginning Levels need to learn the 'to be' and 'not' contractions. Intermediate Levels should add in the 'will, have and is' contractions. Advanced levels can expand their knowledge by adding 'would and had' contractions.
English speakers read and write differently than they speak. When teaching contractions, repetition is the key. English has formal and informal forms and it is important to teach this distinction. I do this by demonstrating the difference on the board.
Read & Write - Say & Hear
I am a teacher. I'm a teacher.
You are a student. You're a student
In addition, I recommend playing games and role playing to develop a natural usage of contractions.
*Would and had contractions are not included in this chart because of infrequent usage.