Review Part I of this collection of tips.

As a teacher, you probably spend a lot of time preparing engaging lessons, grading student work, and attending professional development. But, do you take the time to think about the questions you are asking your students? Do you pay particular attention to what they are asking you? Asking good questions and promoting discourse is an integral part of the teaching and learning in a classroom. It is worth your time! See some tips below on how to get started:

 When using closed questions, encourage all students to respond. It is good to mix up the kind of questions you ask. When using Yes/No questions, for example, ask students to use thumbs up for yes or thumbs down for no. This will include everyone and serve a dual purpose: all students will be more attentive if their participation is often required throughout the class, and you will be able to do informal formative assessment by taking a quick count of how many students seem to be grasping the ideas.
PreKGrade 8

Prefer more specific tips about how to differentiate mathematics instruction for particular topics at your grade level?
Two new books, by math education expert Marian Small, cut through the difficulties of differentiated instruction with two powerful and universal strategies that teachers can use across all math content: Open Questions and Parallel Tasks. Both are organized by grade level and NCTM content strand.

Grades 612

 Use a game or other fun activity in your classroom, but be sure to reinforce the learning by asking students to think about their thinking process afterward. Require students to reflect on their experience by asking powerful reflection questions. Explicitly tell students that you would like them to explain their reasoning and sensemaking. Ask questions about their strategy such as, “Was there a particular move that you could make to limit your opponent?” For more on types of powerful mathematical questions and an example of an elementary game, see “Designing Questions to Encourage Children’s Mathematical Thinking.”
 Use students’ questions to evaluate your own progress. Are you creating an atmosphere so permeated with intellectual curiosity that your students are asking the questions that lead to the discovery of new relationships? It is a very powerful event when students take over asking the questions that get at the big ideas rather than just the procedures. Take note of the questions that your students ask. Are they asking more questions like, “Will you work number six?” or questions like “What would happen if we changed this parameter?” Strive for more of the latter.

Choose questions carefully to motivate students at home. Motivating questions can be those that have no ‘right’ answer and no ‘right’ approach. 
Consider the Dollar Word Problem. This is within reach of upperelementary students, but can also motivate algebra students. It goes like this: “Each letter of the alphabet is worth a value corresponding to its place in the alphabet. For example, the letter A is worth a penny, B is worth 2¢, C is worth 3¢, E is worth a nickel, and so on, with Z worth 26¢. Your job is to create a word that is worth exactly $1. Get as many as you can.” Keep a running list in your classroom. Find more engaging problems for students to work on with their families at Figure This! 
 Pose an unanswered question to challenge your students. Don’t tell them right away that the question has no solution or a predetermined answer. Allow them to wonder about a problem, research it, and find that their speculations turned out to be wrong, or to come up with an original solution. If we give students only problems whose solutions are neat and clear, we are not preparing them for the kind of mathematics that exists in life. Real data sets are conducive to asking openended questions. Ask students, “What kinds of conclusions can you make from this data set? Which graphical representation is best for showing this and why?”
 Base the success of your lessons on the extent of engagement of ideas and not on the students’ happiness. Teach your students how to acknowledge and pursue the struggle and process of learning. You are doing your students a disservice if you present them with questions that they always know how to solve. You need to present them with problems that give them the foundation to struggle and move toward understanding. When they don’t know where to begin, coax them by asking, “Is there something you can try that might work?” and “Are there any mathematics tools (technology or manipulatives) that could help?”
 Leave a question unanswered at the end of a class period. Telling students which solution is correct is never as powerful as letting them figure it out for themselves. The extra time it takes for learning to occur is worth it! This may seen uncomfortable to a teacher at first, but it is more like problemsolving in the real world. Students will begin to appreciate the challenge and work harder outside of the classroom to come back with new approaches.
 Use a partner quiz every once in a while, and allow each pair to ask the teacher just one question. This will encourage students’ ability to ask good questions, while, more importantly, will promote studentstudent discourse. Since the students are granted only one question, they will tend to save it and justify their process with each other. Make sure that the questions chosen for the partner quiz are more complex than those chosen for individual assessment so that they have a reason to collaborate. Allow them to ask for anything but the answer, and be surprised that often a pair will turn in their work without even asking a question. For more on how partner quizzes work, see “If I Only Had One Question: Partner Quizzes in Middle School Mathematics.”
 Give students the answer, and ask them to come up with the question. This can be modified to fit the needs and abilities of your students. If you are working with younger children, make sure you are very specific. For example, “Write a story problem that has an answer of 20 cookies.” Notice that you should include the units so that the students have an idea of what to write about. You may even add, “…that requires subtraction,” for example. With older students, ask them to trade papers with another student without providing the answer. Follow with a discussion focusing on what words in the problems gave hints of how to solve them, what information was extraneous, what difficulties the student solving the problem encountered, and so on.