I have known people who dropped out of going to a group and never came back because someone called upon them to pray. They were embarrassed and they never came back. The same can be said, by the way, for calling upon people to read the Bible out loud. Little things can be a big deal for some folks.
On the other hand, if I were a new comer and you never called upon me to pray, I might feel like I am not really an insider. Everyone wants to be in the inner ring. (Google C.S. Lewis’ article on the Inner Ring.)
Last week I asked for a volunteer to pray. Someone volunteered that is a new comer to the church. I would not have been sure how she would have felt to be called upon. Now I know.
Ask for a volunteer to pray out loud from time to time. You never know who might raise their hand. Do the same thing with reading the Bible out loud. From time to time say, “Who would like to read the first five verses of the text.”