It is a teacher's role to effect change in a student, to 'teach' the student something.
We need to ask an important question: How does a teacher know that he/she has effected a change in the student? How does the teacher know that something has been taught? In fact, isn't it true that unless teachers know that something has been taught then they haven't done their job; they haven't completed the teaching? This is an important point: a teacher's role is to know with a high degree of certainty that a student has learnt something.
It is a teacher's role not just to effect a change in a student, but also to confirm that there has been a change.
There are many types of evidence which a teacher can use to assess whether a student has understood something. Some teachers will think about the clarity of their own explanations, and not about anything the student says or does. Some teachers will ask a student to state whether or not they have understood something, asking "do you understand?" and taking an affirmative response to mean that the student does understand. However, these methods overlook the crucial point, which is that the change takes place within the student, and the teacher should seek evidence of the change.
Another method is to use a student's body language and/or try to empathise with them to judge whether the student has understood. Many psychologists will say that this can be an effective tool, but will also concede that body language can be faked or misunderstood.
The solution is to ask the student to demonstrate understanding. This doesn't require students to judge for themselves whether they have understood something, and it doesn't require the teacher to use indirect signals to assess a student's level of understanding. By asking students to explain an idea, to verbalise or demonstrate their thought process, the teacher can say with virtual* certainty that a student has understood an idea or not. It also lets the teacher know exactly what students are thinking; if students don't understand something, then asking for an explanation will communicate to the teacher (and hopefully to the students themselves) where the understanding is lacking.
(*It is arguable that it is impossible to prove whether someone has actually understood something. Even a 'perfect' explanation could have been a lucky guess, or could overlook an important point which is not understood. However, eliciting response is the best way to demonstrate with as much certainty as possible that an idea has been understood, and it's interesting to note that even if the response doesn't absolutely guarantee perfect understanding, it does demonstrate an attempt to understand, and that the student has thought comprehensively about the ideas.)
A teacher must elicit responses which demonstrate understanding
This idea must be at the cornerstone of any one-to-one teaching. There are other methods which 'can' work, but if a teacher doesn't require a demonstration of understanding from a student, then the teacher cannot guarantee to have effected a change in the student.