If you want specific information, you have to ask a question-- Questions evoke answers. Better yet, carefully crafted questions, evoke well crafted answers. As a teacher, it is important to ask both low and high level questions. According to Bloom's taxonomy, low level questions make sure students understand basic and foundational concepts-- they are able to remember, understand, and apply. High level questions allow students to dig deeper into concepts and analyze, evaluate, and create. It is important to ask questions to spark students curiosity and inspire them to ask their own questions.
Strategies:
Low and High Level Questions: With this strategy, students are asked to answer lower level questions independently and then work as a team to answer high level questions. It is important they are able to answer low leveled questions on their own because it proves they understand and comprehend basic concepts. As a team they can then work to answer the high level questions, ones that ask them to analyze, evaluate, and create. I created a handout of math problem I found in 5 Practices for Orchestrating Productive Mathematics Discussion by Margaret S. Smith and Mary Kay Stein. The first few questions are for students to work through independently because they are low level and the last few questions are for students to work on together since they are more challenging and require discussion.
Multiple Intelligences: Every students learners different because every student has different intelligences. Since there is more than one way to solve a math problem using different intelligences, I can use Gardner's theory on Multiple Intelligences to ask different questions that tap into different intelligences.
Peer Tutoring: Pair students together and have them "tutor" one another by prompting each other with questions about the assignment they are required to complete.
Student-Led Inquiry: The teacher will lead a discussion, but prompt students to ask questions of the teacher and of their peers. This strategy is typically the most valuable after completing an overview of a lesson and students have been equipped with the basic knowledge necessary to enable the making of connections.
Students Questions for Purposeful Learning: Prompt the class with a question provoking statement based on the lesson that is about to be taught. Have students generate questions based on the statement. Write questions on the board and put check marks by questions that arise multiple times. This activity should generate curiosity about the topic and encourage discussion.