Part of independence for students is learning to ask their own questions. Too often, however, we are the ones asking all the questions. I like the meaning of this quote: A teacher's purpose is not to create students in his own image, but to develop students who can create their own image. ~Author Unknown It reminds me of something my dad told me. He said the purpose of education was to "teach students how to figure out what to do when they don't know what to do." Isn't that true independence? And a part of that is teaching students how to ask their own questions.
One way to do that is to use a simple review game. The detailed instructions and handout grid are here. In a nutshell, what you do is put students in a small group and give them an envelope or bag that includes the question prompts. Each student, in turn, pulls a card and asks a questions for the group, which then answers it. It shifts the responsibility to students, but by providing them a starting point, it also provides scaffolding. In my experience, just asking students to make up questions was too open-ended, so this is a good bridge.
If you teach younger students, or students with special needs, or second language learners, you can easily adapt this. Just make big cards with who, what, when, where, how, why, and which. After you read a story, such as The Very Hungry Caterpillar, ask a student to come pick a card (put the cards upside down so they can't see what they are choosing). Then, have each student create a question about the story using the starter word on the card. They can turn to a partner and ask the question, or if you have a small group, they can ask the group.
Simple, and effective. My favorite kind of activity.