Which one is correct?
I taught national curriculum Mathematics as a part-time teacher in the following institutions:
I taught national curriculum Mathematics as a part-time teacher at the following institutions:

Question

Answer

i think technically speaking,  they are both correct. the second is better though. using at instead of in better describes what you are trying to say. it also sounds more fluent.

Answer

To be "in an institution" is to be a patient or inmate of some kind.  A teacher, student, or course would be "at" an institution.