Any problem can be broken down into tiny pieces and solved bit by bit. This approach works for everyone. Some may solve little bits faster than others, or group a couple bits into a chunk, but the approach of breaking down a problem into minute pieces applies to any student and makes hard problems less intimidating.

I'll take a few minutes to introduce myself to him/her but I'd want to get into the subject matter pretty soon - it's the best way to discern his/her learning style and the concepts with which he/she needs help most.

All I can give is my approach. I'll never explain an answer straight up, but I'll guide her through a problem that (to her) seems intractable my way. The goal would be for her to habitually and independently break down a problem into small steps and tackle each step sequentially.

Presumably, a student would have plenty of external motivation or goals in mind, or else he wouldn't ask to be tutored in the first place. What I can do is enforce the idea that he can grow and get better at his subject with correct practice; this would help keep him from being discouraged, as well as provide some internal drive for him.

Often this happens because a student tries to grasp a complex concept all at once. In that case, the concept in question would have a number of smaller, simpler components that can be tackled bit by bit. Gradually, those little components will become the complex concept.

The key in reading comprehension is isolating key words in a given sentence that form key ideas. Once the idea is found, the rest of the sentence makes sense.

Lack of engagement often comes with lack of confidence in a subject. By focusing on small wins first, this creates a positive cycle in a given subject that serves as a motivator for future progress.

The best way of checking for comprehension is practice problems in that area. I would give a student a practice problem and have them explain their method to me; by having them teach me, in a sense, they gain greater facility with the material.

Small wins. Any initial positive progress creates a positive cycle that begets larger wins later on.

1) She may tell me. 2) If not, when going through a problem, what concepts does she get stuck on? What forms of encouragement and education seem to work best? The experimental approach is good here.

Going through a wide range of problems in whatever field my student is studying in and paying close attention to their problem-solving process is my main strategy. That way, if she falters, I'll know exactly what conceptual leap she'll need to take, and guide her there.

I alter my approach based on the material each student goes through - for instance, I'll need to pay attention to a wider breadth of material when teaching the ACT than when working with a student on geometry. After a few sessions I'll have a better handle on exactly what way of presentation is most helpful for my students. My style, however, is fairly consistent student-to-student.

Whatever they have and are comfortable with, first and foremost. If they don't know, or if they're studying for a test like the ACT and GRE where materials matter, I'll recommend specific books for them.