"get to the bottom, get to the root, figure out, work out" I am not sure if these are you wish for but you may state more context to your need.

There seems to be no expression that fits what you're thinking of exactly. I suppose such a teacher is dedicated, passionate, and courageous in what he or she is trying to achieve. Such a person might be described as: - giving all they've got to their cause. - trying to change the status quo. - seeking to bring about real changes. - grappling with the deep issues.

Thank you for your answer.

also self-scrutinizing. or adaptable (i.e. they adapt to the teaching style needed for a certain student)

I would say that the teacher is very self-reflective (in the example that you gave after the question mark), but I'm not really sure if there's an expression for the first part (about digging for truth)