Native English speakers, could you please help me with these issues?

Question

1. Does this sentence make sense:

"He is known among students as being a TIGHT teacher."

2. And if so, what does it mean?

Answer 1

No, it makes no sense.  Shoes are tight; teachers are not.

Answer 2

'Tight' is not appropriate in his instance. 'Strict' would be OK. 

Answer 3

No - it doesn't.

I don't know what you are trying to say.  Strict?  Firm?  Narrow-minded?  It's hard to guess!