What makes for good tutoring? Is it the tutor? Is it the student? Is it the right tutor with the right student?
From my experience and in my opinion it is definitely the dynamic between the tutor and the student. You may have a great tutor but a student that is very resistant to being tutored. Or you may have an eager and interested student but have a rough mannered tutor that is unwilling to meet a student at the level they are at. There are obviously a million different combinations, but again, I believe it comes back to the synergy that can happen between a good fit of tutor and student.
The student has to do their part: engaging actively with the session, asking questions, knowing what they want to go over, taking notes, etc. The tutor has to have a good grasp of the material they are working with, have access to good learning materials, and be able to create a good space for learning.
Am I genius mathematician that can download into a student's brain everything they could possibly want/need to know about math? No. But I have been tutoring students part-time for many years and full time for many years (approx. 25 years in total) and I keep coming back to creating a good space for learning to occur. I respect the students I work with never talking down to them, always being encouraging, celebrating their successes, and working with them to overcome their stumbling blocks in a compassionate way(I've been there...learning math can be challenging).
As a parent you may have to try a tutor or two or three to find a good fit for your son or daughter. So, don't be afraid to try a session or two with a tutor and gauge how your child responds.
Helping students succeed in math for over 15 years. Individualized attention makes the difference!