One thing I see off and on is students who are overly tired. Sometimes students are tired after school, sometimes it is early in the morning, and still others after eating. Being tired makes learning math so much tougher. Pay attention to when you are most alert and awake and focus on doing your math studies then. Everyone is a little different but you want to get the most benefits from your time spent. With the longer days the tendency to stay up later is also present so make sure you are getting enough rest so you can finish the year strong!
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!
I'll share another story about a student I worked with for a couple of years. Her parents had her contribute $5 of her own money to the tutoring sessions and her parents paid the remainder. This student was a Junior and Senior while I worked with her and she had a part time job so she had a source of her own money. Although the parents could have just as easily paid for the tutoring I believe she wouldn't have gotten the same amount out of it. She had a sense of ownership and she wanted to make sure she got a good return on her investment. When we met she knew what she wanted to work on and what questions she wanted answered. She was efficient with the time because now it was 'her' time and now it had 'value' for her. Hmmm, maybe this would work for you too?!
When most students think of the final exam they shudder at the thought of what amounts to not just a test but a comprehensive one at that covering sometimes 6 or more chapters. Before you panic, or worse yet give up before you start, realize what an opportunity this can be. Finals can be anywhere from 10% of your grade in middle school to 20% in high school to 50-60% in college! However, if you score well this can oftentimes mean a jump of one whole letter grade. The final usually differs from the chapter tests in that it doesn't go into the same depth. There is limited time to test on everything covered during the semester so it is the MAIN concepts that are tested. Start going over your old tests and quizzes NOW to fill in gaps in your understanding. Oftentimes, what seemed difficult before will be easier now that all your other math skills have been improved. Lastly, math as a whole is cumulative. Not just chapter to chapter but from year to year. So taking adequate time to study for your final will SOLIDIFY what you have learned and set the stage for a successful year next year in math as well. Make it a good one!
Helping students succeed in math for over 10 years. Individualized attention makes the difference!