✔ 最佳答案
My suggestion:
While I was studying the diploma course, I had six months' practical experience taking up system administration work in different secondary and primary schools.
Further elaboration:
1. You study a course, not study a diploma. You can also take a course.
2. If you had been a system administrator, you can say that you "had six months' practical experience serving as system administrator in..."
3. You can use 'various ' to replace 'different ', or omit them and just say ' in secondary and primary schools'.
Hope it helps!