As far as mathematics tuition is concerned, being able to converse at the students’ level of understanding is the key to being a successful tutor.
This means, for example, using vocabulary and mathematical language that the student is already familiar with, rather than speaking in high-brow terms that only the tutor can comprehend.
If a student has difficulty understanding a particular concept in maths, no matter how basic the concept may be, I always try to begin with simple analogies and easy-to-understand notation and ideas.
Once the student has a feel of what I am trying to convey, then I will try to guide him or her to a more advanced level of understanding.
Only when the student is sufficiently prepared do I introduce formal mathematical notation and abstract reasoning.
Mathematics learning has to be progressive because maths is one subject in which concepts build upon each other. You have to grasp the more elementary concepts first before you can grasp the more advanced ones.
At the same time however, tutors like myself have to be very careful not to oversimplify, or else the student would be unable to tackle examination-style questions which may test high-order understanding.