Different people have different learning styles, and I do my best to tutor accordingly. I believe that being flexible with my methods allows me to be a better teacher.

I would work through some problems with them and try to determine any points of confusion. From there, I would try a few different teaching approaches to find the best way of helping them understand.

Being an independent learner doesn't necessarily mean that the student is good at the subject, but that there is no fear involved. I can help students become independent learners by keeping them curious and interested in the work, and by making sure they are not intimidated by it.

I would try approaching the problem from different angles, maybe using a real-life example (if applicable), or by taking the problem completely out of context. It would definitely depend on the student.

By using puzzles, games, or fun out-of-context examples.

At the end of every unit/chapter, I would give a few problems and ask the student both to complete the problem and explain, in words, how and why he/she did what they did.

Making sure their foundation in the subject is solid will help make future work much less intimidating. Often students just need an initial push to start work, and once the initial hurdle has been passed there is much less uncertainty.

I would do this by working through problems with them, and by asking a series of questions about what they want to get out of our sessions.

I'd ask them how they think they learn best: are they visual or auditory learners? Do they work best from seeing an example or by doing it themselves? I would also adapt my approach after seeing them do some problems.

I'd ask them to paraphrase, or I'd read them a paragraph and ask them to tell me what happened verbally.

Being positive and encouraging, and establishing a good foundation of knowledge before moving on to more complex concepts.

I use a lot of colored pencils/markers and scratch paper.