My preferred approaches is to help students build a strong understanding and intuition by:
- My basic tutoring approaches are to:
- Guide students (with questions) to discover principles/methods for themselves
- Start with simple problems, and use them to build up to understanding the theory or more complicated problems.
- Break more complicated problems into manageable ones
- Emphasize intuitive understanding over technical details
- Ask questions to help students solidify their understanding
- Create quick homework problems and structured revision schedules to solidify student's understanding of key points learned
- Explain problems and concepts when I can't figure out how to guide students to discover them for themselves.
- Ask students to explain stuff back to me to help them integrate their understanding, while I identify remaining areas of confusion
- Use technology to tutor better and more efficiently
- Make screencasts of tutoring sessions, so that students can review their tutoring session afterwards, and also benefit from each other's tutoring sessions! Some students find these very useful! This requires using my computer, which has its own limitation.
- In addition I sometimes:
- Direct students to other resources, such as Khan Academy
- Teach students easier/better methods than are taught in class
- Help students to focus on just what they need to do well in the course.
- Drill specific aspects of problem-solving that students find most challenging. For example, many students find that figuring out which strategy to use is the most challenging aspect of solving integrals, and so we work on figuring out the strategy for solving numerous integrals, without getting lost in the algebraic details of actually solving them.
- Help students deal with expectations/anxieties that are interfering with their learning
Overall, from the feedback I have received from my students (some of whom have first tried other tutors), I believe I am quite an effective tutor.
Here's a screencast of part of a tutoring session (posted with the student's permission). This student likes to talk out loud as he works, and knows the material fairly well. Notice that I just let the student work until the 4 min 30 second mark, when he seems to be getting off track. I get involved when students start thinking unproductively, but don't disrupt students when they are already doing great thinking on their own! The learning is happening in your brain - My aim is to keep that on track.