The concept of apprenticeship is an interesting one as it's different from sitting in a classroom learning carefully planned out lessons. Rather you learn a lot by watching, absorbing, doing, and asking. You are learning not necessarily by being 'taught' but by seeing someone model what you are trying to learn. What does this have to do with math tutoring? Well, one time I had a parent insist that I try and help a nephew as I had helped two other family members and she wanted me to do what I could for him too. It was quite a distance and I tried to politely decline but she insisted, ' just meet with him whatever it takes.' So to make a long story short it turned out that this student was already an excellent math student, had scored a 35 on the ACT, and was being actively recruited by many universities...what could I possibly offer? We talked about school, colleges, jobs, goals, etc. for an hour without hardly a mention of mathematics, yet they were so happy I came over? Why? I happened to mention that he should 'shadow' some people whose careers he was thinking about pursuing and he and his parents had never thought of this possibility. We all learn math in school but for most this is just a means to a different end. This summer think of what that 'end' is and consider interning, volunteering, shadowing or working in an career you are interested in even if without pay. The experience will be invaluable!
Helping students succeed in math for over 15 years. Individualized attention makes the difference!