Not to split hairs, but the compass didn't represent that he found direction as a teacher. If the beginning of his career, Jacobs tells Holland that they have two jobs as educators: fill young minds with knowledge, and give them direction in life, which she said is more important (it's been awhile since I have seen it, but that is the overall idea). She then said they needed a compass, representing of course the direction he was supposed to give.
So, giving him the compass showed him that he had indeed fulfilled what she thought was the most important of their job: he became a great compass for the kids.
Incidentally, I've been a teacher for 11 years now, and the president of the Community College I first attended handed me a compass along with my diploma on stage, because she knew my passion for wanting to be a teacher, and we had discussed loving Mr. Holland's Opus. I keep the compass on my desk every year as that reminder!
There are 10 types of people in the world: those who understand Binary, and those who don't
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