If you are a piano teacher, I bet you run into some shy, not so outgoing, but perfectionist students. Some of these students also may not participate in sports either. If that's the case, these piano students can get really stiff, not flexible, afraid to make mistakes, and even frustrated with themselves.
Students who play sports have the ability to accept losses. They try different things physically and learn from their experiences. They are also accustomed to their coaches, pushing them to do some repetitions over and over whether they like it or not. But if these shy piano students are not participating in sports and still being stiff, I encourage you (piano teachers) to give them a lot of opportunities to improvise on the piano with you. Tell them nothing is right or wrong. Give them a space to experiment.
I'm sure many of you (piano teachers) are already incorporating improvisations into your students' lessons whenever the time allows. However, in my teaching, for these shy students, I always make sure to start their lessons with improvisations FIRST at EVERY lesson. And amazingly, these students always open up gradually, have fun with it, & enter into more experimental mode. After doing the improvisation, they feel more refreshed, and they take their lessons with a more open-minded attitude.