There is no better way for kids to learn to play instruments correctly than one on one with a private instructor that specializes in their instrument.
What benefit is there to paying for my child to have private lessons when they have band class at school?
Playing a musical instrument is a complex task, especially for beginners. Coordinating pitch reading, counting, fingers, tonguing, lips, posture, grip, movement, breathing, and listening all at the same time is daunting for most kids, and it is difficult for any band teacher to guarantee that every child in their classroom is understanding and doing all of those things correctly. Often kids will have problems with one or more of these things, and it doesn't come to light until months or years later. If a child has at least a few regular one-on-one lessons with a private instructor, these issues get nipped in the bud right away and decrease potential frustrations and difficulties. There are no classroom distractions with a private instructor; their only focus is your child.
Private lessons teach students HOW to practice. Individual practice is how students will learn most of their skills and repertoire, so it's very important that they know how to use their practice time efficiently and evaluate their progress.
Private lessons also help motivate kids and get them ahead of the curve. A private instructor can cover a lot more in-depth instrumental technique that is specialized for your child than a band director can in an average band class. Band class is where kids learn to play as a team, but lessons and individual practice are where kids learn to be musicians.
Lessons are like conditioning, while band class is team practice. In lessons and individual practice time, students develop their instrumental technique (like the skills they need for the specific position they play). In band class, we combine everyone's collective skills and strengths to perform our parts together as a team.
Private lessons are always a good idea: extra attention, instruction, motivation, and advice can only help your child grow.