An Example A teacher may assign a report on animals. She leaves the assignment very open-ended so students can research on whatever animal they want. There may be some guidelines of what needs to be included. The students can present their information in the form of a poster, a video, a diorama, or some other form--it's up to the student to decide. Students work on their projects over several days. In the end, they show their projects to the rest of the class or perhaps for their parents in a special science night.
An Example A class may be studying verbs. The teacher will ask the students what they know about verbs. The students will tell what they know. Then the teacher would have students act out different actions to show what verbs are. The teacher would then introduce linking verbs. The teacher would have activities for students to do that show the verbs linking the two parts of the sentence. The teacher will be asking lots of questions as she guides the students through the learning of the new concept of linking verbs. Students and teacher will keep evaluating if students are understanding. Students are also free to ask questions about the topic, with the goal of extending their learning.
An Example Students have been studying the Civil Rights Movement. The teacher posts a question on the board: When is it ok to disobey authority? Students spend the class period discussing if and when it is ok to do such a thing. They give examples to support their opinion. Every student gets equal opportunity to speak. In the end, they may not have a conclusion, but they have wrestled with the concept together.