an English question

approve-check for correctness,and found to be so.like a test in school. approve of-more of agreeing with something in a personal opinion. you might say "i approve of your choice of a blue shirt today"

In this case it means that the teacher passed John's work as being of an acceptable standard, so John's work would have passed the test. If he had approved of it he would have personally thought it was good, though that doesn't mean he would have passed the test, it just means he personally liked it.

"Approve" is used with an object and "approve of" doesn't have an object. -The teacher looked at John's work and approved it. -The teacher didn't approve of him. Hope this helped :)