HI everyone!! How are you?
I think that in the Grammar Translation Method teachers correct errors on the spot and accuracy is emphasized vigorously because their goal is to make students learn a foreign language in order to be able to read its literature,learn its grammar rules and produce accurate sentences and perfect utterances.They translate from L1 to L2 and memorization is a must.
On the other hand,in the Natural approach Teachers are not so much concern as to whether the student produces perfect uttarences or whether he knows a text by heart. Language is viewed as a vehicle to communicate,therefore the teacher will correct only the errors that will interfere with meaning.