See Part II 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:

 Observe another teacher. Pay particular attention to the questions the teacher asks the class and also individual students. Were the questions effective? How can you tell? Did the questions result in single answers or explanations from the students? Were you able to tell if the students had true understanding of the mathematical topics? What kind of questions would you suggest to the teacher? If you aren’t able to set up a time to observe another teacher, take a look at this lesson analysis on questioning and discourse from NCTM's Reflections webpage, and do the same analysis.
 Reflect on the questions that you pose in your own classroom. Use the technique of QuestionListenQuestion. Get an audio recorder, and record yourself teaching. When reviewing the conversation, concentrate on the interaction after you pose a question as a means to evaluate whether or not your questions promote deeper mathematical thinking. Do your questions prompt students to develop deeper understanding or to get them to a desired answer? Is the student learning from the series of questions? Listen to students’ responses and guide them based on what they are thinking. For examples of effective initial and followup questions, see “Questioning Our Patterns of Questioning” and “Questioning Your Way to the Standards.”
 Set up classroom norms so that everyone knows their role in the classroom. The teacher’s role includes orchestrating discourse by:
 posing questions to challenge student thinking;
 listening carefully and monitoring understanding;
 encouraging each student to participate – even if it means asking, “Who can repeat what Andrew said?” or “Who can explain in another way what Bailey did?”
The student’s role includes:
 listening and responding to the teacher and one another;
 using a variety of tools to reason, make connections, solve problems;
 communicating, and make convincing arguments of particular representations, procedures, and solutions.
 Ask questions that assess the students’ learning. Try ThinkPairShare. Call on students by name to invite them to contribute. These questions are not, “Do we all get it?” or, “Does anyone have any questions?” Rather, these questions must give the learners an opportunity to communicate their reasoning process – why they chose a particular method and how their choices made sense. Transform some of your closed questions, those that can be answered with one word, to open questions, those that require explanation.
Be careful to make this transformation gradually. Some students may not answer openended questions because they are only comfortable answering questions that they can be confident they know what constitutes an appropriate response. One way to encourage students to contribute to the discussion is to use the thinkpairshare method. First, allow students to think alone about their solutions. Then, allow them to talk through their ideas with a partner. Next, ask two pairs of students to share their ideas with each other. Last, facilitate a wholeclass discussion.
 Identify, in advance, the big ideas that your lesson examines and the mathematical outcomes that students should achieve. Take time to brainstorm the multiple approaches that could be taken to work through similar problems and the misconceptions that students might have. Make sure that you prepare questions that address these multiple approaches and misconceptions, prompting a discussion about when particular approaches are better than others and how to explain why each misconception is faulty. Close each lesson with a summarizing question that reiterates the big ideas.
 Use Fermi questions in your classroom to encourage multiple approaches, emphasize process rather than product, and promote nontraditional problemsolving strategies. Fermi questions are unexpected questions about the natural world whose answers are rough quantitative estimations. For example, you might ask your class, “How many drops of water are in Lake Erie?” or “How many balloons can fit in the school gym?” Encourage students work in pairs to construct a detailed argument and present it to the class. After the presentations, ask students which pair they think was closest and why.
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
