1. Arrive five minutes early. One of the simplest things you can do to maximize your time with your teacher is to ensure that you get to your lesson on time - which means early. I know that most lessons take place after school and during rush hour when traffic is at its most frustrating. It is definitely worth it to find the best route to your teacher and to plan your schedule so you can arrive a few minutes early. This allows you to catch your breath, focus your attention, and unpack your instrument so that your lesson can start precisely on time. Most teachers won't give you extra time if you arrive late. In my studio, if you're scheduled for an hour-long lesson but you arrive 15 minutes late, you only get a 45 minute lesson. So, ensuring that you are on time and present for every scheduled minute of your lesson is one of the easiest ways to make the most of things.
2. Practice. This might seem obvious, but you would be surprised how many students show up at lessons without having practiced. A good teacher won't let you get away with this! I had a student last year who absolutely hated practicing her rhythm exercises. She wouldn't practice them at all at home, and in lessons she would often try and steer me away from the rhythm book. However, because I knew that developing her sense of pulse was necessary for her playing, I didn't let it slide. I gave her two options: either we would spend a lot of time practicing rhythm in her lesson and have less time for her pieces OR she could practice her rhythm at home and spend less time on it in the lesson. She opted for the second one once she realized that there was no way out of it.
Everyone wants the student to improve quickly and learn new pieces and new skills. This will only happen if practicing is happening consistently at home. Otherwise, the teacher will spend valuable lesson time explaining the same concepts over and over, which will lead to the student and their parents becoming very frustrated.
3. Record your lessons and watch them at home. Ask your teacher if you can record your lessons. I keep a digital video camera in my studio for my students' use. They can bring their own memory cards and record their lessons. Watching your lesson back at home will help you by allowing you to hear the teacher's instructions more times and by letting you see yourself playing from the outside. In your lesson, you might really feel that you are using a lot of bow and wonder why your teacher is so insistent on you trying to use even more. However, when you watch yourself, you may see that you really aren't using much at all.
4. Tell your teacher how you feel. Despite how it may seem at times, your teacher can't actually read your mind. If your teacher says that you don't understand, say out loud to your teacher, "I don't understand what you're saying." It is your teacher's job to find a way to explain things to you in a way that makes sense for you and your learning style! Don't just nod and smile - say what you're thinking and feeling. If your teacher is going too fast for you, say "Can you give me a second to process what you said before? I'm still trying to figure it out."
Two other important things to tell your teacher: "This makes me feel really uncomfortable" and "My hand/wrist/finger/back/neck hurts when I do it this way." Teachers are trained to be on the lookout for tension in your playing, but it makes things go a lot smoother if you can communicate with them clearly.
It is especially important to communicate clearly and directly with your teacher when you are new to each other. The teacher might use a metaphor that doesn't work for you, or they might start changing aspects of your playing that you thought were just fine before you came to them. Please don't just go home and complain to your parents about it. Give your teacher a chance to explain something in a different way or to tell you their reasoning behind something.
5. Write down questions for your teacher as you practice and bring them to your lesson. As you practice during the week, keep a notebook or a practice journal and write down questions for your teacher. If you run into a problem area, such as a shift that you consistently miss, or doublestops that just don't feel right in your hand, write it down and ask your teacher about them in your lesson.
6. Clarify any confusion with your teacher before your lesson. If you're unsure about a fingering, or even just an illegible word in your notebook, send your teacher an email or give them a call during the week to ask. Don't practice confused!
7. Keep your instrument in good working condition. It's critical to keep your instrument in shape just for your own playing. This means changing strings and getting your bow rehaired at least twice a year. It means taking your violin to the shop and having the pegs worked on if they're consistently slipping or sticking, and having any other needed repairs completed promptly. Chances are that your teacher is not a repair technician. Speaking from personal experience, I can put on strings and fix a bridge that's fallen over and that's really about it. Time that your teacher has to spend fighting with your instrument to tune it or fix anything with it is time taken away from your lesson. I've had experiences where a student purchased a very cheap instrument that had horrible pegs that wouldn't hold a pitch. I routinely spent 5 to 10 minutes of his 30 minute lesson just trying to get his violin to stay in tune, which wasn't how either one of us wanted to be spending the time. So, schedule repairs and maintenance in a timely manner!
I hope at least some of these tips are helpful to you as you continue your studies! Feel free to comment with any of your own suggestions for getting more out of your lessons!