I can show you the direction of the next step and catch you if you slip, so you can cross your learning obstacle with confidence.

In a first session, I would look at the student's syllabus and see how the student approaches practice problems. I would identify strong and weak areas of knowledge and skill, and consider the student's learning and problem-solving style.

I can help a student become an independent learner by leading them to the answer using Socratic questions. I like to be hands-off as much as possible, letting the student try independently to solve the problem or formulate their ideas, only stepping in at mistakes. This way the student can find their own preferred problem-solving techniques.

A student is best motivated by their own success, and to do so there must be enough difficulty to challenge, but not too much to overwhelm. Easy problems are useful for establishing basic patterns and review, but eventually boring. Problems that introduce too many new concepts at once can be overly difficult and cause the student to lose interest. Give moderate new problems, or creative variations on old ones, and show the student that they can do interesting things on their own. Then they will learn that the world is comprehensible, and the good grades might only be a bonus.

A difficult skill or concept can be illustrated with simpler examples, or approached from different directions. Thought experiments can reduce the difficulty to a core or kernel of truth that is intuitively obvious, and there are usually multiple formulations of any problem or idea. Cater to visual, auditory, and kinesthetic learners with pictures and diagrams, different explanations, or even physical demonstrations.

A student struggling with reading comprehension can slow down and focus attention line by line, or even a word at a time. Draw attention to the structure of a passage, whether at a scale of chapters, paragraphs, sentences, or words, and work out how the piece of writing is put together.