The most successful tutors have an excellent command of the subject matter, which allows them to very rapidly integrate and synthesize skills and techniques from various topics and apply them flawlessly to any question.
The best tutors always establish good rapport with tutees and are able to empathize with their tutees’ struggles in tackling challenging problems or in having to manage a large volume of classroom work.
The good tutors do not simply give out the solution to math problems, but also engage their students with continual prompting and probing, trying to elicit from the student possible approaches to the given problem.
The best math tutors are able to quickly assess their student’s level of understanding at the start and are able to structure the lessons in a way that leads the student from simpler problems to more challenging questions in a progressive manner.
The best tutors never criticize tutees directly or overtly, but instead draw attention to mathematical errors by implication and questioning, so that the tutees themselves are led to rethink their approach to the problem or recognize the flaws in their own working.
Effective tutors often ask students to describe or articulate what they are doing, what formulas they are trying to use, or what method they are employing.
Effective tutors regularly motivate and encourage their tutees by creating an inquisitive atmosphere, piquing their curiosity with mathematical problems relevant to their daily lives, and providing frequent, positive feedback.