How to get shy students to participate.
This kind of depends on why they're not participating. If it's that they're afraid that they might not have the correct answer, that's one thing. If they just have a fear of public speaking, that's another thing. But here are two ideas that might help.
This first idea is called "Over the Shoulder". So you pose a question to your class, and then instead of having them raise hands and or even calling on volunteers, you say, "Everybody right down a possible answer. Or draw something that represents a possible answer." And as your students are doing that, circulate around your room and look over the shoulder of Sally to see what she is writing or drawing. If you see that she has written a very interesting answer or the correct answer, then you bend down and you whisper in her ear and you say, "Sally. That is a fantastic answer. I really think that should be shared with the rest of the class."
So now she knows she has the correct answer, and might be less shy about sharing that answer with the class. If she has a fear of public speaking, that's OK, too. I'll talk her answer. I will read it to the class. I will give her the credit. The key is, I'm trying to get her to take that first step on to the escalator of participation. And sometimes a strategy like "Over the Shoulder" can be that first step.
Another strategy you might try is something I call "All Raised Hands". This is when you pose a question to your class and you say, "Everybody has to raise their hand. Now if you know the answer, I want your hand straight up, elbow locked. If you think you know the answer, or you have a partial answer or something interesting you want to contribute, give me an ell, or a right angle. And if you have no idea what the answer is, thumb to the head." Now, no matter how shy a particular student might be, they can still pick a hand position that represents what they feel like they could contribute to the answer to that question.
If Sally, who is my shy student, has her hand straight up, then I can call on her knowing that she feels confident she has the correct answer. If she has her thumb to the head then I won't call on her, because I know she feels like she doesn't have the correct answer.
Those are two ideas about helping a shy student participate more in class.