"Putting it on" is an idiomatic expression used to express that something is being faked, usually some kind of minor illness like headaches, stomach aches or cramps. Some kids try to get out of going to school by pretending that they are ill, or as it seems to be in this case, when they are at school they pretend to be ill so that they can go home. This sentence sounds like a parent telling their child who was pretending to have a headache/stomach ache that "the teachers know when you're putting them (the fake pains) on". In other words, the teachers can tell when you are pretending to be ill.

The context is that the student is trying to show that he is listening the teacher, but actually he's not, he is putting him on/misleading/deceiving. Am I correct? Peachey, you also helped me to understand this object. Thank you. :)

I think there's a little confusion about "them". If you mean fake pains (in Shizenai's answer), then it means to pretend to have those pains. If "them" refers to the teachers, then the meaning is "mislead/deceive": "Teachers know when you're misleading them". Of course, if it's an item of clothing, it means to dress oneself. Like many other phrasal verbs, the meaning changes with the context, so check what the object actually is.