Generally, there are two factors that contribute to quiet playing:
1.) They are insecure with their part - not comfortable physically playing the music. For children, it is often because they don't practice enough. For older kids and adults, it's often because they don't practice enough. :)
2.) Social psychology: by playing as a soloist they are excluding themselves from "the group" and so because they are different they are afraid of being judged or made fun of. As a soloist, there's nowhere to hide and if you feel insecure about your playing, then playing in front of others can be terrifying.
1.) Make sure (to the best of your ability) that each student is as comfortable with their part as possible - encouraging them to come to you after school if necessary. If they feel like they know their part, it will go a long way toward building confidence when it comes time to perform.
2.) Make sure that you have a gentle, supportive rehearsal environment. It is important for the kids to know that they won't be judged or made fun of if they mess up or make a funny noise by accident. Here are a few ideas as to how you could go about creating that dynamic:
- Tell the students directly: "This is a good class and we need to support one another - playing solos are hard! Congratulate each other on a job well done!"
- Let them know teasing about it won't be tolerated - punishing students if necessary.
- If they make mistakes (and they will) talk about the importance of over-coming them and moving on, not focusing on them.
- Add humor. If the students think of what they're doing as fun rather than scary and high-pressure, they'll be more comfortable and more likely to play out.
- Be the example. Equalize a situation by making even goofier sounds than they make on their instrument. If they honk on their instrument, make a goofy sound while singing a part to them in rehearsal. If they see how successfully you handle your own mistakes, they'll use that information to handle their own mistakes.
- Use imagery. Using goofy imagery is a great way to get them to focus on something. For example, tell them that they're in a giant arena of stuffed animals and the animals in the back of the arena have to hear the solo. Using imagery allows them to pretend and take the focus off "okay, this is my big solo now."
By and large though, preparedness with parts will take care many, many problems by itself.
Hope that helps.